VAN ATTA C. M. > VAN ATTA VACUUM SCIENCE AND ENGINEERING Properties of Gases at Low Pressure; Vacuum Measurements;
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VAN ATTA
VACUUM SCIENCE AND ENGINEERING Properties of Gases at
Low Pressure;
Vacuum Measurements;
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VACUUM SCIENCE AND ENGINEERING Properties of Gases at Low Pressure; Vacuum Measurements Design and Operating Features of Vacuum Pumps and Systems ;
C.
VAN ATTA
M.
Consultant on
Vacuum Technology
McGRAW-HILL BOOK COMPANY New York
San Francisco
Toronto
London
Sydney
FOREWORD
The dynamic character of the vacuum industry caused by the
b6->lSi*i2**
HARRIS
6 '3-^
£
,,._.
*^*---.--.^.2r
of these worn, dog-eared manuals on engineers' and scientists' desks, as well as the great demand for new and replacement copies, stands as testimony to Dr. Van Atta's success in meeting the needs of prac-
jifi^
797%>— - --
titioners in the field.
^ '^
c^
ever -increasing variety of applications, as well as advances in technology, clearly presents the need for a current text on vacuum science and engineering. On two other occasions in the past the author, Dr. C. M. Van Atta, in conjunction with the Kinney Vacuum Division of The New York Air Brake Company, saw this need and supplied the
is
far superior to
prior book.
We
—
Vacuum Science and Engineering and is certainly much more comprehensive than the believe that Dr. Van Atta has achieved in this new
By comparison,
this
new
effort
and up-to-date coverage of his subject, which should again meet the needs of the industry and become a standard text and reference for all those who wish to study or practice in the writing a complete
field
of
vacuum
science
and engineering.
been a privilege for the Kinney Vacuum Division to encourage and support this work. It is with admiration and respect for the eminently qualified author that we submit this book for your use. It has
VACUUM SCIENCE AND ENGINEERING
J. E. Chappell, General
Manager
Kinney Vacuum The New York Air Brake Company Division
©
Copyright 1965 by McGraw-Hill, Inc. All Rights Reserved. Printed in the United States of America. This book, or parts thereof, may not be reproduced in any form without permission of the publishers. Library of Congress Catalog Card
Number 65-17497
66854
23456789-MP-9876
PREFACE
Over the past forty years vacuum technology has evolved from an incidental but essential tool of scientific research to a rapidly growing
branch of engineering. In the 1930s the principal engineering application of vacuum technology was in the manufacture of light bulbs and radio tubes, for which processes ingenious equipment was developed largely by an empirical approach to the problems of evacuating and surface conditioning. The transition from a research tool engineering application was greatly accelerated during World II, particularly by the multilateral attack on the release of atomic energy by the Manhattan Project. Many divisions of that
to
War
vacuum equipment of more than had ever been contemplated
project required the development of diverse
and greater
previously.
capabilities
Subsequently the
particle accelerators for nuclear
design and construction of large and high-energy physics and the
development of such processes as vacuum coating,
distillation,
and
metal degassing made further engineering applications of the vacuum technology developed during the war. More recently the requirements of controlled thermonuclear research and space simulation have converted to an engineering scale the techniques of ultrahigh vacuum which had previously been applied only to small scale laboratory experiments.
The process of evolution and growth of vacuum engineering is by no means complete. Requirements in many fields of research and materials processing are even now inadequately met, either because the desired vacuum conditions cannot be reliably attained, or because the cost of doing so is excessive. Improved methods of vacuum
pumping, surface degassing, and the measurement of low pressures are needed to meet these present requirements. The role of sorption (adsorption, absorption, and chemisorption) on surfaces is imperfectly understood, so that significant further progress will depend upon a concerted experimental and theoretical effort to understand the basic phenomena involved in the interaction between gases and surfaces at low pressure.
Vlll
PREFACE
In Vactmm Science and Engineering the objectives are to give in form the scientific basis of vacuum technology, to describe in some detail the performance characteristics and limitations of vacuum pumps, gauges for measuring gas pressure, and other components of vacuum systems, and finally to provide design criteria in sufficiently general form to be useful in designing vacuum systems for a wide range of applications. Throughout the text an effort has been made to describe in some detail the physical processes which determine the operating features of the various devices which are discussed. The object in doing so has been to give the reader not merely a catalogue of typical vacuum components and perform^ance data, but in addition a basis for judging the importance of various phenomena which occur in vacuum systems. It is my belief that only by this approach can one provide guidance for the optimization of the design of vacuum systems for a variety of uses. Aside from my own experience in large scale experimental research and industrial vacuum development, I have drawn heavily upon the expanding technical literature dealing with vacuum technology. The emergence of the published proceedings of the American Vacuum Society and its predecessor organizations, and those of the International Organization for Vacuum Science and Technology, as well as such journals as Vacuum (Pergamon Press, London), Le Vide (la Societe Francaise des Ingenieurs et Techniciens du Vide, Nogentsur-Marne (Seine) France), and Vakuum-Technik Springer- Verlag OHG, Berlin) has greatly eased the task of locating literature on new developments in vacuum technology. With the kind cooperation of Dr. J. H. Leek, I have found his excellent book. Pressure Measurement in Vacuum Systems (published for the Institute of Physics and the Physical Society by Chapman and Hall, Ltd., London), most helpful in writing Chapter 3 of the text. It is with deep appreciation that I acknowledge the incentive and support provided by the New York Air Brake Company for undertaking the task of writing a book of this character. The critical comments of R. R. Cyr and Z. C. Dobrowolski of the Kinney Vacuum Division of the company contributed significantly to the final version, particularly of Chapters 5, 6, 7, and 8 of the text. I am deeply indebted to Miss Margaret R. Thomas, who not only typed the manuscript with its many revisions, but also maintained order in the growing lists of references, permissions, and credits. I also wish to thank the many authors, publishers, and vacuum equipment manufacturers who have responded so generously to requests to use illustrative material and who, in many cases, have provided the glossy prints necessary to reproduce photographic illustrations. C. M. Van Atta fairly classical
CONTENTS
Foreword
v
Preface
vii
Chapter
1.
The Nature and Behavior
of
Gases
......
1-1.
The General Gas Law
1-2.
Molecular Constitution and Kinetic Theory of Gases Pressure Related to the Average Molecular Kinetic Energy
4 8
1-7.
The Maxwell-Boltzmann Distribution Law Velocity of Sound in a Gas Flow of Molecules through a Hole Molecular Mean Free Path
1-8.
Van
1-9.
Dependence of Viscosity on Molecular Diameter
18
BEFEBENCES
22
1-3.
1-4. 1-5. 1-6.
12 13
der Waals' Equation of State
15
...... Chapter
Gas Flow
2.
Vacuum Systems
2-1.
Gas Flow
2-2.
Pumping Speed and Conductance Viscous Flow Poiseuille's Law Pressure Drop Formula Turbulent Flow in Vacuum Systems Correction to Poiseuille's Law Due to Surface Slip Gas Flow in the Transition Pressure Range Gas Flow at Low Pressure Conductance of a Long Tube at Low Pressure
2-3. 2-4. 2-5. 2-6.
2-7. 2-8. 2-9.
2-10.
2-11.
in
—
2-13.
t^*
3-2.
23
26
.
30 31
34
....
Conductance of an Aperture Conductance of a Tube at Low Pressure Corrected
36
43 44 47
for
End Effect
......... ......... ........ ......
49
and Monte Carlo Corrections to the Knudsen Conductance Formulas Summary of Gas-flow and Conductance Formulas
51
RErEBENCES
62
Chapter
3-1.
23
.
2-12. Clausing
5
11
.
(
1
3.
Pressure Measurement in
Liquid Manometers The Diaphragm Manometer
57
Vacuum Systems 63 65
3-8.
The Dubrovin Gauge The McLeod Gauge Thermal Conductivity Gauges Hot-cathode Ionization Gauge The Bayard-Alpert Ionization Gauge Hot -cathode Magnetron Ionization Gauge
3-9.
Magnetically CoUimated Electron
3-3. 3-4. 3-5.
*
CONTENTS
CONTENTS
X
3-6. )C_3-7.
6-5.
69
.
3-10. Cold-cathode Ionization
Beam
78
90 103
Gauge
Ionization
.... ......
Chapter
7-2.
124
7-3.
128
jfJ:"^-
^^-1. The Vacuum 143
8-3.
152
8-4.
Vacuum
159
8-5.
Vapor
161
8-6.
167
8-7.
..... ......
BErBBBNCES
Chapter 5-1. 5-2. 5-3. 5-4.
......... .........
Gas Ballast
Pump
...... .
5-13. Molecular-drag
...... .... ........
Pumps
5-14. Axial-flow Molecular Turbine
RErBBENCBS
Chapter 6-1.
Pump
Vapor-jet
Pumps
6-3. Theoretical
.
.
for Diffusion
Pumps
.
274 277 291
293 302
.
Pump
.........
The Design
Vacuum Systems
of
303 307
313
Valves
318
and Traps Absorption Traps
328 341
The Pumpdown Time of Vacuum Components BEFEBENCES
348
Baffles
Chapter 9-1. 9-2.
358
..... ....
179
183
9-5
Two -region Vacuum Systems
185
9-6
186
9-7
Pumping Absorption Pumping
194 199
202
Getter-ion
204 205
APPENDIX
I
214
APPENDIX
II
APPENDIX
230 240
Author Index Suhj ect Index
.
.
.
•
.. III
APPENDIX IV APPENDIX
.
V
.
.
.
.
•
.
.
.
•
.
.
365 370 378
.
..... ..... .
363
.
.... .... ....
.
..... .
Evaporative Deposition of Reactive Metals 9-9 Cryogenic Pumping 9-10 Ultrahigh-vacuum Systems 9-8
BEFEBENCES
218
Vacuum
The Dominance of Surface Phenomena High-temperature Bakeout
9-3
362
.
Ultrahigh
9.
Metal Gaskets 9-4 Bakeable Valves
177
219 227
.
Compression Ratio for a Vapor-jet
Working Fluids
172
Vacuum Pumps
The Steam Ejector
6-2. Diffusion
6-4.
6.
Pumping Speed
Seals
169
Perform
Other Methods of Preventing Contamination by Condensables 5-7. Mechanical Booster Pumps 5-8. Analysis of Mechanical Booster-pump Performance 5-9. Computed Performance Curves for Mechanical Booster Pumps 5-10. Measured Performance Curves for Mechanical Booster Pumps 5-11. Overheating of Mechanical Booster-pump Rotors 5-12. Vapor Compressor Action of a Mechanical Booster Pump
8.
Vessel
169
.
5-6.
of
8-8. Selection
Vacuum Pumps
Functions of Mechanical Pumps General Features of Oil-sealed Mechanical Pumps Pumping Speed of Oil-sealed Mechanical Pumps The Effect of Condensable Vapor upon Mechanical ance
5-5.
.
Mechanical
5.
.
Chapter Detectors
4-2.
Leak-detection Techniques
The Measurement
.
Demountable Motion Seals
4-5.
7.
272 272
....
8-2.
4-4.
268
Pumping Speed Measurement of Gas Flow Mechanical Pump Speed Measurements Measurement of the Pumping Speed of Diffusion Pumps RBFBBENCES
133
Mass Spectrometers The Omegatron Mass Spectrometer Linear High-frequency Mass Spectrometers Halogen Leak Detector
257
Alternative Definitions of
4-1. Magnetic-deflection
4-3.
,
7-1.
123
254
Pump
131
Vacuum Analyzers and Leak
4.
122
249
Resume of Diffusion-pump Performance BBFERENCBS
Chapter
113
3-11. The Alphatron Gauge ^3-12. The Knudsen Radiometer Gauge 3-13. Calibration of Vacuum Gauges 3-14. General Remarks on Ambiguities of Pressure Measurement in Vacuum Systems
KEFBBBNCES
6-9.
111
.
..... ........ ..... .......... ..... ....... Pumps
of Diffusion
Limiting Forepressure for Diffusion Pumps 6-7. Factors Contributing to the Ultimate Pressure of a Diffusion 6-8. Fractionation and Purging
6-6.
107
....
Gauges
Pumping Speed
XI
•
.
382
.
385 398
.
.
401
.
408 434
.
.
435
.
439
.
440
.
441
.
442
.
445
.
447
.
451
COMMONLY USED SYMBOLS
In some cases it has not been convenient to avoid the use of a symbol for more than one purpose. The most prevalent meaning of each commonly used symbol is defined in the following list. Exceptions are clearly indicated in the text.
a
A B c
C
radius of aperture or tube
area
magnetic flux density nozzle coefficient
conductance heat at constant pressure
Cj,
specific
C^
heat at constant volume diameter of aperture or tube electronic charge
D e
E /
¥ h,
specific
energy, electric field intensity
molecular sticking coefficient, frequency force
height of a column of liquid
R Ho ij^
coefficient
positive ion current
i_
electron current
1
electrical current
Ic
gas constant per molecule (Boltzmann constant)
/v
conductance factor
L
length
m
mass of molecule
M
molecular weight
n Wmoi
N
number of molecules per unit volume number of molecules in one mole total number of molecules present
p
probability of ionization
P
pressure
gas flow in molecules per second
COMMONLY USED SYMBOLS PdVjdt
Q
gas throughput,
R
general gas constant
Rg
gas constant per mole,
Re
Reynolds number
s
S
w,,,^]/^
sensitivity
pumping speed displacement speed of a mechanical
pumping speed t
at the inlet of a
time
T
temperature
u
drift velocity of
U V
F w
W z
Z
a gas
velocity velocity
volume mass flow power, mass of gas
number of electronic charges per atomic number
a
accommodation
y
ratio
coefficient
e
slip coefficient, efficiency
viscosity
A
ion
GJC^
r]
A
pump pump
mean
free
path
free molecular
heat conductivity
V
number
I
molecular diameter
p a
density,
T
period
of molecules impinging on one square centimeter of surface in
one second
mass per unit volume
collision cross section
VACUUM SCIENCE AND ENGINEERING
CHAPTER
1
THE NATURE AND BEHAVIOR OF GASES
1-1.
The General Gas Law.
of permanent gases
is
Our understanding of the behavior based upon the experiments of Boyle, Charles,
and Gay-Lussac which lead
to the general gas law. Experiments by Boyle resulted in the conclusion that the volume of a body of gas at constant temperature is inversely proportional to the pressure, which is
equivalent to the expression
PV =
const
(1-1)
where the pressure is defined as the force per unit area exerted by the gas on the walls of the containing vessel. Charles and Gay-Lussac observed that if the volume of a body of gas is kept constant and its temperature varied, the pressure increases linearly with the temperature, so that
^1
=
-Po(l
+
aT)
(i_2)
which T is the temperature on any chosen scale, such as centigrade F^is the pressure of the body of gas at zero on the same temperature scale, and « is a constant. If Eq. (1-2) is multiplied by V^, the initial standard volume of the gas sample, in
PiFo Then if the volume
=
PoFo(l
+
ocT)
(1.3)
changed to some other value, such as V, we have accordmg to Boyle's law is
PV =
P„F„(1
+
aT)
(1.4)
which can be written as
PV = P.V^T + The experimental
fact
centigrade scale, 1/a
(1.5)
the temperature is measured on the 273.I6°C, that is, the volume of a body of
is
=
that
1/a)
if
^^^ changes by an amount equal to 1/273.16 of its value T^^o^''?* at C for each degree change in temperature. This constant is essentially the same for a large number of gases (hydrogen, helium
I
THE NATUEE AND BEHAVIOR OF GASES
VACUUM SCIENCE AND ENGINEERING
2
and others) and therefore has very broad signifione chooses a new temperature scale such that —273.16 C zero, then one can write
nitrogen, oxygen,
cance. is
If
PV = PoFoaT where now the temperature
(1-6)
measured on the absolute centigrade,
is
or Kelvin, scale.
The implication
of Eq. (1-6)
is
that the pressure exerted
by a gas
volume approaches zero as the temperature approaches Although many common gases follow Eq. (1-6) over a wide
at constant
0°K.
Table
1-1.
Molecular Weights of Some Common Gases* Chemical Scale
Chemical formula
Molecular weight
Ha He Xe
O2 Ar
2.016 4.003 20.18 28.02 28.98 32.00 39.94
CO2
44.01
CL
70.91
^'2
Air (mean)
* See, for
gases
B„ The
ratio
= universal gas constant per mole W/M is the number of moles (gram
molecular weights) of the gas present. The numerical value of E^ depends upon the units of mass, pressure, volume, and temperature used. If the pressure is measured in torr, the volume in liters (1 hter = 1,000.027 cm^), and the temperature in degrees Kelvin, then for 1 mole (W/M 1) of gas
=
PV = R,T
real gases depart
the product the product
same pressure contains twice the mass, proportional to the mass of the body of gas. Thus
volume
PF is PF in
write
P,V„^T
WRT
(1-7)
i? is a constant of proportionality. Equa,tion (1-7) is one form of the general gas law which describes the behavior of an ideal gas is
approximately correct for
many common
For the
E(,
P= F = T = = PV T
760 torr 22,415/1,000.027
273.16°K
=
22.415
liters
0°C
760 X 22.415 273.16
=
=
62.364 torr liters/°K g mole
common choices of units In many situations
the numerical value of E^ is given in the mass of a body of gas is of no concern, but the changes in pressure, volume, and temperature are of interest. In this case a convenient form of the general gas law is
Table
where
and
so that
(1-6) is proportional
PV =
(i-sa)
Under standard conditions
at the
not only to the absolute temperature but also to the mass of the body of gas W, and we may
Eq.
(1-8)
W = mass of the sample of gas
Returning to Eq. (1-6), since at constant temperature the product PV for a given body of gas is constant for a given mass of gas, and since twice the
is
M = molecular weight of the gas
from this relationship at sufficiently large values of the pressure and low values of the temperature. Thus only for an ideal gas would the pressure actually approach zero as the temperature approaches absolute zero. all
given in Table 1-1. A more comprehensive table of molecular weights of gases is given in Appendix I. By referring to Eq. (1-7) we can now write the general gas law in terms of the molecular weight of the gas, as follows:
where
1957), pp. 7-9-7-12.
range of temperature and pressure,
some
common
^^=|^oT
example, American Institute of Physics Handbook (McGraw-Hill
Book Company, New York,
3
temperature and pressure the mass of a standard volume of gas is proportional to its chemical combining (or molecular) weight. Consistent with Avogadro's law, precise experiments have shown that under standard conditions of temperature (0°C or 273.16°K) and pressure (normal atmospheric pressure defined as 760 torr) 1 gram molecular weight of any gas occupies a volume of 22,415 cm^. This is the volume occupied by 32.00 g of oxygen (0^) at STP standard temperature and pressure, which is the arbitrary standard on the chemical scale of molecular weights. A partial list of molecular weights of
1-2.
PiFi
P2F,
gases over a wide
range of practical conditions. Further understanding of the nature of gases was contributed by Avogadro, who demonstrated experimentally that at the same
(1-9)
which follows directly from Eq.
PVjT
is
a,
constant.
(1-8), since for
a given
body
of gas
VACUUM SCIENCE AND ENGINEERING
4
Table
1-2.
THE NATURE AND BEHAVIOR OF GASES
KuMERicAL Values of Bg Gas Constant peb Mole fob Vabious Systems of Units* f
p
T
V
dynes/cm^ newtons/m^
cm^
torr
cm^
torr
liters
atm
cm'
"K °K °K °K "K
psi
ftS
"R
mS
i?„
8.314 X 10' ergs/°K joules/°K 8,314
62,364 62.364 82.057 1,546
torr
cm'/°K
torr liters/°K
atm cm'/°K lb ft/°R
ti,
=
6.023 X 1023
^^^Y5
=
^-^^^ ^
In engineering units,
1
lb
1958), 6th ed.
1-2.
Molecular Constitution and Kinetic Theory of Gases.
From the time of the Greek philosophers is made up of tiny indivisible particles
the concept that all matter called molecules had been
sporadically put forward to explain one or another of the observed On the basi s of the experimental results reported properties of matter by a number of independent investigators, Avogadro concluded that .
equal volumes of all gases under the same conditions of temperature and pressure contain equal numbers of molecules. We have already seen that under standard conditions (760 torr pressure and 0°C) a gram molecular weight of any gas fills a volume of 22.415 hters. The number of molecules contained in this standard sample of gas is obtained from the precise measurement of the faraday,
F =
96,488 coulomb
the electrical charge necessary to deposit a gram equivalent of a substance in electrolysis, and the charge on an electron, e
=
1.602
X 10-19 coulombs
which is the unit of ionic charge, determined quantities "^.^i ''mol
—
The
96.488 1.602
X
10-1-
ratio of these experimentally
6.023 X 1023
known as Avogadro's number; it is the number of molecules in a gram molecular weight of a substance, and is therefore the number of
is
^^" molecuIes/cm3
is worthwhile pausing to note the magnitude of this number. Its meaning can perhaps be visualized best by noting that if the molecules in a cubic centimeter of gas under standard conditions were arranged
It
at the corners of tiny cubic cells, the
mole of gas occupies 359 ft' at 32°F and atmospheric pressure (14.67 psi). The Bankine absolute temperature scale is based upon the Fahrenheit scale for which absolute zero temperature is — 459.69°F. Thus T °R = T °F + 459.69 just as T °K = T "C + 273.16. Physical Tables (Smithsonian Instit Sources: W. E. Forsythe, Smithsonian tution, Washington, D.C., 1954, 9th rev. ed.; T. Baumeister (ed.), Marks' Mechanical Engineers' Handbook (McGraw-Hill Book Company, New York, *
5
molecules present in 22.415 liters of any gas under normal conditions. The number of molecules in a unit of volume of gas under normal conditions is therefore
number of such
cells in
a centi-
meter length would be (2.687
X
lO^")!^ *
where
c,
effect at the wall
(2-33)
M
-f I
D^
Pi
f (2-34)
=
(2-35) 128>;
and
'^^
~
16\2 lW~/
~
/
(2-36)
When the pressure Pav is sufficiently high, the term c^P^yD^ dominates the term c^D^ and the flow follows Poiseuille's law as given in Eq. (2-20). When the value of the pressure is such that in (2-34) the term CiPav-D* is equal to the term c^D^, the character of the flow departs significantly
from that of
is
The pressure
Poiseuille's law.
for
which
be referred to as the transition pressure Pj
given by
c,P,D*
=
c,D3
16^
P.=
or
e is
would be no "drag"
-/
Pl-P2
(2-32)
the coefficient which determines the velocity of the gas at the inner surface of the tube. The interaction of the gas with the walls can be analyzed in terms of two distinct processes. Some gas molecules in striking the wall experience specular reflection and thus retain the same component of If all molecules velocity in the direction of flow as before the impact. there reflection specular striking the tube wall were to experience
in
2
where / is the fraction of molecules which are absorbed and reemitted, and 1 — / is the fraction which are specularly reflected. By substituting this expression into Eq. (2-32) one obtains for the gas flow through a tube of circular cross section
and
128»yL
Pi)(
by
given
this condition occurs will
Q = -^Pav(P.-Pi)(l +
D
is
U R^Tl
vacuum system,
dependent upon low-pressure range, where the performance is critically altered by the be not need pipe, the dimensions of the connecting of the pumpportion high-pressure the occurrence of turbulent flow in systems, vacuum in occur does therefore flow down cycle. Turbulent requirement.^ design additional any imposes but not in a way which Slip. 2-6. Correction to Poisseuille's Law Due to Surface confirmed been has (2-20) Eq. given in as flow Poiseuille's law for viscous experimentally over a wide range of gas pressure and tube diameter.
35
and the gas velocity would be
uniform over the cross section of the tube. Other molecules strike microscopic irregularities in the wall and bounce several times. Under these conditions a molecule may be absorbed by the wall and then reemitted later with a random distribution in angle and velocity.
(2-37)
c^D
At pressures
significantly below P^ the viscous flow term c^Ps^vD* is of decreasing importance and the nonviscous term CjD^ dominates. The correction to Poiseuille's law due to slip is therefore negligible at values of the pressure which are large as compared with the transition
pressure, but
becomes so important below the transition pressure that the character of the flow is completely altered. From (2-34) and the definition for conductance
Q
C= P.
-P.
C^P^yD*
+
CaD^ (2-38)
VACUUM SCIENCE AND ENGINEERING
36
GAS FLOW
From the disare given by Eqs. (2-35) and (2-36). and the form of Eq. (2-38), the character of the conductance of a tube can be seen to change radically, depending upon the
where
Cj
and
c^
cussion above
is
If the pressure
is
compared with
large
P(, the conductance
is
given by Eq. (2-21) and is (a) proportional to D*, (6) proportional to the pressure, and (c) inversely proportional to the viscosity. is 2. If the pressure is small compared with P„ the conductance inde(c) and (a) proportional to D^, (6) independent of the pressure, pendent of the viscosity.
An exact 2-7. Gas Flow in the Transition Pressure Range. treatment of gas flow in the pressure range in which both viscous and molecular flow are important is difficult and unsatisfactory because the coefficient of slip, the e which appears in (2-32) and is defined in (2-33),. An empirical approach to this is not calculable from first principles. problem was offered by Knudsen^* based upon a series of carefully controlled experiments on gas flow. Knudsen found experimentally that the coefficient Cj given in (2-36), which determines the magnitude of the nonviscous term in the corrected form of Poiseuille's law (2-34), can be expressed in the form
=K in
1
-f fciPav
(2-39)
kari 2^ av
which
^x4(5^f. 12 n^X m
A-=-«.,
J
substituting the value of Vav given in Eq. (1-23) value for {2kTlm)''^ given in (1-27). The values
by
M
that the value of / (the fraction of molecules which are absorbed and reemitted randomly when they hit the wall) is approximately 0.74, and therefore the fraction specularly reflected is about 0.26. If the pressure is sufficiently, high the terms k^Pa,^ and k^P&Y are very large
^
compared with unity and c^ Kikjk^) = corresponding value of/ is then about 0.85.
x lO^TIM)'^. The Thus Knudsen's results imply that the fraction of molecules absorbed and reemitted, as contrasted with those which are specularly reflected, changes slowly in the transitional pressure region. Including Knudsen's results in the 3.07
complete expression for the conductance of a tube given in (2-38), the final result is
C
(cm3/sec)
=
^
Pav
128??
^+
x
3.81
M^f ^-^1^5^ ^ k^Pav
(2-43)
L'
which the values for k^ and fcj are those given in (2-41) and (2-42), the viscosity is measured in poises, the dimensions in centimeters, the in
pressure in dynes per square centimeter {fi bars), the temperature in degrees Kelvin, and the mass in grams, so that the conductance is measured in cubic centimeters per second. Converting units to torr for pressure
3.81X10.(1)" \M]
X 103
3.81
If the empirical expression for c^ at very low pressure given in (2-39) compared with the theoretical expression given in (2-36), one finds
pressure. 1.
K=
so that
37
and to
C
volume, the above expression becomes
liters for
(2-40)
P
(liter/sec)
3.269 X
—L
Z)*
10-2-^ rj
and the numerical
3.81
ITV^l T\^ 1 + \m) 1 +
1. 1.333
X
103A;iPav
D^
1. 333
X
lO^jfcoPav
i"
(2-44)
(2-41)
This latter expression can be written
and
k.
1.24
5(i!L)"=1.38xlO-.:?(|| \ TJ n \kT/
(2-42)
C-
=3.269
10-
rj
fitting the experimental results of many measurements of gas flow and pressure difference. At sufficiently small values of the pressure the terms JfcjPav and AjaPav are both negligible compared
/TWl +
PavJ> 3.81
n
\m)
1
+0.1 81(MITf^{P^^DIrj) (2-45)
were obtained by
with unity, and 1 1
*
References indicated
chapter.
by
+ +
0.1 .liliMITf^iP^^DIr])
The quantity on the left side of (2-45), the conductance multiplied by the length divided by the cube of the diameter of the tube, is therefore a simple function of the variable Pav-D/»? as shown graphically in Fig. 2-3.
fciPa 1
fc^Pa
superscript numbers are listed at the end of the
Equation (2-45)
is
of the form
y
=
ex
ax
-\-
b I
+
dx
(2-46)
GAS FLOW
VACUUM SCIENCE AND ENGINEERING
38
y=^C-
where
X
the conductance, reaches a minimum. For pressures less than Pmin the conductance increases asymptotically toward the low-pressure value to be discussed in the next section, and at pressures greater than Pmin
L /MY'
=
the conductance increases with increasing pressure and eventually becomes proportional to the pressure as given by Poiseuille's law (2-21). In (2-37) the transition pressure P, is defined as that value of the pressure for which the viscous term CjD^Pav in the expression for the
n
a
=
3.269 X 10-2
^
=
0.181
(ff
with respect to x and setting the resultant has a derivative equal to zero determines the value of x at which y
Differentiating
minimum
(2-46)
value.
The
result
39
conductance of a tube given in (2-38) is equal to the nonviscous term When (2-38) is compared with (2-45) and (2-46) it is evident
C2D^.
when Pav
that in the notation of (2-46)
=
P(,
is
ex 3^Tnin
—
ax
14
'b(d
dx
(2-47)
,.
Solving this expression for x yields Substituting the values of the various quantities into (2-47) yields
1
{(be
2ad
(E^) =5.47(^f \
(2-48)
\M/
/mm
ri
the value of Pav£>/»? at which CLjD^ has a According to (1-58) the viscosity is given by
This
is
T]
by
=
0.499 wmUavA
=
1 ^ ^ 1.497 «av A
=
1.145
and Table
1-3
^ By
pressure
is
Since 10* dynes/cm^
measured
=
in
I
\m)
''Am)
dynes per square centimeter
at the transition pressure
(/xbars)
8.59
D
D
(2-56)
11.14
That (2-506)
\
is, at the transition pressure the diameter of the tube is about 11 times the molecular mean free path. Since for air at 20°C the viscosity r] 1.829 x 10"* poise, the mean
=
free
when the
pressure
is
From (2-48) and in torr. minimum conductance
measured
follows that at the point of
-^ so that
„,n
=
1.57i)
is,
when the mean
path according to (2-506)
is
(2-49) it
A
=
/
8.59
293
Y
1
829 X 10-*
(2-51)
(2-52)
5
P P
\28.98/
path of the molecules is 1.57 times the diameter of the tube, the parameter GLjD^, and therefore also
That
^'-''^
'l
X 750 X 10"'l]^l \
10*
(2-53)
T\^
= ''-Am)
96?7
X
iabdf"'}
(2-50a)
10^
750.06 torr,
1.145
+
combining (2-54) with (2-506) we obtain
Thus
when the
ay
in which the negative sign leads to a meaningless negative value for x. Using the positive sign, substituting the values for x, a, b, e, and d given above into (2-53), and noting that Pav is now the transition pressure Pj, we have
(2-49)
(2-49), (1-27),
X
value.
-
[(be
P.D
— XP Vav
1.497
Thus from
substituting from (1-11).
minimum
-a) ±
x 10-3
P
(2-57)
where A is given in centimeters and in torr. Thus for air at room temperature the minimum value of the conductance of a tube occurs at a pressure
free
-i
min
—
5
X 10-3
5
X 10-3 1.57Z>
3.18
X
D
10-3
given in torr and the tube diameter in centithe Correspondingly, in the case of air at room temperature
which the pressure
in
GAS FLOW
VACUUM SCIENCE AND ENGINEBBING
40
meters.
is
transition pressure occurs at
Ft-
5
10-3
X
5
X 10-3 X 11.14
X
so that the transition pressure range within which the character of the lOP, to P, O.IP,. flow changes ranges essentially from P„ 28.98 and 293°K, rj 1.829 x 10^* poise, For air at 20°C g,
=
M=
=
P,
(air
20°C)
=
293 95.7
=
predominantly viscous region over which the conductance changes from defined in terms of be can character to predominantly molecular in limit P„ and a lower upper an between bracketed
and
and is If the first term on the right
ax
I
=
106 I
is
+ +
much greater than
ex
(2-59)
dx
Solving this expression for x yields
X
=
—-{(106c -a)
±
2ad
-
a)'
^
is
= 948(^f
(2-55),
=
P„
first,
9.91P,
(2-61)
10 the second term on the right side of (2-46) is character. in then the flow is predominantly molecular
Correspondingly,
That
(2-60)
(2-65)
0.557
lOPt
so that
(2-66)
D 5.57
and
O.IP,
X 10-3 (2-67)
D
is given in torr and the pipe diameter in centimeters. given the range of pressure for the transition region for various pipe sizes in the case of air at 20°C.
when the
pressure
In Table
2- 1 is
2-1.
Transition Pressure Ranges for Various Pipe Sizes fob Air AT 20°C Transition pressure range, torr
Pipe diameter
by comparison with
times the
X 10-2
D
40abdf^}
meaningless negative in which, as before, the negative sign leads to a for a, 6, c, and d, value of X. Using the positive sign and the values
so that,
5.57
X 10-4
D
28.98,
Table [(106c
1.829
V-^
-
(2-46)
the second limit Pi. convenience For character. in viscous term, the flow is predominantly Then greater by a factor of 10. let us require that the first term be
the result
is
(2-58)
1 cm is a tube of i) so that, for example, the transition pressure for 5.57 X 10-2 torr or 55.7 fi. . r dependence ot At the transition pressure as defined above, the The pressure conductance on pressure is inconveniently complex.
(2-45)
=
=
the transition pressure from (2-55)
10-2
D
D
K
5.57
41
Centimeters
Inches
Pi
Pu
Pt
0.254 0.635
0.1
2.2 X 10-2 8.8 X 10-3
8.8
0.22 X 10-2
2.20
0.25
1.27
0.5
4.4 X 10-3
2.54
1.0
2.2
4.4 X 10-2 2.2 X 10-2
0.44 0.22
5.08 10.16
2.0
1.1
4.0
5.5 X 10-4
5.5 X 10-3
5.5
20.3
8.0
2.8 X 10-4
2.8
X 10-3
2.8
40.6
16.0
1.4 X 10-3
1.4
1.4
X 10-3 X 10-3
1.1
X 10-4
0.88
X 10-2
0.11
X 10-2 X 10-2 X 10-2
if
is,
lOax
=b
1
I
+ cx + dx
^2-62)
Also for air at 20°C the conductance of a long tube in the transition is obtained bj^ substituting the above constants into (2-45), with the result
pressure range
Solving for the value of x yields
C
rfsM
=
10.99
(2-63.)
(liters/sec)
=
1)4
178.7Pa
252.lPavi)-D3 12.12
(2-68)
311.7Pavi)T
when the pressure is measured in torr and the dimensions in centimeters. so that,
by comparison with
(2-55),
Pi
=
0.114P,
(2-64)
Note that the first term on the right side of (2-68) is and is therefore the viscous-flow term. Equation
identical to (2-23a) (2-68)
may
also be
GAS FLOW
VACUUM SCIENCE AND ENGINEERING
42
pass through the transition region rapidly as the system is pumped down. In such cases the laborious calculation of conductance in the
written in the form
C
D'
=
(liters/sec)
12.12
1
^|l4.74Pav-D
+
^
+
252.lPav-D
not justified and the operation of the by using the viscous-flow or Poiseuille form of conductance given in (2-23a to c) from atmospheric pressure down to the transition pressure P^ and the molecular-flow form of conductance to be discussed in the next section for values of the pressure below P^. transition pressure range
311.7Pav£>
system
=
12.12
—
(2-69)
G = 14.74Pav^ +
where
1 1
At
sufficiently large values of the 1 1
+ +
+ +
252.lPav-P
43
(2-70)
311.7Pav-D
is
sufficiently well represented
is
parameter Pav-D the fraction
252.1 Pay J>
311.7Pavi>
252.1
~
=
r
r rr
r"
0.808
r
Conductance curve from Eqs.(2-45) and (2-68)
311.7
[
viscous Term only, as given
first term which is then negligible as compared with 14.74Pavi>. The viscous for to (2-23a) in the bracket then dominates, and (2-69) reduces becomes However, when P^^D is very small, the first term flow. approaches unity for negligible as compared with the second, which The value of G is then 1 and sufficiently small values of the parameter.
in
t%\Z-Zt^]
/ 1
1
[ill
1
/ / 180 1
160
1 1
/
1
/
/
limiting
low-pressure the conductance is given simply by 12.12D3/L, the next section. In the in discussed be to conductance the of value parameter Table 2-2 are given values of G from (2-70) as a function of the
1
2-2.
Values of the Factor O fob Vaeious Values OF THE PaBAMETER P^yD
f J
ll
1
/
1
7154"
_
^
1
Pe^yD, torr
,
^ '11
io-« 10-3
0.9994 0.9957 0.969
10-2
1.002
10-1 1
10 102 103
2
IQ-5
3
5
7jQ-4
2
3
5
7|q-3
2
3
5
7 jq-2
_
'.-'
^ji 2
3
40
yj
20
K**
L 5
7 ]q-I
2
3
5
7
1
Fig. 2-3. Conductance of a tube as a function of the pressure.
2.289
2-8. Gas Flow at Low Pressure. At low pressure, i.e., at values of the pressure at which the mean free path for collisions between molecules is long as compared with the dimensions of the tube or
15.55 148.2
1,475 14,740
These values may be obtained from Fig. 2-3 by dividing the Pav-D. values of the term CL/D» plotted in the graph by the factor 12.12. In designing a vacuum system in which prolonged operation is expected to occur in the transition pressure range, calculation of conductances by (2-45) or (2-68) may be justified. However, in most practical systems the pressure in the forevacuum portion of the system remains in the viscous-flow regime during the crucial period of operation,
60
/; i
1
80
;
12.12
1
cm
10-5
;
;
-
rt:
100
/
/
y
1
Air at 20°C
120
f
00 rrJ
Table
140
whereas the piping and main chamber beyond the diffusion
pump
conduit through which gas flows, the mechanics of flow are entirely from those at high pressure. The gas molecules move in random directions with a velocity distribution characteristic of the temperature as given by the Maxwell-Boltzmann distribution law diff"erent
(1-21), and by pure chance individually progress from one point in the system to another. Collisions between molecules are very rare events, whereas collisions with the walls of the system dominate so that the molecules, instead of jostling each other by collision processes, move independently of one another. Pressure is not transmitted from one
GAS FLOW
VACUUM SCIENCE AND ENGINEERING
44
momentum from region in the system to another by direct transfer of region of lower molecule to molecule, thus producing a flow toward the the molecules pressure; instead, the transfer of momentum is between character of and the walls of the system. In spite of the independent occur motion of the individual molecules, net flow does nevertheless lower of from the region of higher density (or pressure) to the region a leaving molecules density. Net flow results because the number of the to proportional unit volume of any given region in the system is in the unit of arriving number the whereas region, that density in those other volume from elsewhere is proportional to the density in By a purely statistical effect, therefore, net flow is always in
per second
is
45
thus
dn mn (2kT\^ mu—- = ^m su
dp
I
2tt^\
dt
'di
m
1
Az
(2-72)
J
Since the rate of change of momentum represents a force exerted by the gas molecules on the tube A/ = dpjdt, the tube reacts with a retarding force on the flow of gas of this same magnitude. This retarding force acts over the cross section of the tube so that the change in pressure
is
A
1
dp
A
dt
(2-73)
regions.
and thus from the direction tending to equalize the density everywhere In the pressure regions of higher to regions of lower density or pressure. process is called regime for which the above conditions hold the flow molecular-flow rates molecular flow. Approximate formulas for princithrough tubes and apertures of various shapes were developed pally
by Knudsen.^ Conductance
2-9.
of a
Long Tube
at
Low
Pressure.
In a
(see Fig. 2-4) tube through which gas is flowing at very low pressure wall at the the the molecules move in random straight lines, striking Maxwell-Boltzmann end of each free flight. If the molecules have the
distribution (1-21)],
of
velocities
[Eq.
V
pressure.
Thus the number tube
A
(2-72)
we have
is
=
WWav
1
Combining
the cross-sectional area of the tube. for the change in pressure
(2-73) with
mnl2hT\^s 277-^ \
m
I
(2-74)
A
nkT, the pressure gradient
Since, according to Eq. (1-16)
nkTI m \'^g _ _ P m \-^i ~i^\^kT) a'^~ 7T'^\2kT/
AP
-^1
"a7
The quantity of gas flowing through the tube
then the number of gas
molecules impinging on a square centimeter of surface area each second is given by Eq. (1-31) as Fig. 2-4. Motion of molecules at low
where
Q = PAu from which
Pu =
QjA.
is
(2-75)
is
/jh&T cm*/sec
(2-76)
Substituting this expression into (2-75) yields
/2)fcT\^
2n^
striking the wall each second in the length
For an extended section of a tube of uniform cross section
AP/Az
Az of the
=
(Pi
-
Pa)/^
which Pj and Pj are the values of the pressure at the ends of a section of tube of length L. Substituting this value of AP/Az into
in
is
dn dt
^
n /2kTf Stt'-^V
m
(2-77) /
and solving
for
Q gives for the gas flow through a tube of uniform
cross section
the periphery of the cross section of the tube, which might be circular or have any other shape. If each molecule is completely stopped by the impact at the surface and then reemitted randomly, there is a net momentum transferred to
in
which
P,A^
s is
the wall of the tube, provided that there is a mean drift velocity u in the direction of flow. The momentum transferred to the increment of length Az of the tube will therefore be mu on the average for each molecule hitting the wall in the segment Az. This momentum transfer
\
m
(2-78) I
The above derivation contains the implicit assumption that a uniform u is superimposed upon the random Maxwell-Boltzmann distribution of the molecules. Knudsen has shown that one should more reasonably assume that the superimposed drift velocity of a molecule is proportional to its thermal or random velocity. On this drift velocity
GAS FLOW
VACUUM SCIENCE AND ENGINEERING
46
numerical factor in modified assumption Knudsen found that the along a tube of flow the (2-78) must be multiphed by S/Stt, so that uniform cross section is given correctly by
_ _8_ (2JcTf P^ -Pi A^
(2-79)
=
/2fcr\^^^
8
Q
~ 3^\ m
'P^^Hp^
= ^,(1.29xl0^)y 3.44
sL
J
measured Cair
when
D
is
and
in inches
L
in centimeters,
=
13.82-—
in feet.
and
cfm
(2-82a)
Equations (2-80) to (2-82) apply to
L
of a long, straight tube well removed from the ends. They also apply to the case of a tube for which the length is very large as compared with the diameter so that the end effect is small. If the tube is short, however, an end correction is required to obtain results which are even
approximately correct. Consider a tube of circular cross
^
X 10V?'\'^^'
D and L are
a segment of length
of which proves to agree with experimental results. The conductance therefore is section cross uniform a segment of a long, straight tube of
C
when
47
section
and
length
finite
L connect-
ing two regions, one at pressure P^
cm^/sec
and the other
at pressure P^, as indicated in Fig. 2-5. If the length
_34^/T\^£^
(2-80)
liters/:
by
The conductance of a tube of uniform
substttuting from (1-27).
circular cross section, for
=
which A^js
ttD^JW,
therefore
is
X
103
[mJ
cm^/sec
T
is
is
an aperture of
sectional
area
decreased to zero,
A =
IP (2-81)
liters/sec
1i
when
D and L
(2kTY^
277^^
i2kT^
C when
B is
measured
=
cfm
4.34
in inches
and
L
For
in feet.
(2-81a) air at
Fig. 2-5.
room temper-
\
D^
m
so that
(7air
=
molecules/sec
Z)2
(2-84)
28.98/
The net flow from the region
Z)3
(3,810)(3.181) 9'
=
g-i
-
^2
12.12
X 10^^^
12.12-— Li
cm^/sec
liters/sec
^i\mkTIY 277
(2-82)
since in each region
n
at
=—
I
Pj to the region at Pg
-:-
8 \
i)3
=
(2-83)
n^7T''^(2kTY
,
Ml
ttD'^
-^
molecules/sec
q^=v^A=-i--\ \
effects.
Similarly, the number of those which pass through the aperture from the region at pressure P^ on the right is given by
ature (20°C)
.if,
Tube end
The
% M =im\—) m
=
and
are measured in centimeters,
cross-
ttD^I^.
formula for the conductance of the tube must become equal to that of the aperture as the length of the tube shrinks to zero. In order to complete the derivation of the conductance of a short tube, including end effects, it is necessary first to derive the conductance of the aperture. 2-10. Conductance of an Aperture. In accordance with (1-32) the number of molecules which pass through a circular aperture from the region at the left is
C 3.81
of the tube
the result
D"^
(Pj
= PjkT
m —
)
(wi
-
is
then
n^)D^
/
Pj)
molecules/sec
(2-85)
put in terms of the volume of gas leaving the flow occurs, then region of higher pressure Pj from which the net If this net flow
is
q (molec ules/sec)
^
^^.^^^^
=
The flow in quantity of gas is defined as Q and in this case from (2-86) is given by
Q
A
at low pressure
(dldt)PV(fihaT cm'/sec)
of which (2-85) an aperture is
_L-I
=
= !^(?^f Z).(P, _ 8
\
is
m
3.64
X lO'(^) '^(Pi
C=
10^ (-^)
-
P2)
/^laar
cm^/sec
Thus the conductivity of an aperture of any shape
=
Q=!^(1.29xlO*)(|)V(Pi-P.) X
molecules/sec
Pa)
(2-91)
D%Pi -
/^bar cm^/sec
P2)
(2-92)
(2-87)
P„ :)
/
expression becomes
2.86
-
Correspondingly, the gas flow through
a special case.
Referring to (1-27), one finds that this
substitution from (2-85).
=
J(Pi
1
= P,±=qkT n.
by
=
is
(2-86)
Pi
n^ (molecules/cm^)
of area
q
^JcT
49
GAS FLOW
VACUUM SCIENCE AND ENGINEEBING
48
(2-88)
when
A
is
measured
a circular aperture.
/ T'Y X lOH T7I ^
3.64
I
3.641
—TY A
at
is
cm^/sec
liters/sec
1
low pressure
(2-93)
in square centimeters, corresponding to (2-89) for
Also rp\Vi
The conductivity of a
C
=
Q
P,-P /
2 86
when
D
is
circular aperture
=
2.86
—TY D^
is
C=
thus
X lOM-—
I
D^
cm^/sec
when
A
measured in square inches. 20°C these expressions become is
(2-89)
liters/sec
C =
\MI
when
measured in centimeters, and
A
is
11.6^
when
when
D is measured in centimeters, C =
when (TIM)'-^'
=
3.181, (2-90)
cfm
(2-90a)
D is measured in inches. Note that the above derivation could have been carried out for an aperture of any shape since the result given in (2-89) depends only on the cross-sectional area. In general, the net flow through an aperture
when
A
2-11.
159 A
(2-94a)
cfm
is
measured in square inches.
Conductance
Tube return now of a
at
Low
Pressure Corrected for
to the conductance of a tube of Joining circular cross section and limited length, as shown in Fig. 2-5. may be tube the two regions at pressures Pj and Pj respectively, separated and the are which considered as an aperture, the two sides of
End
and
125.31)2
(2-94)
liters/sec
(2-89a)
cfm
D is measured in inches. For air at 20°C, since liters/sec C = 9.16Z)2
Again, as in (2-90), for air at
measured in square centimeters, and
C = C = 39.i/-|f Z)2
(2-93a)
cfm
49.
Effect.
Let us
tube of length L connected between them. The result is a combination of two conductances in series, that of the tube C^ and that of the aperture Co, so that according to (2-9) the resultant conductance is
-=
or \
C=
——
7;
(2-95)
GAS FLOW
VACUUM SCIENCE AND ENGINEERING
50
which C^ is given by (2-81) and Cq is given by (2-89). Thus for a tube of limited length L the conductance at low pressure is
in
which,
when combined according
C (3.810)(2.86)
C
X 103(T/Jf)'^Z)2
2.86
X \0^{T j M)'^^
X
3.810
(—1
lO''
y\!^
3.810
when
D
and
L
cm^/sec
2)3
(2-96)
(I)
are
measured
in centimeters,
MI
C
and
direction of flow
D is measured in inches and L in feet.
with (2-82) we see that for air
C =
Comparing this expression
is
X
109
when
D
and
L
are
L +
measured
C =
liters/sec
%D
in centimeters,
(2-97)
and
7)3
13.82
cfm
O.llD
(2-97a)
when D is measured in inches and L in feet. The above calculation was carried out for a tube of circular cross section. The conductance of a tube or conduit of uniform cross section of any shape can be derived by combining the conductances given
in (2-80)
and
(2-93) in accordance with (2-95), using the appro-
A
and the periphery s. Thus, for a channel of rectangular cross section with sides a and h and length L, the conductance at low pressure is made up of the two components
priate values for the cross-sectional area
C,
9.71
X
103
TV Ml
a^ft^
{a
+
(2-98)'
b)L
/rpVA rpVA
and
Co
=
3.64
X
lO^I
—
I
ab
is
T ab^ Ml L + %b
narrow
a
slot
also large {L
C =
Z>3
12.12
(2-100)
'^ b,
> 6),
(2-101)
liters/sec
in
which the length in the
the conductance
is
ab'' (2-102)
liters/sec
»"ls
by
cm^/sec
%
L +
liters/sec
+% ab
+b)L
In Eqs. (2-100) to (2-102) the conductance for air at 20°C is obtained setting 9.7l(TjMy-^^ = 30.9, so that, as an example, the conductance of a slot from (2-102) is
Z)3
12.12
(a
9.71
C
at 20°C the conductance of a tube with
the correction for the end effects
cm3/sec
% ab
b)L
b and in which the length L of In the case of a long slot in which a the slot in the direction of flow is not necessarily very large as compared with the width b of the slot,
Finally, for a long,
when
+
(a
^
*AD liters/sec
W)
j'VA
'
{D'' j L)
9.71
=
to (2-95), yield a262
103
X
9.71
X 10/»? (2-45)
High-pressure or Viscoiis Flow. The pressure region of viscous flow is that for which the molecular mean free path is short as compared with the diameter of the pipe or conduit. For these conditions the
conductance of a tube of circular cross section
is
in
which
G is measured
in liters per second,
Pav is in torr, T is in °K, 20°C the conductance is
M
is
in grams,
L and D are
and
r]
7)3/
C
(liters/sec)
=
3.27
x
10"
(2-226) rjL
D and L are measured in centimeters, the viscosity rj is in poises, and the pressure is in torr, where Pav = (Pi + P2)/2, in which Pj and
if
C
(liters/sec)
^
12.12 .^(l4.74
P..D
is
in centimeters,
in poises.
\
_j_
252
^
^
3,/,
+
1
For
air at
P D\
^J
(2-69)
For accurate calculation of the conductance of a long tube, these formulas should be applied over a range of pressure from lOP^ to 0.1 Pj,
gas flow
VACUUM SCIENCE AND ENGINEERING
60
where P;
is
the transition pressure given
P,
which
for air at
20°C
=
95.7
X 10-2
5.57
D Calculation of conductances (2-69) is
seldom
by the
justified in practice.
Conduit of Rectangular Cross Section
by
MI D
is
61
C =
(2-55)
G
a^b^
9.71
[mJ
1m, (a
(a in
which a and
h)L
+
b)L
(2-100)
+ %ab
a%^ 30.9-
(air)
(2-58)
transition formulas (2-45) and It generally suffices to use the
+
b are the
+
(2-lOOa)
y^ab
dimensions of the cross section and
L
is
the
length in the direction of flow.
viscous-flow value of the conductance as given in (2-22) and (2-23) from atmospheric pressure down to the transition pressure given in
1.0
o1 T_. n _. L —ll-^^ U Ll_L_L
and the molecular-flow conductance such as that given in (2-97) from the transition pressure on down. Molecular Flow at Low Pressure. At sufficiently low pressure, i.e., when the mean free path is large as compared with the cross-sectional
.
(2-58)
1
I
I
•
Calculated points
°
Expenmentol points
/
'
I
fnr(R/R/
=
dimension of the tube or conduit, the conductance is independent of the For most purposes the conductance formulas derived partly pressure. empirically by Knudsen are sufficiently accurate. In the following formulas the linear dimensions are measured in centimeters, areas are in square centimeters, conductances are in liters per second, temperature The values for air are given is in degrees Kelvin, and mass is in grams. The less frequently needed equivalents for conductance in at 20°C. cubic feet per minute and dimensions in inches and feet are given in the text.
L/Ro
Circular Aperture
Fig. 2-11. Molecular -flow factors for a tube with two restricted ends.
C
(2-89)
C(air) in
which
D is the
=
9.16i)2
(2-90)
Fig. 2-12. Molecular-flow factors for a tube with two restricted ends and a circular blocking plate. [Taken with permission from L. L. Levenson, N. Milleron, and D. H. Davis, in 1960 Vacuum Symposium Transactions
[Taken with permission from L. L. Levenson, K. Milleron, and D. H. Davis, Le Vide 18, 42 (1963).]
diameter of the aperture.
(Pergamon Press, London,
1961).]
Aperture of Any Shape
in
which
A
is
C
^ ZM{^fA
C
=
(air)
Slot of Long,
C 11.6^
C
Tube of Circular Cross Section 'pVA
=
\m] L
Long, 2)3
(air)
Narrow Slot with
=
in
which
D is the
(air)
=
diameter and
12.12
a
the length of the tube.
6
C
+ %b
(2-101)
L
+%b
(2-lOla)
> 6 and L ^b
(2-96)
IT 9.71
T
(2-102)
(2-97)
C L
>
ab^ 30.9
\M.
C
a
ab^ 9
(2-94)
the area of the aperture.
C ^ 3.810(-)
Narrow Cross Section
(2-93)
(air)
=
30.9
~L
(2-103)
VACUUM SCIENCE AND ENGINEERING Annulxjs between Concentric Tubes
Two
G = 3.810
T\^ {D/ L \MI
CHAPTER
- D,^)(D, - D,) + %{D^ - A)
3
PRESSURE MEASUREMENT IN VACUUM SYSTEMS
(2-104)
C
(air)
- D,')(D, - -Di) L + %{D, - D,)
{D^ 12.12
(2-105)
Fig. 2-13. Molecular-flow factors for
a tube with one restricted end and a [Taken with circular blocking plate. permission from L. L. Levenson, N. Milleron, and D. H. Davis, in 1960 Vacuum Symposium Transactions
By combinations of the above formulas the conductances of many comphcated shapes, such as baffle, structures, can be roughly approximated. The Knudsen formulas are generally
only
approximate
and
for short tubes give conductances
may be greater than the true value by as much as 11 per cent. The results of more accurate calculations and measurements for some shapes are given in the text and in
(Pergamon Press, London,
which
1961).]
Figs. 2-6 through 2-13.
REFERENCES 1.
2. 3.
4. 5.
6.
M. Knudsen, Ann. Physik 28, 75 (1909). M. Knudsen, Ann. Physik 28, 999 (1909). P. Clausing, Ann. Physik 12, 961 (1932). D. H. Davis, J. Appl. Phys. 31, 1169 (1960). L. L. Levenson, N. Milleron, and D. H. Davis, in 1960 Vacuum Symposium Transactions (Pergamon Press, London, 1961), p. 372. L. L. Levenson, N. Milleron, and D. H. Davis, Le Vide 18, 42 (1963).
The most important parameter to be measured in a vacuum system the gas pressure. The pressure of interest may be the total pressure, including both the easily condensable and the permanent gas components present, either the condensable or permanent gas components is
separately, or finally the partial pressure of each of the constituents,
such as oxygen, nitrogen, hydrogen, carbon dioxide, etc. The range of pressure over which reasonably accurate measurements are of interest extends from atmospheric pressure down to 10"^^ torr or lower. Gauges and techniques have been developed by which any of the various types of pressure mentioned above can, in principle, be measured with the necessary sensitivity; but particularly for values of the pressure below about 10~* torr ambiguity and error arise from parasitic effects within existing gauges which make accurate determination of the pressure difficult.
rU
3-1.
Liquid Manometers.
A
liquid
manometer
tube partly filled with liquid. One end of the to the system in which the pressure is to be measured. The other end either
is
U
consists of a
tube
is
connected
open to some reference
pressure, such as atmospheric, or
closed off with the
To the
is
system
volume above
the liquid level evacuated.
Open
and closed manometers are
illus-
To the
system
trated in Fig. 3-1.
Open manometers
are generally
used to measure pressure relative to atmospheric pressure and may be filled with any liquid, of which water,
and mercury are commonly The engineering term gauge pressure and units such as inches of water and millimeters of Hg for the pressure difference grew naturally from the use of open manometers. oil,
used.
63
Open
Closed
Fig. 3-1. Liquid manometer.
VACUUM SCIENCE AND ENGINEERING
64
PRESSURE MEASUREMENT IN VACUUM SYSTEMS
Closed manometers are more generally used for measurement of pressure small as compared with atmospheric. An exception to this statement is the mercury barometer, which is in fact a closed manometer designed specifically to measure atmospheric pressure in absolute units,
i.e.,
A
relative to zero pressure.
manometer
closed
is
first
thoroughly evacuated and then filled to the proper level while still under vacuum so that the gas pressure over the liquid in the closed arm is negligible as compared with any pressure to be measured. The open end is connected to the system so that a difference in level or head between the surfaces of the liquid in the two arms will be just proportional to the total pressure in the system. level h is related to the pressure according to
The
difference in
P=gph in
which the pressure
(3-1)
P is in dynes per square centimeter or /
The
sensitivity of the
Dubrovin gauge from dh
Tdi2
n
^ +7 4
{d^
_
di^)ps9L
=J
W
d^')Pm9{^
-
h)
(3-3)
dj^
-
h)
(3-6)
(3-6) is
1
(3-7)
dP~d^-d,^'^
which is to be compared with (3-1) for the mercury U-tube manometer which the sensitivity is l/gp^. The sensitivity of the Dubrovin gauge is thus greater than that of the mercury U-tube manometer by for
the factor dx'
F d^^
it
the gauge so that the residual pressure throughout the gauge, including the region Fig. 3-5. The Dubrovin gauge. inside the steel tube, is very low. While still evacuated the gauge is returned to the vertical position with the steel tube floating in the mercury, as shown When gas is admitted through the connection at the top in Fig. 3-5. of the gauge, the steel tube is pushed down by the pressure more deeply into the mercury. For some pressure P in the gauge the balance is reached when the weight of the tube plus the force exerted on the closed end of the tube by the gas pressure is equal to the change in weight of the displaced mercury. If d^ and d^ are respectively the inner and outer diameters of the steel tube and p, its density, then
9Pm(K
d,^
cury.
laying
d,^
For a factor
F=
-
(3-8)
dj^
=
=
10 and d^ 1 cm one finds from (3.8) that d^ 1.05 so that the wall thickness of the steel tube must be about 0.025 cm, or 0.010 in. For such a gauge a change in A of 1 cm represents a
cm
change in pressure of 1 torr, so that pressure changes of 0.1 torr can be detected with ease. With a sensitivity of this order the Dubrovin gauge is a convenient instrument for the measurement of pressure in the range below that easily read on a manometer, but above that normally reserved for the McLeod gauge discussed below. 3-4. The McLeod Gauge. 7 By combining a liquid manometer with means of compressing a sample of gas as is done in the McLeod* gauge, the range over which the pressure can be measured can be extended considerably below the practical limit of about 10-^ torr for the mercury manometer. The essential elements of a McLeod gauge are shown in Fig. 3-6, and consist of a glass bulb with a capillary tube extension on the top, a side arm connnecting to the vacuum system,
and some means of
raising
and lowering the
liquid level within the
PRESSUBE MEASUREMENT IN VACUUM SYSTEMS
VACUUM SCIENCE AND ENGINEERING
70
The fluid normally used in McLeod gauges
gauge.
is
mercury, although in a few exceptional instances organic fluids of low vapor pressure have been used.
which holds
for all values of h^
From
system.
{K
When the mercury level in the gauge is lowered below the branch point A the bulb of volume V is connected arm B. The gas in the as that in the pressure bulb is then at the same raised, the bulb level is system. When the mercury of gas sample the is cut off from the side arm and
to the system through side
compressed into the capillary Cj. The capillary C^ is in parallel with a section of the side arm B and has the same bore as C^ so that the surface tension or capillary effect is the same. The difference in level of the mercury in G^ and Cg is therefore due to the pressure difference resulting from compression of the
sample from the large volume V into the small -'volume of Cj above the mercury level. The pressure of the compressed gas in the closed capillary is proportional to (Ag — ^i) + ^O' ^^ which hi and h^ are the heights in millimeters of the mercury in capillaries G^ Fig. 3-6 gauge.
McLeod
the system ratio
pared with
A.2
—
is
K- The
thus just equal to h^
still
and
C^,
and P^
typically very large,
is
the pressure in
Since the compression
present in Cg.
P„
is
negligible as
com-
pressure of the compressed sample of gas is torr within the limit of reading error when
—K
and ^2 are measured in millimeters. manent gas only during the compression
If the
hi
system contains per-
cycle, according to the general
gas law (1-1)
PV = P'V
-
is
and
P
(^0
K){K
-
1,000
h)-
h^-hi = P^ =
P=
(^2
—
raised in the
PV =
const
(3-12)
const
(3-13)
hi){h„—hi)a (3-14)
-
A McLeod
gauge may conveniently be read by bringing the mercury up to the point where ^2 = h^ (i.e., the level in the open capillary opposite the end of the closed capillary) or the mercury level can be set at some standard level h^ in the closed capillary. In the first method level
with ^2
hi)a
=
^0 the pressure
is
(3-10)
=
{h,
-
1,000F is its
is
which is in considerable contrast with the criterion in (3-12). If the vapor pressure of the contaminant in the system is fairly low and some permanent gas is also present, a behavior somewhat in between that of (3-12) and that of (3-13) will result. The important point is that if criterion (3-12) is not obeyed, the pressure readings as determined by a McLeod gauge will not be valid. One can then conclude that the system or the gauge itself is contaminated by a condensable material, the room-temperature saturated vapor pressure of which is given approximately by (3-13). Returning to the measurement of permanent gas pressure with a McLeod gauge we find that the pressure from (3-11) is
1,000
the effective height of the closed end of capillary Cj and a cross-sectional area in square millimeters. Then h^
mercury
1,000F
F'
where
h^ as the
evident that
provided that the pressure is due to a permanent gas as defined by In using a McLeod gauge this point should be periodically (3-9). checked, i.e., the mercury should be raised to two or more levels, the values of A.2 a-nd h^ measured, and the criterion given in (3-12) checked. In an extreme case the remaining gas present in the system may be due to a substance for which the vapor pressure at room temperature is In that case the pressure will increase during compression only P^. to the point at which P = P^, beyond which condensation will occur and the pressure will be independent of the volume of the sample. In that case for a condensable vapor
(3-9)
and P' are the pressures before and after compression, respectively, V is the volume of the bulb (i.e., the volume of the closed portion of the gauge above the cutoff point A), and V, the volume of the closed capillary above the mercury level h^, is given by
in which
(3-11) it
71
h,Y
is
PV =
(^2
—
hi){ho
1,000
—
in
which the constant of the gauge
method with
h^
=
(3-11)
ki(M)i^
=
a/l,000F.
(3-15)
In the second
h.
„
hi)a
k^
=
^=
a(h„
—
h,)
1,000F
^^'
~
^^^
=
^^^^^^'
(3-16)
VACUUM SCIENCE AND ENGINEERING
PRESSURE MEASUREMENT IN VACUUM SYSTEMS
which the constant of the gauge k^ = a(^o - h^)j\,()()QV. In each method A^ is the difference in mercury level in the open and closed capillary when the mercury level is set in the prescribed manner. The first method leading to the formula (3-15) results in a pressure reading proportional to the square of the reading, whereas the second method leads to (3-16), in which the pressure is proportional to the first power of the reading. The sensitivity can perhaps best be defined from (3-15)
^0 can more easily be determined and also to avoid an exaggerated tendency of the mercury column to stick whenever the mercury level comes within a millimeter or so of the closed end of the capillary. The effective height of the closed end of the capillary cannot, in general, be determined accurately by eye because of irregularities near the end of the capillary produced in sealing the end. The true value of h^ can be determined by applying criterion (3-12) to the gauge, which is thoroughly trapped to eliminate condensable vapors, and choosing a value of h^ which fits (3-12) best for several values of h^ and h-^. The McLeod gauge is inherently a cumbersome instrument to use in the pressure range from 10-3 to 10-« torr, in which it is most needed as an absolute gauge. Since it must be made at least partly of glass, it is a fragile device in which the shifting load of mercury must be carefully supported or disastrous breakage will occur. The interior of the McLeod gauge and the mercury used must be scrupulously clean and particularly free of oil and grease, otherwise readings are meaningless and the mercury sticks in the capillary, refusing to come down when
72 in
when AA
= 1 mm,
which
with reasonable accuracy.
gauge
is
about as small a value as can be estimated
On
this basis the sensitivity of the
McLeod
is
P.
=
3.9
X 10-« torr
(3-17)
4,000 X 200
is a practical and useful sensitivity for vacuum measurements. The McLeod gauge has a unique role in the measurement of pressure in vacuum systems and is frequently used as the standard gauge for calibrating most other types of low-pressure gauges.* As can be seen from Eqs. (3-15) and (3-16), the cahbration of a McLeod gauge depends only upon the measurement of the volume V of the bulb and the crossThe volume of the bulb can be sectional area of the capillary tube. measured with great precision by inverting the gauge, filling the bulb and tubing up to the branch point A with mercury, and weighing the mercury. The cross-sectional area of the capillary can best be measured by filling a measured length of the capillary with mercury and weighing
which
the mercury level is lowered. The connecting tubing for a portable McLeod gauge is frequently a source of error since to be convenient in use its diameter must be fairly small and its length typically a meter or more.
The conductance of such a connecting tubing is very small, usually not more than 0.1 liter /sec, so that a small leak at the gauge end of the tubing can give rise to an unexpectedly large discrepancy between the and that seen by the gauge. Such an error can and estimated if the gauge connection can be closed off next to the system and the pressure rise in the gauge due to leakage measured for a specific time interval, such as 5 min. The procedure is pressure in the system
the small sample of mercury. Since capillary tubing is not necessarily of uniform cross section, a length of tubing must be tested and a section of sufficiently uniform diameter chosen. By placing a drop of mercury in the tubing, moving it along the tube, and measuring the length of the mercury column formed at several positions along the tube, the
easily be detected
to take a normal reading P^ with the gauge, then close off the line near the system and wait several minutes and take a second reading P^.
variations in diameter can be easily determined and an acceptable section found for making both the open and closed capillaries Cj
and
C2.
73
Any
appreciable increase of P^ over P^ is an indication that the gauge due to leakage may be serious. To evaluate the gauge error the total volume being filled by the leak must be estimated. This total error
mm
is imExperience has shown that a bore diameter less than 1 practical because of the tendency for the mercury column in a finer capillary to separate, leaving a bead of mercury plugging the closed capillary after a reading has been taken and the mercury level lowered For high sensitivity it is therefore necessary to to empty the bulb. increase the volume F of the bulb rather than to decrease the capillary bore to less than 1 mm. The end of the closed capillary must be sealed off as squarely as possible in order that the zero point of the gauge
volume consists of the gauge volume (the bulb and side tube) and the volume of the connecting line up to the cutoff point. As an example, assume that Pj
P2
1
L
1
/ 1
1
1
50/iAatO.Ol/i^
100
1
— —1—1
is
while the voltage is on, observing certain precautions will contribute The gauge tube to greater operating life by avoiding contamination. should not be mounted in a position where it is in a direct line with a source of hydrocarbon vapor. It should not be operated at pressures in excess of 10 torr nor during the pumpdown period. A simplified circuit diagram for the Penning discharge gauge is shown in Fig. 3-47, and the pressure response curve is shown in Fig. 3-48.
Kinney Penning discharge vacuum gauge.
1
N.
1
y
/
/
/
/
^
—
/
1
1
1
lu
1
10'
/ 10"
/
/
7
10"*
/
10"*
10"
10"
10"'
Pressure, torr
Fig. 3-48. Calibration curve for Kinney Penning discharge gauge.
VACUUM SCIENCE AND ENGINEERING
118
PRESSUEE MEASUREMENT IN VACUUM SYSTEMS
The gauge
is calibrated over the pressure range from 2 x 10~' to 10 torr, the response above about 2 x 10~* torr being much flatter than at lower pressures as shown in the figure. A further development of the cold-cathode ionization gauge was
carried out by Beck and Brisbane,*^ Haefer,** and Redhead*' and has culminated in a gauge of high sensitivity and reliability. The added
cathode
H
is which E is the electric field intensity in volts per centimeter and is velocity oersteds. Since the drift in strength field magnetic the in H, electrons move E and the both perpendicular to everywhere circular cycloidal paths at a constant average radius from the center. Only upon collision with a gas molecule is the electron disturbed from Each time such a this path because of energy loss in the collision. collision occurs the electron moves into a new circular cycloidal path
in
closer to the anode.
Auxiliory
119
With a proper
choice of the parameters the drift velocity of the electrons is sufficient to ionize gas atoms so that an
-Anode
appreciable fraction of the collisions results in the production of positive ions which are attracted imCothode
start of electron
o o o
oo oo o oo o
ooo
A xiol magnetic field
Fig. 3-49. Schematic of the Haefer inverted -magnetron type of cold-cathode ionization gauge. [Taken with permission from Hel-
mut Schwarz, Vacuum
11,
Cutaway view of inverted magnetron cold-cathode ionization gauge. [Taken with permission from P. A. Redhead, in 1958 Vacuum Symposium Transactions (Pergamon Press, London, 1959).] Fig. 3-50.
151 (1961).]
is the use of crossed electric and magnetic fields to increase by a large factor the path of the few electrons emitted by the cold cathode, and thus also the efficiency of the electrons in producing positive ions.
feature
A
schematic representation of the Haefer inverted-magnetron gauge is in Fig. 3-49. The cathode is a cylinder (actually the metal case of the gauge tube) about 5 cm in diameter, and the anode is a small diameter metal rod located on the axis of the cathode. A magnetic field of about 2,000 oersteds intensity parallel with the axis of the tube is maintained by an external coil. A potential difference of several
shown
kilovolts
is
superimposed upon the axial magnetic field. An electron between the anode and cathode will move on a cycloidal path in the E x (azimuthal) direction with a drift velocity in the region
H
given by v^
=
lO^E/H)
cm/sec
,0-11
,0-9
,0-7
Pressure, torr
gauge developed by Redhead*' in Fig. 3-51. lon-current-vs. -pressure which the cathode is surrounded by relationship for inverted-ion-magnean auxiliary cathode outer shell tron gauge. [Taken with permission with cylindrical shields protruding from P. A. Redhead, 1958 Vacuum through the openings into the cath- Symposium, Transactions (Pergamon ode. The auxiliary cathode acts as Press, London, 1959).] an electrostatic shield and protects the edge of the openings through the cathode from field concentrations, thus preventing field emission. The cathode and auxiliary cathode are both grounded, but the current to the cathode alone is taken as the measure of the true positive ion current. The anode rod is typically maintained at 6 kV and the magnetic field intensity at 2,000 oersteds. In the pressure range from 10"" to 10"* torr the positive ion current was found to conform to the relationship i+
applied between the anode and cathode so that a radial
electric field is
anywhere
mediately to the cathode. By this process each electron emitted from the cathode produces a large number of ionizing events before it finally spirals into the center of the gauge and is caught on the anode. In Fig. 3-50 is shown a cutaway view of an inverted-magnetron
=
cP"
which n varied from 1.10 to 1.15 and c was a constant. Above 10-3 torr the space charge changes from negative to positive with
in
the result that the characteristics of the gauge change completely. Calibration curves for several models of the inverted-magnetron gauge are shown in Fig. 3-51, together with a similar curve for the
120
VACUUM SCIENCE AND ENGINEERING
PEESSUBE MEASUREMENT IN VACUUM SYSTEMS
Table
Bayard-Alpert, 10
mA.
Cold-cathode Gauge Chaeactebistics*
3-2.
Gauge
121
Anode
Ion-current
voltage,
pressure.
kV
A/mm Hg
.
5.0
Pumping
Pretreatment of gauge
Gas
rate, 1/sec
0.1
Outgassed
Argon
0.080
4.0
Baked
Argon
0.200 0.140 0.150
at 400°C
Nitrogen
Oxygen
Anode 5.0
4.0
Operated hotirs in
Reduced -size cold
Cathode
5.0
4.4
Fig. 3-52. Cold-cathode magnetron gauge. [Taken with permission from P. A. Redhead, 1958 Vacuum Symposium Transactions (Pergamon Press, London,
for several
Argon
oxygen
Nitrogen
Operated for several hours in argon Baked at 400°C Induction heated to 800-900°C
Oxygen
0.050 0.100 0.120
Argon
0.018
Argon Argon
0.042 0.350
Argon Argon Oxygen
0.110 0.330 0.340
1959).] Reduced-size cold
Bayard-Alpert gauge. As in the case of the hot-cathode magnetron gauge discussed in the previous section, the X-ray hmit of the inverted-magnetron gauge is well below that of the Bayard-Alpert
1.2
0.46
0.3
0.03t
Induction heated Induction heatedf Induction heatedf
Reduced-size cold
gauge.
The type of gauge generally
referred to as the Redhead gauge
is
an
and designated the coldcathode magnetron gauge by Redhead.** The cathode, as shown in Fig. 3-52, is in the form of a spool consisting of a small-diameter central cylinder and two end disks. The anode is a cylinder with a diameter about equal to that of the end disks and is perforated with many holes to ensure good conductance beinversion of the geometry discussed above
Pressure, torr
Fig. 3-53. lon-current-vs. -pressure relationship for magnetron gauge in the range 10"* to 10-9 tQj.r. [Taken
with permission from P. A. Redhead, 1958 Vacuum, Symposium, Transactions 1959).]
(Pergamon Press, London,
tween the regions inside and outside the gauge volume. An auxiliary cathode in the form of an electropolished ring is placed at each end of the cylindrical anode in the gap between the anode and cathode to reduce field emission currents to a minimum. Redhead found that in the pressure range from 10~^ to 10~* torr the cold-cathode magnetron gauge with anode potential of 5 kV and magnetic field of 1,070 oersteds has a linear characteristic
shown in and helium. as
Fig. 3-53 for nitrogen
As can be seen from the graph, the ion current in amperes
Vacuum Symposium
* Taken with permission from T. N. Rhodin and L. H. Rovner, in 1960 Transactions (Pergamon Press, London, 1961), p. 228. f Prolonged treatment with some evaporation of metal. % Ratio of ion current to pressure is not constant.
for
nitrogen
is
given approxi-
=
lOP
mately by i^
Helium 10-'
which the pressure is given in It was also observed that at a pressure of about 2 x lO^^" torr there is a break in the response curve so that below this in
,y
torr.
-->
eio''
value of the pressure the curve is no longer linear but takes the
form
• Run
Magnetron gauge operating alone
Run 2 'SkV Run 3 J B=l,060 gauss
10'1-12
,/59'
shown for helium in Fig. 3-54. Redhead reports that the coldcathode magnetron gauge has a pumping speed of approximately 0.15 liters/sec. Rhodin and Rovner** have made extensive measurements of the pumping speed of cold-cathode magnetron
1
X
Bayard-Alpert gauge operating alone
as
10 10
10"
Pressure, torr
Fig. 3-54. lon-current-vs.-pressure relationship for magnetron gauge in the range 10~' to 10~l^ torr. [Taken with permission from P. A. Redhead, in 1958 Vacuum Sym,posium Transactions
(Pergamon Press, London,
1959).]
VACUUM SCIENCE AND ENGINEERING
PRESSURE MEASUREMENT IN VACUUM SYSTEMS
gauges similar to that of Redhead and report that the principal disadvantage is the high pumping speed of such gauges, leading to some ambiguity in interpretation of the ion current reading. The results of their measurements are summarized in Table 3-2 in which the pumping speeds of the normal size (Redhead) cold-cathode magnetron gauge and one of reduced size are compared with that of a Bayard- Alpert type of hot-cathode ionization gauge. In spite of the high pumping speed and its dependence upon the
1 torr of dry air. An improved version of Vacca'^ is provided with six ranges with full described by the Alphatron scale readings of 10-^, 10"^, 10, 100, and 1,000 torr. The low range is accomplished by an improved electrometer tube and circuit capable of amplifying currents as low as 10-^* A. The higher ranges are obtained by using a second ionization
122
Section
previous history of the gauge, as illustrated in Table 3-2, the cold-
A-A
30 to 40 contoined
volts in
amplifier
power supply
Qutput
cathode magnetron gauge is useful 10~ii in the pressure range below the well below torr, a pressure Alpert gauge. Bayardrange of the The high pumping speed is apparently associated with the very high efficiency of ionization
Housing
trons
in
by the
circular
their
elec-
cycloidal
in a high positive ion high sensitivity, with that of compared current, as operating gauge the Bayard- Alpert
which
orbits,
results
i.e.,
at the
same
3-11. 2
1
l'Mi|i|i|
I
II
I
3-55. The Alphatron gauge. [Taken with permission from J. R. Downing and G. Mellen, Rev. Sci. Instr. 17, 218 (1946).]
Fig.
pressure.
The Alphatron Gauge.
Any
process which causes ionization of the residual gas in a tube or
chamber
2
X
10-1"
A for a pressure of
new gauge
be within 2 per cent of
is
said to
full scale for
ranges.
3-12.
The Knudsen Radiometer
Gauge.
The Knudsen*^ radiometer
gauge
perhaps the most widely
is
known and described^' of the less common vacuum gauges. The basic element of the radiometer gauge consists of two parallel plates, one of which is heated, separated by a distance which is small as compared with the dimensions Fig.
of the 3-56a.
plates,
as
shown
The unheated
in
plate
Fig. basic
3-56.
The
two
alternative
elements of the Knudsen radiometer vacuum gauge. [Taken with permission from J. H. Leek, Pressure Measurement in Vacuum Systems (Published for the Institute of Physios and the Physical Society
by Chapman and HalI,Ltd., London, 1964),
2nd
ed.]
is
supported on a sensitive suspension so that a small force acting upon An alternative form is shown in Fig. 3-566 in which it can be measured. the unheated vane is suspended between two fixed plates, one of which The force per unit area on the susis heated and the other cooled. pended vane or plate is given approximately by
can, in principle, be used
as a basis for an ionization gauge.
X
The
chamber of very small volume. linearity of the
all
123
alpha particles, beta particles, and gamma rays are all ionizing agents, the advantages of which may be considered as possible means of ionizing gas for the
f
rays,
purpose of measuring its molecular density. A practical development of this type is the Alphatron (National Research Corporation) gauge of Downing and Mellen'" which utilizes a small source of alpha particles, for example, 0.5-mg piece of an alloy of gold and radium sealed in a capsule. The gauge consists of a source holder and two grid structiires inside a small metallic ionization chamber which serves as the gauge tube (see Fig. 3-55). A diiference in potential of 30 to 40 V is maintained between the two grid structures to sweep out the ions and electrons formed by the ionization process. The ionization current is found to be substantially a linear function of the pressure over a wide range, from 10-* to 40 torr for the first version of the Alphatron, the current being
-I
©% {^
dyne/cm^
(3-36)
which T^ and T^ are the temperatures respectively and the vane, T is the ambient temperature of the In the second case walls of the gauge tube, and P is the gas pressure. for the first case in
of the heated plate
/2
=
w^ m
T,V^"
dyne/ cm ^
(3-37)
which T^ and T^ are respectively the temperatures of the heated and cooled plates and T is the ambient temperature. In this latter case the force on the vane does not depend on its temperature T^. In either
in
case the force depends directly
upon the pressure
in the strictest sense,
124
the force per unit area exerted by the gas, with no dependence upon the molecular weight of the gas. In this respect the Knudsen gauge may be considered an absolute pressure-measuring device. A more exact treatment of the theory of the Knudsen gauge, taking into account the accommodation coefficients for the vane surfaces and the inside surface of the gauge tube, leads to much more complicated expressions for the force per unit area on the vane. Differences in accommodation coefficients at the various surfaces result in responses which differ for various gases, with the response to helium and hydrogen
125
PRESSURE MEASUREMENT IN VACUUM SYSTEMS
VACUUM SCIENCE AND ENGINEERING
A needle valve is provided so that any chosen gas can be admitted to the system at a controlled rate to vary the pressure. For calibrating thermocouple and Pirani gauges, usually from 10'^ to large1 torr, only a rather insensitive McLeod gauge (small bulb and diameter capillary) is required, and no serious difficulties are reported. However, for calibrating ionization gauges over a sufficient pressure range in the region of linear response, the greatest McLeod gauge sensitivity system.
Gas input through drying tube
being particularly low for some gauge designs. The linear expressions for the response of the Knudsen gauge are valid only in the pressure region for which the molecular mean free path is large as compared with the spacing between the vane and fixed By using the smallest practical spacing and a closed plate or plates. box structure about the vane system, linear response up to a pressure
Gauges to be
of 10-» torr can be obtained. At higher pressures the response is always less than the linearly extrapolated value and eventually begins to decrease with increasing pressure. The useful range of the radiometer gauge thus tends to be from about 10"* to 10-* torr. practical designs of the Knudsen gauge pressures as low as 10-^
coiibrated
Severe
McLeod gauge
I
locations
around
chamber
In
Since a sensitive suspension is required, all designs of the Knudsen gauge thus far developed are too cumbersome and Many special adaptations have been fragile for most applications. made and successfully applied, however, when the unique features of
torr are detectable.
Liquid-
Liquid-
nitrogen trap
nitrogen trap
does occur in all types of ionization gauges. 3-13. Calibration of Vacuum Gauges. For many years the accepted standard for calibrating other vacuum gauges in the pressure range below that easily accessible to the simple mercury U-tube manometer has been the McLeod gauge. The limitations of the McLeod gauge and the precautions necessary to obtain consistent It is clear from that discussion that results are discussed in Sec. 3-4. the calibration of other vacuum gauges is limited to gases which obey Boyle's law up to the maximum pressure to which it is compressed Accepted practice has been to in the operation of the McLeod gauge. provide a glass- or metal-walled chamber evacuated by a liquidnitrogen-trapped diffusion pump to which the McLeod gauge and the
gauges to be calibrated are connected each through a liquid-nitrogen-
The use of liquidthe ionization gauges is essential to protect from mercury vapor from the McLeod gauge and also to protect the McLeod gauge from contamination by hydrocarbon vapor from the cooled trap, somewhat as
nitrogen-cooled traps
shown
in Fig.
3-57.
Liquid-nitrogen and
ffiK^'\K.'\K
154
diagram of the complete
circuit for the
helium leak detector version of
1
Ion
gouge
-^
—
-^
1
In |U
1
i_
^
—
15-
^^-i
(2)
/ "a
(4) -
R-f
250
volts
power
1-
/ .'.,
volts
supply
(2)
,..,.„,
375
power
regulator
(21
modulotor
+
Filament
oscillator
supply (4) (4)
z'
\
+
A-c
Preomplifie
amplifier (2)
-^
(2)
Fig. 4-22. Block circuit diagram for linear r-f helium leak detector. [Taken with permission from R. E. Moody, in 7956 Vacuum Symposium Transactions
(Pergamon Press, London,
1957).]
the device is shown in Fig. 4-22. In the vacuum analyzer version the applied high frequency is swept over the range necessary to bring into = 100. In Fig. 4-23 is 2 to synchronism ion masses from
M
M=
shown the electrode structure
An
for the r-f
alternative form of linear r-f
vacuum
analyzer.
mass spectrometer featuring an
array of equally spaced grids as an e/m
filter,
illustrated in Fig. 4-24,
155
potential
e?7j(,t ill passing through the r-f filter will reach the partial collector and be recorded as a partial pressure. The highly negative grid between the ion source and the r-f filter is designated the total collector since it intercepts a uniform fraction of ions of all masses and thus provides a current indication which is proportional to the total pressure as read by an ionization gauge. The grids of the r-f filter are equally spaced, and are alternately connected to the opposite polarities of a variable-frequency r-f oscillator so that successive grids are driven 180° out of phase. Each group of three adjacent grids constitutes a sorting structure of the Bennett type.^^ In passing through the sorting structure, ions, in general, experience a succession of accelerating and decelerating impulses and on the average gain or lose kinetic energy. The change in energy AlFy for an ion depends
upon the number the
N
of Bennett stages in
the
structure,
entering
the amplitude
accelerating
U
of the r-f
Fig. 4-23. Linear r-f mass spectrometer vacuum-analyzer
electrode
structure.
was originally proposed by Redhead^" for use as a vacuum analyzer. Ehlbeck et al.^i have discussed the theory of this type of mass spectrometer and given results of measurements on the resolving power and Ions are produced sensitivity as a function of operating parameters. by electron bombardment in the ion source, accelerated through an r-f filter consisting of {2N + 1) precision-made grids, decelerated by a retarding grid, and finally selectively recorded on the partial-collector
potential
electrode, provided a particular type of ion has gained sufficient energy
The transit angle is the phase interval of the applied r-f which a particle would spend in traversing the distance d between two adjacent grids of the ion sorter at the velocity v„ = [2(e/m)f7„] at which it enters the sorting structure. The entering phase
surmount the potential applied to the retarding grid. Between the ion-retarding grid and the collector is an additional grid at high negative As potential to prevent any electrons from reaching the collector. to
shown in the d-c potential plot in Fig. 4-24, the filament and partial ion collector are at ground potential, the ion chamber at a positive
?7o,
potential, the phase
cp
of the r-f at the in-
stant the ion enters the transit angle
oc
first stage,
where
2nfd\2-U„
m
interval
A
positive
and the
99
and the
[Taken with permission from R. E. Moody, in 1956 Vacuum Symposium, Transac(Pergamon Press, tions London, 1957), and through the courtesy of Beckman Instruments, Inc.Fullerton, CaUf.]
AW
N
over which the change in energy ^- after stages is fractional gain in energy AW^I^U^ are both critical
VACUUM ANALYZERS AND LEAK DETECTORS VACUUM SCIENCE AND ENGINEERING
156
Table
functions of the ion e/m ratio when the remaining parameters (d, U„, U, f) are held constant. Alternatively, if all other parameters are held constant and the radio frequency varied, then ions of different e/m ratios receive the maximum energy gain at discrete values of the frequency.
Pump
4-2.
157
Operating Parameters for R-F Mass Spectrometer Vacuum
Analyzer*
mA
electron current. Total yield of ion source at 4 Half width of energy distribution of ions Total current sensitivity (signal to total ion collector) Partial current sensitivity at U (r-f amplitude) = 140 volts Resolving power at U = 140 volts Upper limit of pressure at which the partial current is proportional to the partial pressure
x 10~^ A/torr
1
.
.
4.5
eV
8 x 10"^ A/torr 2 X 10-" A/torr
100 5 x 10—* torr,
approx
Taken with permission from H. W. Ehlbeck, K. H. Loecherer, J. Ruf, and H. J. Schuetze, in 1960 Vacuum Symposium Transactions (Pergamon Press, London, 1961), p. 407. *
Resolving power of 100 could only be attained by using such a highA mass spectrogram obtained with the precision grid structure.
instrument at a total pressure of 1 X 10"^ torr and resolving power of about 100 is shown in Fig. 4-25. Assuming that a partial-collector current of 10-1* A can be detected above 3.10""amp background, the minimum partial pressure detectable with the sensitivity of 2
X 10-« A/torr
5
is
X 10-»
By sacrificing resolving power torr. this limit of detectable partial pressure Fig. 4-24. Schematic drawing of electrode arrangement and d-c potential distri[Taken with permission r-f mass spectrometer according to Redhead. from H. W. Ehlbeck, K. H. Loecherer, J. Ruf, and H. J. Schuetze, in 1960 Vacuum Symposium Transactions (Pergamon Press, London, 1961).]
bution for
can probably be reduced somewhat, at least for the lower range of mass
10 12 14 16
shown
in Fig. 4-24, the resolving
R=
power
/m
is
=
al.^i
using five stages as
defined as
100
compact and relatively simple type of r-f mass spectrometer, called the Farvitron, has been described by Reich. 23 The electrode system for the Farvitron is shown schematically potential
JL
22
28
M
Mass spectrogram at of 1 x 10^^ torr and resolution of i? = 100 from
Fig.
4-25.
total
pressure
r-f sorter
distribution.
Because
type of
r-f
spectrometer
of Ehlbeck et al. [Taken with permission from H. W. Ehlbeck, K. H. Loecherer, J. Ruf, and H. J. Schuetze, in 1960 Vacuum Symposium Transactions (Pergamon
in Fig. 4-26 together with the axial
X(f2-A)
18
values.
A
In the instrument developed by EhllDeck et
oLLuIIL
of
in which /max is the radio frequency for a given e/m value at which the collector current is maximum and f^ and /a the frequency values below' and above /max at which the collector current reaches half the maximum value. The operating parameters of the instrument are given in Table
the geometry of the electrodes and the d-c voltages applied, the axial poten-
The authors emphasize that the transparency of the grid structure They found is a critical feature in determining the resolving power. that a grid structure in which each grid was a square mesh of 5 X 10"* cm diameter molybdenum wire with a spacing of 0.05 cm transmits only 7 per cent of the incident ions, whereas a structure in which each grid
between the two end electrodes and the central ring electrode. An ion of charge-to-mass ratio e/m injected into such a field experiences an
4-2
.
consists
of parallel wires precisely aligned transmits
tial
distribution
parabola, that
is
is,
99
Press,
approximately a = F — kx^, in which
axial oscillation of frequencj^
f
=
C!\-
35 per cent.
V
V
V
London, is
1961).]
the voltage applied
VACUUM SCIENCE AND ENGINEERING
158
C =
where which the
and
L
VACUUM ANALYZERS AND LEAK DETECTORS
the distance between the end electrodes at 0. If an alternating potential of g9 superimposed upon the d-c potential, an ion of e/m
4/7rL
is
electrical potential
=
frequency / is satisfying the above frequency relation will resonate and gain sufficient energy to escape from the potential pocket.
frequency is varied periodically by a 50 cycles/sec wobbler signal over the range of 0.13 to 1.8 megacylces/sec. For the dimensions and d-c voltages chosen by Reich the resonant frequencies are given by
W
J
A
S
r-'r-i-ii
r
I"-!-"!
:
Tube R-f amplifier
I
i^i'-r-'.
3
1 Demodulator
R-f generator
0,l3-l8Mc
Wobbler
50cps
Fig. 4-26. Schematic diagram of the electrodes and of the axial potential distribution of the Farvitron mass spectrometer. [Taken with permission from G. Reich, in 1960 Vacuum Symposium Transactions
London,
(Pergamon
D (Pergamon
is
the molecular weight of the atomic or molecular ion involved.
The frequency swing imposed by the wobbler can be varied in breadth anywhere over the available frequency range so that either the full mass range from ilf = 2 to ilf = 250 can be displayed, or a much narrower mass range can be chosen and expanded to the full width of the oscilloscope trace.
The Farvitron is a relatively simple and compact form of r-f mass spectrometer which can be conveniently constructed for baking out at high temperature. The sensitivity is apparently limited, at least in the form described by Reich, to partial pressures not less than about 10~^ torr. The high scanning rate of 50 cycles/sec makes the Farvitron ly changing conditions in a
Press,
London,
1961).]
Press,
1961).]
In the Farvitron the ions are produced by accelerating a regulated current of electrons from a tungsten filament axially into the electrode on the left, the end of which is a wire mesh. The electrons start from a cathode potential of —100 V, as shown in the schematic circuit diagram in Fig. 4-27, and will therefore penetrate the parabolic field to a depth of —100 V, producing positive ions by collisions with any molecules present. These ions oscillate in the parabolic field, most of them not having sufficient energy to reach the cup-shaped electrode on the far end. However, when an r-f voltage is applied to the electrode on the left, ions of the e/m corresponding to the above frequency relation gain in amplitude of their motion and escape to the collector
on the right. The r-f current to the collector electrode is amplified and then rectified to produce a d-c voltage which is applied to the vertical deflection electrodes of an oscilloscope. The radio
electrode
M
megacycles/sec
particularly useful in following rapidOscilloscope
Fig. 4-27. Circuit diagram for the Farvitron mass spectrometer. [Taken with permission from G. Reich, in 1960 Vacuum, Symposium, Transactious
= 2AM-
/ where
D-c supply
159
LflMfiiJ
vacuum
system. 4-4.
A
Halogen Leak Detector.
discussion
of
leak
detectors
would not be complete without mention of the halogen leak detector based upon the enhanced positive ion
output
diode.
of
a
halogen-sensitive Air flow-
Langmuir and Kingdon^*'^^
had demonstrated the production of positive ions by ionization of gas
diagram of halogen leak detector. [Taken with permission from W. H. White and
molecules coming into contact with a hot surface provided the therm-
J.
FiG.
S.
4-28. Schematic
Hickey, Electronics 21, 100
(1948).]
work function of the surface White greater than the ionization potential of the gas molecule. and Hiokey^" utilized the greatly enhanced production of positive ions
ionic is
which occurs when a gas containing any one of the halogens (fluorine, chlorine, bromine, and iodine) comes in contact with a hot (^^900°C) platinum surface as the basis for a leak detector. Their detector consists of a platinum cylinder mounted on a ceramic-clad heating element placed centrally within a larger platinum cylinder, as shown
The heated inner cylinder is made positive and the ion current is read on a microammeter, as shown in the diagram, or by means of an schematically in Fig. 4-28.
(100 to 500 V) relative to the outer cylinder,
VACUUM SCIENCE AND ENGINEERING
160 amplifier.
detector
VACUUM ANALYZERS AND LEAK DETECTORS
The halogen detector is most effectively used as a leak by placing it inside the vacuum system and probing the
system with a
Loudspeaker Sensing
element
Freon-12 or other halogen-containing gas. Torney^' has made a study of the optimum conditions for operating a halogen detector to ensure stability and sensitivity. The platinum diode produces a background current of positive ions even when no halogens are present. The background current due to this effect varies with the gas pressure and the temfine jet of
perature
The
of the
signal
inner
presence of a
halogen- containing gas also depends upon the gas pressure (of air).
The dependence of the
sidual ionization current for
re-
two
different values of the heater curipOO
and of the signal in detecting a calibrated leak of 10~^ cm^/sec
Halogen leak detector backgroand positive ion current for 1.60-A and 1.75-A heater current and signal
on the pressure in the system is shown graphically in Fig. 4-29. The operating range (70 to 200 fi)
rent 20
40
100 200
400
Pressure,;!
Fig. 4-29.
current for standard leak of 10~* cm^/sec as a function of the pressure in the system. [Taken with permission from F. L. Torney, Jr., in 1957 Vacuum Symposium Transactions (Pergamon Press,
London,
1958).]
crosshatched in the figure is so chosen that the background current
relatively independent of
the pressure in the system and the ratio of signal to background is
optimum
is
^C;
Amplifier relaxation oscillator
ond power supply
O
Requloted ,.
voltages
O
1
element.
due to the enhanced
ionization in the
161
relatively large, resulting in
an
ratio of signal to background.
Torney also observed that the background positive ion current changes slowly with time provided that the pressure and circuit parameters are steady, whereas the signal due to the introduction of a halogen gas rises much more rapidly. Utilizing this difference in response, Torney developed a circuit which facilitates discrimination between background fluctuations and signals due to a leak. The circuit, a block diagram of which is shown in Fig. 4-30, contains a network between the detector and the amplifier which constitutes a bandpass filter which bypasses through C2 the high-frequency noise generated in the detector, is unresponsive to the very low frequencies associated with changes in the background ion current, but transmits an intermediate band of frequencies typical of changes in the signal due to detection of a leak by use of a halogen gas. Subsequent amplification of the signal beyond the bandpass filter then permits the sensitive detection of the enhanced positive ion current due to the application of a halogen gas to a leak even
Fig. 4-30. Block diagram of circuit for halogen leak detector. [Taken with permission from F. L. Torney, Jr., in 1957 Vacuum Symposium Transactions
(Pergamon Press, London,
1958).]
though this change is small as compared with typical changes in the background ion current. One feature of halogen leak detectors which can cause difficulty is the relatively long "memory" of the detector once it has been exposed to a surge of halogen gas.
To
re-
duce the memory period, Torney^' devised a mounting for the detector which provides for the purging of the detector
by the introduction
Sensing head
From system under test
of gas free of halogen contamination, as is
shown
in Fig. 4-31.
The unit
From regulated source of
To vacuum pump
clean uncontaminoted air
either connected in series in the
forevacuum
shown
line of the
in parallel as
The
system as
in Fig. 4-31a or connected
shown
Coble to
in Fig. 4-316.
control unit
principal disadvantage of the
series arrangement is the resulting low conductance for gas flow. The parallel arrangement in Fig. 4-316 may be permanently installed in a system without impairing pumping
performance. According to Torney, 2' leak rates of 2 X 10~* atm cm^/sec will produce a full-scale deflection on his version of the halogen leak detector, and leak rates as small as 2 x 10"^
To vacuum
pump From system under test
Fig. 4-31. Methods of connecting halogen leak detector into a vacuum system. [Taken with permission from F. L. Torney, Jr., in 1957 Vacuum. Symposium Transactions
(Pergamon
Press,
London,
1958).]
atm cm^/sec can be detected when proper precautions are observed. 4-5. Leak-detection Techniques. Leakage through flange seals, welded or soldered joints, and flaws such as cracks and porous sections of metal is an important cause of vacuum-system failure. The degree
VACUUM ANALYZEBS AND LEAK DETECTORS
VACUUM SCIENCE AND ENGINEERING
162
as a function of the time, as
shown
in Fig. 4-33.
163
The system assumed
which leakage must be eliminated in vacuum systems is far greater than that required for pressure and most other vessels in common engineering experience. Because of the importance of eliminating leakage, methods of detecting and localizing leaks constitute an impor-
pump. When the pressure has reached a nearly steady value during pumpdown, the trap is cooled by liquid nitrogen removing the condens-
tant element in vacuum practice. Larger leaks in vacuum systems
able vapor, after which a base pressure is reached depending upon the outgassing and leak rates. The valve between the diffusion pump and
to
relatively crude methods.
may be detected by any of several The system may be pressurized slightly by closing the valve to the pump and
Hole to view flame
Burner
Copper plote
flir-intoke tube used to hunt for leaks
example has a liquid-nitrogen-cooled
the liquid-nitrogen-cooled trap
by
painting
ing for bubbles.
and look-
eokoge
A very large leak
can be detected most easily if the gauge pressure is kept very low. Alternatively, the system may be Now York, 1949).] pressurized with a halogen-containing gas such as Preon-12 and a sniffing method used to detect the halogen gas coming out through the leaks. A hahde torch such as that illustrated in Fig. 4-32 is convenient for this purpose and reasonably sensitive. The air-intake hose shown in the figure is used to explore the system for leaks. When the inlet end of the hose sniffs the halogen gas, the flame in the torch turns green. Small components of a vacuum system can be separately sealed, connected to a compressed-air supply, and immersed
A trail of bubbles indicates the location of a leak.
According
and Wakerling,^* the pressurizing methods are limited in sensitivity to a leak rate of the order of 10^^ atm cm'/sec, which is entirely adequate for locating the larger leaks that would prevent pumping a system down to the region of ionization-gauge operation. When the leak rate in a vacuum system is low enough that the diffusion pumps can be put into operation and a pressure less than 10~^ torr attained, more sensitive methods are required to locate the remain-
to Guthrie
In this case ionization gauges may be operated in the portion of the system and heat-conductivity gauges in the forevacuum section. The behavior of a vacuum in this condition has been described by Briggs, Jones, and Roberts^^ in terms of the pressure fine
vacuum
then closed and the pressure
rise
suspicious rote
I
from A. Guthrie and R. K. Wakerhng (eds.), Vacuum Equipment and Techniques (McGraw-Hill Book Company,
ing small leaks.
over the diffusion
an unsafe overpressure. Gas will then flow out through the leaks, the larger of which can then be areas with soap solution
in water.
is
baffle
connecting a tank of nitrogen to the system through a regulating valve set at a gauge pressure of a few pounds per square inch, carefully avoiding the risk of applying
located Fig. 4-32. Halide torch and auxiliary equipment. [Taken with permission
for this
Punnping
Liquid nitrogen
storted
introduced into
Pump volved off
from system
trap
Time
>
vacuum system with a significant leak present. [Taken with permission from W. F. Briggs, A. C. Jones, and ,T. A. Roberts, in 195S Vacuum. Symposium Transactions (Pergamon Press, London, 1959).] Fig. 4-33. Pressure vs. time for a
followed in time.
Since the outgassing rate diminishes with time, the pressure-rise curve typically has a decreasing slope as long as the curve
dominated by outgassing. However, if the curve becomes a straight some time, the pressure rise may be assumed to be dominated by a leak, the value of which \s Q = V dPjdt, where V is the volume of is
line after
the system.
When
has been determined that a leak is present, the next step is The procedures which may be used are many, but only some of the most efficacious will be mentioned. Briggs et al.29 describe the use of a null method in the circuit of a cold-cathode (PIG) type of ionization gauge as shown in Fig. 4-34 to detect with high it
to localize the source.
sensitivity
leak
any change
in the
system pressure.
Usually when a definite
present, the system pressure remains fairly steady at a value determined by the leak rate and the pumping speed of the system. is
Under these conditions the steady reading due to the system pressure can be balanced out as shown schematically in the figure and any changes in pressure, up or down, detected with increased sensitivity.
VACUUM SCIENCE AND ENGINEERING
164
If
—
I
Ionization
d^
gouge
Sr To
vacuum system
o
Shunt
Null indicotor
Reference voltage
rate
VACUUM ANALYZERS AND LEAK DETECTORS can
J.
decrease in the leak rate or using some gas other than
by air,
such as Freon, COj, or helium, to cause a change in the gauge response, the balance in the gauge circuit will be disturbed and the of a leak indicated. location Methods such as these are generally capable of detecting leak rates
of the
order of lO""
atm
cm'/sec.
The next order of
sensitivity
is
P"iG. 4-34. Null method for detecting changes in system pressure during
the halogen leak detector described
hunting. [Taken with permission from W. F. Briggs, A. C. Jones, and J. A. Roberts, in 195S Vacuum Symposium Transactions
already stated, this device is installed in the forevacuum line of the vacuum system and has a
(Pergamon Press, London,
sensitivity of
leak
1959).]
in the previous section.
about 2 X
As was
lO"**
atm
cm*/sec.
By far the most sensitive and versatile of the leak detectors is the mass spectrometer helium leak detector, several types of which are In application the helium leak which has its own complete vacuum system, is connected into the forevacuum of the system being tested through a control valve as Equipment under test\ illustrated in Figs. 4-35 and 4-36. In Fig. 4-35 the system to be leak tested is enclosed in a hood into which helium is injected so that the system is surrounded by a mixture This method is of air and helium. particularly effective if the problem Envelope containing is to determine whether a vacuum helium-air mixture device has a leak greater than some Fig. 4-35. Hood method of applying specified value, but it does not
described earlier in this chapter. detector,
help to locate the leak.
On
very large systems the hood method can be applied to sections of the system by enclosing portions of the system
165
now be
changed by squirting water or other liquid on suspicious parts of the system to cause a momentary
D-c power supply
leak
the
helium leak detector. [Taken with permission from W. F. Briggs, A. C. Jones, and .T. A. Roberts, in 1958 Vacuum Si/mposium Transactions (Pergamon Press, London, 1959).]
thus roughly localizing any leaks present. The is very widely applied since it facilitates localizing the leak within a small area. A tank of helium with a regulator valve and a hose terminated by a small nozzle is used When the probing gas jet hits to explore the vacuum system in detail. the leak, the helium leak detector responds in a time depending upon the capacity of the system and the size of the leak. Most leak detectors produce an audible signal, the sensitivity of which can be set for detection of small or large leaks. The sensitivity of a helium leak in
hoods of plastic
method
gas probe
detector
is
foil,
illustrated in Fig. 4-36
defined in terms of the
smallest air leak rate to which the
respond when air is replaced by pure helium at atmospheric pressure. In the earlier sections of this chapter the sensitivities of several helium leak detectors are given on this same instrument
basis.
leaks
However,
in searching for
vacuum systems conare much less favorable
in
ditions
'
a
C3
^
—®
than those under which the tivity is measured. In any
S7
w
/?=^
y
rn
will
Equipment Leak detecto
Roughing
under test
^^|,^^
pump
Fig. 4-36. Gas probe method of apply[Taken with ing helium leak detector. permission from W. F. Briggs, A. C. Jones, and J. A. Roberts, in 1958
Vacuum Symposium Transactions gamon Press, London, 1959).]
(Per-
sensicase, detection of leaks of 10"^
atm cm^/sec
and detection of leaks as small as 10^1" atm cm^/sec is entirely possible under good conditions. No matter what probe gas is used in leak detection, precautions must be taken to avoid excessive flooding of the system and its surroundings with probe gas. The objective is to determine the precise location of the leak, not simply to determine whether one is present. If there is an
is
usually relatively straightforward,
amount of probe gas about the system, the leak detector will continue to respond for some time, whether or not the gas probe is A fine gas directed at a leak, so that time is lost in localizing a leak. jet which is turned on only for brief intervals and then turned off again
excessive
is
best.
and
will
The leak detector can then be kept operating at high sensitivity respond when the leak is struck by the gas probe with whatever
delay
is characteristic of the system. In Chap. 9 the operation of getter-ion pumps is discussed in some detail. Ackley et al.^" describe how the current drawn by a Vac-Ion type of pump may be used as a sensitive indicator for leak detection.
One property of this type of pump is that for a given type of gas the current drawn by the pump is proportional to the throughput. Thus for gas of type a
Qa
and
similarly for each
=
(4-11)
S,xPa
component gas
in the system,
where
7„ is the
VACUUM SCIENCE AND ENGINEERING
166
current
drawn
for a given
throughput Q^, P„ the resulting partial
pressure of the gas component in question,
pump
of the getter-ion
for that
of a system with a leak present.
I
VACUUM ANALYZERS AND LEAK DETECTORS
and S^ the pumping speed
same component. Consider the case The getter-ion pump current is
=h SPh
(4-12) '
pump
current
is
Mit)
since
presumably
lit)
Since the measurement depends upon the change from the substitution of the gas at
electrometer circuit.
in the value of the current resulting
the leak, the limit of sensitivity for leak detection by this method depends upon how small the fluctuations in the getter-ion pump current may be before making the substitution. The authors state that by taking proper precautions the fractional change in the getter-ion pump current can be of the order of 1/2,000.
value of the getter-ion
where Qg represents the internal outgassing load and Q^ is the leakage throughput of gas of type 1. If, now, at time t = 0, gas of type 1 is replaced by gas of type 2, then after a time t the change in the getter-ion
pump
Relative Values of Pumping Speeds, Leak Rates, and IjP Factors Used in Determining the Change in Getter-ion Pump Current Due to Substitution of One Gas for Another* Probo gas
1
(^h.
1
-exp(^^^)_ -exp(-^
the average pressure through the slot, Co is the low pressure or molecular-flow conductance of the slot similar to that given in (2- 102), 6^ and 62 are constants similar to k^ and Ajj used in (2-39), and Ci is a constant which replaces the constant TrD*ll28rjL of (2-39) in
first
sufficiently large.
straight line given
&lPa
C„
is
than unity as has been shown for the case of a tube in Eq. (5-25) can be written in the form
This assumption appears to be valid for P^ > Pc defined in (5-30), i.e., in the region of viscous flow, in which (5-21) reduces to a simflar exHowever, for P^ < P^ the pression to that given by Winzenburger. and an expression of the molecular, flow through the clearance slots is form given in (5-21) is then valid. In the foregoing discussion the conductance through the clearances of the pump G, and the reverse pumping speed 8^ due to imperfections in the rotor contours have been tacitly treated as constants independent
C =
which the
when Pav
cAP, T^^
w
is
191
Since
is
The clearance slot, the conductance of which we wish to represent in general form, is one for which the width is a minimum at the line of near contact between the rotors or between rotor and cylinder and increases with the contour of the parts on either This slot can be represented by one side of this minimum clearance. of a uniform width equal to the minimum clearance and of a length in the direction of flow, which depends on the details of the geometry. The conductance is in any case given by an expression of the general form of (5-23), although the exact values of the constants Cq and C^ which depend upon the geometry must be determined empirically. Note that for very small values of the pressure Eq. (5-23) reduces to
by
definition the average pressure
through the clearance
slot
is
Pav
=
^^^
(5-28)
in the case of a slot.
C =
Pav
"
4'
(5-30)
Pj/2 will be called the critical pressure.
(5-24)
Several rather gross approximations are made in the transition from the exact expression (5-23) for the conductance through a slot to the
(5-23) reduces to the approxi-
combination of Eq. (5-24) for Pg < P(/2 and Eq. (5-30) for P2 > Pf/2. For an analysis of the performance of a mechanical booster type of vacuum pump, however, these approximations lead to a sufficiently accurate representation of the conductance through the clearances
'
-^av "^ 7~
CjPa
(5-25) 61
62
MECHANICAL VACUUM PUMPS
VACUUM SCIENCE AND ENGINEERING
192
is 10 or more times P^ of interest. range (the inlet pressure) over most of the pressure narrow slot for air at low low-pressure The conductance of a long, pressure is given by Eq. (2-102) of Chap. 2. For our present purposes
since in practice
we
Pj
(the interstage pressure)
when the interstage pressure Pg = P(/2 = P^, at which pressure the mean free path is twice as long as it is at the pressure P^. Thus at the value of the pressure Pa at which the sharp break appears in the approximate conductance curve
write this equation in the following form
=
C,
k—
d (5-31)
which the constant k depends upon the units used. The clearance between the rotors of a Roots type of compressor, however, is not of uniform width for a clearly defined depth z, but is defined by curved surfaces. Nevertheless it can be seen that the low-pressure conductance of such slots will have the form
For
air at
=
=
k^d^
varies as the square of the radial clearance d.
=
fc^rf*
=
x 10-^ cm
where
/Ij
torr.
Thus at the
Pc
(5-35)
5
=
critical
2
free
path
= -'
x 10~^
(5-36)
in. is
the
mean
free
path at
P =
1
pressure P^ the width of the clearance slot
related to the corresponding
mean
free
path as follows
(5-33)
which k^ is in part a geometrical constant. Note that in the above discussion no mention is made of conductance through the clearances at the ends of the rotors. The reason for this omission is that the flow path \z in Eq. (5-31)] for the end clearances is very long between flat surfaces. Thus for very adequate end clearances this conductance is negligible as compared with that through
P
or in
=^d
(5-37)
which d
is the average rotor clearance. the above discussion of the conductance of gas through slots can be seen that the conductance through the mechanical clearances
From it
high values of the pressure the conductance through a slot is proportional to the pressure. Also in the case of a slot the conductance at high pressure is proportional to the cube of the slot width. Thus it is clear that in Eq. (5-30) as applied to the conductance through the radial clearances of the pump, Cj must be of the form (5-30), for sufficiently
Ci
=
(5-32)
where d is the root mean square of the mechanical clearance between the rotors or between each rotor and the cylinder wall, and fcj is in part a geometrical constant averaged over all orientations of the rotors. What is of main significance is that the low-pressure conductance
As can be seen from Eq.
Y
20°C we have from (2-57) for the mean A
is
=
^2
62,
in
Co
193
of a positive displacement type of compressor used as a
vacuum
pump may
booster
be represented with reasonable approximation by the lowing expressions, each applied to its proper pressure range C,
and
C^
k^d^
=
k^d^
for
+
k^d^
P,
'-^
(5-39)
d
in
the radial clearances.
The transition pressure Pj has been related to the mean free path arid diameter in the case of gas flowing through a tube. In Eq. (2-56) it is seen that at the transition pressure the diameter of the tube D is about 11 times the mean free path 1< of the gas molecules. Approximately this same factor applies to a slot in which case the width of the slot d at the transition pressure is d
The sharp knee
in the
=
12L
approx
(5-34)
approximate conductance curve in (5-30) occurs
The general form of the pumping speed 8^ of the mechanical booster
pump
now be seen from Eq. (5-20). independent of the pressure until the interstage pressure reaches the transition value and then increases linearly with the pressure above this value, as given in Eqs. (5-38) and (5-39), is of fundamental importance. When the gas flow Q is zero and the interstage pressure is at the limiting pressure of the backing pump, that is, 82 = 0, the pumping speed 8-^ of the booster pump will also be zero. At this point the limiting value Pq of the inlet pressure will be determined by the zero-flow compression ratio as in Eq. (5-14). The pumping speed will then rise rapidly as the gas flow and pressure increase, primarily because the pumping speed of the backing pump is increasing. When the pumping speed of the backing pump reaches its normal plateau value at an interstage pressure of about 0.1 torr, the pumping speed of the booster pump will also reach a plateau value. The
as a function of the pressure can
fact that C^
is
T MECHANICAL VACUUM PUMPS
VACUUM SCIENCE AND ENGINEERING
194
As the pressure
is
further increased this plateau value of the
pumping
then be maintained until the interstage pressure reaches the speed 5' P^, which in practical cases may be in the range 1 to value critical Above this point the pumping speed is expected to decrease with torr. increasing pressure, primarily because C„ the internal leakage through the clearances, is increasing rapidly with the pressure. Thus one expects a very broad pumping-speed curve which rises from zero at the ultimate pressure to a flat plateau value and then decreases as the will
increased beyond the critical pressure. If the zero-flow compression ratio given in Eq. (5-14) is high as compared with the staging ratio between the displacement of the booster and its backing pump, the plateau pumping speed should be very nearly equal to the
interstage pressure
the preceding test and Eq. (5-14) amounts to a determination of the parameter S^. In addition, the value of the interstage pressure at which begins to decrease as the pressure increases is identified as
K
the critical pressure P^.
f
14
I
12
70
of the backing
pump
.,
h-i
---
B
-/
Hj /[
J
Average
=
of the pressure, the performance curve of a positive displacement compressor used as a mechanical booster pump can be computed point by point from Eq. (5-20). The performance of the first experimental
mechanical booster pump was predicted in this manner and was later confirmed in its general features by pumping speed measurements. However, for a more accurate test of the theory and a better understanding of mechanical booster-pump performance subsequent calculations of pumping-speed curves have utilized the results of two preliminary tests designed to measure directly the parameters C,
and K:
r"
With the pump
rotors at rest but set in turn at equally spaced
positions throughout a complete revolution, the conductance through the clearances of the pump was determined by admitting a measured flow of air into the inlet with the forepump in operation and measuring the pressure at the inlet P^ and that at the interstage P^. By appli-
cation of the conductance formula
Q =
C,{P,
-
P,)
to these observations for a small gas-flow rate and averaging these results, the low-pressure value Co of the conductance C, through the
was determined. With the booster pump
clearances
in operation but without any flow into the was varied from the limiting pressure of the backing pump up to several torr, and the pressures at the inlet and interstage were measured. The ratio of these pressure readings, K = P2IP1, is the zero-flow compression ratio, which combined with C^ from 2.
inlet the forepressure
i
1.J
.
90
135
^
"
50 ''°
30 20 10
180 225 270 315 360
10"'
10"^
Angular position of rotors, deg
Fig. 5-12. Curve for obtaining experimental value of conductance through pump clearances. [Taken with permission from C. M. Van Atta, in 19S6
Symposium
Vacuum
Transactions
(Pergamon Press, London,
1957).]
.
I O
8.0 cfm
10"'
1
10
100
Interstage pressure, torr
Compression -ratio curve mechanical booster pump. [Taken with permission from C. M. Van Atta, in 19S6 Vacuum, Sym,-
Fig. for
5-13.
a
Transactions posium London, 1957).]
(Pergamon
Press,
The significant dimensions of the positive displacement type of mechanical booster pump, on which extensive calculations and tests were carried out, were as follows Cylinder length: 16 Cylinder bore 9-M :
1.
._.. ._..
multiplied
45
o
^~60 Q_
^"110
is
by the staging ratio. 5-9. Computed Performance Curves for Mechanical Booster Pumps. By; choosing reasonable values for the parameters C^ and function 8^ and knowing the pumping speed of the backing pump as a
pumping speed
195
in.
in.
Radial clearances, d 0.008 in. average Displacement speed at 1,740 rpm, Sj^: 1,230 cfm Displacement speed of backing pump: 130 cfm :
measurements on the conductance through the clearances as described in the first of the two preliminary tests outlined above are given in Fig. 5-12. From these measurements the average value of Co = 8 cfm. The dependence of the compression ratio on the Although these latter results interstage pressure is shown in Fig. 5-13. show an unanticipated droop in the compression ratio at the lower limit of the pressure range, an average value for the low-pressure range is taken to be ii' = 50. These values of Co and K substituted into Eq.
The
results of the
(5-14) yield S^
=
16.8 cfm.
The
results of the second test also yield a value for the critical pressure. Since begins to decrease sharply at an interstage pres-
K
sure of 1.5 torr, P^
0.008
in.
=
1.5 torr, consistent
with a rotor clearance of
VACUUM SCIENCE AND ENGINEERING
MECHANICAL VACUUM PUMPS
The remaining undetermined constant is C^ appearing in Eq. (5-30). The value of this constant has been arrived at by trial-and-error fitting of the high-pressure end of the experimental performance curve. The value chosen by this procedure is Ci = 2.8 cfm/torr.
experimental performance curve of the 130-cfm backing pump used. Dotted lines connect points on the booster-pump performance curve with those on the backing-pump curve from which they were computed.
196
From
these results
we have
Eq. (5-30)
for
The staging repetition
=
C,
+
8.0
-
1.4(P2
ratio for the standard
very nearly 10 to
combination
197
is
1,230 to 130, or
The curve plotted in Fig. 5-15 as Case I is a of the computed performance curve shown in Fig. 5-14. 1.
cfm
1.5)
1,200
Mechanical booster pumf
1,000
o
r
\,
'i"
;;'K
\ \
\
\
I
V
I
\
O
/ \'
\ >
\
1
\
/.
600
\
\
\
\
f:
\
\
\
V
\
^
\
\
\
V
\
\
>
\
\
I
L
\
I
\
\
I
800
\
\
\
e
wn
\
^°
\
\
I
\
400
I
i
\
\
\
\\
I
Q.
P
I
\\
\
\
»
\
\
\
/
V
\
\
s. 10"
V
\
^
;^
-^
^^
^
1 ^Backing pump ',J
10-
10"
McLeod gauge pressure,
1
.
i
\
S
10-"
\
\
\
10"
*
1
>
1
•
200
V
\
1
\
k
10
1
_i..l
100
torr
Fig. 5-14. Pumping-speed curve for a mechanical booster pump. [Taken with permission from C. M. Van Atta, in 1956 Vacuum Symposium Transactions
(Pergamon
Press,
London,
With the numerical values of the above constants measured or assumed and the pumping speed 8^ of the backing pump as a function of the interstage pressure Pg known from previous measurements, the
pumping speed S^
of the booster
Pj can be calculated using Eq. 8i
=
-;;;
8^
S, —TT^ 24.8
+
1,238
8^
+
+
24.8
Pressure
(McLeod
1957).]
for
1.4(P2
+
The corresponding value
pump as a function of the inlet pressure Thus we have
(5-20).
-
1.4(P2
Pj
1.5 torr
1.5)
of the inlet pressure
Case II of Fig. 5-15
^2
a similarly calculated performance curve
illus-
is
by a factor of 2 from 130 to 65 cfm. For simplicity it is assumed that the pumping speed of the smaller backing pump would be just half that of the measured value for the standard backing pump at each value of the pressure. Conversely, the performance curve illustrates the
Pi
is
trating the expected effect on booster-pump performance of doubling the staging ratio, i.e., decreasing the displacement of the backing pump
1.5 torr
1.5)
-
Fig. 5-15. Pumping-speed curves showing dependence of mechanical boosterdisplacement of the backing pump. [Taken with Atta, in 1956 Vacuum Symposium Transactions (Pergamon Press, London, 1957).]
pump performance upon the permission from C. M. Van
n
8,
The calculated performance curve for the standard combination of parameters given above is shown in Fig. 5-14 together with a typical
expected
shown
as Case III in Fig. 5-15
on the booster-pump performance of decreasing the staging ratio by a factor of 2, that is, by increasing the displacement of the backing pump from 130 to 260 cfm. Figure 5-16 illustrates the effect of radial clearances on the performance of the mechanical booster pump. The calculated performance effect
VACUUM SCIENCE AND ENGINEERING
198
"*
.,,
1,000
c
y' •"
/:^ 800
s
,„.
• '
/
/ 1
// 1
200
\
0.008 0.004
in.
IJ [
0.01 6
in.
10"'
Case!
*s«
in.
Ro cking-pump displacement
=
1
Bo oster-pumpdisplocement
=
1
\,
±'.
30cf I 230cfm
in
is
the throughput admitted as a steady flow at the inlet to P„ is the resulting pressure at the point of interest.
if this
definition of pumping speed
is
to bear
any
relation-
\
10"^
10"-'
ship to the analysis of the
100
10
pumping action given
sections, the significant pressure at
Pressure (Mc Leodl, torr
in the previous
each point in the system where
pumping speed is to be measured is that due to the gas admitted at the inlet. Under the usual conditions of test, the pressure of permanent gas in the system is due to air and the remaining pressure is due to condensable materials originating, for example, in the backing pump. Since a McLeod gauge measures the pressure due to the permanent gas and is very little affected by the vapor pressure present under these circumstances, the pressures used for pumping speed measurements are McLeod gauge readings. The role of condensable materials backstreaming from the backing pump is a separate matter and will be the
Fig. 5-16. Pumping-speed curves showing the effect of radial clearances on the performance of the mechanical booster pump. [Taken with permission from C. M. Van Atta, in 195(i Vacuum Symposium Transactions (Pergamon Press,
London,
which Q
Q_
P.
the system, and
However,
n 10"^
I
\ s '''
(
i
Case
\, Rotor
Cose
// 400
CoseE
^^
/
1
199
mechanical booster pump of 1,234-cfm displacement speed backed by a roughing pump of 130-cfm displacement speed is shown in Fig. 5-17. The shaded area where the two curves join represents the changeover from the booster-pump operation to the booster bypass. 5-10. Measured Performance Curves for Mechanical Booster Pumps. The pumping speed at any point in a multistage system may be defined in accordance with Eq. (5-6) as
s
/
600
..
\^
MECHANICAL VACUUM PUMPS
1957).]
curve for Case I with standard clearances of 0.008 in. is shown for comparison with similar curves calculated for radial clearances of 0.004 Note that for this latter case in. (Case IV) and of 0.016 in. (Case V). curve falls off pumping-speed the and the plateau has disappeared that at the peak. below and pressure above rapidly for values of the of a consisting combination typical a The throughput curve for
discussed later.
Experimental results for the pumping speed of a 1 ,230-cfm mechanical pump backed by a 130-cfm forepump are shown in circles in Fig. 5-14. These results compare favorably with the calculated pumping-speed curve for which the basic parameters are in good agreement. Experimental pumping-speed results are also shown as circles in Fig. 5-15 for the 1,230-cfm booster pump backed by a 220-cfm forepump. These results should correspond fairly closely with the calculated curve designated as Case III of Fig. 5-15, although the backing speed is not quite as high as that assumed for the calculated curve. Comparison between the experimental and calculated pumping speeds shown in Fig. 5-15 indicates that the theory developed for the operation of a positive displacement rotary compressor as a vacuum booster pump is approximately correct. However, examination of the experimental results reveals minor deviations in behavior from that booster
10°
^
-^ 'i^ T ,-my//.
with the upper surface moving with respect to the lower surface with separated by a distance
Fig. 5-22. Plane representation of the molecular-drag pump.
velocity v
=
rio,
which yields
the solution of which
d^v __
1
bP
dy^
7}
dx
(5-47)
of the form
is
as illustrated in
to the plane of the figure, multiplied by the pressure difference which occurs in the distance bx, so that
bP
=
u
By
Ay^
differentiating (5-48) twice
+ By + C
and comparing the
result with (5-47),
(5-49)
bx
2rj
Since the gas in contact with the lower plate so that the constant
C =
upper plate moves with
0.
its
at rest,
is
m
=
at y == 0,
Also, since the gas in contact with the
velocity
(5-43)
=
u
v,
v at y ==
Ji.
Putting these
is
1
bP
2,7]
bx
Bh
h^ this force is balanced by the difference between the viscous forces from the gas above and below the thin layer under The component of viscous force from the gas below consideration. the layer can be written by reference to the definition of viscosity given
(5-48)
one finds that
conditions into (5-48), the result
=wbP by
(5-46)
dy^
A,
The peripheral disFig. 5-22. tance between the inlet and outlet in Fig. 5-21 is L, which is the length ofthelower or stationary plate in Fig. 5-22 in the plane case. Following a procedure analogous to that in Sec. 2-3, the gas contained in a thin layer of thickness by at height y above the stationary plate, and of length bx in the direction of the motion, experiences a force opposite to the direction of motion of the upper plate given by the crosssectional area w by, where w is the width of the plates perpendicular
F
— by
—
riw bx
(5-50)
At equilibrium
in (1-54) as
B
so that
= -.,^s'^=-yjwbx[^^^
(5-44)
1
which u
layer
is
is
the velocity of the gas in the sample layer, since the area
The negative sign arises since the gas below the sample moving more slowly and therefore retards its motion. The
bx.
^P
ir^y bx 2r]
=w
(5-51)
bx
Substituting the above values for A, B,
dy
S
1
2rj
and C
into (5-48) gives for the
velocity distribution
F,
in
^-P,
V
h
which
is
/v
h
I
bP
2r]
bx
h y
(5-52)
a parabolic form.
The net volume flow of gas from the region at the pressure Pi to that at Pj is given by integrating the flow from y = Since to y = h.
MECHANICAL VACUUM PUMPS
VACUUM SCIENCE AND ENGINEERING
208
level y the volume flow in the layer of thickness by at the total flow is
dV
wu
is
wii by, the
by
v=o
'dt
1
bP
.2rj
bx
=W Jy=i Jy=0
^
dy
y
\h
bx
2ri
/
.
w bP
wvh ~^
h^
wvh ~2~
-
increased since the pressure diff'erence depends inversely on h^. If the molecular-drag pump is backed by a pump which maintains
has
the interstage pressure P^ at such a low value that the mean free path of the gas molecules is long compared with the dimension h of the pumping channel, viscosity no longer plays a role and the relationship In this (5-56) between the inlet and outlet pressures no longer holds. and stationary the with alternately collide molecules gas the regime moving surface. Consider the flow across an element of length bx of the channel. 12 Each molecule which strikes the moving surface of
-Pi)
w bP
~
12r]
QrjV
(5-54)
bx bx
(5-55)
bP
so that
h^
If the length of the channel
L, then
is
by
integrating (5-55) one obtains
the pressure difference f
^^
6-nv f
^
bx
QrjvL
The compression ratio P2IP1 for the pump described above large, therefore, unless the outlet pressure were only become not would The simple molecular-drag pump here 1.71 torr. than greater slightly as the first stage of a two-stage only effective therefore is described is fairly low. By decreasing pressure interstage the which in system difference pressure maintained the channel h, pumping of the depth the also the therefore backing and regime, viscous-flow the in pump by the substantially can be ratio, compression large for a required pressure cylinder.
(5-53)
Ur] bx
Under equilibrium conditions the pressure difference (Pj such a value that the net flow is zero. Thus from (5-53)
209
(5-56)
area
w
bx receives drift velocity equal to
v,
the velocity of that surface.
Each molecule which strikes a stationary surface, either opposite to the moving surface or at the two sides of the channel, receives a The resulting average drift velocity is the velocity zero-drift velocity. times the ratio of the area of this surface to the surface moving of the total surface of the channel element of length bx,
wv
h^
(5-57)
independent of the pressure. The molecular-drag pump operating in the regime of viscous flow is thus expected to maintain a pressure difference between inlet and outlet under conditions since the viscosity
"
The flow due
directly proportional to the peripheral velocity and proporthe length of channel between inlet and outlet and inversely pressure this for order In depth. channel tional to the square of the necessary difference to give rise to a large compression ratio P2IP1, it is
of zero flow which
is
much larger than a pump in which the
that P2 not be
Consider
inner cylinders
is
h
=
0.2
in.
=
the pressure difference (P^ - Pi)clearance between the outer and 4 in. = 10 cm; the 0.5 cm, r
V
=
is
rm = poise, the expected pressure difference
and
= = 1.04
x 10^ radians/sec 10,000 rpm, so that w 1.83 x 10"* rj 20°C air at 10^ for Since cm/sec. 1.04 x
rotational speed
^1
=
2(w
is
=
Qa
to this drift
motion
If a pressure difference
bP
103
X 750 X
assuming a distance of 50
+
torr cm^/s^c h)
w%v torr liters/sec
(5-58)
h
produced by the above pumping action,
a flow will occur in the opposite direction because of this pressure The counterflow difference through the conductance of the channel. is
given by
=
2.28
X
10^ /xbar
2{w 10-«
cm between
1.71 torr inlet
and
outlet ports
m
9 71
the
—
^p
w%2
34.4/ T\'^
0.25
X
2{w
is
X 1.83 X 10-* X 1.04 X 10* X 50
2.28
is
10-«Pis
h)
IV%V
^^-^^^^ = 5X
+
\M/ w
+
+
h)
bx torr liters/ sec
h bx
(5-o9)
MECHANICAL VACUUM PUMPS
VACUUM SCIENCE AND ENGINEERING
210
by
reference to (2-79) and no flow into the system Q^
9-^1 hr7
Q^, so that
7
—=
lO-^i^V
~~
~P
10*
5
P
h dx
_5x
dP
or
= +
\MJ w
Under equilibrium conditions with
(2-80).
P=
Integrating this expression from = L, the result is
dx
\t} h
9.71
w%v w
P^ to
(5-60)
P=
P^ and x
=
to
X
\nP^=k —
vL
InP,
P P
Thus
(5-61)
5
where the pressure
(5-62)
T~\t)
P^, is sufficiently
number
of alternative designs
for molecular-drag
pumps have been
devised with two considerations in mind. The first is to ensure a low
conductance leakage path from outthrough the running clearances of the pump. The second is to vary the depth of the pumping channel to provide a decreasing channel depth as the gas is comlet to inlet
pump. For
above.
A
low that the flow is molecular, the compression ratio maintained by the simple molecular pump described above is independent of the pressure and depends exponentially on the quantity vLjh, which is made up of the parameters of the if
Gaede reports and Dushman^^ confirms compression ratios of the order of 10^ attained by a multistage molecular pump based upon the principle of the simple design described
10-
X
k
From the foregoing calculation the zero-flow compression ratio for a simple molecular-drag pump is predicted to be so very large when operating in the molecular-flow regime that the limitation in a real pump is due to factors not specifically considered. In the simple pump described, leakage from the outlet region back into the inlet through the clearances at the ends of the rotor and the imperfect sealing between the rotor and cylinder, where the radial clearance is assumed to be zero, would prevent the attainment of the theoretically predicted compression ratio. Even so,
h
or
air at
20°C the constant (T/Jf)'^ io-«
=
3.181
1
k
1,62 9.71
so that (5-61) then
X 10-5
(5-63)
(3.181)
becomes
pressed so that the cross section of the channel at the inlet of the pump
P
will
Y =exp(l.62 X 10-s^j Taking as an example the same values for parameters of a pump,
vL
_
T^
1.04
X
10*
v,
L,
X 50 1.04
(5-64)
and h
X
as before for the
10"
(15
so that the compression ratio for air should be
is
==
exp
(1.62
=
exp
(16.8)
surprisingly large.
X 10-5 X
=
lO'-^"
1.04
x
lO")
Fig. 5-23. Cross section of molecular-drag pump design due to S. Siegbahn with pumping channels in the form of Archimedes' spirals cut
[Taken with in the two flat sides. be as large as possible to ensure permission from S. Von Friesen, good pumping speed, but still to Rev. Sci. Instr. 11, 362 (1940).] ensure that this depth will be small relative to the molecular mean free path over as much of the comIn Fig. 5-23 is shown a cross pression range of the pump as possible. section of a design due to S. Siegbahn^* in which pumping channels in the form of Archimedes' spirals are cut in the two flat sides of the housing, within which a disk rotates at high rotational velocity. The clearance between the disk surface and the flat section of the end plate between the adjacent spirals
P2/P1
which
211
is
made
as small as practicable for
periphery of the disk and the discharge at the hub. In the unit shown, three spiral grooves are cut in parallel, starting 120° apart, providing three times the pumping speed of a single channel.
free rotation.
The
inlet is at the
MECHANICAL VACUUM PUMPS
VACUUM SCIENCE AND ENGINEEEING
212
213
Pj according to cP,
Pi
where Pq was the lowest pressure attainable and
a constant of the
c is
order of 10^^.
The performance of a pump somewhat analogous to that of Siegbahn The rotor in this case is (see Fig. 5-24) is described by Beams.^^ induction through the vacuum driven magnetically and by suspended material bearings. seal and of shaft the problems wall, eliminating 10* which is about cm/sec, of 1.4 of the order x Peripheral speeds typical for the are room temperature, air molecules at for one-third Vav sealed and is is completely the unit Since model tested." preliminary trap, liquid-nitrogen-cooled with a diffusion pump an oil Ijacked by the forepressure can be very low. A composite curve of the observed compression ratio P2/P1 for various values of the forepressure Pg and the rotational speed is shown in Fig. 5-25.1^ A theoretical curve for the
Fig. 5-24. Molecular pump of Williams and Beams. Rotor is suspended magnetand driven by induction. [Taken with permission from C. E. Williams and
ically
W. Beams, London, 1962).]
J.
in
1961
Vacuum Symposium
Transactions (Pergamon Press,
Because the computed compression ratio for a pump of this description is tremendous when the internal leakage is ignored, the pump acts as though it has a forward pumping speed which is independent of the pressure shunted at intervals of pressure between Pj and Pj t>y leakage conductances. Examination of this model leads to the conclusion that the zero-flow compression ratio should have the form
compression ratio as a function of rotational speed is shown for comparison. It is evident that P2/P1 departs further from the theoretically predicted value as the forepressure Pg is decreased, indicating the influence of outgassing from surfaces at the lower values of Pj attained during the test. As an example, with a forepressure of 4 x 10"' torr the untrapped ionization-gauge reading at the inlet was 2 X 10"* torr, yielding a compression ratio of only 200 compared with the predicted value of nearly 3,000 for
- = exp ^'iri
olxlO'^torr
10-^
A 10
-
''
which w
is
the rotational velocity,
A;
is
P310-
,--©' ,-'-'
1.2x10
y:° ,-'-^9'xio>^ Theoretical
'^^'\,''^''
y^
depend upon the forepressure
^^^^
y^
s
pumping speed
lo.i
_ ,-2
2
3
5
7 ]Q-I
2
3
Iff
5 7 1
Throughput, torr
10
liters/sec
Fig. 6-22. Limiting forepressure as a function of throughput for 6-in. diffusion pump.
for
low gas flow
decreases as the power input and limiting forepressure increase. Increase in the power input,
and therefore the temperature and density of the vapor in the firststage jet, causes greater expansion
VAPOB-JET VACUUM PUMPS
VACtrUM SCIENCE AND ENGINEERING
256
of the jet in leaving the nozzle and therefore more vapor molecules adversely directed on the surface of the jet exposed to the high vacuum. The result is a greater proportion of gas molecules knocked away from the jet by backward-moving vapor molecules before penetrating to the core of the jet where they can be propelled toward the fore vacuum.
The
10"
o
o 10"
-
CO
— oo
o—O o
o
1
10"*
o
* * * oo o
o o ro
§ - o, o
T3-
r.
-
1
5
evident from the
\\
1.0
I
1
°
NX.
z
I
A
~
in Fig. 6-38.
The angle of the conical surface of the lower member of the nozzle was varied from +15° (protruding) to —45° (receding) relative to the^ vertical. Curve A was obtained with normal heater power input and curve B with heater input reduced about 18 per cent. The dotted curves are corrections to curves A and B due to a measurement of the backstreaming contributed by the lower jets of the pump. It is
average angle above the plane of the nozzle
1
'
'
1
Society.]
condensed on the top of the test chamber. The oil flow from each of the collecting surfaces was conveyed by a tube to a separate buret so that the accumulation during a specified period of time could be measured. The backstreaming total rate was measured as a function of the nozzle, as
_
1 '
-
©
member
p
line to boiler
American Vacuum
of the angle of the lower
carbon deposits resulting from the
Correction
_ bosed
^
^
on effect of
B
-
installation of a baffle
under the first stoge
.1,1,1 0°
+ 15°
Angle
-30°
-15°
of inner wall of
,
1
-45°
nozzle
40
20
60
Angle, deg
rates of total various nozzle [Reprinted with per-
Fig. 6-39. Distribution of relative rates of backstreaming as a function of the angle above the plane of the
mission from The Macmillan Company, from D. L. Stevenson, in 1963
diffusion-pump nozzle. [Reprinted with permission from The INIacmillan Company, from D. L. Stevenson, in 1963 Vacuum Symposium Transby actions. Copyright 1963
Fig.
6-38. Relative
backstreaming configurations.
Vacuum
Symposium
Copyright
Vacuum
for
©
1963
Society.]
Transactions.
by
American
©
American Vacuum
Society.]
VACUUM SCIENCE AND ENGINEERING
268
decomposition act as a catalyst.
Insufficient quantitative
VAPOR-JET VACUUM PUMPS
work on the
role of materials in catalyzing the decomposition of diffusion-pump
has been reported to permit a detailed discussion of the subject. However, the decomposition rate in glass pumps is apparently sigHot aluminum in nificantly less than in comparable metal pumps. However, undesirable. as regarded with the working fluid is contact are so fluids used of the properties differences chemical individual in fluids
radially inward
toward the center of the
269
reservoir.
If this flow
is
impeded by barriers with small openings, the fluid is heated substantially while it is still near the outer portion of the reservoir so that high-vapor-pressure constituents are boiled off near the outside. As the fluid flows toward the center it is further heated and lowervapor-pressure components are vaporized. The nozzle stack is constructed of concentric tubes arranged such that each nozzle receives
great that generalizations are not valid. The products of decomposition of diffusion-pump fluids consist of materials of both higher and lower vapor pressure than the original
Those of
fluid.
sufficiently high
vapor pressure act as permanent
gases in the sense that their vapor pressures are so large that they are
not condensed on liquid-nitrogen-cooled baffles. Other products are heavy liquids and solids of very low vapor pressure which accumulate in the boiler and eventually clog the nozzle system with a dark deposit. Because an appreciable decomposition rate is typical of diffusion-pump operation, the ultimate pressure, even with good liquid-nitrogen-cooled baffles, is limited by the rate of decomposition and production of high-
vapor-pressure products which migrate into the high-vacuum system beyond the baffles and must then be pumped out again. Best results
low ultimate pressure are obtained when a diffusion run with low power input and with a fluid of greater than
in terms of very
pump
is
normal
stability.
and Purging. From the time high-boilingintroduced by Burch^" in 1928 for use instead of mercury in diffusion pumps, the need for continual purification to eliminate high-vapor-pressure components initially present in the oil, or produced during operation by decomposition, was realized. Hickman'i and his collaborators were largely responsible for the systematic study of decomposition and contamination of diffusion-pump fluids and the development of specific mechanisms for purging the pump6-8. Fractionation
point fluids were
first
and separating the remaining Figure 6-40 shows a two-stagb glass diffusion pump with boiler compartments to separate the fluid roughly according to the vapor pressure of the constituents and catchment lobes on the exhaust arm of the pump for elimination of high-vapor-pressure components into the backing pump. Large horizontal pumps of metal construction based upon the glass fractionating designs were developed but have not proved to be as convenient boiler
of
undesirable
constituents
constituents in the proper order.
in practice as
The
pumps
of vertical design.
have been incorporated into the design of metal vertical pumps. One of many such designs is illustrated in Fig. 6-41. Fluid returning from the jets to the boiler flows principles of fractionation
Fig. 6-40. Two-stage fractionating glass diffusion pump. [Reproduced through the courtesy of ConsoHdated Vacuum Corp., Rochester, N.Y.]
vapor from only a
specific
annular region of the
boiler.
The backing
from the outer portion of the boiler where the vapor pressure is highest, and the first jet receives vapor from the central section where the vapor pressure of the fluid is the lowest. One advantage claimed for the mechanism of fractionation is that the high-vacuum jet is supplied only by the relatively low-vapor-pressure constituents of the working fluid, contributing to a lower backstreaming rate and vapor pressure at the inlet of the pump. Another advantage or flnal jet receives vapor
claimed is a higher forepressure tolerance because of the relatively high vapor pressure of the constituents forming the backing or final jet.
However, these advantages have not been as clearly demonstrated commercial diffusion pumps of metal construction as in glass pumps
in
of the type fllustrated in Fig. 6-40, at least in part because of the process of reverse fractionation discussed by Hickman. ^^'^^
270
VAPOR-JET VACUUM PUMPS
VACUUM SCIENCE AND ENGINEERING
271
disadvantage in the construction of a metal fractionating pump is the low conductance for vapor flow to the nozzles inherent in the concentric tube design for the nozzle stack. Because of the relatively small gain
vacuum
by the introduction of fractionathe limitations imposed by the presence of the concentric tubes against significant improvements to the in ultimate
actually achieved
tion in metal diffusion boiler
pumps and
and jet system, the design trend has been away from fractionation some of the features described in the previous section. All
to gain
recent commercial
and
pump
designs, such as those illustrated in Figs. 6-9
6-10, as of the date of this writing (1964), achieve better perform-
ance without the fractionating feature than earlier designs of either fractionating or nonfractionating pumps.
Distinct from the question of fractionation of the diffusion-pump
components according to vapor pressure is the problem of purging the pump fluid of high- vapor-pressure components by ejection into the forevacuum. Hickman^^ and Latham, Power, and Dennis^^ have demonstrated that complete ejection of the more volatile constituents of the working fluid from the pump is more effective than fractionation. The rate of ejection of volatiles in a design such as that shown in Fig. 6-9 is influenced by the vertical spacing from the bottom nozzle to the liquid level in the reservoir and the temperature of the pump housing on which the oil condenses. The temperature of the pump housing near the top must be cool to ensure efficient condensation of the fluid from the first jet. In some applications the top few turns of tubing are separated from the rest of the cooling coil and either cooled by chilled water just above the freezing point or by a mechanical refrigerator to reduce further the vapor pressure at the inlet of the pump. However, the wall temperature should preferably increase from the region of condensation of the first jet to a considerably higher temperature below the bottom jet so that higher- vapor-pressure components which are condensed near the top are evaporated as the fluid into
Fig. 6-41. Three-stage fractionating oil diffusion pump of metal construction. Effective fractionation can only be obtained by careful separation of the respective boiler zones. This is obtained by shaping the component resting on the pump base plate as shown (shaded). The lower jet cap is at the same height asthe lower end of the cooling jacket. As a result, the oil flowing down the walls is
warmed,
Vacuum
facilitating degassing.
[Taken with permission from H. G.
Nollei-,
V, 59 (1955).]
The partial condensation of the vapor on the inner walls of the tubes supplying vapor to the nozzles in fractionating pumps, such as that shown in Fig. 6-41, is held to be responsible for a reversal of the desired direction of fractionation. Furthermore, the separation of the fluid into constituents according to vapor pressure is not as well controlled or efficient in the commercial metal pumps as in the glass fractionating pump, such as that shown in Fig. 6-40, since the concentrically divided boiler of the vertical metal pump is not the equivalent of the separated boiler compartments of the horizontal glass pump. Another serious
down the housing wall toward the backing jet and pumped out with the permanent gas into the forevacuum. The forevacuum section of the diffusion pump must also be allowed to run warm so that the more volatile constituents of the effluent will not be condensed and permitted to flow back into the boiler. The optimum temperature distribution is a compromise which allows a sufficiently high rate of ejection of volatiles from the pump without
fluid drains
permitting an excessive rate of loss of pump fluid into the forevacuum. For a given pump design the stability and vapor pressure of the fluid are factors which determine the optimum temperature distribution along the pump housing and forevacuum connection. An extreme example mentioned in Sec. 6-4 is OS- 124 (Monsanto Chemical Company)
VAPOB-JET VACUUM PUMPS
VACUUM SCIENCE AND ENGINEERING
272
which best performance was obtained by Batzer" when the lower end of the pump housing was allowed to run at 90 to 100°C. his6-9. Resume of Diffusion-pump Performance. Although upon was based torically the original development of diffusion pumps
3;
eff'ort mercury as the working fluid, since about 1930 the far greater diffusion has been devoted to understanding and improving "oil" oil pumps. With a few important exceptions listed in Sec. 6-4, nearly used on diffusion pumps instead of mercury diffusion pumps are certain inherent of spite In systems. electronuclear and industrial all
6.
for
factor advantages of mercury, such as chemical stability, the speed mercury greater than for (6-37) for oil diffusion pumps is significantly diffusion
pumps.
usually referred to as oils, now available for use that about equal to in diffusion pumps range in vapor pressure from vapor mercury down to such low values that the room-temperature
Organic
fluids,
high-temperature pressure can only be estimated by extrapolation from hydromeasurements. Narrow cuts of petroleum oils, chlorinated been have carbons, and a wide variety of synthetic organic fluids high of In the development of synthetic fluids used.
4. 5.
7. 8. 9.
10. 11. 12. 13. 14. 15.
19.
Warren W. Chupp, Lawrence Radiation Laboratory, Berkeley,
(1959).
20. 21.
22.
23.
of the order of lO^' torr
26.
The base pressure
for baflftes at 20°C
is
using Silicone 705 or OS- 124 fluid. g/cm^ min. 2. The backstreaming rate is of the order of lO"" the order of 0.5. of is (6-37) 3. The speed factor as defined in Eq. 4.
The
limiting forepressure
is
24. 25.
27.
28.
0.3 torr or higher. 29.
System designs should be based upon the assumption that diffusion pumps meeting approximately the above performance specifications
30. 31.
can be obtained.
32.
REFERENCES 1.
2.
M. LeBlanc, in L. Dunoyer, Vacuum Practice, trans, by Nostrand Company, Inc., New York, 1962), pp. 41-42.
33. J.
H. Smith
(D.
Van
V. V. Fondrk, in 19S7 Vacuum Symposium Transactions (Porgamon Press,
London, 1958),
p. 88.
A
18.
17.
forebase pressure, backstreaming rate, speed factor, and limiting Several industrial vacuum firms have demonstrated difpressure. fusion pump designs for which 1.
Saul Dushman, Scientific Foundations of Vacuum Technique (John Wiley & §ons, Inc., New York, 1949). W. Gaede, Ann. Physik 46, 357 (1915); Z. Tech. Physik 4, 337 (1923). R. Jaekel, in Proceedings First International Congress on Vacuum Technology, 1958 (Pergamon Press, London, 1960), p. 21. R. Jaekel, Kleinste Drucke (Springer-Verlag, 1950), pp. 140-197. H. G. Noller, Vacuum V, 59 (1955). N. A. Floresou, Vacuum 10, 250 (1960). E. H. Kennard, Kinetic Theory of Oases (McGraw-Hill Book Company, New York, 1938), p. 108, p. 194. P. Alexander, J. Sci. Instr. 23, 11 (1946). Smithsonian Physical Tables, 9th rev. ed. 1954, p. 40. D. Latham, B. D. Power, and N. T. M. Dennis, Vacuum II, 33 (1952). 188, 62 (1946). J. Blears, Nature 154, 20 (1944); Proc. Roy. Soc. (London) K. C. D. Hickman, Nature 187, 405 (1960). T. H. Batzer, in 1961 Vacuum Symposium Transactions (Pergamon Press,
London, 1962), p. 315. K. C. D. Hickman, in 1961 Vacuum Symposium Transactions (Pergamon Press, London, 1962), p. 307. B. D. Power, N. T. M. Dennis, and D. J. Crawley, in 1961 Vacuum Symposium Transactions (Pergamon Press, London, 1962), p. 1218. S. A. Vekshinsky, M. I. Menshikov, and I. S. Rabinovich, Vacuum 9, 201
16.
successfully
an molecular stability and low vapor pressure there would appear to be stable Highly opportunity for continued improvement in the future. to meet an fluids with a wide range of vapor pressures are needed extreme range in performance from high pumping speed at low ultimate pressure to high throughput at high backing pressure. The performance of diffusion pumps can be judged in terms of the
273
Calif.,
private
communication T. L. Ho, Physics 2, 386 (1932). H. G. Noller, G. Reich, and W. Bachler, in 1959 Vacuum Symposium Transactions (Pergamon Press, London, 1960), p. 72. D. L. Stevenson, in 1959 Vacuum Symposium Transactions (Pergamon Press, London, 1960), p. 134. C. E. Normand, Oak Ridge National Laboratory, private communication. B. D. Power and D. J. Crawley, Vacuum IV, 415 (1954). H. R. Smith, in 1959 Vacuum Symposium Transactions (Pergamon Press, London, 1960), p. 140. M. H. Hablanian and H. A. Steinherz, in 1961 Vacuum Symposium Transactions (Pergamon Press, London, 1962), p. 333. M. H. Hablanian, in 1962 Vacuum Symposium Transactions (The Macmillan Company, New York, 1962), p. 384. Norman Milleron and L. L. Levenson, in 1961 Vacuum Symposium Transactions (Pergamon Press, London, 1962), p. 342. D. L. Stevenson, in 1963 Vacuum Symposium Transactions (The Macmillan Company, New York, 1963), p. 134. R. C. Burch, Nature 122, 729 (1928). K. C. D. Hickman, J. Franklin Inst. 221, 215 and 383 (1936). K. C. D. Hickman and J. J. Kinsella, in 1956 Vacuum Symposium Transactions (Pergamon Press, London, 1957), p. 52. K. C. D. Hickman, Rev. Sci. Instr. 22, 141 (1951).
THE MEASUREMENT OF PUMPING SPEED
275
of surfaces reach a balance in a relatively short time, particularly for permanent gases, so that if Q (the admitted flow) is kept constant, (the outgassing rate) rapidly approaches zero
Qf,
and the pressure
reaches the value given in (7-3) rather quickly.
CHAPTER
Also, in the case of mechanical
7
vacuum pumps,
the
pumping speed
varies considerably with the inlet pressure, decreasing rapidly with
decreasing pressure near the ultimate pressure Pq of the pump. Thus the ultimate pressure is determined not so much by the outgassing
THE MEASUREMENT OF PUMPING SPEED
in the
system as
it is
by the decreasing pumping speed approaching
zero at the ultimate pressure.
Pumping
7-1. Alternative Definitions of
equation for the pressure in a
PS in
which
P
vacuum system
V
dP Q
dt
+
Speed.
The
Whether the outgassing basic
is
Qo
the
S is
the effective
pumping
speed,
important
that
S
=
0.
Then with the flow Q
dP
Qo
'dt
V
(or
by
=
whether there
is
an
closing off a valve at 0,
Eq.
(7-1)
becomes
(e.g., in torr liters/sec) of gas flowing into the system, and Qg the gas flow due to interior surface outgassing. Thus, in general,
pumping speed
p -u9if
or
Observation of the pressure several times during the pressure rise which is Qo/ V. By putting the result-
yields a linear curve, the slope of
=
=
and dPjdt 0, the ing value of Qo into (7-1) with Q speed at the ultimate pressure can then be determined from
is
VdP
^^-P^
Q
Qo
P
P a
In order to measure the pumping speed, conditions are imposed on the system so that a simplified form of Eq. (7-2) is applicable. For example, if the outgassing rate is negligible {Qq = 0) and the system is operated at constant pressure with a steady flow of gas {Q = const) entering the system, then dPjdt = and from what remains of (7-2)
-I
(7-3)
as given in (2-1).
This expression is sometimes used as the definition of pumping speed and is a valid basis for measuring the pumping speed in the pressure range of most oil-sealed mechanical pumps, provided the pressure measured actually corresponds to the gas admitted to the system, as discussed in Sec. 5-3. If air is admitted to the system at a measured flow rate Q and the pressure measured with a McLeod gauge, then because of the compression effect of the McLeod gauge, as described in Sec. 3-4, the pressure reading will be just the partial pressure of the permanent gas (in this case air) admitted to the system at the
measured flow rate Q.
Also, in the pressure regime of oil-sealed mechanical pumps the sorption processes (adsorption and desorption)
274
;7-4)
Q is the through-
put the
is
is
system, S is the system for which is
pump so
(7-1)
the pressure measured at some particular point in the the pumping speed at that same point, V is the volume of
rate Qg
excessive leak in the system) can be ascertained
On
=
^0
pumping
(7-5)
-;^
system is free of accidental leaks then, for mechanical pumps, generally very small as compared with the value of S at higher
If the Sf, is
and can be neglected. In the case of diffusion pumps, however, the situation is quite different. As discussed in Sec. 6-5, the pumping speed of a diffusion pump is essentially independent of the pressure over the range in which measurements are normally carried out. The ultimate pressure is then not the result of the pumping speed approaching zero but of a limitation on the attainable pressure due to the outgassing rate Q^. The situation is frequently such that a base pressure is soon reached which then
pressures
changes only very slowly with the time because the outgassing rate becomes nearly constant. Returning to (7-1) for the case in which the system is operated at constant pressure, we have
PS = Q + and
Qo (7-6)
276
VACUUM SCIENCE AND ENGINEEEING
THE MEASUREMENT OF PUMPING SPEED
we have the equivalent
In the pressure regime of diffusion-pump operation (7-9) and (7-10) do not generally apply because the outgassing rate is an important However, in this case the outgassing factor near the base pressure. rate rather soon reaches a nearly constant value, changing slowly enough that it may be regarded a constant during the period required In this case Eq. (7-1) can be written for a pumpdown test.
SO that instead of (7-3)
of (6-34)
(7-7)
which is unambiguous only if the pumping speed is essentially independent of the pressure. In this case it also follows that
dP_
S
=
(7-11)
Q,
dt
(7-8)
P2-P1
PS +
277
pumping speed of a diffusion pump is independent of the since for periods of interest the outgassing rate Q„ may and pressure constant, the value of Q^ can be substituted from (7-6) regarded as be Since the
Thus
if the
equilibrium pressure
P is measured for each of several values
of the gas flow Q, in sequence, and then the slope of the curve is the
Q
is
plotted against the resulting P,
pumping speed
so that
S, as illustrated in
dP
Fig. 7-1.
F
another way in which the pumping determined is by observing the pressure as a function of the time as the system is pumped down. If the and the outgassing gas flow Q = rate Q^, is negligible, then from (7-1) speed can, in principle, be
Still
where
P,, is
the base pressure.
(7-9)
by integrating and arranging we have that
S
=
V 2.30
so that
re-
When
^
Unfortunately, there are very few real situations to
which
this ideal
pumpdown
equation applies. In Fig. 7-1. Graph of throughput the regime of mechanical roughing against resulting pressure for determination of the pumping speed. pumps, the pressure usually changes so rapidly during the pumpdown operation that the outgassing rate is not negligible and is changing with time. Only if the volume of the system is very large as compared with the displacement speed of the pump, so that the pressure changes slowly during pumpdown, will observations based upon Eq. (7-10) check approximately with the known pumping speed of a mechanical vacuum pump. In this case the walls remain nearly in equilibrium with the pressure in the system and outgassing does not play an important role.
~ V k dt P P-Po 8 P Po = - T7 V Pi~Po V S = 2.30 (*2
H
^1)
P1--P0 logi
(7-12)
^1
the assumptions leading to Eq. (7-11) are vahd, then Eq. (7-12)
provides a basis for pumping-speed measurement which has certain Measurement of the gas flow is not required, and distinct advantages. the gauge constant cancels out, provided that the gauge is linear over the pressure range of the measurement. The volume of a system can generally be determined with fair precision from external dimensions. The procedure is simply to pump down the system to a steady base
(7-10)
Pressure, P
In
and
P,
login
Rearranging terms and integrating
yields
dP
so
Po)
at
Jp,
Sdt
^ = -S(P -
enough air (preferably through a drying tube) to bring the pressure back up by a factor of 10 or more, and flnally to read the pressure at several specific values of the time as the system pumps down again. This procedure works well on large systems,
pressure, then let in
,
when the rate of change of pressure during pumpdown rapid as to make pressure readings difficult.
particularly is
not so 7-2.
Measurement
of
Gas Flow.
Pumping-speed measurements
vacuum-pump performance are predominantly carried out under conditions of constant flow. The full range over which gas
for determining
must be controlled and measured for the routine measurement of pumping speeds of commercial vacuum pumps extends from about 10" flow
THE MEASUREMENT OF PUMPING SPEED
VACUUM SCIENCE AND ENGINEERING
278
is normally admitted through a an appropriate test dome mounted on the pump and the flow rate controlled to a value at which the desired pressure is maintained. The gas flow must be measured in such a way that the volume per second and the pressure are both known, so that In those cases in which the throughput Q = P{dVjdt) is determined. no significant pressure drop occurs in the flow-measuring device, the
to about 10-5 torr liters/sec.
Gas
control valve or standard orifice into
279
pound. The parameter c is the nozzle coefficient and generally has a value close to unity. Since from Eq. (1-8) the gas density is feet per
W
MP
V
R,T
the critical volume flow through the orifice
is the barometric pressure when the test is in In those cases in which there is a pressure drop, the value of the pressure at which the flow dVjdt is measured must be determined. Some of the devices commonly used for throughput determination in
is
pressure of interest
various flow ranges will be briefly described. Calibrated Orifice. For large flow rates a calibrated orifice connected to the test dome through a gate valve is convenient and
atmospheric pressure or any desired gas maintained at a controlled pressure in a tank upstream from the orifice flows into the system at a rate determined by the diameter of the reliable.
The surrounding
= by
substituting R^
For
air,
for
=
which
4904c|—
Ml
62,364 from Table
M = 28.98,
cm^/sec
Z)2
at a
(7-15)
1-2.
normal room temperature of
20°C
air at
and the temperature, average molecular weight, and pressure of the gas upstream of the orifice. The flow rate is independent of the pressure downstream from the oriflce, provided that the pressure is less
p dt
dt
progress.
—=
dY
15.6
X
cm^/sec
103cZ)2
dt
=
(7-16)
liters/sec
15.60c7)2
oriflce
than the critical pressure given in Eq. (6-1), as in the case of the flow of steam through an ejector nozzle. For the common diatomic gases y = 1.40, so that the critical pressure from (6-1) is P,
where P^
The
=
(7-13)
0.535Pi
the pressure upstream from the orifice. mass flow through an oriflce under these conditions Eq. (6-7), which for a diatomic gas becomes is
critical
given by
dM = HI
when the
pressure
is
0.538c(Pipy^'D^
measured
g/sec
is
orifice,
is
in centimeters
19.64c(Pip)'^^Z»2
g/sec
(7-14a)
dt
when
the pressure
is
measured
in torr.
915c(Pi/Fi)'^i)^
in the usual engineering
pounds per square
Ib/hr
=
213.3cZ'2
cfm
(7- 16a)
dt
D is measured in inches. For example, the approximate critical flow of atmospheric air through an orifice of 1 in. throat diameter under the above conditions is 100.6 liters/sec or 213.3 cfm, obtained by setting c = 1 in the above equation. If atmospheric pressure is 760 torr, then the throughput for air through when
a
1-in. -diameter orifice is
Q
= P— =
760 X 100.6
=
7.65
X
10* torr liters/sec
dt
=
760 X 213.3
=
1.62
x 10^ torr cfm
In practice the values of the temperature and pressure at the time of the measurement must be substituted in (7-15). The exact value of the nozzle coefficient depends upon the flow For testing the conditions and the detailed shape of the orifice.
(7-146)
of which
is
shown
institute for the
form in which D is in inches, the pressure is in and F^ = 1/p is the specific volume in cubic
inch,
in centimeters, or
"capacity" or pumping speed of steam ejectors, the Heat Exchange Institute! * has developed a standardized long radius orifice, the design
Finally,
dW 11
measured
dV
(7-14)
dW
-^ =
D is
in /ibars (dynes per square centimeter)
and D, the diameter at the throat of the or
when
*
in Fig. 7-2.
The arrangement prescribed by the
mounting of the standard
orifices in
pumping-speed
References indicated by superscript numbers are listed at the end of the
chapter.
THE MEASUREMENT OF PUMPING SPEED
VACUUM SCIENCE AND ENGINEERING
280
measurements is shown in Fig. 7-3. The above reference also gives tables and graphs of flow rates in pounds of air per hour for a sequence of standard nozzles ranging in throat diameter from 0.0625 in. to 1.0 in. Table 7-1 contains a sample of the data given in one section of the above reference with the flow rates in pounds per hour as in the original, and also for convenience
-Manometer
ly^^^ Downstream pressure tap To ejector suction
with the flow rates converted to torr cubic feet per minute and These to torr liters per second. values differ very little in general from those calculated from (7-15)
by assuming that
c
=
1,
coefficient
HEI standard orifice
c
for
shape
is
the
very
nearly equal to 1. The tables and curves permit accurate determination of the critical flow rates
Fig. 7-3. Arrangement of standard orifice for critical air-flow tests. [Reprinted from the Standards for Steam Jet Ejectors, 3rd ed. Copyright 1956 by the Heat Exchange Institute, 122 East 42nd Street, Xew Yorlc, N.Y. 10017.]
Table
of standardized orifices Table 7-1. Also in Ref. 1 a detailed method given for computing the nozzle
P3 (7-13),
>>
pump
n
J
>>>/!?>
/7-r
side
^W^ yj^j^^/zf ////// ///r9n^
Fig. 8-24. Cross section of butterfly type of
vacuum
valve.
VACUUM SCIENCE AND ENGINEERING
THE DESIGN OF VACUUM SYSTEMS
flow with reasonably steady throughput at a given setting, a needle valve of special design is required. An early but quite successful type of needle valve is that described by Bush" and illustrated in Fig. 8-26. The principal feature of the design is the slowly tapering needle fitting
in their use at the inlets of primarily to condense vaporized pump fluid and products of decomposition of the pump fluid. The backstreaming of diff'usion pumps is discussed in some detail in Chap. 6, and the use of water-cooled baffles and refrigerated traps is also briefly described.
328
snugly into a carefully reamed conical seat. For some applications a bellows seal may be substituted for the packing shown in the figure. Such valves are now commercially available. As Bush" mentions,
Vapor traps are most widely known
diffusion
The
direct blast of
'^^^^^fp^^^^"J0 1
n
10
60
90
120
150
210
240 270 300 330
Min.
Fig. 8-50.
down
Pumpdown
factor F.
curve compared with that computed by use of the pumpData of Table 8-6.
are contaminated
by
adsorbed water, and possibly other between the observed and calculated pumpdown times may conveniently be called the system factor, values of which for the pumpdown data in Table 8-6 are given in the last column. Because of minor errors in pressure readings, changes in temperature during the period of the pumpdown, minor discrepahcy in the actual as compared with the assumed rotational speed of the pump, etc., a system factor in the range 0.95 to 1.05 may be considered not to be significantly different from 1.00. It will be noted, however, that the computed system factor in this case rapidly exceeds 1.05 when the pressure drops below 1 torr. The very large increase in the system factor for pumpdown to 0.14 torr is not typical and was most probably caused by the presence of a leak of the order of 40 torr cfm. The pump is capable of reaching an ultimate pressure of the order of condensable materials.
oil
should not exceed 10 per cent of the pressure. However, during atmospheric pressure this pressure drop is negligible as compared with the pressure itself. The conductance of the connecting piping is proportional to the pressure in this pressure range so that over most of the pumpdown cycle the conductance is very large indeed as compared with the pumping speed of the pump and is therefore not normally a significant factor in determining the
/ Obse rved
\ r ompu ^pH
30
pump is such that the not likely to be a measurable factor
pumpdown from
\ a
is
in determining the pumpdown time. As discussed in Sec. 2-4, the pipe size is selected to ensure an acceptably small pressure drop when the system has reached its normal operating range (i.e., the lowest pressure of practical interest). The criterion frequently applied is that the pressure drop in the line (up to the inlet of the mechanical pumps)
s.
100
353
films,
The
ratio
pumpdown
time within the range of mechanical pump operation. Many pumpdown experiments have been carried out under both favorable and unfavorable conditions. When there are sizable leaks present in the system or when puddles of water have accumulated at some low point in the plumbing, then the pumpdown process becomes stalled and the system factor approaches infinity. However, when there are no leaks present, when the interior of the system has been cleaned section by section before assembly, and when no unforeseen
event has created puddles of water somewhere in the system, then experience shows that rather definite values of the system factor apply to the pumpdown time, depending upon the pressure limit involved, such that ^(actual)
=
(system factor)^ (system factor)
(calc)
V -—
i^^^^^
(8-11)
The recommended system factor makes allowances for the normal outgassing of surfaces exposed to atmospheric air and provides a basis for judging whether the system is pumping down normally or whether some problem exists which must be corrected. On the basis of experience, therefore, recommended system factors are given in Table 8-7 not only for single-stage mechanical pumps, but also for compound
pumps and mechanical by
special
care,
booster pumps.
such as letting
down
emphasized that the system to atmospheric
It should be
THE DESIGN OF VACUUM SYSTEMS
VACXJUM SCIENCE AKD ENGINEBBING
354
shorter pumpdown times than
by admitting only dry nitrogen, be reahzed. those computed using the recommended system factors can apsystematic and Naundorf25 has attempted a rather complete the into extending time proach to the determination of the pumpdown solution a to leads approach lange of diffusion-pump operation. His typify based upon the graphical representation of two quantities which
pressure
Table
8-7.
and ceramics.
The
a calculation of the gas load as a function of the time for most practical situations would be a formidable task. However, in the case of the relatively simple case of a stainless steel chamber 4 ft in diameter and 6 ft in length, evacuated by a 32-in
pump, Naundorf was able to demonstrate good agreement between the predicted and actual pumpdown schedule. The outgassing rate was determined experimentally by closing the valve into diffusion
Recommended System Factors System factor
•
V
Qi Oi
Pressure range, Single-stage
torr
mechanical
pump
Compound mechanical
pump
I
(J
pump* £
1-0.5 0.5-0.1
1.0
1.0
1.1
1.1
1.15
1.25
1.25
1.15
10
-
1.5
1.25
1.35
1.25
1.35
3
10
\
-
^^Gos
f Net pumping
.
/
5-0^
capacity
load
-
o
/
10'
2.0
0.02-0.001
V
">
\
10
0.1-0.02
\
10^
Mechanical booster
S
760-20 20-1
355
difficulty is that
Q2
^10'
/ /
Based upon bypass operation until the booster pump is put into operation. the Larger system factors apply if rough pumping flow must pass through gettmg and valves operating for needed time Any idling mechanical booster. the mechanical booster pump up to speed must also be added.
T2
T,
,0°
10"^
10"^
10"
10"
10"'
Pressure P.torr
Fig. 8-51.
1
10"'
10"
Time
Throughput of a diffusion-
pump system
^^^
P,,
Pz
10" -
*
as a function of the
'
10'
1
10^
t,hr
Fig. 8-52. Gas load as a function of the time. [Taken with permission from C. H. Naundorf, in 1960
the throughput as a function of the pressure as represented in Fig. 8-51 and (2) the gas load as a function of the time as represented in Fig. 8-52. At every instant of time, in order for the pressure to be the observed value P, the throughput of the system Q must equal the gas load L existing at the time of the observation.
pressure.
will Unless there is a dominating leak in the system, the gas load There 8-52. Fig. in decrease with the time more or less as illustrated the throughput as a is no difficulty about determining the form of function of the pressure. This curve can be quite accurately predicted from the pumping speeds of the pumps used and the conductances of traps and other components introduced. At each value of the pressure the throughput Q = PS, where S is the resultant pumping speed of the
pump once each hour and measuring the rate of pressure which multiplied by the volume of the tank gave the gas load due to outgassing. The data thus obtained were plotted as shown in Fig. 8-53, and prove to be in excellent agreement with the data on outgassing of stainless steel contained in Dayton's paper. The result of combining the gas-load curve with the throughput-capacity curve of the pumping system is shown in Fig. 8-54. A horizontal line drawn through any value of the throughput and gas load intersects the throughput-vs. -pressure curve and the load- vs. -time curve. Dropping vertical lines down from each intersection yields the pumpdown time
the system:
(1)
combined system. The gas load L as a function of the time is somewhat more difficult to construct. In order to predict the form of the gas-load curve as a function of the time one must know a great deal in detail about the processes of the adsorption, chemisorption, diffusion of gases through materials, and are topics These solubilities of gases in materials of construction. are data of tables discussed at length by Dayton^" in a paper in which given for
all
these processes for
many
metals, plastics, elastomers,
from
C.
Vacuum
[Taken with permission H. Naundorf, in 19(i0
Symposium
Transactions
(Pergamon Press, London,
Vacuum
Si/m,posium,
Transactions
(Pergamon Press, London,
1961).]
1961).]
the diffusion
rise,
for a particular value of the pressure.
This procedure
is alleged to provide an excellent prediction of the time provided the pressure in question is not seriously limited by some other process than outgassing, such as leakage and permeation. In the event that these other processes are important.
pumpdown
THE design of VACUUM SYSTEMS
VACUUM SCIENCE AND ENGINEERING
356
357
and pumping speed of the system, to lead to the expression
state as well as dimensions
gration of (8-12)
is
shown
Throughput vs. pressure
\
Inte-
f-
for
mcf-15,000 system
\.
used
Gas load (by rate-of-rise
method)
« Pressure read at
gas lood
vs.
time
^y*
•
\
Measured values
Note: Untrapped ion
and McLeod gauge
\
f
data
10°
I ^
10''
10"'
10°
10'
10^ Time,hr
10"'
10"^
10"'
10"^
10"' Pressure, torr
Log time.hr
Fig. 8-54. Gas load as a function of the time combined with throughput as a
Fig. 8-53. Experimental gas load as a function of the time for a stainless steel tank of total surface
A vertical of the pressure. at any value of the pressure to the throughput curve, then a horizontal line drawn to the intersection with
function
area of 165 sq ft. [Taken with permission from C. H. Naundorf, in 1960 Vacuum Symposium Trans-
line
drawn
the gas-load-vs.-time curve, and finally a
(Pergamon Press, London,
vertical line drawn down from this intersection gives the pumpdown time for
1961).]
the chosen value of the pressure. [Taken with permission from C. H. Naundorf, in 1960 Vacuum Symposium Transactions
(Pergamon Press, London,
1961).]
the gas-load curve must be corrected and in general will have the form
shown
+C
(8-13)
valve inlet
».
Predicted
actions
V S P
.''Key:
pumpdown time, provided P^ > P >
Here P^ is a paramwhere a is the same as that in Eq. (8-12) and V is the volume of the system. The wide range over which the above pumpdown time relationship holds in practice is demonstrated in Fig. 8-57. When organic materials such as elastomers and plastics dominate the outgassing properties of a system, however, the pumpdown relationship is more complicated. In this case (P — Pe)~^ is more nearly a linear function of the pumpdown time, and the equation cannot be integrated to anything approximating Eq. (8-13). From this discussion of pumpdown time in the range of diffusionfor the
eter of the system being defined as
pump
P^
=
Pj^.
aj V,
evident that firm predictions are much more in the pressure range for mechanical pumps. Factors not taken into consideration are the use of refrigerated traps and the application of mild heating to the vacuum chamber. The operation
difficult to
it is
make than
vacuum designer make reasonable choices in pump sizes to make possible the attainment of the desired pressures in the specified time. However, the
references cited in the above discussion will assist the to
precautions taken during preparation and operation of the system will
in Fig. 8-55.
Further understanding of the problem of predicting pumpdown times that for a metal is provided in a paper by Kraus" in which it is stated by the expressed is time the of function a apparatus the pressure as equation following differential
MO"'
/ Sio^ Adsorbed and absorbed
dt
d{P
-
S
=
gas load
(8-12)
const
S^
Total gas load
vsJimeX^
vs.
/
time 5-10"
the pressure attained after pumping for the time t, P^ is the ultimate pressure attainable after pumping for a long time, and S is the pumping speed of the system. The prediction of this equation is that P^)"! is a linear function of the pumping time the quantity (P
-
provided that the pumping speed
*S is
a constant.
That
this is indeed
shown by the graph in Fig. 8-56. The two curves in the figure were obtained from the same system, the steeper curve after the system had been exposed to atmosphere for only 2 mm and the less steep curve after an exposure to atmosphere of 2 hr. The value of the constant a in the above equation depends upon the initial
true in cases of interest
is
Inleakage and 10'
permeation 10"
y
/
2'10"'
P^;)-
P is
1
1
/A ,'V
^t
,;> 10°
10'
10^
10
Min
Time.hr
Fig. 8-55. Gas load as a function of the time corrected for the presence of significant leakage and
[Taken with permission from C. H. Naundorf, in 1960 permeation.
Vacuum Symposium Transactions (Pergamon Press, London,
6
4
1961).]
Fig. 8-56. Relationship between 1/(P = P^) and the pumping
[Taken with permission t. from Th. Kraus, in 1968 Vacuum Symposium, Transactions (Pergamon Press, London, 1959).] time
THE DESIGN OF VACUUM SYSTEMS
VACUUM SCIEKCE AND ENGINEERING
358
many cases affect the performance much more than minor changes in
in
\,
10"
8-8.
/ y' Switchover to
pump
diffusion
^:) \
i
\
-3
V
10'
Log(P-PE) t
\
\
^-Log(t10"
K V
1
10
1
choice
of
design
100
Min
Fig. 8-57. Pressure-time curve for a vacuum annealing furnace demonstrating the wide pressure range
over which Eq. (8-13) is applicable. [Taken with permission from Th. Kraus, in 195& Vacuum Symposium Transactions (Pergamon Press,
roughing pumps required for this function can be computed with very uncertainty from Eq. (8-11) using the system factors given in Table 8-7. Whether this battery of roughing pumps consists of
little
single-stage
Selection of Vacuum Com-
ponents. The conventional vacuum system consists of mechanical pumps, diffusion pumps, valves, vapor traps, vacuum gauges, and interconnecting plumbing all assembled for the purpose of attaining and maintaining the specified environment in a vacuum chamber. Because the vacuum designer is faced with several alternative combinations of components which will meet the specified per-
•
•
original
parameters.
\> 10"
the
359
single-stage Nude
ion
Ion
pumps alone or mechanical booster pumps backed by pumps is an economic question which can only be answered gouge
Cold trap
Gote valve
Interconnecting
valve
Roughing ,0
-—@)-^14
formance, the final choice involves judgment regarding the most convenient and economical combination of components which will serve the purpose. In this section the functions of each of the
^Thermocouple
components in
Diffusion-pump^
meeting the operating requirements of the system will be discussed
be briefly and some London, 1959).] combinathe specifying given for tions and capacities of components needed. Mechanical Pumps. The mechanical pumps of a conventional high-vacuum system have two rather separate functions: (1) to pump down the system to the level necessary for the diffusion pumps to be put into operation and (2) to maintain the backing pressure during regular operation at an acceptable pressure for optimum operation of the diffusion pumps. These two requirements frequently lead to very different values of the capacity for the mechanical pumps. In many large systems the time for roughing down the system is much longer than that required to reach operating pressure once the diffusion pumps and refrigerated traps can be put into operation, after which the mechanical-pump capacity required to maintain the needed backing pressure is very small. In such systems, as illustrated in Fig. 8-58, it is economical and convenient to install a battery of largecapacity mechanical pumps connected directly to the vacuum vessel by means of a bypass line to rough out the system to a pressure below that at which the diffusion pumps can operate. The capacity of the criteria
will
wjvolve
foreline trap
Freon^ compressor Roughing pump
conventional high-vacuum system. (1) Vacuum chamber; (2) internal liquid-nitrogen thimble trap; (3) liquid-nitrogon-cpoled diffusion pump baffle; (4) gate valve (in optimum design the connecting pipe would be as short as possible; (5) Freon-cooled baffle; (6) diffusion pump with Freon-cooled exhaust condenser; (7) forevacuum oil vapor trap; (8) forevacuum valve; (9) backing pump; (10) roughing pipe and valve with oil vapor trap; (II) roughing pump; (12) interconnection between roughing and backing lines with close-off valve; (13) ionization gauges nude and tubulated in vacuum Fig.
8-58. Representative
—
—
chamber;
(14)
thermocouple gauges in roughing and backing
lines.
by computing the pumpdown time for various combinations of pumps and their associated plumbing and then comparing the resulting performance with the cost of each combination. In principle the determination of the capacity of the backing pump is a simple matter. If the throughput Q of the system during normal operation is known, then the pumping speed for backing is Sj, = QjPi,, where Q is the throughput and P^ is the backing pressure required during operation. This determination is generally much more difficult to judge in advance than the pumpdown capacity required because of the uncertainty in the value of Q due to gas flow, outgassing, and
VACUUM SCIENCE AND ENGINEERING
360
furthermore
have
THE DESIGN OF VACUUM SYSTEMS
some
excess
permeation. The system should capacity to override minor leaks sufficiently to get the diffusion pumps An interconnection between into operation and expedite leak hunting. in Fig. 8-58 can be invaluable the backing and roughing pumps as shown with this added flexibility even However, during periods of difficulty. backing pump above the the of capacity ill the system, a factor of 2 in calculated from the anticipated throughput is recommended. Because of uncertainty in the knowledge of the value of the throughput, an even larger margin in capacity may be required. Even with a fairly generous factor applied to the throughput for determining the
minimum
capacity of the backing pump, however, in most cases that capacity is very much smaller than that required for the roughing pump. Operation of a system thus usually consists of pumping the system down through the bypass and roughing pumps to a pressure of perhaps 0.1 or 0.2 torr, then closing the bypass valve and opening the gate valve The diffusion pump has presumably already into the diffusion pump.
been in operation with the gate valve closed and backed by the backing pump. The next step is then to cool down the liquid-nitrogen-cooled baffle over the diffusion pump and also to fill the thimble trap with Meanwhile the liquid nitrogen (assuming a thimble trap is used). system down the roughing used for pumps mechanical capacity large
from atmospheric pressure can be stopped. Diffusion Pumps. The pumping speed required for the diffusion associated baffles and gate valves must also be considered from the point of view both of pumpdown time and of the required operating pressure. The pumpdown time can best be approached by
pump and
method ofNaundorf^^ outlined in the previous section. For various combinations of diffusion pumps, gate valves, and baffles one can estimate the throughput capacity of the system as a function of the pressure. From the outgassing data supplied in the paper by the
Dayton^' and the exposed areas of various materials one can construct a gas-load curve as a function of the time. By combining these curves as in Fig. 8-54 the pumpdown time as a function of the pressure can be roughly predicted for any particular combination of diffusion pump, baffle system, and gate valve for which the overall pumping speed is known. The choice from this point of view must then be compared with the pumping speed required to maintain the desired operating pressure for the predicted gas load by applying S = QjPo, where P„ is
the operating pressure.
gate-valve pumping speed sideration.
The choice of diffusion-pump, usually determined by this
is
Although additional construction cost always
oversizing the system
by providing excess pumping speed
baffle,
and
latter con-
results
from
to override
361
accidental leakage or a larger gas flow for whatever process is involved, this additional construction cost will in most cases be at least partly compensated for by the reduced pumping and processing time which usually result from excess pumping capacity. A vacuum system with
pumping capacity which
is too small to do the allotted job is much less economically sound than one which has a moderate excess capacity. Loss of time during operation can be very expensive and in a short time dissipate the initial savings one might make by installing insufficient
pumping
capacity.
Accessories.
ventional
The
accessories
which are useful to include
in a conas that illustrated in Fig. 8-58, aside in the drawing, are
vacuum system such
from those
specifically
shown
1. Multiplicity of ionization gauges. In many large systems it is convenient to install ionization gauges in pairs, one with and one without a glass liquid-nitrogen trap. The discrepancy between the gauges
due primarily to condensables (mostly water vapor) so that an experienced operator can readily ascertain the condition of the system and diagnose many troubles. is
2. Thermocouple or Pirani gauges are indicated in Fig. 8-58, but the advantage of a multiplicity of such gauges in the roughing and backing sections of the system should be emphasized. 3.
Although vacuum valves are expensive, the
into the system
by the
flexibility
introduced
inclusion of valves at strategic points
is
well
worth the cost. Aside from the gate valve for isolating the diffusion pump from the vacuum chamber, valves should be installed at the following positions (a) at the vacuum chamber end of the roughing line, (b) in the forevacuum line near the outlet of each diffusion pump, (c) at the inlet of each mechanical pump, either roughing or forevacuum, and (d) in a line interconnecting the forevacuum and roughing lines. Also recommended are small, normally closed valves installed between each shutoff valve and its mechanical pump for testing and diagnosing the source of trouble in the system, and a small, normally closed valve on the vacuum chamber for letting down the chamber to atmospheric pressure. Provision should be made to admit commercial dry nitrogen or dry air through a drying unit. :
Conventional vacuum systems of the type described above should give excellent service with base pressure (untrapped ionization-gauge reading) of 10^' torr and should perform well in the range of 10-^ torr. When operation at significantly lower pressure is desired, the techniques of ultrahigh
next chapter.
vacuum
are required.
This
is
the topic of the
VACUUM SCIENCE AND ENGINEERING
362
REFERENCES 1.
2.
3.
4.
5. 6. 7. 8. 9.
10.
11.
12. 13.
14.
15.
16.
17.
18.
L. L. Levenson, Xorman Milleron, and D. H. Davis, in 1960 Vacuum Symposium Transactions (Pergamon Press, London, 1961), p. 372. Transactions I. Farkass and E. J. Barry, in 1960 Vacuum Symposium (Pergamon Press, London, 1961), p. 35. A. Guthrie and R. K. Wakerling (eds.). Vacuum Equipment and Techniques
(McGraw-Hill Book Company, New York, 1949), pp. 148-158. R. R. Addis, Jr., L. Pensak, and Nancy J. Scott, in 1960 Vacuum Symposium Transactions (Pergamon Press, London, 1961), p. 39. R. R. Wilson, Rev. Sci. Instr. 12, 91 (1941). R. H. V. M. Dawton, Brit. J. Appl. Phys. 8, 414 (1957). R. W. Roberts, Rev. Sci. Instr. 32, 750 (1961). J. F. Gerber, Rev. Sci. Instr. 34, 1111 (1963). F. N. D. Kurie, Rev. Sci. Instr. 19, 485 (1948). J. S. Wahl, S. G. Forbes, W. E. Nyer, and R. N. Little, Rev. Sci. Instr. 23, 379 (1952). William E. Bush, A. Guthrie, and R. K. Wakerling (eds.). Vacuum Equipment and Techniques (McGraw-Hill Book Company, New York, 1949), Chap. 4, p. 179. J. W. Johnson and W. M. Good, Rev. Sci. Instr. 32, 219 (1961). Norman Milleron, in 1958 Vacuum Symposium Transactions (Pergamon Press, London, 1959), p. 140. J. R. Ullman, in 1957 Vacuum Symposium Transactions (Pergamon Press, London, 1958), p. 95. L. L. Levenson, Norman Milleron, and D. H. Davis, in 1960 Vacuum Symposium Transactions (Pergamon Press, London, 1961), p. 372. A. R. Taylor, in 1961 Vacuum Symposium Transactions (Pergamon Press, London, 1962), p. 1328. H. R. Smith and P. B. Kennedy, in 1959 Vacuum Symposium Transactions (Pergamon Press, London, 1960), p. 271. John Strong in collaboration with H. Victor Neher, Albert E. Whitford, C. Hawloy Cartwright, and Roger Hayward, Procedures in Experimental Physics (Prentice-Hall, Inc., Englewood
19.
20.
21.
22.
23.
24. 25. 26. 27.
Cliffs,
N.J., 1938), pp. 105, 124.
D. Alpert, Rev. Sci. Instr. 24, 1004 (1953). J. H. Carmichael and W. J. Lange, in 1958 Vacuum Symposium Transactions (Pergamon Press, London, 1959), p. 137. M. A. Biondi, in 1960 Vacuum Symposium Transactions (Pergamon PreSs, London, 1961), p. 24. N. Milleron and L. L. Levenson, in 1960 Vacuum Symposium Transactions (Pergamon Press, London, 1961), p. 213. L. L. Levenson and N. Milleron, in 1961 Vacuum Symposium Transactions (Pergamon Press, London, 1962), p. 91. T. H. Batzer and R. H. McFarland, Rev. Sci. Instr. 36, 328 (1965). C. H. Naundorf, in 1960 Vacuum Symposium Transactions (Pergamon Press, London, 1961), p. 60. B. B. Dayton, in 1959 Vacuum Symposium Transactions (Pergamon Press, London, 1960), p. 101. T. Kraus, in 1958 Vacuum Symposium Transactions (Pergamon Press, London, 1959), p. 38.
CHAPTER
9
ULTRAHIGH VACUUM
The term ultrahigh vacuum has come into use in recent years to designate the range of pressure below about IQ-' torr which cannot easily be attained by the conventional methods and techniques described in the previous chapter. In order to reach significantly lower pressure, additional or alternative techniques must be applied. The techniques thus far found to be useful in attaining operating pressures in the range IQ-s to lO"" torr or lower will be briefly described in this chapter. 9-1. The Dominance of Surface Phenomena. From the papers of Daytoni-3* on the outgassing of "clean" metal surfaces at room temperature it is evident that after exposure to normal atmospheric air for several hours the amount of gas readily available for desorption
from the surface at room temperature amounts to many molecular layers. As an example, Dayton's tables^ show that after 10 hr of
vacuum pumping the
outgassing rate for a stainless steel surface is and is decreasing very slowly. Therefore to maintain a base pressure of IQ-s torr in the presence of such an outgassing rate requires a pumping speed of at least 20 liters/sec for each square foot of internally exposed surface. Most large vacuum
about
2
X 10-5
torr liter /sec ft^
chambers consist of outer walls and a complex inner structure, the which must be considered. Also the wall area
total surface area of
vacuum pumping is usually limited by the many other demands of the system for access ports, high voltgage insulators, and a variety of accessories essential to the vacuum process. The result is available for
that a design figure of 20 liters/sec for each square foot of internal surface can generally be realized or even somewhat exceeded in practice so that the base pressure is limited to about lO"" torr even after many hours or days of pumping.
In the previous chapter mention was made of speeding process of outgassing by increasing the temperature of the
up the
vacuum
References indicated by superscript numbers are listed at the end of the chapter.
363
VACUUM SCIENCE AND ENGINEEBmo
ULTRAHIGH VACUUM
chamber, and this practice has been followed for many years. Howsystem is not ever, the gain in the ultimate pressure attainable by a The factor. large a by 100°C) to (say baking improved by a mild typical the reach to required time the that principal advantage is To reduce significantly limit of the system may be greatly reduced. at temperatures baking requires pressure the attainable operating
experimental data of this type in the curves shown in Fig. 9-1 for steel and in Fig. 9-2 for aluminum. Based upon the macroscopic surface area, the total amount of gas given off by metal surfaces at room temperature over a period of 10 to 50 hr of vacuum pumping ranges from 20 to 100 molecular layers. What is perhaps more to the point is that untreated
364
365
This requirement introduces a number of complications into the design which are not encountered in conventional
much
greater than 100°C.
vacuum-system design. Experience has shown that outgassing from metal surfaces in vacuum The character of the surface is predominantly due to water vapor. discussed by many investiis surfaces metal deposition of water on Hebling,« Mongodin and and Lichtman gators: Kraus,* Hayashi,^ the surfaces of metals Because Noller.* and Prevot,' and Flecken consist of somewhat construction vacuum-chamber generally used in state of the physical exact the defining of problem porous oxides, the metal is complicated. the of surface the on contaminants water and other As Dushman* has explained, there are three mechanisms by which a the gas can be taken up by a solid material, all generally included under general term sorption.
Chemisorption refers to the formation of a chemical compound by interaction of a gas with the wall material, as in the case of the formation of an oxide film. on a metal 2. Adsorption refers to the surface condensation of a gas of only film a in This process is generally believed to result surface. 1.
a very few molecular layers of gas. molecules penetrate 3. Absorption refers to a process by which the gas dissolved into the interior of the wall material and in a sense the gas is
5
9-1. Outgassing rate versus time for steel at room temperature. Curves for rusty steel, sandblasted
Fig.
steel, and stainless steel (curve 1) from the data of Blears et al.^" Stainless steel curve 2 from the data of Gellor,!' and curve 3 from that of Basalaova'^ on untreated stainless steel. [Taken with permission from B. B. Dayton, in 1961
Vacuum Symposium
in the solid.
The outgassing history is expected on theoretical grounds to depend incritically upon which of these three mechanisms of sorption are is extensive, very been has which question, volved. Research on this The area. surface effective the of complicated by the definition roughness factor (i.e., the effective microscopic surface area compared with the gross, or macroscopic, surface area) inferred by various investigators ranges from about 20 to 100 depending upon the details applied of outgassing experiments and the assumptions of the theory lack the and theory the of complexity the Because of to the situation. the of sufficient detailed knowledge of the microscopic character of experiupon based problem the to surfaces, an empirical approach mental outgassing results at various temperatures seems to be the only practical course to follow at the present time
.
Dayton^ has summarized
Transactions
(Pergamon Press, London,
1962).]
10-7
J'iG. 9-2. Outgassing rate versus time at room temperature. Curve 1, untreated duraluminum, and curve 3, duraluminum scoured and washed with benzol and acetone, are based on the data of Basalaeva.i^ Curve 2, duraluminum, is based on the data of Geller.ii Curve 4, aluminum bright-rolled and cleaned in Stergene, and curve 5, anodized aluminum, are based on the data of Blears et al.^" [Taken with permission from B. B. Dayton, in 1961 Vacuum Stjmpo-
sium Transactions (Pergamon Press, London, 1962).]
metal samples outgas at the rate of about I0-' torr liter/sec cm^ after 1 hr of vacuum pumping at room temperature, and this rate of outis about inversely proportional to the pumping time. These statements have to do with room-temperature outgassing for which water vapor is by far the dominating substance. At high temperature other factors, such as diffusion of absorbed gases through the metal, become important so that high-temperature outgassing cannot be inferred simply by integrating the room-temperature curves and compressing the resulting output over a shorter period of time. 9-2. High-tetnperature Bakeout. In the previous section it was stated that operating pressures much less than about 10^* torr
gassing
VACUUM SCIENCE AND ENGHSTEEEING
366
ULTRAHIGH VACUUM
cannot easily be attained because of the long-persisting outgassing of The total amount internally exposed surfaces at room temperature. of gas available on metal surfaces is so great that even with the inverse dependence upon the pumping time of the outgassing rate the base pressure attainable is seldom as low as lO"' unless some action is taken to change drastically the source of gas available for desorption.
Mc X system
te
mp
400°C
=
on first bake
10-^
Base pre ssure before
/Sp
//I / /
bokeout
'
/Max / /
10'* -
\\^
\ \
N.
system
>\
^'^~\
385
Another example of a two-region system is described by Metcalfe and Trabert^^ ^^d illustrated schematically in Fig. 9-26. The outer vacuum chamber is 48 in. in diameter and is evacuated by a conventional diffusion-pump system consisting of a 12-in. diffusion pump with
is shown in Fig. 9-27. An interesting feature of the curve the series of ionization-gauge peaks which are observed as the liquidnitrogen supply to the chevron baffles is shut off and the baffles slowly is
pump Quick cooling
warm
up.
These peaks are interpreted as being due to the fractional condensed gases off the baffle surfaces.
distillation of the Rotary pump
9-6. Getter-ion
Pumping. Thus far in this chapter we have ways in which the performance of the conventional diffusion pump and vapor-trap combination, together with various modifications in the methods of sealing and the technique of baking to high temperature, could be improved for the purpose of attaining considered various
Fig. 9-25. Two-region ultrahigh-vacuum system with thin-wall inner chamber. [Taken with permission from H. Ehlers and J. Moll, in 1959 Vacuum Symposium Transactions (Pergamon Press, London, I960).]
VACUUM SCIENCE AND ENGINEERING
ULTRAHIGH VACUUM
much lower pressures than are typically obtained in conventional vacuum systems. The diffusion pump and its mechanical backing pump are sources of contaminants
the ions and electrons formed by ionization are constrained to move in more or less tight spirals along the lines of force. A neutral molecule
386
which must be prevented from backstreaming into the highvacuum portion of the system and limiting the base pressure to
much
some
higher pressure than that
desired.
Rather than combat
this
problem of backstreaming, engineers in recent years have made an intensified effort to exploit methods of pumping which do not generate hydrocarbon contaminants and give promise of providing "clean" vacuum spaces with relatively simple combinations of
equipment. One approach to this problem which has had some 30
40-
Time.hr
Fig. 9-27. Typical bakeout and pumpdown cycle of the two-region vacuum
system shown in Fig. 9-26. [Taken with permission from R. A. Metcalfe
and F. W. Trabert, in 1961 Vacuum Symposium Transactions (Pergamon Press, London, 1962).]
degree of success was discussed toward the end of Chap. 5, where recent progress in the development of molecular pumps and axial-flow molecular turbine pumps was de-
We
devote the remainder of this chapter to other scribed.
shall
methods of pumping, some of which have already been demon-
strated to provide important capabilities in the ultrahigh-vacuum
pressure range. It is well
discharges have the ability to pump to some particularly true of discharges in magnetic fields, since
known that gas
This
degree.
is
Exit-gas leak
Pressure
~10'^
torr
Side magnet
Hollow cold ttiode
-300 volts
Pressure ~5)(10" torr
Anode constriction'
Pressure~5xlO"''
Fig. 9-28.
torr
End view
"To forevocuum
An ion pump based upon the pumping action of an intense discharge in
a magnetic field. [Taken with permission from .J. S. Foster, and E. J. Lofgren, Rev. Sci. Instr. 24, 388 (1953).]
Jr.,
E. O. Lawrence,
387
which wanders into a discharge column in a magnetic field quickly becomes ionized, trapped in a spiral path in the magnetic field, and forced to leave the region where it entered the discharge by spir'aling along the magnetic field. The pumping action of discharges in magnetic fields has therefore been well known for a long time. However, the first serious attempt to develop a vacuum pump utilizing this
appears to be that of Foster, Lawrence, and Lofgren. ^s The device took the form shown in Fig. 9-28, which illustrates a discharge eff'ect
ion
pump
The
axial magnetic field
capable of pumping at the rate of about 5,000 liters/sec. was produced by an array of coils mounted on the long, cylindrical body of the pump, except for the central region where the pump housing is enlarged to provide high entrance conductance. Across this enlarged section of the pump the coil was in the form of a rather open spiral conductor carrying a large current to maintain the magnetic field strength and still permit gas molecules to diffuse freely into the discharge.
The distribution of currents in the coils determines the shape of the magnetic field which is optimum when the lines of force bulge slightly in the central section of the pump and converge somewhat symmetrically toward both ends.
The discharge is a large PIG discharge first investigated by Penning. »« There are two cathodes, one on each end of the device. Experience with a variety of hot- and cold-cathode designs resulted in the final selection of a hot, hollow cathode
on one end and a cold, hollow cathode The anode for the discharge is the long cylindrical pump body reaching from the enlarged pumpinlet section to the anode constriction on each end. The discharge column is limited in diameter by the anode constrictions. The shape of the magnetic field and the diameter of the cylindrical anode from the constriction to the pumping section of the device are sensitive parameters. In order to maintain the proper discharge conditions in the central region of the pump it was found to be necessary to maintain a neutral gas density in the cathode chambers not less than about 5 X 10-* torr, which is the forevacuum against which the ion pump works. The gas from the cathode chambers fiows in from both ends of the pump, is ionized, and as positive ions is carried back to the cathodes, where the ions are neutralized. Molecules fiowing into the discharge column in the central section are ionized and also are carried out the ends as ions and are neutralized at the cathodes. Many of the on the other, as shown in the
figure.
ions striking the cathodes interact chemically. This process proceeds at such a rate that the forevacuum valves at the two ends of the
pump
could frequently be closed and even then gas had to be bled
VACUtTM SCIENCE AND ENGINEERING
ultrahigh vacuum
chambers in order to maintain the minimum operating pressure of 5 x 10"* torr required to maintain the discharge. The operating characteristics of the pump are shown in Table 9-1. From these characteristics it is evident that the ion pump of Foster,
about 12 in. in diameter. (2) An electron-emitting filament and double grid system which accelerates electrons radially outward, ionizes residual gas molecules, and drives the ions with energies up to 1,000 eV into the walls of the pump body which are coated with the evaporated
Lawrence, and Lofgren cannot be classed as an ultrahigh-vacuum pump since the typical base pressure was about 1 X 10"* torr. However, the pump did have the specific advantage of not producing hydrocarbon impurities. The feature of continuing to pump even
titanium.
388 into the cathode
Table
Opekating Pabametbes of the Ion Pump Shown in Fig. 9-28*
9-1.
Pumping speed Base pressure Arc voltage Arc current Cathode
Magnet power
3,000-7,000 liters/sec 0.8-5 x 10"* torr
400-300 V 20-10 A Radiantly heated tungsten cathode Heating power, 4.5 kW Side magnets, 20 kW Center helix, 12 kW
when the forevacuum of the
valves were closed contributed further to the system relative to hydrocarbon contaminants.
Unfortunately, the pressure in the cathode region had to be maintained at least at 5 x 10~* torr, and the compression ratio which the pump could maintain against the pressure in the cathode chambers was never better than about 10^, so that pumping at pressures much lower than 10~* torr with this particular type of ion
pump
does not appear to be
promising.
During studies of the performance of closed-off systems with a Bayard- Alpert gauge in operation Bayard and Alpert^^ observed a very definite pumping action of the gauge involving chemisorption and ion Herb and his collafcoraburial in metal coatings in the gauge tube. ^Qj.g36,37 have reported on the operation of a large device designed The specifically to exploit these mechanisms for vacuum pumping. device, known as the Evapor-ion pump, is illustrated schematically in Fig. 9-29, and involves two principal features: (1) A feed mechanism by which titanium wire is fed in a sequence of discrete steps from an '
down a guide so that the tip of the wire periodically touches a post of tantalum-tungsten alloy which is heated by electron bombardment to such a high temperature that a short length of the wire is evaporated each time the tip of the wire touches the post. The evaporated titanium coats the walls of the pump housing, which is
internal spool
is
very active in the chemisorption of gases. These latter gases
most of the common gases except the noble are ion
pumped
in the Evapor-ion
pump, driven into the wall coating, and covered up by subsequent layers of evaporated metal.
Pumping speeds measured for various gases by Swartz^* were as given in Table 9-2 when the rate
* Reproduced by permission from J. S. Foster, Jr., E. O. Lawrence, and E. J. Lofgren, Rev. Sci. Instr. 24, 388 (1953).
cleanliness
Freshly evaporated titanium
389
of titanium evaporation was 5.3
Filament F
mg/min. The most extensive use of the Evapor-ion type of pump is on the 30 X lOi'-eV AGS proton synchroton at Brookhaven, where over 50 units have been in use for
Inner grid G|
several briefly
years.
Outer grid Gj
Gould^^ reported
on experiences and
diffi-
encountered in the early use of these pumps in such great multiplicity. The method of evaporation of titanium has been changed to one of sublimation from a heated titanium rod as described by Gould and Mandel*" and also by Herb, Pauly, Welton, and Fisher.*! The Evapor-ion pumps which have been changed over to the new continuous sublimation technique are operated as culties
described by Gould and Mandel" under the control of an automatic
Bleeder system
Fig. 9-29. The Evapor-ion pump. [Taken with permission from R. H. Davis and A. S. Divatia, Rev. Sci. Instr. 25, 1193 (1954).]
pressure detector in the pressure range 2 x 10"' to 2 x 10"* torr. The ultimate pressure thus far attainable using the new technique is 2 x 10^' torr, which the authors believe is determined by the impurities present in the commercial (non-vacuum-processed) titanium which is used.
The pumps equipped with three sections of titanium rod for sublimation deposit, as shown in the photograph in Fig. 9-30, are expected to
ULTRAHIGH VACUUM
VACUUM SCIENCE AND ENGINBEBING
390
Table
9-2.
Pumping Speeds for Various Gases for the Evapor-ion Pump* Gas
Partial pressure, torr
Air
370
X 10-5 3 X 10-6 1.7 X 10-6 5 X 10-6
1,000
2,000 3,300 1,000
X 10-5
20
5 X 10-5
5
1
Nitrogen
Hydrogen Carbon monoxide Methane Argon
.
.
.
speed,
liters/sec
X 10-5
1
Oxygen
Pumping
1
* Reproduced by permission from J. C. Swartz, in 1955 Vacuum Symposium Transactions (Committee on Vacuum Techniques, Boston, 1956), p. 38.
391
operate satisfactorily for a period of about two years before replacement of the titanium rods will be required.
Although as used on the Brookhaven AGS the operating pressure is not very low, it is an acceptable range for the present needs. What is important is that the system appears to be essentially free of hydrocarbon contaminants. The system is initially pumped down to a pressure of about 10-* torr by a group of compound mechanical booster pumps backed by single-stage mechanical roughing pumps. The system is then isolated from the mechanical pumps and the Evapor-ion pumps are put into operation. The relative simplicity of the Penning Penning gauge gauge system in other respects seems to have fully justified the considerable expenditure of effort in perfecting the Evapor-ion pump to the point of high reliability. A getter-ion pump in which the ionization
and gettering processes
more
completely separated than in the Evapor-ion pump has been described by Gale.*^ The pumping unit together with the test reservoir for admitting various are
gases under controlled conditions is
shown
The pumptwo chambers
in Fig. 9-31.
ing unit consists of
Tungsten filaments
overwound with titonium
Fig. 9-31. Getter-ion together with test
pump
of Gale*^
reservoir
for
admitting various gases under controlled conditions. [Taken with permission from A. J. Gale, in 1956 Vacuum Symposium Transactions
(Pergamon Press, London,
1957).]
within one titanium metal is evaporated from heated tungsten filaments wound with titanium wire, and within the other is a Penning type of ionization gauge. One interesting feature of this arrangement is that
formed in the Penning discharge unit cannot strike directly the walls on which the titanium metal is deposited. Even so, there is a marked difference in the pumping characteristics, depending upon whether the Penning discharge is in operation Particularly in the pumping of argon and helium the pumping speed is greatly enhanced. To determine the pumping effectiveness of the combined unit, the procedure followed was first to pump out the entire system with a diffusion pump and outgas the pump and structure by heating the tungsten filaments below the evaporating temperature. The valve to the diffusion pump was then closed and the filaments were raised arbitrarily to a temperature at which titanium was evaporated onto the walls of the chamber and then the filament current was turned off. The valve between the reservoir and the getter-ion pump was then closed and gas admitted to the reservoir to a predetermined pressure. The gas sample was shared with the ions
.
Fig. 9-30. Inner structure of Evapor-ion pump with three sections of titanivim for sublimation coating. [Reprinted with permission from The Macmillan Co.,
from
C. L.
Copyright
Gould and P. Mandel, in 1962 Vacuum, Symposium, Transactions. 1962 by The American Vacuum Society, Inc.]
©
VACUUM SCIEKCE AND ENGINEERING
392
ULTRAHIGH VACUUM
opening the interconnecting valve, and finally Since the pressure in the reservoir was observed as a function of time. the volume of the reservoir, which was about 700 cm', was about equal to that of the pumping unit including the Penning discharge chamber,
pump chamber by
Table
9-3.
^'^
in pressure with time provided a measurement of the pumping speed. In the test runs reported, the initial pressure in the reservoir
was
7
X 10^2
torr
or
3.5
S
Absorption choVocteristic of getter-ion
pump
for
dry oir
pumping 5
10
15
20 25 30 35 40 45 50 55 60 Elapsed time.min
Fig.
9-32. Pressure-vs.-time
curves
from which the performance of the getter-ion
pump shown
in Fig. 9-31
dry air. [Taken with permission from A. J. Gale, in
was determined 1956
for
Vacuum Symposium
Transactions
(Pergamon Press, London, for a large
number of
1957).]
speed,
is
cmfijsec
Nitrogen
ig
Carbon dioxide Helium
24 9
Reproduced by permission from A. J. Gale, in 1956 Vacuum Symposium Transactions (Pergamon Press, London, 1957), p. 12.
pumping unit
is
the anomalously high
pumping speed
for
helium and
argon.
When an its
evaporated metal coating has reached saturation and loses efficiency, the surface can be restored to its original
pumping
00 60s molecule o6as atom >Gos
Anode
ion
• Titoniumatom • Electron
t3
generally less
than that for the next lower pres-
and furthermore defrom run to run as the getter surface appears to become sure range,
^
creases
saturated;
(2)
the pressure range
from 3 X 10-* to about 5 x 10-« torr, over which the pumping speed is the same from run to run
pumping speed in the amount of gas already
cycles, indicating that the
this pressure range is relativelj' insensitive to
absorbed by the getter surface; (3) the pressure range from about 5 X 10-* to 6 or 7 X 10-' torr, over which the pumping speed decreases toward zero at an ultimate pressure at which the absorption and desorption rates of the getter surface appear to reach equilibrium. The pumping speed in the pressure region (2), in which it is constant insensitive to the gas absorbed by the getter surface, is shown in Table 9-3 for several gases. According to Gale*^ the pumping speed for hydrogen is much greater than that for other gases, with the result that the slopes of the curves were too steep to permit a measurement of its value. The most interesting feature of the performance of the
and
fob
*
The results of nine ion pump. runs in sequence are shown graphiThree regions cally in Fig. 9-32. of performance can be distinguished: (1) the pressure range from 3.5 X 10-2 cio^n to about 3 x 10-* torr in which the slope of the pumpdown curves, and therefore the
10"
Fig. 9-31
16 28
Oxygen
x lO-^
torr after sharing with the getter-
Pum,ping speed,
Air
the operation of opening the valve to the reservoir and sharing the gas sample between the two volumes accounted for an immediate drop in pressure to one-half that initially Thereafter, the in the reservoir. fall
393
Pumping Speed op the Getter-ion System of Various Gases*
Fig. 9-33. Schematic drawing of the
Vac Ion pump. [Taken with permission from L. D. Hall, in 1958 Vacuum Symposium Transactions (Pergamon Press, London, 1959).]
Cathode
9-34. Assumed pumping mechanism of the Vac Ion getter-ion pump. [Taken with permission from L. D. Hall, in 1958 Vacuum, Symposium Transactions (Pergamon Press, London, 1959).]
Fig.
performance by heating the filaments for a few minutes and depositing a new coating of evaporated titanium. This process can be repeated until the titanium wound on the tungsten filaments has been essentially completely consumed by evaporation. A major advance in the development of getter-ion pumping was initiated by Hall« in the development of the Vac Ion pump, which is illustrated in Fig. 9-33.
which
is
mounted an
The device
box within "egg crate" electrode made
consists of a rectangular
electrically insulated
VACUUM SCIENCE AND ENGINEERING
394
of thin metal plates (usually titanium) arranged to produce an array On each of the inner flat surfaces of of cells with square cross section. the boxlike stainless steel casing a plate of titanium or other active
secured with a small clearance between the surface of the two The rather flat fiat electrodes and the insulated cell structure. assembly is put between the poles of a magnet so that the field lines pass through the square cells of the insulated electrode and are perpendicular to the surfaces of the two titanium plates on either side. When a positive electric potential is applied to the insulated electrode,
metal
is
each cell of the device acts like a separate PIG or Penning discharge. Because of the large cathode area involved the pressure at which the discharge will start and continue to pass current is very low when a potential difference of the order of 5,000 V is applied to the central
ULTRAHIGH VACUUM of these two processes
395
In a test of this point a small Vac Ion pump was heated to 400°C while it was in its magnet with the voltgage applied to the anode. The pump continued to operate at this temperature and reduced the pressure at this temperature to about 2 X 10-* torr at the end of a 3-hr bakeout. After the system was allowed to cool 5
X
down
is
to
reached.
room temperature, the pressure reading was
10-10 torr.
^
diQ^: I
>
electrode.
The mechanism of pumping by the Vac Ion pump as visualized by Hall" is illustrated in Fig. 9-34. As in any PIG discharge any electrons which are present oscillate in the electric field between the cathodes and are restricted from moving to the side and striking an anode plate by the magnetic field. The electrons are thus very efficiently used for producing ionization, i.e., not only is a positive ion produced and drawn cathode but in addition in each ionizing event another electron is produced which carries on the process of producing more ions. The ions are propelled into the cathode plate with energies of several kiloelectron volts and sputter cathode
by the
electric field into the surface of the
material (such as titanium), some of which settles on the surfaces of the anode plate structure. The freshly deposited active metal has strong chemical affinity for most gases with the result that gas atoms are
accumulated and held by chemisorption on the anode plates. The cathode plates are slowly eroded by the sputtering process. Figure 9-35 is a photograph of a cathode plate after long service showing the deep holes eroded opposite each cell of the anode. Hall" reports that hydrocarbon contamination of the Vac Ion type of pump can easily prevent the pump from starting to operate. Several hours of exposure to the pumping action of a mechanical vacuum pump Baking the Vac Ion will make the Vac Ion pump difficult to start. pump to 400°C for 2 hr in air may restore the pump to normal operation. However, repeated contamination by hydrocarbons eventually results in the pump no longer responding to air baking and the cathodes must be replaced to put the pump back into operation. The gas which is absorbed on the anode surfaces is partly very tenaciously held and is partly rather weakly bound. A pump will therefore both pump and release gas during operation, and the question is what limit of base pressure can one hope to realize when the balance
2i
Fig. 9-35. Cathode plate of of erosion due to sputtering.
'
i
'3'
Vac Ion pump
after long service showing pattern [Taken with permission from L. D. Hall, in 1958 Vacuum Symposium Transactions (Pergamon Press, London, 1959), and through the courtesy of Varian Associates, Palo Alto, Calif.]
The earliest pumps of the Vac Ion type were quite small and typically had pumping speeds for air of the order of 5 liters/sec. Zaphiropoulos and Lloyd*^ have discussed some of the design considerations which arise in scaling up the Vac Ion tjrpe of pump to much larger sizes. Figure 9-36 shows schematically a quadrupole and an octupole configuration for very large pumps of this type. Figure 9-37 is a photograph of a 5,000-liters/sec Vac Ion pump, showing one example of a satisfactory scaling up of the Vac Ion concept. For the 5,000-liters/sec
ULTEAHIGH VACUUM
VACUUM SCIENCE AND ENGINBEBING
396
397
pump the applied voltage is 6 kV and the current is 65 mA at a pressure Since the current is proof 10-« torr, which is about 400 watts. would portional to the pressure for this type of pump, the power problem this alleviate become excessive at a pressure of IQ-^ torr. To
the power supply is current-limited beyond a specified value and the In some applications of large pumps, potential drops to about 500 V. the sections are brought into operation one at a time in order to avoid Inner bore Cathode -anode
power drain, and all units are turned on only when the pres-
sections
excessive
sure has decreased to 10"^ torr or
W=W
less.
A
problem in the operation of the Vac Ion type of pump is an in
instability
pumping of
the
Surprisingly, helium, for
argon.
which normal sorption by any material L' =
2L
Fig. 9-36. Illustration of configuration for large Vac Ion pump designs
(magnets not shown). [Taken with permission from R. Zaphiropoulos and W. A. Lloyd, in 1959 Vacuum Sympo-
sium Transactions (Pergamon Press, London, I960).]
is
insignificant,
is
pumped
apparently by being rather deeply buried in the cathode material. With argon the quite well,
situation
quite different,
is
and
the problem is discussed in some A typical detail by Jepsen et al.*« pattern of the pressure versus time for a getter-ion pump exhibiting
argon instability 9-38.
The
is
periodic
shown j
in Fig.
umps in pres-
One sure by a factor of 10 or more are characteristic of this difficulty. incorto is Brubaker*' solution to this problem which was proposed by the porate a third electrode in the form of a grid between the anode and cathode true the outer plate electrode, such that the new grid becomes 9-39. and the side plates become auxihary electrodes as illustrated in Fig. suita By pump. This arrangement is referred to as the triode getter-ion pump triode the for able choice of design and operating parameters the Brubaker was able to show a generally improved pumping speed for However, air. and noble gases and completely stable pumping of argon principal one of there are several disadvantages to the triode design, the cathodes. the of which seems to be the very much shortened life loss of cathode lifetime
In order to avoid the complexities and et al.* resulting from the triode getter-ion pump design, Jepsen type of diode the of investigated the effect of slotting the cathodes
pump
in the
manner shown
in Fig. 9-40.
The
result of the slotted
Fig. 9-37. Photograph of 5,000 liters/sec
Vac Ion pump. [Taken with permission from R. Zaphiropoulos and W. A. Lloyd, in 1959 Vacuum Symposium Transactions (Pergamon Press, London, I960).] cathodes appears to be to provide an optimum solution. (1) Pumping and the pumping speed slightly higher than with the plane cathodes. (2) The pumping speed for argon is about 10 per cent of that for air and is stable for all values of the pressure for air is completely stable,
below 10-^
torr.
(3)
The cathode
life
does not seem to have been
XlO"''
MO"' xlO"^ xlO"''
Time
Fig. 9-38. Typical pattern of pressure vs. time for a getter-ion pump exhibiting the argon instability. [Taken with permission from R. L. Jepsen, A. B. Francis, S. L. Rutherford, and B. E. Kietzmann, in 1960 Vacuum Symposium Transactions
(Pergamon Press, London,
1961).]
.
VACUUM SCIENCE AND ENGINEERING
398
ULTRAHIGH VACUUM
399
impaired by the slotting nor do the benefits of the slotting disappear with aging of the cathode. Aside from the problem of rather extreme sensitivity to hydrocarbon contamination of the cathodes, the getter-ion pump of the Vac Ion type has undergone steady improvement and certainly must be regarded as one of the most effective available means for ultrahigh-vacuum pumping. The question of hydrocarbon contamination can be completely Auxiliary
V=V| "-*
electrode
^^^^^^^^^^'-^^^^^^^^^^ ^^^^v^^^'^
Cathode
^=°~-Hl
D
D
D
^—
D
D
ID
D
-j^Clouds
r
v=oSlotted
of tropped
cathode
V=V,
Positive
Sputtered
atoms of A^xx^xxs! of cathode material
Fig. 9-39. Cross section of the triode getter-ion pump showing the open
cathode structure and the side plate as an auxihary electrode. [Taken with permission from R. L. Jepsen, A. B. Francis, S. L. Rutherford, and B. E. Kietzmann, in 1960 Vacuum Sympo-
sium Transactions (Pergamon Press, London, 1961).]
Fig.
9-40. Cross
section
of slotted
cathode configuration of the diode getter-ion pump. [Taken with permission from R. L. Jepsen, A. B. Francis, S. L. Rutherford, and B. E. Kietzmann, in 1960 Vacuum Sym,posium, Transactions
London,
Artificial zeolite* as a
vapor-trap
The recent more zeolite absorption pumps for roughing out vacuum systems of large volume in order to avoid the possibility of hydrocarbon contamination from the sealing oil of a mechanical material has already been discussed at length in Sec. 8-6.
practice of utilizing one or
roughing
pump
is
6
zeolite
(b)
pressure.
Absorption Pumping.
5
lOOg
1961).]
avoided in systems in which the roughing-down operation is carried out by a mechanical pump with an artificial zeolite trap in the pumping line or by the use of absorption pumping starting from atmospheric 9-7.
4
L(760mmHg)
(Pergamon Press,
of considerable practical interest.
* 1 3X Zeolite is an alkali methal aluminosilicate of unusually porous structure manufactured by the Linde Division of the Union Carbide Cornpany.
Fig. 9-41. (a) Pumping speed of a molecular sieve pump at 0.1 torr as a function of amount of gas already pumped. (6) Final base pressure as a function of the amount of gas pumped. [Taken with permission from P. F. Varadi and K. Ettre, in 1960
Vacuum Symposium
Transactions (Pergamon Press, London, 1961).]
Varadi and Ettre''* have carried out a series of tests on a 13X Zeolite type of "molecular sieve" absorption pump to determine (1) the pumping speed of the absorption pump for various gases as a function of the amount already absorbed, and (2) the final pressure attainable as a function of the amount of each gas absorbed. The pumping-speed measurements were all made at a pressure of 0.1 torr. The results of these two types of tests are shown graphically in Fig. 9-41. The absorption pump contained 100 g of 13X Zeolite which was cooled by liquid nitrogen.
I
VACUUM SCIENCE AND ENGINEERING
400
The rather
ULTRAHIGH VACUUM
pumping speeds for different species of be noted by the very small line near the origin of the figure, the ability of 13X Zeolite to absorb hydrogen is almost nil. Another interesting feature of the tests is the apparent fatigue effect due to repeated absorption and expulsion of air. It will be noted that there are two curves for air in the figure: (1) for the first run on a new sample of zeolite and (2) for zeolite which had been recycled several times through the absorption and degassing routine. gas
is
large variation of
As
very striking.
will
liquid-helium cryogenic
pumping
401
to obtain the lowest possible base
pressure.
Evaporative Deposition of Reactive Metals.
9-8.
Getter-ion evaporation or sputtering of active metals, usually titanium, together with ionization of the gas by electron collisions
pumps
utilize the
to enhance the gettering effectiveness of the newly deposited reactive metal. This combination provides very satisfactory vacuum pumping
and freedom from hydrocarbon contaminants.
However,
for
many
applications the evaporative deposition of an active metal without ionization of the residual gas has also been found to be useful and Liquid helium
800
Main chamber
material in the manufacture of electronic tubes.
\
Main ion -getter
Liquid
Bellows valve
Omegatron
Auxiliary
ion-getter pump.
Work spoce
8 liters/sec
Support
5W
pump
helium trap
lonizotion
gouge
25
I
iters /sec
Bellows Front View
gouge Sorption
pump
Fig. 9-42. Schematic diagram of ultrahigh-vaouum system incorporating sorption, ion-getter, and liquid helium cryogenic pumping. [Taken with permission
From
Simultaneously the tube is subjected to induction heating of the internal metallic parts and oven heating of the The tubulation is then glass envelope to ensure thorough outgassing. sealed off and a getter capsule is flashed dispensing barium metal as a operating at lower pressures.
Pironi
from R. H. Honig, London, 1962).]
For many years barium particularly has been used as getter In the mass production of receiving tubes, vacuum pumping is normally accomplished by mechanical pumps arranged in groups on a rotating and indexing machine having a large number of ports to which the tubes being evacuated are connected. As the machine rotates, each tube is connected in turn to a rough pumping section followed by stages effective.
trap liters/sec
in
1961
Vacuum Symposium
these quantitative figures
Transactions (Pergamon Press,
getter material to clean
up by chemisorption the residual gas remaining vacuum pumping provided in the
in the tube after the rather rough
The use of a getter for completing the evacuation process by a large factor the cost of initial evacuation of electronic tubes and in addition provides a means of continued chemisorption of any gases which might be produced during the operation of the tube
process.
reduces it
should be possible to design zeolite pumping speed based
traps with fair assurance as to the capacity and
upon the amount of zeolite contained. The use of a sorption pump under conditions
in service.
In recent years there has been an intensive investigation of the
which avoidance of hydrocarbon contaminants is necessary is represented in the system shown in Fig. 9-42, which illustrates the arrangement developed by Honig.*' The system is one of fairly small volume and is roughed out to 10~^ torr by a sorption pump cooled to liquid-nitrogen temperature. The system is then further pumped by the getter-ion pump and finally liquid nitrogen is introduced to cool thoroughly the sur-
effectiveness of evaporated coatings of reactive metals, particularly
roundings of the liquid-helium thimble trap before introducing the liquid helium. When the pumpdown cycle was preceded by a bakeout at 350°C for 15 hr, the base pressure realized in this system was judged to be less than IQ-i" torr on the most favorable run. Typical pressure readings were between 10""' and 10"!" torr. This system represents most of the more advanced techniques of fully bakable systems with freedom from hydrocarbon contamination and the introduction of
chamber itself, in which case the evaporated metal is deposited directly on the walls of the vacuum chamber. In case 1 ) the getter pump must be connected to the vacuum chamber and is therefore limited in pumping speed by the conductance of the connecting tube or manifold. In case (2) the walls of the vacuum chamber itself become absorbing with the result that a much larger effective pumping speed can be
in
titanium and molybdenum, deposited on surfaces within a vacuum chamber in pumping out residual gas by chemisorption. This technique has proved to be effective in two specific situations: (1) as a separate pumping unit acting as a getter pump which can be attached to a
vacuum chamber,
the evaporated metal being confined in this case pump itself, and (2) within the vacuum
to the inner walls of the getter
(
achieved.
VACUUM SCIENCE AND ENGINEERING
ULTRAHIGH VACUUM
In contrast with the performance of a getter-ion pump (see Sec. 9-6) which is capable of pumping the noble gases to some degree, a getter device without ionization has no such capability. Only those gases which interact chemically with the evaporated metal are effectively pumped. Getter pumps are therefore usually supplemented by the
formation of a molten drop of metal, which is supported on the tip of the wire by surface tension forces. For metals such as titanium and molyb-
402
Negatively biased
0.030 tungsten wire
cylindrical grid
electron emitter
pumping action of a well-baffled diffusion pump. Since the noble gases make up a small fraction
5'
(about
1
per cent) of atmospheric
Nickel supports
metal pumping of high pumping speed for reactive gases supplemented by a trapped diffusion pump of relatively small pumping speed is an effective combination for many applications. Such a getter pump may, for example, consist of a chamber with one or more units for evaporating a reactive metal on the interior surfaces connected to a well-baffled diffusion pump backed by a mechanical vacuum air at sea level, active
-Molten
ball
5-10 kv/^"
0.030-1 0.1
amp
High
'^
Capillary tube
surrounded by water
vacuum 2
Feeder rolls
through liquid metol vacuum seals
Wire degassed
byl^R heating
.
Etficient
_liquid-nitrogen,
trapped 4 oil
in.
diffusion
pump Insulated
Fig. 9-43. Device for evaporating active metals by electron bombardment. [Taken with permission from N. Milleron, in 1957 Vacuum Symposium Transactions (Pergamon Press, London, 1958).]
is
stored on a reel in an auxiliary
pump. Several methods of evaporating
metals such as titanium, zirconium, and molybdenum, all of which have been used as getter materials, have been developed. Milleron^" has described a method of evaporation from the end of a wire, the tip of which was heated by electron bombardment in the device
illustrated in Fig. 9-43. The wire vacuum chamber, where it is outgassed
by being heated to as high a temperature as the material will stand by an electric current. The wire is then fed by a system of rolls through a water-cooled copper capillary tube into the evaporation chamber. The small conductance around the wire through the capillary tube prevents any appreciable flow of gas desorbed by the wire from entering the evaporation chamber. The end of the wire protruding from the capillary tube is bombarded and heated by electrons from a circular filament at 5 to 10 kV negative potential relative to the wire. The end of the wire is heated beyond the melting point, resulting in the
403
denum
there is no serious problem in controlling the electron bombardment heating so that the molten ball at the end of the wire is stable and the rate of evaporation steady. Typical evaporating rates are given as 0.05 g/min, which could be maintained for several hours by feeding the wire at the proper rate from the reel in through the capillary channel.
Using the above method of evaporating molybdenum, Milleron and Popp^i have measured the pumping of hydrogen gas admitted to the chamber in pulses. The conditions of the test were as follows
—
Volume
of chamber 70 liters Projected area of coated wall
— —
7,500 cm^ Microscopic area as measured by low-temperature adsorption of argon on molybdenum surface more than 20 times the projected area
—
Base pressure less than 10~i° torr Quantity of hydrogen per pulse 10~^ torr liter Time duration of gas pulse less than 1 sec Maximum pressure rise per gas pulse with newly coated walls
—
—
—
1
x 10~'
torr
—
Equivalent pumping speed greater than 10* liters/sec Quantity of hydrogen to saturate coating and raise pressure to 10~^ torr approximately 1 torr liter
—
Molybdenum, zirconium, and titanium are all effective in the above type of gettering device, but molybdenum is found to be more effective in pumping hydrogen (the gas of major concern in the Milleron and Popp development) in the pressure range below 10"^ torr, whereas titanium was found to be capable of absorbing more hydrogen gas. The reason for this difference would appear to be that molybdenum may be heated to a higher temperature without the danger of melting than titanium or zirconium, resulting in a more thorough outgassing of the metal before it is evaporated into the pump chamber, whereas the latter two metals have a greater total capacity for reacting with hydrogen. Other methods of evaporating the most commonly used reactive metals, titanium and molybdenum, than that described above are mentioned in Sec. 9-6, particularly as an adjunct to the Evapor-ion pump. The simplest and most convenient method thus far developed is similar to that described by Gale,*^ in which a wire of the metal to be evaporated is wound on a somewhat larger-diameter tungsten wire, which acts as a heater element. In one of the large thermonuclear research machines at the University of California Lawrence Radiation
ULTRAHIGH VACUUM
VACUUM SCIENCE AND ENGINEERING
404
Laboratory (Livermore) known as ALICE, both titanium and molybdenum units are used in a beam tube in which the pressure must be reduced from about 10~^ torr of hydrogen and water vapor at one end to an operating pressure of about 10~' torr over a distance of about ten feet. Titanium evaporation combined with well-baffled diffusion pumps is used in pumping units as shown schematically in Fig. 9-44 in portions of the system in which the pressure Metollic is comparatively high and the main evaporotor requirement is that of relatively Liquid-nitrogen Flap valve high throughput. In the main cooled liner " " n nn vacuum chamber where the pressure must be maintained at 10~' or less with the beam on, molybdenum is evaporated directly on a liquid-
may require many hours before the system can be cooled the evaporative deposition process started under conditions which will ensure effective pumping at pressures less than 10"* torr. The practice of coating a liquid-nitrogen-cooled inner liner of the vacuum chamber has become accepted for certain classes of controlled-
outgassing
down and
One of the most famous such installation the Ogra machine of the Kurchatov Institute for Atomic Energy in Moscow. The central chamber of the machine is 1.6 in diameter
fusion research devices. is
m
and 19 Table
m
9-4.
units in each case consist of a 0.060Diffusion
pump
in diameter
wound with
Pumping
unit consisting of a titanium evaporator unit backed by
Fig. 9-44.
an
diffusion
filament
0.020-in. -diameter
or molybdenum wire. The heating current for the titanium evaporators is about 125 A, whereas that for the molybdenum
titanium
pump
with a liquidnitrogen-cooled baffle. [This drawing was kindly provided by Mr. William S. Neef, Jr., Lawrence Radiation Laboratory, Livermore, California.] oil
tungsten a
about 190 A, consistent with the high-temperature characteristics of the molybdenum. Herb et al.*^ quote the data given in Table 9-4 from the RCA Review of June 1957, from which it is evident that vapor pressures for titanium of the order of 10~' torr are attainable for sublimation,
i.e.,
before the melting point
is
reached.
Herb
et
al.
estimate that
1715°K sublimation from a titanium surface of 10 cm^ should produce a pumping speed for active diatomic gases of about 1,000 liters/sec
when
results.
is
10~^ torr, or should absorb a
liter/sec at
whatever equilibrium pressure
the pressure
This capacity or pumping speed
is
increased
by a
factor of 10
the temperature of the titanium is raised to 1850°K. Whether performance of this order is realized in practice will depend greatly upon the extent to which the titanium metal is outgassed before evaporation. The process of evaporative deposition of active metals for getter pumping includes a preliminary baking of the system and thorough outgassing of the getter metal at a temperature which is high enough not to evaporate any significant portion of the metal but high enough to drive out absorbed gases. In some cases the baking and if
is
about 38,500
liters.
The
1 1 1 1 1 1
X 10-8 X 10-' X 10-6
X 10-^5 X 10-« X 10-3
4 x IQ-^ 1 X 10-2
Quoted with permission from the RCA Review, June, 1957. These values of vapor pressure are considerably lower than those quoted in the Smithsonian Physical Tables (Smithsonian Institution, 1954) from the results of Brewer, The Thermodynamic and Physical Properties of the Elements, Report This suggests that many of the older data on for the Manhattan Project, 1946. *
t
vapor pressures of metals are suspect.
is
at a temperature of
throughput of 10"^ torr
volume
The Vapob Pressure of Titanium at Various Temperatures* Ti vapor pressure,'\ torr °K 1330 1415 1500 1600 1715 1850 1945 (melting point) 2000
which covers a large fraction of the chamber wall. The evaporator
cooled trap
in length, so that the
Temperature,
nitrogen-cooled stainless steel liner
Liquid -nitrogen-
405
steel
vacuum chamber has been equipped with a
thin-walled stainless
evaporated periodically from several evaporating units placed along the length of the chamber. An electron beam of current up to 1 A at 3 keV bombards the end of a 2-cmdiameter titanium rod on each evaporator, resulting in a maximum evaporation rate of about 50 g/hr of titanium. According to Simonov, steel liner
on which titanium
is
Kleimenov, Mileshkin, and Kochnev^^ the combination of the active metal coating on the cooled liner backed by an array of well-baffled mercury diffusion pumps provides a pumping speed for hydrogen of 2 X 10" liters/sec, a base pressure of 1 x lO-i" torr, and an operating pressure during injection of a powerful molecular ion beam of about 5 X 10-" torr. Effective pumping speeds of millions of liters per second could not possibly be achieved unless the walls of the chamber themselves are highly absorbing. Only limited portions of the chamber walls, primarily the ends, are available for openings into pumping manifolds, so that no matter how high the pumping speed of the pumps connected to these manifolds the net pumping speed limited by the conductance of the openings alone would not exceed 100,000 liters/sec.
(
VACUUM SCIENCE AND ENGINEERING
ULTRAHIGH VACUUM
If in addition one allows for the conductance of the chamber itself toward both ends from the middle, the net conductance from the median plane (where most of the gas originates in this machine) to both ends, assuming that both ends of the tank are completely open, is only about 50,000 liters/sec. From this it is clear than the only possibility of
the probability of absorption per surface encounter is stated to be about 0.1 that is, about 10 collisions with the coated wall are necessary on the average for a hydrogen molecule to stick under the conditions
406
achieving
pumping speeds of several
million liters per second in such a
machine
Fig. 9-45. Apparatus for the investigation of the sorption of gases at low pressures on renewable surfaces
of reactive metals and surfaces of structural
chamber; tion
of
materials.
(1)
Vacuum
surface for condensametal; (3) evaporator of (2)
metal under study; (4) sample of structural material under investigation; mass spectrometer for (5) analysis of the gas desorbed from the surface of the specimen; (6) mass spectrometer for analysis of the gas in the chamber; (7) mercury vapor pump with liquid-nitrogen-cooled
is
to
make
the walls as
completely absorbing as possible. Simonov et al.^^ investigated the sorption of hydrogen gas by renewable surfaces of chemically active metals as a function of the temperature of the surface using the apparatus shown schematically in Fig. 9-45. The metal to be investigated was evaporated either continuously or periodically and condensed upon a substrate, the temperature of which could be controlled and measured over the range
-195
+100°C. Two time-ofmass spectrometers were used, one for determining the comto
flight
position of the gas desorbed
by the
specimen under test and the other for determining the composition of the gas generally throughout the chamber. The authors state that one of the most important characteristics of baffles; (8) getter -ion pump. the sorption of hydrogen by a reactive metal is that the sorbed hydrogen molecules are dissociated into atoms which migrate over the surface of the metal and readily react with other sorbed atoms producing volatile compounds which may be desorbed. This process at least partly defeats the purpose of the original sorption process, resulting in a portion of the sorbed hydrogen and other gases being reemitted from the surface in a form which is no longer effectively sorbed by the surface but must be pumped out through the diffusion pumps or otherwise disposed of. Gases whose presence greatly affects the rate of permanent sorption of hydrogen are oxygen and nitrogen. For a typical freshly deposited surface of titanium exposed only to pure hydrogen
407
;
of the experiments.
As gases
are
sorbed by the surface, the probability of absorption of hydrogen decreases markedly. The process of dissociative chemisorption of pure hydro-
Dz
/
(a)
H2
/
> AV
PotO withnnf argo n addit ion 1
/ X
.
w
"y
i
found to pass through
the lower inflection points of curves (a) and (6). Auxiliary scales showing flow rates in terms of molecules
-«
I
~
°-io
A
and
I
10
ing the surface are trapped. straight line is drawn at 45° in the figure
427
J
V
1
V
.
1-2= U.I
'
•
/
Iio'Ve
A
A
10
10'
10"'
n-9 10 '
10 °
610
'
lO'"
IlO
Argon partial pressure, lorr
9-61. Hydrogen cryotrapping by argon for different values of hydrogen and argon flow rates. [Reprinted with permission from The Maomillan Co., from J. Hengevoss and E. A. Trendelenburg, in 2.963 Vacuum Symposium Transactions. Copyright © 1963 by American
Fig.
sponds to the case in which one hydrogen molecule is trapped by one condensed argon molecule. Curve (c) is taken at a hydrogenflow rate which is great enough that Vacuum Society.] the hydrogen partial pressure exceeds the saturated value at 4.2°K so that condensation on the cryostatic surface occurs even in the absence of any argon. Thus in curve (c) both condensation and trapping occur at the same time so that the break in the curve corresponding to the onset of cryotrapping by argon occurs at an appreciably lower argonflow rate than that corresponding to the intercept with the 45° line drawn through the inflection points of (a) and (6), indicating that about 10 times as many hydrogen molecules are deposited by the combination of condensation and trapping as are argon molecules. In a subsequent experiment the connection to the diffusion pump was sealed off and a large amount of hydrogen admitted to the chamber. After cutting off the hydrogen flow an equilibrium hydrogen pressure of 1.3 X 10-', corresponding to the saturation value at 4.2°K, was reached. A continuous flow of argon resulting in an argon partial pressure of 4 x 10~' torr was then introduced, and the partial pressure of hydrogen slowly fell to 2 x 10^* torr. The argon flow was then
VACUUM SCIENCE AND ENGINEEKING
ULTRAHIGH VACUUM
an unmeasurable turned value, whereas the partial pressure of hydrogen remained at 2 x 10~* torr, indicating that the hydrogen was permanently trapped by the condensed argon deposit. Similar experiments were carried out to determine whether helium could also be cryotrapped by condensing argon. The results showed that the sticking probability of helium on the argon deposit is about
Figs. and 9-63. Because hydrogen cannot be condensed at liquid-hydrogen temperature, there is great advantage in adding materials which are effective in adsorbing hydrogen, particularly in
428 off
and the
partial pressure of the argon
fell
to
429
9-62
situations in
which hydrogen
is the major gas component present, as in The two adsorption pumps illustrated are of such devices developed by Lazerev and Fedorova
controlled-fusion research.
typical of a series primarily for the purpose of meeting the needs of the Soviet controlledfusion research program. As is evident from Figs. 9-62 and 9-63
together with their captions, the cryogenic adsorption pumps consist of a central, double-walled cylinder, open at one end as the pumping
aperture and lined with small chunks of graphite held in place by a wire mesh. The liquid-nitrogen-cooled shield is designated as component 1 and not only serves to reduce the radiation heat load on the inner liquid-hydrogen-cooled component 2, but also acts as an auxiliary adsorption pump for nitrogen, oxygen, and argon. This feature is said to be important because it permits evacuation of the system to 10~* torr or less of other common gases before pouring in the liquid hydrogen
and cooling the
central component 2 to 20.4°K. The inner adsorbing thus preserved for pumping hydrogen without appreciable contamination due to the adsorption of the other more easily adsorbed
surface
Fig. 9-62. Model of liquid-hydrogencooled charcoal adsorption pump with liquid-nitrogen-cooled shield having an adsorbing section upstream from the liquid-hydrogencooled section and of the same diameter. [Taken with permission from the American Institute of Physics, from B. G. Lazarev and M. F. Fedorova, Soviet Phys.-Tech.
Phys. 6, 624 (1962).]
0.03
Fig. 9-63. Model of liquid -hydrogen-
charcoal adsorption pump with liquid-nitrogen-cooled shield having an adsorbing layer completely surrounding a similar liquid-hydrogen-cooled adsorbing unit except for the pumping aperture. [Taken with permission from the American Institute of Physics, from B. G. Lazarev and M. F. Fedorova, Soviet Phys.Tech. Phys. 6, 624 (1962)[.]
cooled
and that about 30 argon molecules are required to trap one mole-
cule of helium.
Although the process of cryotrapping has been only partially investigated and the mechanism of the process is not understood, the results described above are most encouraging for the enhancement of the normal cryopumping process by the trapping of otherwise noncondensable gases on low-temperature surfaces. The process of adsorption pumping discussed in Sees. 8-6 and 9-7 has been extended into the cryogenic region by Lazarev and Fedorova*" particularly for the purpose of pumping hydrogen with high pumping speeds at low pressure. Several designs of liquid-hydrogen-cooled adsorption pumps were developed, two of which are illustrated in
is
gases.
Each adsorption pump
equipped with a valve
connecting it connecting it to a mechanical vacuum pump for roughing out the system. The sequence of operation is first to rough out the system with both valves open to a pressure of about 10"^ torr, then close valve 5. Liquid nitrogen is then poured into the reservoir of component 1 after which the pressure in the system quickly drops to a value of 10~^ or 10^* torr. Liquid hydrogen is then introduced into the reservoir of component 2 and the adsorption pump is then ready to pump hydrogen, which can then be admitted to the vacuum chamber as needed. The pumping speed of the adsorption pump illustrated in Fig. 9-62 is shown as a function of the pressure (on a logu scale) in Fig. 9-64, in which the pressure indicated is that measured at the inlet to the pump. Over the pressure range tested, the pumping speed for hydrogen increased from about 400 liters/sec at 8 x 10~* torr to about 900 liters/sec at 10~^ torr. is
to the vessel to be evacuated
From
and a valve
the dimensions of the inlet
(4) for
(5) for
it is clear that even at the higher not choked by the conductance of the inlet, which for hydrogen must be at least a factor of 5 greater than the measured pumping speeds. The lower curve 2 is the pumping speed as a function of inlet pressure which would normally be realized in the second step of the evacuating procedure when the valve 5 is turned off and component 1 of the pump is cooled with liquid nitrogen. Curve
pressure the
pump
is
VACUUM SCIENCE AND ENGINEERING
430 3
is
similar to curve 2 except that both
2 were cooled with liquid nitrogen.
component
ULTRAHIGH VACUUM 1
and component
Substitution of liquid-hydrogen
cooling (20.4°K) for liquid-nitrogen cooling (77°K) appears to increase the pumping speed of the adsorption
pump for hydrogen by 1,000
a factor of 3 or
more and reduces the attainable base pressure by nearly a factor of 10. If is worth noting that the liquid-nitro-
800
baffles not only serve as heat shields but also condense gases such as nitrogen with very high effective pumping speed. The pumping speed for hydrogen achieved was about 2,000 liters/sec and that for nitrogen was about 3,000 liters/sec. The consumption rate of helium was about 0.5 liter/hr. According to measurements of Bachler et al. and those of Borovik, Grishin, and Grishina,^^ the equilibrium vapor pressure of hydrogen is approximately lO-^ torr at about 3.3°K, so that at
2.5°K
gen filling lasts for a period of 20 to 40 hr and that of liquid hydrogen for 24 hr or more depending on the
600
431
Pressure gauge
Vacuum chamber
details of design. 400
Preliminary tests have been made on a similar design of adsorption pump by Lazarev and Fedorova using liquid-helium (4.2°K) cooling on the inner component for the cryogenic
200
10
10'"
10"'
10
Pressure, torr
Fig. 9-64. Porformance of the adsorption pump illustrated in Fig. 9-62. Curve 1: Pumping speed for hydrogen as a function of the pressure, liquid-hydrogen cooled. Curve 2: Pumping speed of the adsorption pump with liquidnitrogen cooling in component 1 only as a function of the pressure. Curve 3: Pumping speed of the adsorption pump with liquidnitrogen cooling in both compo-
nent 1 and component 2. [Taken with permission from the American Institute of Physics, from B. G. Lazarev and M. F. Fedorova, Soviet Phys.-Tech. Phys. 6, 624 (1962).]
7
is
Auxiliary
pump
pumping
of helium in the pressure range 10~^ to 10~* torr. Bachler, Klipping, and Mascher*^ have made a study of cryopumping in the temperature range from 4.2 to 2.5°K by controlling the pressure over liquid helium. Because of the very steep dependence of the equilib-
rium vapor pressure of hydrogen on temperature in this range, this procedure provides a possible solution to the cryogenic pumping of hydrogen
by condensation.
The pumping and by which the
Liquefied gas reservair
1
2
Fig. 9-65. Arrangement for controlling pressure of cryogenic gas and therefore the temperature of the condenser. By this system temperatures as low as 2.5°K are achieved in condensing hydrogen. [Reprinted with permission from
The Macmillan Co., from W. Bachler, G. Klipping, and W. Mascher, in 1963 Vacuum Symposium Transactions. Copyright © 1963 by American Vacuum Society.]
pressure control system
liquid helium in the cooling coil
is
maintained at any desired temperature, either higher or lower than 4.2°K, is shown in Fig. 9-65. Valve
throttled to obtain the required flow of refrigerant,
and valve
6
is
adjusted to provide the needed pumping speed to attain any desired temperature in the condenser. Bachler et al. report that control of the temperature to within 0.01°K is achievable by this system. In Fig. 9-66 is shown a schematic drawing of a condenser unit to be operated at temperatures below 4.2°K. The low-temperature coil is shielded above and below by chevron brffles which are cooled by the cold exhaust gas evaporated from the low-temperature
coil.
These
the vapor pressure of hydrogen should be well below IQ-i" torr, ensuring that the sticking coefficient and pumping speed for hydrogen due to
condensation on a surface maintained at 2.5°K will be independent of the pressure well into the ultrahigh-vacuum range. Bachler et al. note that whereas in their device nitrogen is pumped with about the maximum speed anticipated from theoretical calculations, hydrogen is pumped with about half the theoretical rate. However, since for hydrogen the theoretical rate is nearly four times that of nitrogen, the is still very favorable for pumping hydrogen. The use of a liquid-helium-cooled condensing surface under conditions in which the heat load from the process going on within the vacuum chamber (in this case a controlled-fusion plasma) may be a problem
result
ULTRAHIGH VACUUM
VACUUM SCIENCE AND ENGINEERING
432
In a series has been investigated by Borovik, Busol, and Kovalenko."' geometries Borovik of experiments with trapping surfaces of various tolerable for the proper et al. determined the maximum thermal load of liquid maintenance of the temperature near the value 4.2°K typical atmospheric helium at normal Since the heat of evappressure. oration of liquid helium is small (about twenty calories per mole)
surfaces were
blackened. of sheet copper, 2 These precautions ensured
made
The liquid-helium-cooled condenser was thick, and was also highly polished. minimum radiation heat load on the liquid-
mm
helium-cooled condenser, preserving as
/
433
much
of the heat capacity as
^^www;^
the conditions of heat transfer become characterized by eruptive boiling at the metal surface if the heat load g (watts per square
UooooocoooppociooooocB
centimeter) reaches some critical
value
g,r-
The experiments were
generally such as to determine the temperature of the condensing surface as a function of the heat load.
From
these experiments
Fig. 9-66. Condenser unit with prochevron radiation baffles tective cooled by the exhaust gas from the These low-temperature condenser. baffles serve to condense gases such
and the low-temperature condenser condenses hydrogen. [Reprinted with permission from The
as nitrogen,
Macmillan
from
Co.,
G. Klipping, and
Copyright
Vacuum
W.
©
1963
Society.]
Bachler,
Mascher, in 1963
Symposium
Vacuum
W.
Transactions.
by
American
load) until a critical value sr„ was reached in the range 3 to 5 x
watt/cm^ above which value the surface temperature increased abruptly due to the onset of erup10^*
tive boiling.
In order to screen the liquidhelium-cooled surface from the source of radiation and still permit fairly effective condensation of gas on the surface, Borovik et devised the condensation al.** pump illustrated in Figs. 9-67
The liquid-helium-cooled, double-walled cylindrical surface chamber wall by a liquid nitrogen-cooled (3) is protected from the unit connected cylinder with skirts above and below the condenser
and
i=LJ# ^^^^^^^
it
was observed that the temperature of the surface was relatively independent of the heat load (increasing very slowly with the heat
9-68.
louver-type baffles. to the reservoir for a set of liquid-nitrogen-cooled and within this assembly is another cylindrical
Concentric with arrangement of louver-type baffles, in this case water-cooled. The brightly outer surface of the liquid-nitrogen-cooled outer shield was water-cooled polished (copper), whereas the inner liquid-nitrogen- and
Fig. 9-67. Vertical cross-sectional
Fig.
view of liquid-helium-cooled lou-
sectional
vers
as
radiation
Chamber outer
shields.
wall;
(2)
(1)
liquid-
nitrogen-cooled .shield; (3) liquidhelium-cooled condensing surface; (4)
liquid-nitrogen-cooled louver;
water-cooled baffle. [Taken (5) with permission from the American
from E. S. Busol, and V. A. Soviet Phys.-Tech.
Institute of Physics,
Borovik, F.
I.
Horizontal crossview of the liquidhelium-cooled condensation pump 9-68.
shown in Fig.
9 - 67 The numbers designate the same components .
listed in Fig. 9-67.
[Taken with
permission from the American Institute of Physics, from E. S. Borovik, F. I. Busol, and V. A. Kovalenko, Soviet Phys.-Tech. Phys. 8, 68 (1963).]
Kovalenko, Phys. 8, 68 (1963).]
possible for the heat of condensation of gas in cryogenic
Borovik
pumping.
et al."* report that:
kW
1. With a heater of 10.5 output inside the inner shield the rate of evaporation of liquid helium due to the heat input was only 0.04 liter/hr, corresponding to a thermal load on the heat transfer surface of only 7.5 x 10^^ watt/cm^, which is about a factor of 5 below the
critical value. 2. The pumping speed of the condensation pump was found to be about II per cent of that of a perfectly condensing surface or about 1.25
liters/sec
cm^ of the
inner, water-cooled louver surface.
The authors
^ 434
VACUUM SCIENCE AND ENGINEERING
ULTRAHIGH VACUUM
assume that the pumping speed for hydrogen would be 4.68 Hters/sec cm^, but did not make the measurement.
and trap combination to provide much higher overall system pumping speeds at low pressure than had been previously attempted. As the requirements of the controlled-fusion program became more valve,
Borovik et al. conclude that cryogenic pumping is an effective means pumping hydrogen in controlled-fusion research devices. Private communication with Professor Borovik reveals that a magnetic mirror machine utilizing liquid-helium-cooled surfaces for cryogenic pumping has been constructed and is now in operation.
demanding, auxiliary techniques were added, such as the evaporation of active metals, first on the walls of the vacuum chamber at room temperature and then on liquid-nitrogen-cooled inner liners. Elimination of hydrocarbon contaminants by the use of either room-temperature or liquid-nitrogen-cooled absorption pumps combined with getter-ion pumps provides another solution to the problem of relatively high-speed pumping in the ultrahigh-vacuum range. The more recent advent of space research and simulation has expanded much further the demand for large ultrahigh-vacuum chambers with extreme requirements of high pumping speed at very low pressure. For this service the combination of very large diffusion pumps with
of
9-10. Ultrahigh-vacuum Systems. In this chapter and to some extent in the preceding chapter the techniques of ultrahigh vacuum have been discussed. The problem of the vacuum engineer is to utilize these techniques in the design of ultrahigh-vacuum systems to achieve the required performance as economically and effectively as possible.
Some
of the techniques described have been applied under rather and are not necessarily applicable to a wide range of vacuum problems. However, the most important parameters to be considered are specialized circumstances
1.
The gas load expected
in terms of the quantities of various
Freon- and liquid-nitrogen-cooled traps, augmented by the extensive use of cryopumping at liquid-hydrogen or liquid-helium temperatures to achieve pumping speeds in the multimillion liters per second range, has been most commonly adopted. Each ultrahigh-vacuum system is itself a special design problem which must be solved by a careful appraisal of the requirements to be met and the selection of the most effective combination of the techniques described in the preceding sections capable of meeting the requirements. Because of the requirements of metal gaskets, bakable
com-
ponent gases. 2. The operating pressure desired for the process to be carried out, either in terms of total pressure or in terms of the partial pressure of a
particular
component
gas.
Ultrahigh-vacuum systems tjrpically utilize some combination of the techniques discussed in this and the preceding chapters. For systems involving essentially no throughput of gas other than the outgassing of the surfaces, the achievement of very low pressures can be accomplished with low pumping speed and the thorough outgassing of the
components, and extreme freedom from leaks, and the difficulties in and the like, an improper choice of techniques to be applied can result in excessive costs of construction and operation and seriously jeopardize the chances of achieving the required performance. However, the means are now available for achieving almost any desired base pressure and enormous pumping speeds at low pressure. If properly applied, the methods already developed are capable of achieving spectacular goals. What is perhaps more important, the development of new techniques proceeds at such a pace
pressure measurement
by baking the system at temperatures up to 450°C or higher. mercury diffusion pumps with a combination of Freon- and
surfaces Oil or
435
liquid-nitrogen-cooled baffles can provide the modest pumping speeds required for such systems. Indeed, as was shown by Alpert,^^ a thoroughly outgassed system can be maintained in the ultrahigh-
that what seems spectacular today will most certainly be commonplace within the near future in the rapidly expanding field of ultrahigh
vacuum range by the pumping action of the ionization gauge alone when closed off from the vacuum pump by a sufficiently tight bakable valve.
vacuum.
Systems of this type may be regarded as static systems in which ultrahigh-vacuum conditions are attained on a small scale with essen-
REFERENCES
tially zero
throughput. Beginning with the requirements of controlled-fusion research, static systems could no longer be relied upon to maintain the desired low
1.
2.
pressure because the experimental equipment was relatively large in volume and an appreciable gas throughput required high pumping speeds. This need was initially met by optimizing the diffusion pump,
3.
4.
k
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T. Kraus,
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14. P. F. Varadi, in 15.
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33.
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Westinghouse Research Laboratories, Research Report 100
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25. 26. 27.
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W. M.
Brubaker, in 1959 Vacuum Symposium Transactions (Pergamon London, 1960), p. 302. P. F. Varadi and K. Ettre, in 1960 Vacuum Symposium, Transactions (Pergamon Press, London, 1961), p. 248. R. H. Honig, in 1961 Vacuum Symposium Transactions (Pergamon Press, London, 1962), p. 1166. Norman Milleron, in 1957 Vacuum Symposium Transactions (Pergamon Press, London, 1958), p. 148. Norman Milleron and E. C. Popp, in 1958 Vacuum Symposium Transactions (Pergamon Press, London, 1959), p. 163. V. A. Simonov, G. F. Kleimenov, A. G. Mileshkin, and V. A. Kochnev, Paper No. 255, Conference on Plasma Physics and Controlled Nuclear Fusion Press,
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(Pergamon Press, London, 1962), p. 1175. T. H. Batzer and J. F. Ryan, in 1963 Vacuum Symposium Transactions (The Macmillan Company, New York, 1963), p. 166. I. Farkass and G. F. Vanderschmidt, in 1959 Vacuum Symposium: Transactions (Pergamon Press, London, 1960), p. 42. D. Alpert, Rev. Sci. Instr. 22, 536 (1951). J. Wishart and G. H. Bancroft, in 1960 Vacuum Symposium Transactions (Pergamon Press, London, 1961), p. 13. R. J. Conner, R. S. Buritz, and T. von Zweck, in 1961 Vacuum Symposium Transactions (Pergamon Press, London, 1962), p. 1151. T. H. Batzer, in 1959 Vacuum Symposium Transactions (Pergamon Press, London, 1960), p. 265. M. Rivera and R. LeRiche, in 1959 Vacuum Symposium Transactions (Pergamon Press, London, 1960), p. 55.
R. H. Davis and A. S. Divatia, Rev. Sci. Instr. 25, 1193 (1954). C. Swartz, in 1955 Vacuum Symposium Transactions (Committee on Vacuum Techniques, Boston, 1956), p. 83. C. L. Gould, in 1956 Vacuum Symposium Transactions (Pergamon Press, London, 1957), p. 39. C. L. Gould and P. Mandel, in 1962 Vacuum Symposium Transactions (The Macmillan Company, New York, 1962), p. 360. R. G. Herb, T. Pauly, R. D. Welton, and K. J. Fisher, Rev. Sci. Instr. 35, 573 (1964). A. J. Gale, in 1956 Vacuum Symposium Transactions (Pergamon Press, London, 1957), p. 12. L. D. Hall, Rev. Sci. Instr. 29, 367 (1958). L. D. Hall, in 1958 Vacuum Symposium Transactions (Pergamon Press, London, 1959), p. 158. R. Zaphiropoulos and W. A. Lloyd, in 1959 Vacuum Symposium Transactions (Pergamon Press, London, 1960), p. 307. R. L. Jepsen, A. B. Francis, S. L. Rutherford, and B. E. Kietzmann, in 1960 Vacuum Symposium Transactions (Pergamon Press, London, 1961), p. 45.
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D. J. Goerz, Jr., in 1960 Vacuum Symposium Transactions (Pergamon Press, London, 1961), p. 16. 20. D. Lichtman and A. Hebling, in 1960 Vacuum Symposium Transactions (Pergamon Press, London, 1961), p. 187; and D. Lichtman, J. Appl. Phys. 19.
Sci. Instr.
331 (1948).
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M. Penning, Physica 4, 71 (1937). R. T. Bayard and D. Alpert, Rev. Sci. Instr. 21, 571 (1950). R. G. Herb, R. H. Davis, A. S. Divatia, and D. Saxon, Rev.
34. F.
p. 149.
John Strong, Procedures in Experimental Physics (Prentice-Hall, Inc., Englewood Cliffs, N.J., 1938), p. 128. C. M. Van Atta, R. J. Van de Graaff, and L. C. Van Atta, Phys. Rev. 51, 1013(A) (1937); C. M. Van Atta, R. J. Van de Graaff, L. C. Van Atta, and D. L. Northrop, Phys. Rev. 57, 536(A) (1940); and L. C. Van Atta, D. L. Northrop, R. J. Van de Graaff, and C. M. Van Atta, Rev. Sci. Instr. 12, 534
437
H. Ehlers and J. Moll, in 1959 Vacuum Symposium Transactions (Pergamon Press, London, 1960), p. 261. R. A. Metcalfe and F. W. Trabert, in 1961 Vacuum Symposium Transactions (Pergamon Press, London, 1962), p. 1211. J. S. Foster, Jr., E. O. Lawrence, and E. J. Lofgren, Rev. Sci Instr 24 388
51.
52.
Research, Conference Proceedings, Salzburg, Sept. 4-9, 1961, AEC-tr-5589, Book 1 (U.S. Atomic Energy Commission, Division of Technical Information,
February 1963),
p. 168.
M. Bailey and R. L. Chuan, (Pergamon Press, London, 1959),
53. B. 54.
W.
56. 57.
Vacuum Symposium
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p. 262.
Moore, Jr., in 1961 Vacuum Symposium Transactions (Pergamon London, 1962), p. 426. Jack Grobman, in 1961 Vacuum Symposium Transactions (Pergamon Press, London, 1962), p. 421. R. T. Brackman and W. L. Fite, J. Chem. Phys. 34, 1572 (1961). D. A. Degras, Second European Vacuum Symposium, Frankfurt am Main,
R.
Press, 55.
in 1958
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438
58.
59.
SCIE^
AND ENGINEERING
June 5-7, 1963 [Proceedings published for the Deutschen Arbeitsgemeinschaft Vakuum by Rudolf A. Lang, Esch (Taunus), 1963], pp. 54ff. F. W. Schmidlin, L. O. Heflinger, and E. L. Garwin, in 1962 Vacuum Symposium Transactions (The Macmillan Company, New York, 1962), p. 197. J. Hengevoss and E. A. Trendelenburg, in 1963 Vacuum Symposium Transactions (The Macmillan Company, New York, 1963), p. 101; and A. Naturforsch. 18a, 481 (1963).
APPENDIX
Lazarev and M. F. Fedorova, Soviet Phys.-Teoh. Phys. 6, 624 (1962). Bachler, G. Klipping, and W. Mascher, in 1963 Vacuum Symposium Transactions (The Macmillan Company, New York, 1963), p. 216. 62. E. S. Borovik, S. F. Grishin, and E. I. Grishina, Zhur. Tech. Phys. 30, 539 60. B. G. 61.
I
W.
Molecular Weights of Gases*
(1960). 63. E. S. Borovik, F. I. Busol,
and V. A. Kovalenko, Soviet Phys.-Tech. Phys.
Formula
Gas
8, 68 (1963).
Helium
He Ne
Argon
Ar
Molecular weight, g/mole 4.003 20.18 39.944 83.70 131.30
Kr Xe
Nitrooren
H2 N2
Oxvoren Chlorine
O2
2.016 28 02 32 000
CI2
70.91
28.98 (mean)
Air
36.47 34.08
Sulfur dioxide
HCl H2S SO2
Nitric oxide
NO
Nitrous oxide
N2O
NH3
30.01 44.02 17.03
CO
28.01
CO2
44.01
Hydrogen Hydrogen
chloride sulfide.
.
.
.
.
.
.
Carbon monoxide .... Carbon dioxide
Ethylene
.
64.06
CH4
16.04
C2-H.2
26.04 28.05
C2H4
* Source: Handbook of Chemistry Co., Cleveland, 1963), 44th ed.
and Physics (Chemical Rubber Publishing
439
APPENDIX APPENDIX
II
Van der Waals' Constants, Molecular Diameters, AND Mean Free Paths Computed from the Constant 6 According to EqS. (1-40) AND (1-38) Critical Constants,
A* Gas
P*
Formula
(cm^/mole)'
atm
atm X
He Ne
Helium
Neon Argon Krypton
Ar
Kr Xe
Xenon Hydrogen Nitrogen
Ha Na
Oxygen
O2
Chlorine
Clj
Mercury
Hg
— 267.9 — 228.7 — 122. — 63.0 16.6
— 239.9 — 147.1 — 118.8 144.0
>1500
0.03412 0.2107
12.8
49.7 76.1
>200
cm^/mole
io-«
2.26 25.9 48.0 54.0 58.2
33.5
cm X
10-
2.62 2.38 2.94
4.194
23.70 17.09 32.19 39.78 51.05
0.245 1.390 1.360 6.493 8.093
26.61 39.13 31.83 56.22 17.0
2.76 3.14 2.93 3.55 2,38
1.345 2.318
3.«(6
3.43
P= T= X
X
Viscosity op Gases at 0°C and 760 Torr together with Computed Values OP Molecular Diameters and Mean Free Paths in Accordance with Eqs. (1-62) and (1-38) A
cm 1
Formula
Gas
torr
Sulfur dioxide Nitric oxide Nitrous oxide.
.
.
.
H2O HjS SO2
NO .
.
.
Ammonia
.
CO .
C02
CH, CgHj C2H4
Acetylene Ethylene disulfide
N2O
NH3
Carbon monoxide Carbon dioxide Methane
Carbon
HCl
.
cs.
51.4 374.0 100.4 157.2 94.0 36.5 132.4
—
— 139.0 31.1
>1550 36.0 9.7
273.0
81.6
217.72 88.9 77.7 65.0 71.7
111.5 35.0 73.0
>200 62.0 50.9 76.0
3.667 5.464 4.431 6.714 1.340 3.782 4.170 1.485 3.592 2.253 4.390 4.471 11.62
40.81 30.49 42.87 56.36 27.89 44.15 37.07 39.9 42.67 42.78 51.4 57.14 76.9
3.19 2.89
3.24 3.55 2.81
3.27 3.09
Viscosity, fi*
micropoises
1
cm X 10-8
O^C
P = T =
1
cm torr
0°C
X 10-3
10-3
9.26 10.3 7.34 6.38 5.40 8.33 6.44
Helium
He
Neon
Ne
Hvdrosren
5.08 11.2
7.61 6.07
5.05 8.08 5.96 6.68
3.16
6.36
3.22 3.24
6.13 6.07
3.44 3.56 3.94
5.38 5.01 4.11
AmericMn Institute of Physics Handbook (McGraw-Hill Book Company, New^York, 1963), 2nd ed.; Handbook of Physics and Chemistry (Chemical Rubber Publishing Co., Cleveland,
2.20
216.5
H2 N2
84.7 166.6
2.68
8.83
3.78
4.45
O2
191.0 124.0 171.2
3.65
4.77
Kr Xe
7.40
6.27
186.9 312.4 208.8 224.9
Ar
Chlorine
Hydrogen chloride Water vapor .... Hydrogen sulfide.
III
CI2
Air
Hydrogen Hydrogen
chloride. sulfide
.
.
.
.
HCl HjS
13.2
2.55
9.82
3.69
4.27
4.67 3.49
4.87
2.68
5.51
7.61
3.76
4.49
132.5
4.53
117.5
4.73
3.10 2.84
Sulfur dioxide
SO2
2.07
NO
117 179.0
5.55
Nitric oxide
3.71
4.62
Nitrous oxide
N2O
136.1
4.69
2.90
NHg
88.9
4.57
3.05
Carbon monoxide Carbon dioxide
* Sources:
Ethylene
.
.
.
CO
165.8
3.79
4.42
CO2 CH4 C2H2
137.6 103.2
4.66
2.93
4.18
3.64
93.5
4.96
2.59
C2H4
93.6
5.05
2.50
1963), 44th ed.
* Source: Handbook of Chemistry Co., Cleveland, 1963), 44th ed.
440
and Physics (Chemical Rubber Publishing
441
APPENDIX IV 1
cubic foot per minute (cfm)
443
1.667 X 10-2 cfs 471.95 cm3/sec = 0.47195 liter/sec 28.32 liters/min = 1,699 liters/hr
= = =
1.699 mS/hr
=
0.0283 m^/min
Throughput or Oas Flow 1
APPENDIX
torr cm^/sec
IV
Units and Convebsion Factoes of Use in Vacuum Technology*
1
torr liter/sec
= = =
Pressure 1
standard atmosphere (atm)
=
760
mm Hg of density
where g
bar
1
= = = = = =
1
1
torr
micron
{/i)
= = =
13.595 g/cm^ 980.665 cm/sec^ = 760 torr
1.0133 X 10«dynes/cm2 14.696 psi = 2,116.2 Ib/ft^ 29.921 in. Hg at 32°F 33.899 ft of water at 39.1 °F 10* dynes/cm^ = 10*/ibar
750.06
1 fi
=
hter/sec
{fi
1/seo)
= = =
mm Hg of density
where g
= = =
=
= = = =
=
13.595 g/cm^ 980.665 cm/sec^ = 750.06 torr
1
atm cm3/sec
=
:
0.98692 atm 14.504 psi 1 Hg of density 13.595 g/cm^ where g = 980.665 cm/sec^ 1,333 fih&T (dynes/cm^) 10^^ torr = 1 millitorr
-
mm
-
cfm
torr
1
-
-
-
1.333 /^bar (dynes/cm^) :
Pumping Speed and Conductance 1
cubic centimeter per second (cm^/sec)
1 liter
per second
1 liter
1
per hour
(liter/sec)
(liter/hr)
cubic meter per hour (m^/hr)
= = = =
= 6 x 10^^ liter/min = 10~' m^/sec 6 X lO-^mS/min = 3.6 x lO-^m^/hr 3.531 X 10-5 cfs ^ 2.119 x 10-3 cfm
1 /i
10-^ liter/sec
=10^
cm'/sec
= = =
=6x10* cm^/min
= 3.6 X 106cm3/hr = IQ-Sm^/sec = 6 X 10-2ni3/jnin = 3.6 m^/hr = 3.532 X 10-2 cfs = 2.119 cfm = 2.778 x 10"* liter/sec = 1.667 X 10-2 liter/min = IQ-^m^/hr = lO^cm^/hr = 1.667 x lO-Sm^/min' = 16.67 cmS/min = 5.886 x 10-* ofm = 9.72 X lO-Scfs = 2.778 x 10-* m^/sec = 1.667 x 10-2m3/min = 10^ Hters/hr = 10* cm3/hr = 0.2778 liter/sec = 277.8 cm3/sec = 0.583 cfm = 9.72 X 10-3 gfg
442
Rubber Publishing
fx
liter/sec
(fi
l/sec)
1,000 n liters/sec (fi I/sec) 1,000 torr cm3/sec 2.119 torr cfm
2,119 /< ofm 1.316 atm om3/sec 10-3 ^Qj.j. liter^ggQ 1 torr cm3/sec 2.119 /< cfm 2.119 X 10-3 torr cfm 1.316 X 10-3 atm cm3/soc 760 torr cm3/sec
760 ^
liter/sec
0.760 torr liter/sec 1.610 torr ofm 1,610 n ofm 1,000 /< cfm 0.4719 torr hter/sec 471.9 torr cm^/sec 471.9 /< liters/sec 0.6210 atm cm3/sec 10-3 ^QJ.J. pfjj^
0.4719 /« Hter/sec 0.4719 torr cm3/sec 4.719 X 10-* torr hter/sec 6.210 X 10-* atm cm3/sec
Length 1
m
contimetor (cm)
meter (m)
1
1
inch 1
foot
= = = = =
mm
= 10 0.01 0.3937 in. 3.281 X 10-2 ft 100 cm = 1,000 39.37 in.
mm
3.281 ft
0.08333 ft 2.540 cm = 25.40
(in.)
12
(ft)
mm
in.
30.48
cm =
304.8
mm
Area 1
Source: Handbook of Chemistry and Physics (Chemical Co., Cleveland, 1963), 44th ed. *
cfm
3.6 liters/hr
\
10-3 torr liter /sec 2.119 X 10-3 torr cfm 2.119 /« cfm 1.316 X 10-3 atm cm3/sec
square centimeter (cm2)
= = =
10-* m2 = 100 mm2 0.1550 in.2 1.0764 X 10-3 ft2
VACUUM SCIENCE AND ENGINEERING
444
=10* cm^ =10' mm^
square meter (m^)
1
square inch
1
1
square foot
= = = = = = = =
(in.^)
(ft^)
1,550.0 in.2
10.764 ft2 6.944 x lO-^ ft^ 6.452 cm2 = 645.2 6.452 X 10-* m2
144
mm^
in.^
929.0
cm2 =
9.290 X 10-2
9.29 x 10*
APPENDIX V
mm^
m2
Volume 1
cubic centimeter (cm^)
1 liter
We 1 liter
cubic meter (m')
1
1
cubic inch 1
cubic foot
(in.')
(ft')
= = = =
= lO^^m' =
0.99997 x 10-' liter 6.1023 x 10-2 in.s 3.531 X 10-5 ft3
10' liters
=
10*
=
mm' = 35.31 ft' ^ i6.39 cm' =
cm'
6.1023 X 10* in.' 1.639 x 10-2 liter 5.787 X 10-* ft' 28.316 liters 2.8317 X 10* cm'
=
Values op Some Physical Constants*
mm'
m'
V
10^
2.8317 x 10'
R 1.639 x 10*
mm'
=
^oln^ol
Temperature °C
32
Rankine to centigrade
°R
= = =
"R °F
°C
Boiling point of water* Melting point of ice* Sublimation point of dry ice* .... Boiling point of liquid Nj* Boiling point of liquid H2* Boiling point of liquid He* Absolute zero
100
-78.2 -185.8 -252.9 -268.95 -273.16
»mol«
°F
+ + +
273.16 459.69 1.8°C
*
1.8°C
°K 373.16 273.16 195.0
77.35 20.3 4.215
212 32
-108.7 -320.5 -423.2 -452.10 -459.69
1.3805
=
1.660 9.109 4.803 1.602 2.893 9.649
°R 671 69 491.69 351.0 139.2 36.5 7.59
pressure.
445
"K
X 10-" erg/°K
X
10-2*
X X
10-28 g 10-"> esu 10-1" coulomb
X X 10" X
10*
g
esu/g mole coulombs/g mole
979.0-980.9 cm/sec^ 980.665 cm/sec^
Publishing Co, Source: Handbook 0/ Chemistry and Physics (Chemical Rubber
1963), 44th ed.
op
X lO'Vcm'
6.023 X 1023/g mole 22,415 cm' 8.3143 X 10' erg/g mole
=
Faraday Acceleration due to gravity: Approximate range over U.S.A. Assumed "standard" value
9
°K =
2.687
=
32 mi exactly) O2 Electronic rest mass Electronic charge
P=
Item
Losohmidt's number (molecular density of a gas at 760 ton- and 0°C) Avogadro's number (number of molecules in 1 g mole) Volume of 1 g mole of gas at 760 torr and 0°C Gas constant Boltzmann's constant Atomic mass unit (chemical scale in which
e
mm'
1,728 in.'
Kelvin to centigrade Rankine to Fahrenheit Fahrenheit to centigrade
At standard atmospheric
^
Value
Name
Symbol
cm' =
1.000027 x 10-' 1,000.027 use hereafter the approximation = 10' cm' = 10-' m' = 10* mm' = 3.531 X 10-2 ft' = 61.025 in.'
= = = = = = =
10'
,
Cleveland
AUTHOR INDEX
Tho page numbers
in italics are those of references at the
Abbott, T. A., 140, 168 Ackley, J. W., 165-167, 1(>8 Addis, R. R., Jr., 312, 362 Alexander, P., 234, 27.3
ends of the chapters.
Burch, R. C, 268, 273 Buritz, R. S., 380, 381,436 Bush, William E., 328, 362 Busol, F. I., 432-434, 438
Alpert, D., 99, 103, 104, 131, 342, 343, 362, 378, 388, 434, 436, 437
Biichler,
W., 250, 252, 273, 289, 302,
430-432, 438 Backus, J., 133, 135 Bailey, B. M., 410-412, 437 Bancroft, G. H., 379, 380, 436 Barrington, A. E., 165-167, 168 Barry, E. J., 309, 311, 312, 362 Basalaeva, N., 365, 436 Batzer, T. H., 243, 272, 273, 347, 362, 371, 372, 375, 376, 381, 382, 436
-^
Bayard, R. T., 99, 103, 104, 131, 388, 437 Beams, J. W., 212, 213, 218, 313 Beck, A. H., 118, 132 Becker, J. A., 89, 131 Becker, Wilh, 214, 215, 218 Bennett, W. H., 155, 168 Benson, J. M., 85, 86, 131 Bills, D. G., 107, 132 Biondi, M. A., 343-346, 362 Blears, J., 100, 131, 242, 273, 365, 436
Borovik, E. S., 431-434, 438 Bowie, R. M., 99-101, 131 Brackman, R. T., 424, 437 Briggs, W. F., 162-165, 168 Brisbane, A. D., 118, 132 Brubaker, W. M., 396, 437 Buckley, O. E., 95, 131
Carmichaol, J. H., 342-344, 362 Cartwright, C. Hawley, 341, 362 Chapman, S., 21, 2^ Charles, D., 145, 147-149, 168 Charpentier, D. E., 139, 142, 143, 167, 168 Chuan, R. L., 410-412, 437 Chupp, Warren W., 247, 273 Clausing, P., 51, 53, 54, 62 Cleveland, J. F. 285, 286, 302 Conner, R. J., 380, 381, 436 Crawley, D. .T., 230, 24.5-247, 258, 260, 264, 273
Davis, D. H., 52, .54-57, 61, 62, 306, 3.34,
335, 362
Davis, R. H., 388, 389, 437 Davis, W. D., 140, 141, 168 Dawton, R. H. V. M., 314, 362 Dayton, B. B., 99, 285, 294-296, 302, 354, 355, 360, 362, 363-365, 435
Degras, D. A., 424, 437 Dempster, A. J., 133, 167 Denison, D. R., 107, 132 Dennis, N. T. M., 241, 244-247, 271, 273 Divatia, A. S., 388, 389, 437 Dobrowolski, Z. C, 200, 218 Doughty, E. G., 140, 168
447
AUTHOR INDEX
448 Downing,
J. R., 122, 132 Dubrovin, J., 68, 131 Dunlop, G. C, 83, 131 Dunoyer, L., 272
Dushman,
Saul, 82, 83, 139, 211, 218,
227, 273, 364, 43G
East, H. G., 65, 131
Ehlbeck, H. W., 154, 156, 157, 168 Ehlers, H., 384, 437 Eklund, S., 212, 218 Enskog, T>., 21, 22 Ettre, K., 399, 437
Farkass, I., 309, 311, 312, 362, 378, 436 Feaks, F., 129, 132 Fedorova, M. F., 428-430, 438 Fisher, K. J., 389, 437 Fite, W. L., 424, 437 Flecken, F. A., 364, 436 Florescu, N. A., 230, 233, 234, 261, 262,
273 Fondrk, V. V., 220, 223, 224, 272 Forbes, S. G., 324, 325, 362 Forsythe,
W.
Hablanian, M. H., 261-264, 273, 289, 302 Haefer, R. A., 102, 118, 131, 132 Hall, L. D., 393-395, 437 Hall, L. G., 142, 168 Hamilton, A. R., 87, 89, 131 Hasse, T., 83, 131 Hayashi, C., 364, 436 Hay ward, Roger, 341, 362 Hobling, A., 150, 168, 364, 373, 374, 436 Heflinger, L. O., 424, 438 Hengevoss, J., 102, 131, 424, 425, 427, 438 Herb, R. G., 388, 389, 404, 437 Hickam, W. M., 375, 436 Hickey, J. S., 159, 168
Hickman, K.
C. D., 64, 131, 243, 244,
263, 268, 269, 271, 273
Hippie, J. A., 139, 143, 167, 168 Ho, T. L., 240, 253, 273 Honig, R. H., 400, 437 Hustrulid, A., 140, 168
Ishii,
H., 125, 127, 132
E., 4
Foster, J. S., Jr., 386-388, 437 Francis, A. B., 165-167, 168, 396-398,
437 Frank, N. H.,
AUTHOR INDEX
16,
22
Gaede, W., 179, 205, 211, 218, 227, 230, 273 Gale, A. J., 391, 392, 403, 437 Garwin, E. L., 424, 438 Geller, R., 365, 436 Gerber, J. F., 317, 318, 362 Goerz, D. J., Jr., 373, 436 Good, W. M., 328, 362 Gould, C. L., 389, 390, 437 Green, C. B., 89, 131 Greer, E. J., 365, 436 Grishin, S. F., 431, 438 Grishina, E. I., 431, 438 Grobman, Jack, 421-424, 437 Grove, D. J., 374, 375, 379, 380, 436 Guthrie, A., 133, 136, 138, 162, 167, 168, 309, 310, 362
Jacobs, Robert B., 209, 218 Jaokel, R., 230, 237, 273 Jaycox, E. K., 99 Jepsen, R. L., 165-167, 168, 396-398, 437 Johnson, J. W., 328, 362 Jones, A. C., 162-165. 168
Kenna, R. A., 180, 218 Kennard, E. H., 78, 131, 231, 235, 273 Kennedy, P. B., 339, 340, 362 Kietzmann, B. E., 396-398, 437 Kingdon, K. H., 159, 168 Kinsella, J. J., 269, 273
Klages, G., 83, 131 Kleimenov, G. F., 405-408, 437 Klipping, G., 430-432, 438 Klopfer, A., HI, 112, 132 Klumb, H., 83, 131
Knox, F. A., 184, 218 Knudsen, M., 36, 44, 53-56, 123, 132
60, 62, 62,
Kochnev, V. A., 405-408, 437 Kovalenko, V. A., 432-434, 438 Kraus, Th., 356-358, 362, 364, 435 Kruger, Charles H., 215-217, 218 Kuhn, H. J., 65, 131 Kurie, F. N. D., 323, 324, 362
449
Moll, J., 384, 437
Mongodin, G., 364, 436 Moody, R. E., 153-155, 168 Moore, R. W., Jr., 412-421, 437 Morse, R. S., 99-101, 131
Nakayama, K., Lafferty, J. M., 107, 108, 110, 111, 132
Naundorf,
Lampson,
Neef,
W., 98, 131 Landfors, A. A., 289, 302 Lane, C. T., 83, 131 Lange, W. J., 342-344, 362 Langmuir, I., 101, 131, 159, 168 Latham, D., 241, 244, 271, 273 C.
Lauer, E. J., 106, 132 Lavender, R., 87, 88, 131 Lawrence, E. O., 386-388, 437 Lazarev, B. G., 428-430, 438 LeBlanc, M., 219, 272 Lech, J., 145-147, 151, 152, 168 Leek, J. H., vi, 67, 77, 87, 92, 94, 97-99, 113, 115, 123, 132, 283, 302 LeRiche, R., 382-384, 436 Levenson, L. L., 52, 54-57, 61, 62, 265, 273, 306, 334, 335, 345-347, 362
Lichtman, D., 150, 168, 364, 373, 374, 436 Little, R. N., 324, 325, 362 Lloyd, W. A., 395-397, 437 Loeb, L. B., 12, 14, 22 Loecherer, K. H., 154, 156, 157, 168 Loevinger, R., 138, 167 Lofgren, E. J., 386-388, 437 Lothrop, C. F., 165-167, 168
McFarland, R. H., 347, 362
McLeod, H.,
69, 131
Mandel, P., 389, 390, 437 Mandoli, H., 165-167, 168 Marks, Lionel S., 4 Mascher, W., 430-432, 438 Mellen, G., 122, 132 Menshikov, M. I., 247, 259, 260, 273 Metcalfe, R. A., 385, 437 Mileshkin, A- G., 405-408, 437 Milleron,
Norman,
52, 54-57, 61, 62,
265, 273, 301, 302, 306, 332-335, 34.5-347, 362, 366, 372, 402, 403, 408, 436, 437
W.
125, 127, 132
C. H., 354-356, 360,
S., Jr.,
362
404
Noher, H. Victor, 341, 362 Nicollian, E. H., 149, 150, 168 Nienhuis, K., 114, 132 Nier, A. O. C, 140, 167, 168 Nightingale, J., 365, 436 Noeller, H. G. (see Noller, H. G.)
H. G., 202, 205, 218, 230, 237, 250, 252, 273, 289, 302, 364, 437
Nollcr,
Normand,
C. E., 253, 273 Northrop, D. L., 371, 436 Nottingham, W. B., 95, 96, 102, 107, 131, 132 Nyer, W. E., 324, 325, 362
Oatloy, C. W., 300, 302
Pauly, T., 389, 437 Pearson, G. L., 89, 131 Peck, A. W., 298, 302 Penning, F. M., 113-115, 132, 387, 437 Pensak, L., 312, 362 Perkins, G. D., 142, 143, 168 Peters, J. L., 141, 142, 168 Pinson, J. D., 298, 302 Pirani, M., 86, 131 Popp, E. C., 403, 408, 437 Post, R. F., 333 Power, B. D., 180, 218, 230, 241, 244247, 258, 259, 264, 271, 273, 375, 436 Pressey, D. C, 67, 131 Prevot, F., 364, 436
Rabinovich,
I. S.,
Redhead, P. A.,
247, 259, 260, 273
68, 105, 118-122, 128,
129, 132, 154, 168 Reich, G., 101, 131, 157-159, 168, 250,
252, 273, 289, 302 Rhodin, T. N., 121, 132
450
AUTHOR INDEX
Riddiford, L., 101, 131
Torney, F.
Riddoch, A., 115, 132 Ridenour, L. N., 98, 131 Rivera, M., 382-384, 436
157,
168 Schwartz, C. M., 87, 88, 131 Schwarz, Helmut, 118 J.,
Simmons, J. C, Jr., 126, 127, 132 Simonov, V. A., 405-408, 437
C,
16,
J. R., 333, 334, 362, 371,
436
Vacca, R. H., 123, 132 Atta, C. M., 186, 195-198, 218, 371, 436 Van Atta, L. C, 371, 436 Van de Graaff, R. J., 371, 436 Vanderschmidt, G. F., 378, 436 Vandershce, T. A., 140, 141, 168 van Oostrom, A., 103, 131 Varadi, P. F., 368, 369, 399, 436, 437 Vekshinsky, S. A., 247, 259, 260, 273 Voego, W., 83, 131 Von Friesen, S., 211, 218 von Zweck, T., 380, 381, 436
312, 362
Shapiro, Ascher H., 215-217, 218 Siegbahn, S., 211
Slater, J.
131,
Van
Schmidlin, F. W., 424, 438
Nancy
129,
SUBJECT INDEX Ullman,
Santeler, D. J., 106, 129, 130, 132 Saxon, D., 388, 437
Scott,
95, 96,
168
Trabert, F. W., 385, 437 Trendelenburg, E. A., 424, 425, 427, 438 Trump, H. G., 83, 131
Roberts, J. A., 162-165, 168 Roberts, R. W., 315, 362 Robinson, C. F., 142, 168 Robson, F. C, 375, 436 Roehrig, J. R., 126, 127, 132 Romann, M. P., 77, 131 Rovner, L. H., 121, 132 Ruf, J., 154, 156, 157, 168 Rufer, C. E., 288, 302 Rutherford, S. L., 396-398, 437 Ryan, J. F., 375, 376, 436
Schuemann, W. C, 104, 105, 73,2 Schuetze, H. J., 104, 131, 154, 156,
L., Jr.,
132, 160, 161,
22
Smith, H. R., 260, 273, 339, 340, 362 Smith, J. H., 272 Smith, P. T., 93, 131 Sommer, H., 143, 168 Stoinherz, H. A., 261-263, 273 Stevens, C. M., 140, 168 Stevenson, D. L., 250, 253, 254, 265267, 273, 287, 302 Stork, F., 104, 131 Strong, John, 341, 362, 370, 436 Swartz, J. C, 389, 390, 437 Sylvester, R. L., 186, 218
Wahl, J. S., 324, 325, 362 Wakerling, R. K., 133, 136, 138, 162, 167, 168, 309, 310, 362 Wallace, R. A., 145-147, 151, 152, 168 Warnecke, R. J., Jr., 145, 147-149, 168 Watson, W. R., 145-147, 151, 152, 168 Webber, R. J., 83, 131 Weinhart, H. W., 99 Welton, R. D., 389, 437 White, W. H., 159, 168 Whitford, Albert E., 341, 362 Williams, C. E., 212, 213, 218, 313 Williams, T. W., 139, 167 Wilson, R. R., 313, 314, 362 Winters, H. F., 107, 132 Winzenburger, E. A., 186, 189, 190, 218 Wishart, J., 379, 380, 436 Worcester, W. G., 140, 168
Tate, J. T., 93, 131 Taylor, A. R., 338, 362 Thees, R., 203, 218
Zaphiropoulos, R., 395-397, 437
Thomas, H.
Ziock, K., 186, 218
A., 139, 143, 167, 168
Absorption, definition of, 364 pumping by ahimina, copper and zeolite, 343-348, 398-400
Accommodation of,
Bayard-Alpert ionization gauge, errors due to accumulation of surface coating, 106
coefficient, definition
limits of operation, 103-105
79
role, in
low temperature cathodes, 106
Knudsen radiometer gauge,
124 thermal conductivity gauge, 79-81 Adsorption, definition of, 364 pumping by graphite at cryogenic temperatures, 428-430 Air, effective molecular weight of, 2 normal composition of, 411 Alphatron gauge, 122 Argon, instability in Vac Ion pumps,
nude gauge construction, 106 principles of operation, 103
in
396-398 normal content of air, 411 Avogadro's law, 2, 4 Avogadro's number, 4
Backstreaming
in
diffusion
effects,
105
reduced x-ray hmit, 103 sensitivity, 103, 107 (See also Ionization gauge, conventional hot cathode type; Magnetron
ionization
gauges; Penning discharge gauge; Pressure gauges) Bellows seals (see Metal bellows) Blears's effect, 100-102, 242, 297 Boiling points of common gases, 409
Boltzmann constant, 7 Booster diffusion pumps, 257 Boyle's law,
pumps,
257-268, 329 catalytic effect of materials of nozzle
assembly, 267 dependence, on pressure, 263 on shape of first-stage nozzle, 265-267 effect on ultimate pressure, 257-268 measurement of, 258, 261-264 reduction by water-cooled cap over first-stage nozzle, 259, 263 role
pumping
Calibration of vacuum gauges, 124-128 aperture method for ionization gauges, 126-128
McLeod gauge,
107 comparison, with conventional ionization gauge, 103 with hot cathode magnetron gauge, 109
as absolute standard,
124-126 error due to use of vapor trap, 72, 125, 127
and Gay-Lussac's law, Chemisorption, definition, 364 Charles's
1
Collision cross section, 21
dependence, on molecular diameter,
of jet from first-stage nozzle,
259-264 Bayard- Alport ionization gauge, 103-
1
21
on viscosity, 21 Compression ratio, for diffusion pumps, 230-240 for mechanical booster (blower) pumps, 185, 188, 199-201, 204 for mechanical oil-sealed pumps, 171 for molecular drag pumps, 205-214
451
SUBJECT INDEX
462 Compression
molecular tur-
ratio, for
bine pumps, 217 Condensable vapors,
accelerated
re-
moval by high-temperature bakeout, 363-370 backstreaming, from diffusion pumps, 258-268, 329 from oil-sealed mechanical pumps, 174, 340 from steam ejectors, 227 dominance of water vapor following pumpdown, 137, 330-332 effect, on performance of mechanical oil-sealed pumps, 177-179, 351 on reading of McLeod gauge, 71
pumping speed, 25, 58 conductances, in parallel, 26, 58 in series, 25, 58 molecular flow pressure range, 43-51, 60-62 annulus between two concentric tubes, 51, 62 aperture in thin wall, 47-49, 60 channel of rectangular cross section, 50, 61
long
tube of circular 44-47
cross
section,
Monte Carlo
calculation of, 51-
57
narrow
slot
with end correction,
51, 61
tube with end correction, 49, 60 summary of, 57-62 transition pressure range, 15, 23,
36-43, 59
dependence on pressure, 37-43 formula for long tube, 37, 41, 59 limits of, 40-42 viscous flow pressure range, 26-30, 34-36, 58 change in character due to surface slip, 34
Displacement
speed
vacuum pumps,
of 172
mechanical
Dubrovin gauge, 68
pressure drop, 30, 59
Conductance
factors,
Knudsen and
Clausing, 52-57
Cryo-adsorption, 421-424, 428-430 Cryogenic pumping, 408-434 boiling points of common gases, 409
combined, with catalytic process, 421-424 with mechanical pumping, 410-412 cryo-adsorption, 421-424 cryotrapping, 424-428 liquid-helium-cooled thimble trap, 400 pumping speed of cryogenic pumps, 411-421
elimination from oil-sealed mechanical pumps, 179-185 vapor compression action of mechanical booster pumps, 204 vapor traps, absorption type, 341348 refrigerated, 328-341 Conductance, definition, 24, 58 general formulas, combined with
SUBJECT INDEX
Conductance, general formulas, viscous flow pressure range, formula for long tube, 29, 58 pipe -size formula based on
shielded
liquid-helium-cooled densers, 430-434
con-
of, 412-421 vapor pressure dependence on temperature, 409 Cryotrapping, 424-428
theory
pump working fluids, 240-249 decomposition of organic, 242-245, 264 mercury and organic, comparative advantages, 244-249 vapor pressures of, 240-244 Diffusion pumps, 227-272 backstreaming, 257-268, 329 Blears's effect, 100-102, 242, 297 booster, 257 compression ratio, 230-240 ejector, oil vapor, 257 forepressure, limiting valvie of, 254257 fractionating, 268-271 Ho coefficient, 248-250, 253 modern types of, 227-229 principles of operation, 227-240 pumping speeds of, 240, 249-254, 293-302 with vapor trap, 240, 252 Diffusion
^
purging, 271
speed factor, 253, 272 ultimate pressure, 257-268 working fluids, 240-249
Elastomers, 307-316 Electron volt, unit of energy, 91 Electronic charge, definition and value, 4 Emissivity, definition, 81 Evapor-ion pump, 388-391
Faraday, definition and value, 4 Farvitron mass spectrometer, 157-159 Forepressure limit of diffusion pumps, 254-257 dependence on design and operating parameters, 255 design compromises, 255 limitation due to decomposition of working fluid, 256 process of jet breakdown, 254 throughput dependence on, 256 booster diff'usion pumps, 257 oil vapor ejector pumps, 257
Gas ballast, 179-183 Gas flow, 14, 23-62, 277-291 through a hole, 12, 47-49 low pressure range, 43-57 methods of measurement of, 277-291 molecular flow, 14, 23, 43-57, 60 Poiseuille's law, 26-30, 34-36
Reynolds number, 31 transition
pressure range, 15, 23, 36-43, 59 turbulent flow, 31-34 viscous flow, 14, 23, 26-30, 34-36, 58 Gas law, general, 1-4 Boyle's law, 1 Charles's and Gay-Lussac's law, 1 Gases, boiling points of, 409 general gas law, 1-4
453
Gases, universal gas constant, 3 vapor pressures at low temperatures, 409 velocity of sownd in, 11 Gaskets, elastomer, 307-316 metal, 370-378
O ring, 307-313, 315 Getter-ion pumps, 385-398 Bayard-Alpert gauge pumping action, 105, 388 discharge in axial magnetic fleld, 386-388 Evapor-ion pump, 388-391 gettering and ionization processes,
391-393 leak detection application of, 165167
pumping action of gas
discharges,
386
pump, 396-398 Vac Ion pump, 393-398
triode getter-ion
argon instability, 396 hydrocarbon contamination, 394 mechanism of operation, 394 slotted cathode construction, 396398 triode getter-ion pump, 396-398 Getter pumping, 401-408 deposition of reactive metals, 401408 molybdenum, 402-404, 408 nickel, 407 titanium, 401-408 zirconium, 402
pumping
effectiveness as function of
temperature of coated surface, 406-408
Halogen leak detectors, 159-161, 162 Helium leak detectors {see Leak detectors)
ideal gas, deflnition, 2
molecular constitution of, 4 molecular weights of, 2 molecules per unit volume, 5 nature and behavior of, 1-22 ratio of specific heats, y, 11, 220 specific heats at constant pressure
and
at constant volume, 11
Ideal gas, deflnition, 2 Ionization of gases, 90-98 cross section for electrons, 93 ionization potential, 92 ionization probability, 93 Ionization gauge, conventional cathode type, 90-102
hot-
SUBJECT INDEX
454
gauge, conventional hotcathode type, alternative methods of operation, 92 Blears's effect, 100-102, 242, 297 cahbration of, 97, 125-128
Ionization
cross section for ionization, 93 design of gauge tubes, 99-101
ionization process (see Ionization of gases)
Nottingham x-ray limit, 102 nude gauge arrangement, 100-102 outgassing of gauge elements, 101 parameters for various gauge tubes, 99 principles of operation, 90-94 range of useful application, 97 regulated power supplies for, 98 sensitivity of, 95-99
simplified electrical circuit for, 94
x-ray limit, 102 (See also
SUBJECT INDEX
Leak detectors, mass spectrometer types double magnetic fociising, 141 linear resonance accelerators, 152154 Nier 60° magnetic deflection, 140 omegatron, 149 Liquid nitrogen (LN), automatic level control, 337 coolant, for absorption traps, 342, 347, 399 for coated getter surfaces, 404408, 435 for vapor condensation traps, 330, 332 cryotrapping on LN-cooled surfaces, 424 intermediate coolant from cryopumping systems, 426-430, 432434 of,
Bayard-Alpert ionization
gauge; Magnetron ionization gauges; Penning discharge gauge) Isentropic flow, 219-221, 278-282
McLeod
gauge, 69-78
calibration methods, 72 criterion for validity, 71
of condensable reading, 71
effect
Kelvin temperature scale, 2 Knudsen radiometer gauge, 123
accommodation
coefficient, effect
Lambert's law of molecular emission, 52 Leak detection techniques, 161-167 bubbles from air pressurizing, 162 halide torch technique, 162 halogen leak detector, 159-161
mass spectrometer leak detection methods, 164 Vac Ion pump current, 165-167 variations in pressure gauge readings, 162-164 Leak detectors, halogen sensitive, 159161 (see
mass spectrometer types
of, below)
due to connecting tube, 73-75, 125 due to liquid-nitrogen-cooled trap, 72, 125, 127 methods of controlling mercury level, 75-77 primary standard for pressure measurement, 72 response formula, 70-72 scales, linear and quadratic, 71
multiple, 77 sensitivity, 72
Magnetron
focusing, 142 deflection,
degree magnetic 137-140
ionization
gauges,
cold
cathode inverted magnetron, 118120 cold-cathode magnetron, 120-122 hot-cathode magnetron, 107-111 {See also Bayard-Alpert ionization gauge; Ionization gauge, conventional type; hot-cathode Penr'ing discharge gauge; Pres-
mass spectrometer types of, cyoloidal Dempster 180
on
error,
on
sensitivity, 124 pressure range, 124 principles of operation, 122-124
helium
vapor
sure gauges)
Manometers, diaphragm, 65-68 hquid, 63-65 (iS'ee
also Pressure gauges)
Mass
flow, definition, 24
relation to throughput, 24 of steam ejectors, 223
Mass spectrometer leak detectors (see Leak detectors) Mass spectrometer vacuum analyzers, 133-159 magnetic deflection types, 133-143 cycloidal focusing, 142
Dempster magnetic focusing, 133140 Nier 60 degree deflection, 140 Vanderslice 90 degree deflection, 140 resonance types, Farvitron, 157-159 linear accelerator, 152-157 omegatron, 143-152
Maxwell-Boltzmann distribution law, 8-11 average molecular velocity, 9 most probable molecular velocity, 9 root -mean square velocity, 7-10 Mean free path, 5, 13-15, 21, 23 Measurement, of gas flow, 277-291 of gas pressure, partial, 133-159 total, 63-128 of pumping speeds, 291-302 Mechanical booster pumps (vacuum blowers), 185-205 analysis of pumping performance, 186-194 compression ratio, 185, 188, 199-201, 204 net pumping speed, 187-190 overheating of exhaust, 202 pumping speed dependence on pressure, 189, 193-202 reverse flow or slip, 186-188 vapor compressor action, 204 Mechanical oil-sealed pumps, 169-185 compression ratio, 171 condensable vapor, effect on performance, 177-179 methods of elimination, 179-185 air stripping (Knox method), 184 drop-out tank, 179 gas ballast, 179-183 hot pump, 184 inlet condensers and vapor traps, 184 oil
purification
184
and
circulation,
455
Mechanical oil-sealed pumps, functions in vacuum systems, 358-360 oil, lubrication and sealing, 172 operating features, 169-172 pumping speed, 171-177, 291-293 selection of sizes, 359 stages, single and double, 171 throughput, 175-178 types, 169
Mechanical vacuum pumps, 169-218 booster pumps (blowers), 185-205 functions of various types, 169 molecular -drag type, 205-214 molecular turbine type, 214-218 oil-sealed rotary types, 169-185
Metal bellows, 316 for rotary motion seals, 317-318 for translational motion seals, 316 for valve-stem seals, 320-323 Metal gaskets, 370-378 aluminum foil, 375-377 copper bead, 372 copper ridge, 373 copper shear, 371 flare seal, 374 knife-edge seals, 373 soft metal ring, 370, 374 reweldable flanges, 378 Molecular drag pumps, 205-214 analysis of performance, 205-210 performance of various designs, 211214 Molecular mean free path, 5, 13-15, 21, 23 derived in terms of molecular diameter, 13 relationship to viscosity of a gas, 21
determining character of gas ''2, 23 Molecular tu.bine pump, 214-218 Molecular weights, 2, 10 role in
flow,
of various common gases, 2 Molecules, diameters of, 13-21 diatomic, 11 elastic sphere
ionization of,
model of, 5-15 by electron impact,
90-94 masses of, 10
Maxwell-Boltzmann velocity bution
mean
of,
distri-
8-11
free path monatomic, 11
of, 5,
13-15, 21, 23
SUBJECT INDEX
456
Pressure, gas, definition of, 1 dependence, on kinetic energy of
Molecules, polyatomic, 11 velocities of, 7-1
Motion
seals,
Nozzles,
SUBJECT INDEX
molecules, 5-8 on mass of gas, 2
313-318
converging-diverging
type,
220 diffusion pump, 227-230, 265-267 isontropic flow, 219-221 mass flow through, 221 velocity of gas flow through, 220 critical pressure,
effects
O
of nonisotropic
kinetic theory of, 5-8
detection
sensitivity, 149 partial pressure analyzer, 150-152
pressure, 124
critical
278-282
gas flow through, 278-281 280 278, gas flow through,
critical pressure for, 278,
mass 280-282
standardized dimensions of, 280 subcritical gas flow through, 280, 282 Outgassing, bakeout procedures and
365-370 on ionization gauge readings,
effectiveness, effect
101
on pumpdown time, 351-358 quantity of gas released by metal
effect
surfaces,
rate
363-369
of gas evolution temperature, 365
pressure
gauges
spectrometer
vacuum
Partial
at
(see
room
Mass
analyzers)
Penning discharge gauge (PIG), 113118
114-116 principles of operation, 113 useful pressure range, 114-118 Pipe sizes, selection of, for viscous flow, 30 Pirani pressure gauge {see Thermal conductivity pressure gauges) Poiseuille's law, 26-30, 34-36 erratic behavior of,
434
30 Pressure gauges, 63-128 caUbration methods for, 124-128 Dubrovin, 68 ionization, 90-123
principles of operation, 143-149 Orifices, calibrated,
Alphatron, 122 cold-cathode types, 113-122 magnetron, inverted Haefer 118-120 Penning discharge, 113-118 Redhead magnetron, 120-122 hot-cathode types, 90-113 Klopfer magnetically collimated electron beam gauge, 111-113 Lafferty hot-cathode magnetron, 107-111 {See also Bayard-Alpert ionization gauge; Ionization gauge, conventionalhot-cathode type) Knudsen radiometer type, 123 McLeod, 69-78 manometer, diaphragm, 65-68 liquid, 63-65 partial {see Mass spectrometer vac-
uum
analyzers) thermal conductivity, 78-90 Pirani type {see Thermal conductivity pressure gauges)
thermocouple type
(see
Thermal
conductivity pressure gauges)
Pumpdown
factor
for
system
factors,
352-354
Pumping
speed, deflnitions, for isotropic molecular distribution,
23-25, 58, 274-277
measurement, ambiguities at low
permanent, 18, 63 vapor pressure, 17, 71, 331, 409 Pressure drop formula for viscous flow,
315 Oil ejector pumps, 257 Omegatron, 143-152 argon vs. helium leak rings, 307-313,
354-358
graphically determined from throughput and load curves, 354-356
distribution, 129-131, 412-416 gauge pressure, definition, 63
partial, 63, 133, 250,
time, formula for roughing
down system, 348-354 functional dependence at low pressure,
on temperature, 1-3 on volume, 1-3 direction
219
Pumpdown
mechanical
for nonisotropic molecular distri-
bution, 416-418 methods of measurement, 291-302 performance, adsorption pumps, 347 cryogenic pumps, 411-421 diffusion pumps, 249-254 Evapor-ion pumps, 390 getter-ion pumps, 391-393
mechanical booster (blower) pumps, 189, 193-202 mechanical oil-sealed pumps, 171177 molecular drag pumps, 212 molecular turbine pumps, 218
steam ejectors, 223-227 Vac Ion pumps, 395
vacuum systems, 26, 277, 360 resultant for pump combined with a conductance, 25, 58 units of, 24
Pumping speed
factor
for
diffusion
pumps, 253 Pumps, vacuum, absorption, 398-400
time, 348-361 effect of outgassing, 351-358 for mechanical pumps, factor
F
349-351
lings, quick connect, 309 groove designs for, 307-309 guard ring with double seal, 309 properties of various elastomers, 311-313
square-cross-section gaskets, 309 Solvents, properties of, 304 Sorption processes, absorption, 364
absorption pumping, 398-400 adsorption, 364 adsorption pumping, 428-430 chemisorption, 364 cryosorption, 421-424 cryotrapping, 424-428 desorption, 365-370 Specific heats of gases, 1 Standard conditions of temperature
and pressure, 3 Steam ejector pumps, 219-227 backstreaming of water vapor, 227 components of, 219 isentropic expansion and compression, 219-221, 223 principles of operation, 219-223 pumping speed of multistate units, 223-227 stalling condition, 226 steam consumption, 227 Stefan-Boltzmann law, 81 System factors for determining pumpdown time, 352-354
cryogenic, 408-434 diffusion,
227-272
diffusion booster, 257
Evapor-ion, 388-391
385-398 mechanical booster (blower), 185205 mechanical oil-sealed rotary, 169getter-ion,
185 molecular drag, 205-214 molecular turbine, 214-218 oil vapor ejector, 257 steam ejector, 219-227 Vac Ion, 393-398
Temperature, absolute
scales, 2, 4 absolute zero of, 2 centigrade scale, 2, 4 dependence, of gas pressure on, 1-3 of vapor pressure at low tempera-
ture, 409 Fahrenheit scale, 4 Kelvin scale, 2, 4
Rankine scale, 4 Thermal conductivity of free
molecul'
.
gases, 78 conduction at low
pressure,, 78
for rarefied gases, 78
Thermal conductivity pressure gauges,
pumDS, 349-351
Pumpdown
457
Seals, elastomer, O-ring gaskets, coup-
Reynolds number, 31
78-90 basic principles, 78-83
Seals, elastomer,
307-318
O-ring gaskets, 307-313, 315
accommodation
coefficient,
79-81
emissivity of gauge elements, 81
SUBJECT INDEX
458
Thermal conductivity pressure gauges, basic principles, energy transfer
from heated element, 78 free molecular thermal conduction, 78
Stefan-Boltzmann law, 81 thermal conduction loss along filament, 81-83 thermal conductivity of rarefied gases, 78
Pirani gauge, 86-90 control circuits for, alternative, 87 pressure range of, 87 principles of operation of, 86 response curve vs. pressure, 89-91 thermistor type of, 87-91
thermocouple gauge, 83-86 compensation for ambient temperature, 85 matched tubes, 84 multi-station control circuit, 85 principles of operation, 83
SUBJECT INDEX
Traps, vapor, creep barrier for organic fluids, 332, 367
exhaust baffles for diffusion pumps, 340 forevacuum, 340-342 functions of, 328-330 inlet baffles for diffusion
pumps,
240, 252, 329-339 mechanically refrigerated, 338340 performance of diffusion pump with, 240, 252, 335-337 surface migration of organic fluids, 332 temperatures for various applications, 244, 246, 329-331 thimble traps, 330-332 Turbulent flow, 31-34 occurrence in vacuum systems, 3234
Reynolds number, 31 Two-region vacuum systems, 382-385
response curves for several gases, 83
Thermocouple
gauge
(see
Thermal
conductivity pressure gauges) Throughput, curves for mechanical
vacuum pumps, 175-178 definition, 24, 57, 175
mass flow, 24 system pumpdown time based upon, 354-356
relation to
Titanium,
getter
pumping
by
de-
position of, 401-408 vapor pressure vs. temperature, 405
Transition pressure in gas flow, 39-41 Trap{s), absorption, 341-348, 398-400
absorption materials, 341-343 bakeout cycle, 342-345, 347 capacity for gases and vapors,
344-348 copper foil type, 342-344 stay-down times for, 342 effectiveness as a pump, 347, 398-400 liquid-nitrogen-cooled, 347 tray design, 344 ultimate pressure, 344-347 vapor, 328-341 automatic liquid nitrogen level control, 337 conductance of baffle systems, 333 337
Ultrahigh vacuum techniques, 363-435 absorption pumping, 398-400 bakeable valves, 378-382 bakeout procedures, 364-370 cryogenic pumping, 408-434 getter-ion
pumps, 385-398
thimble trap, 400 metal gaskets, 370-378 reactive metal deposition, 401—408
Vacuum pumps,
vapor-jet, 219-272
Vacuum
phenomena, dominance
of,
two-region vacuum systems, 382-385 Universal gas constant, 3 value of, in various systems of units, 4
Vac Ion pump, 393-398 tion,
criteria for selec-
358-361
pumps, 360 mechanical pumps, 358-360 pressure gauges, 361 diffusion
valves, 361
Vacuum
gauges
(see
Pressure gauges)
459
Velocities of gas molecules, 7-11
average,
303-307
9, li
Maxwell-Boltzmann distribution
most probable, root
mean
9,
of,
10
square,
7, 9,
sound velocity, relation
n to, 11
Viscous fiow, 14, 23, 26-30, 34-36
pumping
ports, criterion for, 306 solvents, properties of, 304
correction to Poiseuille's law, 34-36 drag, coefficient of, 35
virtual leaks, avoidance of, 306
Poiseuille's law, 26-30, 34-36 pressure drop formula, 30 selection of pipe sizes for, 30
welding specifications, 305 Valves, vacuum, 318-328, 378-382 bakeable, 378-382 functions of, in vacuum systems, 319 gate, 323-328 butterfly type, 324-326 disk typos, 325, 327 modified plumbing types, 323 sliding plate typos, 324-326 globe, 318-323 bellows sealed types, 318, 320323 diaphragm sealed type, 320 elastomer sealed types, 318 needle type, for control of gas flow, 325, 328
Van dor Waals'
equation of state, 15-18
change of phase
(liquid,
vapor and
gas), 17 critical
volume, 16 permanent gas,
baffles
and
pressure,
efficiency
of 172
vacuum pumps, Water
\'apor,
mechanical
contamination of oilpumps, 177-179
sealod mechanical
dominant component gas following pumpdown, 133, 330-332, 364 effectiveness
of
thimble
trap
in
pumping, 330-332 elimination from oil-sealed mechan-
pumps (see vacuum pumps)
ical
Mechanical
steam ejectors, attainable water vapor pressure, 223-225 backstreaming in, 227 vapor pressure as function of tem-
temperature and Zeolite, absorbent material for
definition of, 18
traps, at
triple point, 16
Vapor Vapor
34
slip, coefficient of,
Volumetric
perature, 331
pressure,
vapor
room temperature, 343-
347
\'an dor Waals' constants, 17
363-370 system design, 434
Vacuum components,
vessels,
cleaning of interior surfaces, 304 external pressure requirement, 303 finish of interior surfaces, 304 leak hunting, 161-167, 307 materials of construction, 303
liquid-helium-cooled
surface
mechanical, 169-218
refrigerated, 347,
traps, 328-341
of
gases
at
temperatures, 409 of water vs. temperature, 331
low
398-400
absorbing various gases, 344-347, 399 quantity of vapor and gas evolved during bakeout, 345 effectiveness
in
t
(continued from front flap)
-
Other
special
features
include
a
thorough treatment of the ultrahigh vacuum development, and a discussion of
methods
pumping by the use
of
of
vapor
deposition of active metals.
Here
A comprehensive guide to the
'
unique, comprehensive, and
is
authoritative coverage of
vacuum
modern theories, instruments, and uses of high vacuum
sys-
tems, their components, operation, and
design— a book which enables the reader to solve practical Vifith
FUNDAMENTALS OF VACUUM SCIENCE AND TECHNOLOGY
problems associated
every aspect of
vacuum technology.
GERHARD LEWIN
By
Plasma Physics Laboratory, Princeton University
248 pages. 6x9. 104
illustrations
Designed for the man whose work requires a practical
About the Author
-
knowledge
unique reference
of
vacuum technology,
this
fully explains pertinent kinetic
Since 1935, Dr. C. M. Van Atta has "
been involved with physical apparatus requiring larger than normal vacuum systems. Since 1937, he has acted as consultant
in
vacuum technology
ponents
to in-
in
...
.
.
systems
gas flow .
.
.
.
surface effects
.
.measurements
.
.
.
...
com-
and design calculations.
The book
and has been actively enthe new-product development
effort of the
.
punnping processes
dustrial firms
gaged
theory equations
—
critically
evaluates
all
basic
vacuum
helps you select the most efficient
equipment for your specif ic purposes — and guides you in the actual design of special equipment.
Kinney Vacuum Division of
The NewYorkAir Brake Company. His experience includes teaching and
Filled with
research at MIT; applied physics research at the Naval Ordnance Labora-
graphic analysis of high
tory;
Physical Sciences and Mathematics and
Supervisor of Physics Research, University of Southern California; develop-
ment of high-current particle accelerators and controlled thermonuclear research.
University
of
California,
Lawrence Radiation Laboratory, Berkeley and Livermore, California.
vacuum
as a working tech-
nological tool.
tion ofthe isotopes of uranium. University
Lawrence Radiation LaboraChairman of the Division of the
and
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Washington, D.C.; research and development on electromagnetic separa-
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