Table Of ContentTotal Pressure Measurements
in Vacuum Technology
A. BERMAN
Vacuum Calibration Laboratory
Soreq Nuclear Research Centre
Yavne, Israel
1985
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Berman, A. (Armand)
Total pressure measurements in vacuum technology.
Bibliography: p.
Includes index.
1. Pressure —Measurement. 2. Pressure-gauges.
3. Vacuum technology. I. Title.
QC165.B45 1985 533'.5 84-28454
ISBN 0-12-092440-4 (alk. paper)
PRINTED IN THE UNITED STATES OF AMERICA
85 86 87 88 9876 5 4321
To
Nadya-llane and Eric
Preface
When you can measure what you are speaking about
and express it in numbers you know something about
it; but when you cannot express it in numbers, your
knowledge is of a meagre and unsatisfactory kind.
Lord Kelvin
Vacuum technology is an integral part of a whole range of modern indus
tries, for example, those involved with integrated circuits, semi-conduc
tors, plasma research and metallurgy. In addition, it is of vital importance
to research and development in science and engineering. In industry, the
quality of the end product is directly related to the quality of the vacuum.
This depends on the accuracy of the most adequate method of measuring
the rarefied environment and on the correct interpretation of the results
yielded by measurements.
Vacuum measurement has, however, been a rather neglected area and
only in the last two decades has the question of measurement accuracy
and diagnosis assumed proper significance and attention. Interest in the
subject is therefore increasing and likely to keep increasing with the de
velopment of new technologies requiring very low residual pressures.
The quantitative determination of the rarefied gas environment as well
as the assessment of performance typical of vacuum equipment (e.g., flow
rate, throughput, conductance of ducts) involve measuring pressure.
Pressure measurement is far more complicated than the measurement of
any of the fundamental quantities—length, mass and time—in that the
parameters characterizing both the rarefied environment and the measur
ing process are neither unique nor invariable. Indeed, as the degree of
rarefaction reaches lower values, both density and chemical composition
of the gas keep changing. The measuring process itself interferes with the
gas measured, modifying its chemical and physical properties.
Unfortunately, pressure measuring techniques are used before all the
necessary factors contributing to the rarefied environment are known,
and the interpretation of the results can be misleading. This situation is
further complicated by the fact that there is no single well-established
xi
xii PREFACE
standard measuring technique for the quantities involved and that the
choice of units is still a problem. On the one hand there is the self-
consistent system of SI units which unfortunately is not widespread even
in countries that have adopted it; on the other hand there is a natural
desire to preserve the use of "Torr" a term familiar to vacuum workers.
We decided to use the highly logical system of SI units, and to express
pressure in both Pa and Torr.
The technical literature concerned with pressure measurement in vac
uum technology amounts to hundreds of papers, a few dozen chapters in
specialized books on vacuum technology, and only one excellent text
book published twenty years ago. In all this literature little has been
included on problems concerning particular aspects of low total pressure
measurement, such as in hostile environments of corrosive or radioactive
gases or in the presence of magnetic fields.
In writing this book we have attempted to select and organize an im
mense store of information so as to bridge the existing gap in the literature
on the measurement of low total pressure. Emphasis is placed on the
general processes and problems involved in measurement techniques as
well as on the physical principles on which vacuum gauges operate, rather
than on the detailed description of the gauges. However, where special
instruments are necessary for the determination of "pressure" or gas
density, such as pressure converters or radioactive gauges, both the de
sign and techniques involved in their use are fully described.
The text is mainly intended for both graduate students and re
search scientists who have a good general background in physics and
engineering.
Acknowledgments
I should like to thank Professor A. Roth for his invaluable help in the in-
depth reading and criticizing of substantial sections of the text. I am
grateful to Mrs. Hilda Krumbein and Miss Rhea Plottel who kindly under
took the editing of the manuscript and made many suggestions which
were useful in improving the text. For her skillful and patient preparation
of figures, I express my grateful appreciation to Mrs. Sara Saphier. The
burden of typing has been carried by Mrs. Linda Wolff to whom many
thanks are due. I am grateful to the authors, journals, publishers and
industrial establishments cited in the text for permission to reproduce
figures and tables. The excellent cooperation of Academic Press in the
preparation of this book is gratefully acknowledged.
Finally, I owe more than I can say to my wife for allowing me to work
long hours at home without demanding much of my attention and for
continuous encouragement.
XIII
List Symbols
A Area S Volume rate of flow of gas
a Cross-sectional area or thickness s Absolute sensitivity
B Magnetic field SR Relative sensitivity
C Conductance T Thermodynamic temperature
c Electrical capacitance t Time in general
P
c Average speed of gas molecules Ό.5 Half-time
cp Heat capacity (constant pressure) tm Time to build a monolayer
c Heat capacity (constant volume) u Velocity
v
D Diffusion coefficient of gas V Volume
E Electric field W Constriction of the gas flow
E Elasticity module a Modulation factor for / +
m
Ετ Rate of energy transfer per «t Thermal accomodation coefficient
unit area Polarizability of gas molecules
«8
F Force «a Attenuation coefficient
g Acceleration due to gravity ß Volume expansion coefficient
h Height y Surface tension
I Current or current density δηι Drift from the average value
r Positive ion current in the δ Molecular diameter
gas phase ε Positive charges produced per
/ Electron (emission) current electron, per cm path, per Pa at
/c Collected ion current 0°C
Ir Residual current V Viscosity
h Photo current T?EID Efficiency of electron impact de-
K Thermal conductivity sorption
κ Knudsen's number Θ Contact angle
η
k Boltzmann's constant λ Mean free path
L Leak rate λο Wave length
I Distance μ Actual mean value
3
M Molecular weight V Modulation factor for Ir
m Mass (of molecule) ξ Condensing probability
N Total number (of molecules) P Density
Nr Number of revolutions <rm Macroscopic coefficient of tangen
N Number of scattered molecules tial momentum transfer
s
n Refraction index (light) er Standard Deviation
nm Number density of molecules Te Time constant of electric cables
P Total pressure Tk Gas-kinetic time constant of a ves
P Partial pressure sel
Pv Vapor pressure TP Time constant of a measuring sys
Q Throughput tem
ßh Heat transfer Tt Time constant of a pressure trans
ßm Rate of transfer of momentum ducer
of mass motion Φ« Light yield of fluorescent light
Ro Universal gas constant Φ Molecular incidence rate
Re Electrical resistance ω Angular velocity
XV
CHAPTER 1
Units and Terminology in
Vacuum Technology
1.1 Pressure Units in Different Systems 1
1.1.1 Introduction 1
1.1.2 Expressions for Pressure 2
1.1.3 Pressure in Coherent Systems of Units 4
1.1.4 Pressure Units Not Belonging to Coherent Systems 4
1.2 The Logarithmic Representation of Pressure 7
1.2.1 Pressure Scales 7
1.2.2 Pressure Scale Analogous to the Bel Concept 9
1.2.3 Pressure Scale Analogous to the Decibel Concept 9
1.2.4 Pressure Scale Analogous to the pH Concept 10
1.3 Throughput and Conductance in the SI System 11
1.4 Terminology and Standardization in Vacuum Technology 13
1.4.1 Terms Related to Specific Vacuum Applications and
Graphic Symbols 13
1.4.2 Standardization of Interchangeable Parts, Measuring
Methods, and Equipment Performance 15
References 16
1.1 Pressure Units in Different Systems
1.1.1 Introduction
The root of the word vacuum is the Latin word vacuus (pi. vacua),
which means a space devoid of matter. Such a state, however, can never
be practically attained in a laboratory, nor even in outer space, where
there are a few hydrogen atoms per cubic centimeter at 10-14 Pa (10~16
Torr). In modern usage vacuum is considered to exist in an enclosed
space when the pressure of the gaseous environment is lower than atmo
spheric pressure or has been reduced as much as necessary to prevent the
influence of some gas on a process being carried out in that space.
1
2 1. UNITS AND TERMINOLOGY IN VACUUM TECHNOLOGY
Vacuum developed from the state of an art to a precise science in the
past four decades when scientists throughout the world began the system
atic study of the physics and chemistry of vacuum techniques. As a result
of these studies, the physical phenomena which occur in vacuum could be
explained and quantified by the kinetic theory of gases, the theory of gas
flow through impedances, and the theory of elementary gas transport.
These theories are treated in detail in many excellent reference books,
and it is assumed that the reader is familiar with them.
As a result of the evolution of vacuum science and technology, an
increasing number of physical quantities had to be considered and mea
sured, and a correct terminology had to be established. Pressure, used to
measure the degree of rarefaction (even though not correct for all situa
tions) and to calculate gas throughput and conductance of ducts and ori
fices to gas flow, was being reported in no fewer than 15 units in 1945. The
decision taken to use the pascal (newtons per square meter) belonging to
the International System of Units (SI) as a unit for pressure seemed to
make order in the chaos created by the use of so many units, but it was
not until the past decade that countries all over the world started using the
pascal or the bar (also belonging to SI).
This section is restricted primarily to a short presentation of units for
pressure, throughput, and conductance to gas flow. Nomenclature in vac
uum technique and in standardization of measuring methods and inter
changeable parts is also presented.
1.1.2 Expressions for Pressure
The pressure units presently in use in vacuum science and technology
fall into two categories. In the first, pressure units are grouped within
coherent unit systems; the second contains units that do not belong to
such systems.
Pressure P is defined as the force F which a gas or vapor exerts perpen
dicularly on an area A and is expressed by:
P = F/A (1.1)
Pressure can also be written
P = hpg (1.2)
This expression is obtained by applying the general theorem of the states
of perfect liquids to the equilibrium of a liquid column under the condi
tions of Torricelli's experiment. Here h is the height of the liquid column,
p the density of the liquid in the column, and g the acceleration due to
gravity at the location of the measurement.
3
1.1. PRESSURE UNITS IN DIFFERENT SYSTEMS
The derived unit of pressure, expressed by Eq. (1.1), is in either of the
forms
P = [m][l]-l[x]-2 (1.3)
p = mur2 (1.4)
depending on which of the base units length /, mass m, time /, or length /,
force F of a coherent system of units have been used to express P.
The derived unit of pressure in Eq. (1.2) expressed in the same units as
Eq. (1.3) does not belong to a coherent system.
Figure 1.1 illustrates the derived pressure units in coherent as well as
other systems. Some of the pressure units shown, such as pascal, Torr,
millimeters of mercury, and bar, are frequently used, others rarely, and
some (vac, gaede) never. The vac was proposed to supersede the millime
ter of mercury, which does not belong to a coherent system of units
(Florescu, 1960, 1961). The unit, having a value 1 vac = 103 dyn/cm2, was
not accepted, since it represents another name for the millibar which was
in use at the time (Volet, 1960; Bigg, 1960, 1961). The gaede was intended
to provide a smaller unit than the picotorr, supposed not to suffice for the
measurement of pressures less than 10"12 Torr (Thomas et ai, 1959).
Base units of the system Decimal (sub) multiples of pressure units
Coherent systems length (/) mass (m) time (t)
P=FA-' Unit Derived
ΓΡ1] == l4Hl'f system purneist sure The system Other systems
SI (MKS) Pa (N/m2) bar = IO"5Pa(N/m2) Gd(gaede)=l06Pa(N/m2)
CGS dyn/cm2 millibar vac-millibar
MTS PZ microbar (barye)*=f dyn/cm2
British pdt/ft2
Base units of the system
length (i) force (f) time (t)
Unit Derived
pressure
system
unit
[p].[F][i]- Technical kg f/m2 kg f/cm* tat) (^0η$'βΓβ) cm H20 (guericke f
British tb f/ft2
Other systems
Normal atmosphere (atm)
mmHg
Torr mTorr =/i.Hg=/xmHg
P= h/og in Hg
mm H2O
in H2O
ft H20
Fig. 1.1 Various units of pressure P. * French literature; ** German literature.
