Total Pressure Measurements in Vacuum Technology PDF
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Total Pressure Measurements in Vacuum Technology A. BERMAN Vacuum Calibration Laboratory Soreq Nuclear Research Centre Yavne, Israel 1985 ACADEMIC PRESS, INC. (Harcourt Brace Jovanovich, Publishers) Orlando San Diego New York London Toronto Montreal Sydney Tokyo COPYRIGHT © 1985 BY ACADEMIC PRESS, INC. ALL RIGHTS RESERVED. NO PART OF THIS PUBLICATION MAY BE REPRODUCED OR TRANSMITTED IN ANY FORM OR BY ANY MEANS, ELECTRONIC OR MECHANICAL, INCLUDING PHOTOCOPY, RECORDING, OR ANY INFORMATION STORAGE AND RETRIEVAL SYSTEM, WITHOUT PERMISSION IN WRITING FROM THE PUBLISHER. ACADEMIC PRESS, INC. Orlando, Florida 32887 United Kingdom Edition published by ACADEMIC PRESS INC. (LONDON) LTD. 24-28 Oval Road, London NW1 7DX LIBRARY OF CONGRESS CATALOGING IN PUBLICATION DATA 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.
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