VACUUM Technology

IA-1271

VACUUM TECHNOLOGY P A R T I.

A. R O T H

/

/ ' I

v, * ^ * 1

I ,

IA-127I Israel Atomic Energy Commission A. ROTH

Vacuum Technology

October 1972 582 p. This is the text of a Postgraduate Course

given by the author at the Faculty of Engineering of the Tel-Aviv University,

After an introduction dealing with the main applications and history of vacuum technology,

the course discusses relevant aspects of rarefied gas theory, and treats in detail molecular, viscous and intermediate flow through pipes of simple and complex geometry.

Further chapters deal with relevant physico-chemical phenomena (evaporation-condensation, sorptlon-desorption, permeation), pumping and measuring techniques, and special techniques used for obtaining and maintaining high vacuum (sealing techniques, leak detection). (Parts I & II).

VACUUM TECHNOLOGY

PART I

A. Roth

Israel Atomic Energy Commission October 1972

Head Vacuum Technology Dept. Soreq Nuclear Research Centre

I

CONTENTS

Page

1. Introduction 1

1.1 The vacuum 1

1.11 Artificial vacuum 1 - Vacuum ranges 4 - Composition of the gas 4

1.12 Natural vacuum , 6 Vacuum on earth 6 Vacuum in space 6

1.2 Fields of application and importance 7

1.21 Applications of vacuum techniques 7

1.22 Importance of vacuum technology 13

1.3 Main stages in the history of vacuum techniques .... 14

1.4 Li terature sources 18

2. Rarefied gas theory for vacuum technology 25

Commonly used symbols 25

2.1 Physical states of matter 27

2.2 Perfect and real gas laws 34

2. 21 Boyle' s law 34

- McLeod's gauge 35

2.22 Chales1 law 37

2.23 The general gas law 38

2.24 Molecular density 42

2.25 Equation of state of real gases 44

2.3 Motion of molecules in rarefied gases 46

2.31 Kinetic energy of molecules 46

2.32 Molecular velocities 49

2.33 Molecular incidence rate 51

2.4 Pressure and mean free path 53

2.41 Mean free path 53

2.42 Pressure units 57

II

Page

2.5 Transport phenomena in viscous state 61 2.51 Viscosity of a gas 61 2.52 Diffusion of gases 65

- Diffusion pump (principle) 66 2.6 Transport phenomena in molecular state 68

2.61 The viscous and molecular states 68 2.62 Molecular drag 70

- Time to form a monolayer 71 - Molecular pump (principle) 71 - Molecular gauge (principle) 72

2.7 Thermal diffusion and energy transport 73 2.71 Thermal transpiration 73 2.72' Thermal diffusion 74 2.73 Heat conductivity of rarefied gases 75

-. Heat conductivity in viscous state 75 - Heat conductivity in molecular state 77 - Thermal conductivity gauge (principle) 82

Appendix 83

3. Ga flow at low pressures , 87

Connonly used symbols . < 67

3.1 Flow regimes, conductance and throughput B9 3.11 Flow regimes 89

- The Reynold number 90 -. The Knudsen number 91

3.12 Conductance 92 - Parallel and series connection 94

3.13 Throughput and pumping speed 95 3.2 Viscous and turbulent flow 99

3.21 Viscous flow-conductance of an aperture 99 3.22 ViBcoua flow-conductance of a cylindrical

plpe-Polseuille'a law 103 3.23 Viscous flow-surface slip 107 3.24 Viscous flow-rectangular cross section 108 3.25 Viscous flow-annular cross section 110 3.26 Turbulent flow Ill

I l l

Page

3.3 Molecular flow 112

3.31 Molecular flow-conductance of an aperture .... 112 3.32 Molecular flow-conductance of a diaphragm .... 113 3.33 Molecular flow-long tube of constant cross

section , 115 - Circular cross section ,.....,,.,,.,.......... 117 - Rectangular cross section 117 - Triangular cross section ,,.......,.,,.,...... 118 - Annular cross section 118

3.34 Molecular flow-short tube of constant cross section 119

- Circular cross section 120 - Rectangular cross section 121 - Annular cross section 121

3.4 Conductance of combined shapes .*...-.............. 122 3.41 Molecular flo^-tapered tubes 122

- Circular cross section 124 - Rectangular cross section 125

3*42 Molecular flow-elbows 125 3.43 Molecular flow-traps 126

3.44 Molecular flow-optical baffles 133 - Conductance of baffles with straight plates .. 134 - Conductance of baffles with concentric plates 135

3.45 Molecular flow-seal interface ..* 138 3.5 Analydico-Btatistlcal calculation of conductances... 142

- Transmission probability for elbows .......... 147 - Transmission probabiliry for annular pipes 148 - Transmission probability for baffles 149

3.6 Intermediate flow 154 3.61 Knudsen * s equation , 154 3.62 The minimus conductance ...... 155 3.63 The transition pressure 157 3.64 Limits of the intermediate range 158 3.65 General equation of flow 159 3.66 The viscous-molecular intersection point ..... 160 3.67 Integrated equation of flow 164

IV

Page

3.7 Calculation of vacuum systems 16B 3.71 Sources of gas in vacuum systems 168 3.72 Pumpdown In the viscous range 170 3.73 Pumpdown in the molecular range 174 3.74 Steady state with distributed gas load 178 3.75 Nomographic calculations 181

4 Physico-chemical phenomena in vacuum techniques 187 4.1 Evaporation-condensation 187

4.11 Vapours in vacuum systemB 187 4.12 Vapour pressure and rate of evaporation 188 4.13 . Vapour pressure data 190 4.14 Cryopumping and vacuum coating 195

- Cryopumping 195 - Vacuum coating 200

4.2 Solubility and permeation 203 A.21 The permeation process 203 4.22 Permeation through vacuum envelopes 208 4.23 Consequences of permeation 211

4.3 Sorption 215 4.31 Sorption phenomena 215 4.32 Ad sorption energies 215 4.33 .Monolayer and sticking coefficients .......... 221 4.34 Adsorption isotherms 224 4.35 True surface 226 4.36 Sorption of gases by ahsorbants 229

- Sorption by activated charcoal 229 - Sorption by zeolites 231 - Sorption by silica gel 232

4.4 DeBorptlon-outgassing

V

Page

5. Production of low pressures 243 5.1 Vacuum pumpB 243

5.11 Principles of pumping 243 5.12 Parameters and classifications 244

5.2 Mechanical pumps 248 5.21 Liquid pumps 248 5.22 Piston pumps 250 5.23 Hater ring pumps . 252 5. 24 Rotating-vane pumps 253

- Gas ballast , 257 5.25 Sliding-vane pumps 261 5.26 Rotating-plunger pumps 264 5.27 Roots pumps 265 5. 28 Molecular pumps 267

5.3 Vapour pumps 269 5.31 Classification 269 5.32 Vapour ejector pumps 271 5.33 Diffusion pumps 274

- Pumping speed 274 - Ultimate pressure 276 - Roughing and backing 277 - Pump fluids 279 - Fractionating pumps , 282 - Back streaming and back-migration 283 - Characteristic curves 284

5.4 Ion pumps 286

5.41 Classification 286 5.42 Ion pumping 287 5.43 Kvapor-on pumps ? PS

- Small evapor-ion pumps 289 - Large evapor-ion pumps 290 - The Orbitron pump - 292

5.44 Sputter-ion pumps 294

VI

5.5 Sorption pumps 298 5. SI Mature of sorption pumping 296 5.52 The sorption pump 302 5.53 Multistage sorption pumping 303

5.6 Cryopumping 308 5.61 Cryopumping mechanism 308 5.62 Cryopumping arrays 316 5.63 Cryotrapping 320 5.64 Cryopumps 323 5.65 Liquid nitrogen traps 324

5.7 Gettering 328 5.71 Gettering principles 328 5-72 Flash getters , 331

5.73 Bulk and coating getters 334 5.74 Gettering capacity 336

5.8 Pumping by dilution 337 5.9 Measurement of pumping speed 333

5.91 Methods of measurement 338 5.92 Constant pressure methods 338 5.93 Constant volume methods 343 5.94 Measurement of the pumping speed of mechanical

and diffusion pumps 344

6. Measurement of low pressures 347 6.1 Classification and selection of vacuum gauges 347 6.2 Mechanical gauges 349

6.21 Bourdon gauge 349 6.22 Diaphragm gauges 349

6.3 Gauges using liquids 354 6.31 U-tube manometers 354 6.32 Inclined manometers 355 6.33 Differential manometers 356 6.34 The Dubrovln gauge , 356

VII

Page 6.35 The McLeod gauge 359

- Sensitivity and limitations 359 - Raising systems 365

Forma of McLeod gauges 367 6.4 Viscosity (molecular) gauges 371

6.41 The decrement gauge 371 6.42 The rotating molecular gauge 373 6.43 The resonance type viscosity gauge 374

6.5 Radiometer (Knudsen) gauge 374 6.6 Thermal conductivity gauges 377

6.61 Thermal conductivity and heat losses 377 6.62 Pirani gauge 379 6 ,63 The thermocouple gauge 382 6.64 The thermistor gauge , 384 6.65 Combined McLeod-Pirani gauge 385

6.7 Ionization gauges 385 6.71 The discharge tube 385 6.72 Hot-cathode ionization gauges 386

- Principles 386 " Common ionization gauge 389 - Bayard-Alpert gauge 392 - Lafferty gauge 392 - Klopfer gauge , 395

6.73 Cold-cathode ionization gauges 396 - Penning gauge 396 - The inverted magnetron gauge 397 - Redhead magnetron gauge 398

6.74 Gauges with radioactive sources 399 6.8 Calibration of vacuum gauges 401

6.81 General 401

6.82 McLeod gauge method 401

6.83 Expansion method ,... 401 6.84 Plow method 402 6.85 Dynamical method - 403

VIII

6.9 Partial pressure measurement: ....................... 404 6.91 General 404

6.92 Magnetic Reflection mass spectrometers 405 6.93 the trochoidal mass spectrometer 408 6.94 The omegatron 409

6.95 The Farvifcron 430 6.96 The quadrupola 412 6.97 Time-of-flight mass spectrometers ............ 413

7. Hifth, vacuum technoloj&y 415 7.1 Criteria for selection o materials ................ 415

7.11 General 415

7.12 Mechanical strength , 415 7.13 Permeability to gases 417 7.14 Vapour pressure and gas evolution ............ 417 7.15 Working conditions 417 7.16 Metal vessels and pipes 418 7.17 Glass vessels and pipes . 419 7.18 Elastomer and plastic pipes ....-.......... 420

7.2 Cleaning techniques 422 7.21 Cleaning of metals 422 7.22 Cleaning of glass 428 7.23 Cleaning of ceramics 429 7.24 Cleaning of rubber 430 7.25 Baking 430

7.3 Sealing techniques 430 7.31 General* classification 430 7.32 Permanent sealB 4 31

- Welded seals 431 - Brazed seals 438 - Glass-glass seals ............................ 446 - Glass-metal seals 449 - Cerssaic-metal seals 459

IX

Page 7.33 Semipermanent and demountable seals 460

- Waxed seals 461 - Adheslves (Epony) 461 - Silver chloride 474 - Ground and lapped seals 475 - Liquid seals 479

7.34 Gasket seals 481 Sealing mechanism 481

- O-ring seals 493 - Assembly and maintenance of O-ring seals 502 - Shear seals 504

Knife edge seals 505 - Guard vacuum in the seals 506

7.35 Electrical lead-throughs 508

7.36 Motion transmission 512

7.37 Material transfer into vacuum 518 - Cut-offs 518 - Stopcocks 520 - Valves 521 - Controlled leaks 526 - Vacuum locks 526

7.4 Leak detection 531

7.41 Leak rate and detection 531

7.42 Leakage measurement 537

7.43 Leak location 543

7.44 Sealed unit testing 544

7.45 Sensitive leak detection methods 547 - Halogen leak detector 547 - Detectors using vacuum gauges 548

Principle of operation 548 Single gauge detection 551 Barrier leak detection 552 Differential" leak detection 554

- Mass spectrometer leak detectors 554 - Ion pump as leak detector 555

8. Vacuum systems 559

8.1 Basic criteria of design 559

8.2 Evaluation of the gas load 560 - Leakage 562 - Out gassing 566

X

Page

- Permeation 569

- Pumping requirements 572

8.3 Vacuum chambers * 572

8.4 Pumping combinations 573

8.5 Rules for operating vacuum systems 576

- References (for Figs. 8.1 - 8.3) 579

- 1 -

1. INTRODUCTION

1.1. The vacuum

Although the Latin word vacuum means "empty", the object of vacuum techniques is far from being spaces without matter. At the

lowest pressures which can be obtained by modern pumping methods 3

there are still hundreds of molecules in each cm of evacuated apace.

According to the definition of the American Vacuum Soviety, the

term "vacuum" refers to a given space filled with gas at pressures

below atmospheric, i.e. having a density of molecules less than about 19 3

2.5 x 10 molecules/cm .

It can be concluded that the general 'term "vacuum" includes

nowadays about 17 orders of magnitude of pressures (or densities) below

that corresponding to the standard atmosphere. The lover limit of the

range 1B continuously decreasing, as the vacuum technology improves

its pumping and measuring techniques.

1.11. Artificial vacuum

Here on the earth wcuum is achieved by pumping on a vessel, the

degree of vacuum increasing as the pressure exerted by the residual

gas decreases below atmospheric* Measuring a system's absolute

pressure is the traditional way to classify the degree of vacuum.

Thus we speak of low, medium, high and ultrahigh vacuum corresponding

to regions of lower and lower pressures (Fig.1.1).

At first approach the limits of these various ranges may look as

arbitrary, since for each range there are specific kinds of pumps and

measuring instruments. In fact, each of these various vacuum ranges

correspond to a different physical situation. In order to describe

these situations it is useful to utilize the concepts of molecular

density, mean free path, and the time constant to form a monolayer,

concepts which are related to the pressure, as veil as to the kind of

gas and its temperature.

- 2 -

Molecular density, n(cm~*) L o EL 2L S_

I I I I I I I I I I ' 1 ' I I 1

760

S

S-

S K S * S - " > Molecular incidence rate.Kcnr3***)

5 -

%

1 V - o , -0 I -I 61 q ,-, 2 6,- _ z

- o , * r

3

5?

-1

T T T X X

*

Mean free path Mem) O d O O O Oi Oi

These tarns will be mathematically analyzed in further **h."pters.

For the sake of this introduction, they can be defined as;

- Molecular density Is the average number of molecules per unit

volume.

- Mean free path is the average distance that a molecule travels in

a gas between two successive collisions with other molecules of

that gas.

- Time to form a monolayer is the time required far a freshly cleaved

surface to he covered by a layer of the gas of one molecule

thicknesB. This time is given by the ratio between, the number Ik

of molecules required to form a compact monolayer (about 3 x 10 reolec/(cra ) and the molecular incidence rate (at which molecules

strike a surface).

Tallies 1 .1 , and 1.2 l i s t values of these terms.

TftBUi: 1.1.Aiotecutar Incidrnrt Rair uiut Time To Farm a Mcnvlaytr lor Air el 2 5 ' C

FrnjKiire, torr

MotecitlurilL'nsity. Mi-nn fn-f-

V i-in

Molcrnlnr ini'iilcMivp n i l r v l \

molrc-i]l['/i:m= s>t

Timn to ( n r m l

mcnnlnypr, /.KM.

2.48 X 10'" (1.61) X W" 3.14 X 10" tea x w* I 3.24 X ID" RJXI\ ID* 4.13 X 10" 3.00 X 10"* ID"* 3.24 X 10" JUSX1W 4.13 X 10" 2,00X10* i n * 3.24 X 10'" 5JM X 10* 4.13 X 10" a.on x io*

3.24 X 10' ftflnxiw 4.13 X 10" 2.0ft X I P 10 " 32* X 10' .1 rei y in* 4.13 v 10' M U X 10* IO- 1" 354 X 10' js .mx i " 4.13 X I0 3 2JOO y W

TAILE IZMoletuhr Incidrner Half anil Timr To Farm n Hondaytr for Same Common Hairs at :':i f; unit 10' Tarr

CM Mnlfci i l i i r weight, HI Kraut/moti-

Molrctihir

I.CDl

3 .7JXIO '

M w n f rw It t l l l ,

Mn lmi ln r

i i i u lm iWr in * j r r

1.13 X 1ft"

Timn lo funn I

monolayer f . ( re

Air 29

Molrctihir

I.CDl

3 .7JXIO '

M w n f rw It t l l l ,

Mn lmi ln r

i i i u lm iWr in * j r r

1.13 X 1ft" IJMXlO" 2R 3.7fi r>.m 4.10 i.m

a 32 3fi1 fl.41) SUB 222 i u 2 2.75 na i 1B.64 0.975 l b 4 2.IS M.7* 11. t l 21ft Hrf) . . 18 im 337 S31 1.01 CTO, 44 45Ti 8JM sax 1J A 40 3.67 M l 3 m 2,13

- 4 -

By analysing the ranges shown on Fig.1.1 and the values of the

terms listed In Tables 1.1 and 1.2, It results that the physical

situation* characterizing the various vacuum ranees are;

Low (and Medium) vacuum - the number of molecules of the gas

phase Is large compared to that covering the surfaces, thus in this

range the pumping la directed towards rarefying the existing gas * - 2

phase. The range extends from atmospheric pressure to about 10 Torr.

High vacuum - the gas molecules in the system are located

principally on surfaces, and the mean free path equals ? is greater

than the pertinent dimensions of the enclosure. Therefore the

punping consists In evacuating or capturing the molecules leaving the

surfaces and Individually reaching (molecular flow) the pump. This

is the range where particles can travel %n the vacuum enclosure without

colliding to other particles. The range extends fron about 10~ to

10" 7 Torr.

ultra-high, vacuum - the time to form a nonalayer is eqttijfr or longer than the usual time for laboratory measurments, thus "clean1'

surfaces can be prepared and their properties can be determined before

tha adsorbed gas layer is formed. -7 -14

This vacuum range extends from about 10 Torr to 10 Clover

limit decreasing with progress of technology)*

Composition of the gas. - HTillc the total pr ssure in a vacuum

chamber decreases, the composition of the gas phase changes as well.

In the low vacuum range the composition of the gas mainly reasemblea

to that of the atmosphere (Table 1.3). In the high vacuum range the

composition changes continuously, towards one which contains 80 - 90

percent water vapour. The water molecules come' from the surfaces.

As pumping la continued and heating is applied,the carbon monoxide

content Increases, in the ultra-high vacuum range hydrogen is the

dominant component (Table 1.3), coming mostly from the bulk of the

materials (permeation).

Table l[.3. - Gas compositions

Component: Atmosphere (^ -) ultra-hinh vacuum

Component: Percent by volume

Partial pressure Torr

Partial pressure '

(2) T o r r (3)

N 2 78.OS 5.95 x 1 02 2 x I D ' 1 1 ' -

2 20.95 1.59 x 1 0 2 3 x 1 0 " 1 2 -

Ar 0.93 7.05 6 x 1 0 " 1 2 ;

1 co2 0.033 2.5 x 10" 1 6.5 x I 0 " 1 1 | 6 x 10" 1 Z

Ne 1.8 x 10"? 1.4 x 10" 2 5.2 x l O " 1 1 | I

He 5.24 s l O * 4 x K f 3 3.6 x 10" 1 J

Kr 1.1 x 10" 4 8.4 ,x 10" 4 i H 2 5.0 x 10"

5 3.8 x 10" 4 1.79 x 10" 9 ; 2 x i o ~ u

i X e 8.7 x 10" 6 6.6 x 10" 5

~" i

V 1.57 1.19 x 1 0 1 1.25 x lO^"10 j 9 x 1 0 " 1 3

" 4 2 x lO"4 1.5 x 10 " 3 -11 7.1 x 10 \ , 3 x l a " "

3 7 x 10"6' 5 .3 .x 10 " 5 -. ' N20 5 x 10" 5 3.8 x 10" 4 < -

CO - -' 1.4 x 1 0 - 1 0 9 x 1 0- 1 2

(1) F.J. NOrton, IraoB. 2nd Internet. Vacuum Congress, Pergamon Pres

- 6 -

1.12. *aturl vacuum

'Vacuum on urth

t Katun uses "low vacuus technique*" in some of the function* of

U f a of animals, but no natural high vacuum is known on earth. Some

of these "applications" are very vital* aa our own respiration, others

like the vacuum action of mosqultos, are rather bothering.

Buman beings are pumping to about 740 Torr during their

respiration, and may achieve pressures as low as 300 Torr by suction.

The octopus la able to achieve pressures of about 100 Torr.

Vacuum in space

As the pressure of 760 Torr at sea level is a result of the

"atmospheric column", the pressure decreases with the altitude. Up

to 100 km altitude (troposphere and stratosphere) the pressure

decreases quite regularly by a factor of 10 for each increase in . 3

altitude of 15 km, which results in a pressure of 10 Torr at about

90 km altitude. At higher altitudes high vacuum exists.

The ionosphere (100 - 400 km) contains a large number of ionized atoms, and its pressure decreases only by a factor of 10 every

100 - 200 km. This decrease results in a pressure of about 10~ Torr

at an altitude of 100 km. According to Fig.1.2 above 400 km, ultra

high vacuum conditions exist.

Above this altitude the pressure decreases at an even slower

rate, thus at 10000 km a pressure of about 10 Torr exists.

Since the average spacecraft, travels at a velocity considerably

In excess of that of the average gas molecule, the pressures measured

on spacecrafts is actually determined by the spacecraft velocity and

gas particle concentration, Thus the diagram (Fig.1.2) of the high altitude atmosphere is expressed in concentration (density) units.

The gas molecule concentration (density) is estimated to fall in the shaded area of Tig.1.2, since the density varies with the

time of day and the amount of solar activity. At an altitude below

200 km, the atmosphere Is essentially air. Between 200 - 1000 km the

Particle Conwnlfofion, porHefes/em'

Figure 1.2. - Characteristics of high-altitude atmosphere

surrounding the Earth, to an altitude at 10 5 kllonetres.

gas is principally atomic nitrogen and oxygen, which may be largely

ionized at periods oE solar maxima. There is same evidence of an

appreciable amount of helium at shout 700 - 1000 km altitude.

Above an altitude of 1500 km, the p,as consist a of neutral atomic

hydrogen, protons and electrons.

1,2, Fields of application and Importance

1.21. Applications of vacuum techniques

The large variety ot applications of vacuum can be classified

either according to the physical situation achieved by vacuum technology

(labia 1.4) or according to the f ields (Industries) where th aaellcatioa beloaaa (Fig. 1 .3) .

labia 1.4. - appllcatloae of vacuus Technique

Ifcyaical Objective Applications

fcchieva pressure diffai

Boldins, L l f t lm Transport (pneuaatic, cleaners,

f i l ter ing) Foralng

tove active itaospherlc Eonetituents

Low aolacular

density

Laapa (incandescent- , fluorescent, alactrlc tubas)

Halting, sintering Packaging Encapsulation,' Leak'detection

taaowa occluded at disaolvad

Drying, dehydration, concentration, Freeze drying, Lyophyllsation, Degassing Eaprsgnation

mergy trans far Thermal insulation Electrical insulation Vacuus alcrobalance Space sinulstion

Large

aaan free path

kvold

collisions

Electron tubes, cathode ray, television, photocells, pbotoaultlpliers. X-ray Accelerators, storage rings, ass speetroaatera, Isotope ssparstors Electron adcroscopss Electron beam welding, nesting Coating (evaporation, sputtsring) Molecular distil1stion

Long aooolayar foraation

tiaa

ilean surfaces

Friction, adhesion, ealsalon atudies^Hstariala testing for space.

pnic*TioHs or VACUUM TICHNIOJI

f EVUWItW J f fBM.*!"" ) (

- 10 -

Obviously ach of tha applications of vacuus techosjlogy utilises on* or Mir* physical situations obtained by rarefying the gas. Some of

them achieve products or facllltlss In which the vacuum agists

during all their lif (lamps, tubes, accelerators, ate), others -only

use vacuum technology as a step la the production, the final product

being u**d ia atmospheric conditions (vacuum coating, drying,

taeteammtlon., etc.).

According to the physical situations created by vacuum the

various applications may be resumed (Table. 1,4) as follows:

The pressure difference achieved by evacuating a vessel can

realise forces on the walls up to 1 kg/cm . These forces ass us*d'--*. y

fox holdine, or lifting solids, for the transport of solids or liquids,

emd for forming (shaping) objects. Plastic or rubber cups applied on surfaces so that tha air be

eacdsded from the cup* can hold small objects. The same principle is used to fasten tools on work tables (chucks). Here the middle part of

a larger rubber membrane forming the base of the Cool is mechanically

pulled away, to form a vacuum enclosure with its periphery sitting on

the table.

By using sniffers which are evacuated after being placed with..

their mouth on the object to be lifted, very small objects can be precisely lifted and trensfered (e.g. filaments in the mass production

of leaps). Relatively large (flat) objectB can be lifted (platee, cars) if the mouth of tha lifting cup is large, 5 - 7 tons can be

lifted with a mouth of 1 m .

The vacuum cleaner is the simplest exanpLe of a widely used

vacuum transport system. Vacuum cleaners are usually able to achieve 2

pressures of 600 Torr, thus to euck objects of tens of grans/cm , Vacuum ttansport systems foe grains and powders are based on features

similar to vacuum cleaners.

The pneumatic transport systems connecting post officii in Paris

or London, are examples of very lsrge vacuum transport facilities.

- 11 -

That of Pari* has a length of about 300 km, of double, 60 or 80 mm

bore tubes; they are using a pressure of 450 Torr for the transport

from post offices towards pumping stations, and an over pressure

of C.B atn for transport in the opposite direction. The transport

cylinders containing the letters move at speeds of 8 - 10 m/s.

It is interesting to mention that pneumatic trains working

on this principle were in function at Dublin (Ireland) and Saint-Germain.

(France) in the 1840 - 1860 rears.

Vacuum Is commonly used in laboratory and chemical industry to

accelerate filtering speed. The pressure difference obtained by

evacuation is used in the vacuum forming (molding) of plastics.

Tha necessity of removing the chemically active constituents

of the atmosphere (oxygen, water vapour) by vacuum pumping appeared

together with the invention of the incandescent lamps. In order to

avoid oxidation of the filament heated at very high tmperatures, it

must be in an inert atmosphere. This atmosphere is constituted either

by a high vacuum (about 10 - Torr), or by an in&rt gas filled into

the lamp after its evacuation at a high vacuum.

The possibility of evacuating large chambers at a high vacuum

level is used in vacuum metallurgy to protect active metals from

oxidation during melting, casting, sintering, etc.

Vacuum packaging of food, or materials sensitive to reactions

with atmospheric components is used at a large scale in modern industry,

the level of evacuation being usually in the low vacuum rang*. Vacuum

encapsulation of sensitive devices (translators, capacitors, etc)

is oftan carried out at high vacuum levels. The leak testing

techniques using high sensitivity detectors can control the tightness

of tha encapsulation.

Vacuum technology is uaad to remove humidity from food, chemicals,

pharmaceutic products, concrete, etc., and occluded (dissolved) gas from

oils, plastics, etc. The fabrication of fruit juice, and concentrated milk* ere examples of large scale productions based on vacuum

concentration* This process does not require extensive heating in

- 12 -

order to evaporate th* uttr or solvents contained in th* product* Sy using tb vacuoe drying proceaa In conjunction with cooling,

the protects are first frozen, tht water being than removed by

sublisetion. This a the beale feature of fre*s* dry lag. In the,

product! of freese drying th* final watar content la vary low,

chesdcel cbangaa ar* slnlsal, volatile conatltuanta ara essentially

kept In. th product (e.g. Instant toffee), coagulation la avoided (blood plasm) and storage propsrtlas ar* excellent.

Vacuus impregnation process conalat In removing tbe occludad

humidity ox gaaee, and filling their plaea by another materiel. Although th* comsonly known Impregnation processes arc those used to

improve tba dislsctrlc propartias of insulations (aotor windings, capacitors, cables), acuum impregnation techniques ara also used to ineraasa strength, or dacraaaa combustibility of textiles, paper,

wood, etc.

High vacuus is s thsrsal and alactrical insulant. Ibis property

ia used in th* Dewer flaaka for tha atoraga of liquid air, nitrogen,

helius, etc, as well aa in the "thtrsos flaaks11 used to keep cool

drink or food. Both are double-walled flasks, the space between the

walla being evacuated at high vacuus.

The electrical insulation properties of high vacuum are used

in vacuus switches, as well as in high voltage devices (accelerators, tubes).

As th* snsrgy transfer in outer apace ia similar to that which

occurs In ultrs-hlgh vacuumrSpscs lisulatlon became one of th*

sophltlcatsd sppllcstlons of vacuus technology. Space simulator

chasbers extend to volumes of sore than 1000 m ,and eose of than are

evacuated to the lowest pressures which can be achieved today*

Vacuus slcrobalanc* techniques us* high and ultra-high vacuus

to avoid any "background" provening frost ens surrounding gas.

Th* large seen free paths existing in high vacuus, is used

to svold collisions between molecules, electrons. Ions in electron

- 13 -

tubes, photocells, cathode ray tubes, X-ray tubes, accelerators, mass

spectrometers, electron microscopes, etc. This same property is used

in vacuum coating plants where the coating material evaporated from

its source reaches the substrate being coated, by travelling in

straight lines, without collisions, in this vay thin films are

deposited for a large number of optical, research, or ornamental

uses.

Molecular distillation is another field where high vacuum is used

in order co obtain very pure fractions by evaporating and condensing

the molecules without any collisions to other gas molecules.

Ultra-high vacuum permits to study the real properties of

surfaces (friction, adhesion, emission, etc) since at theee low

pressures the tines of formation of a monolayer are sufficiently long

(hours, Fig.1.1).

1.22. Importance of vacuum technology

The list of applications of vacuum technology include a large

number of items which becaae symbols of the progress. From this

point of view the importance of vacuum technology is evident.

The size of the field can be shown by the number of persons

(scientists, engineers, technicians and workers) involved in the world

in the various aspects of vacuum technology. This number was in 1965

over one million, receiving a total of salaries of about 3 milliard

dollara. At that time it was evaluated that more than 4 milliard

lamps and 1 milliard electron tubes were produced per year.

The number of persona active in the progress of vacuum science

and technology can be evaluated to tens of thousands, according to

the number of members of 1UVSTA. I.U.V.S.T.A. is the International

Union for Vacuum Science, Techniques and Applications, which includes

(in 1970) 18 National Vacuum Societies.

The number of commercial firms producing general and specialised

vacuum equipment ranges to about 100, (companies ranging from 100 to

thousands of persons).

- 14 -

1.3. Main stsE in the history of vecoum techniques

It can bs considered that ths history of vacuum techniques

begins In 1643, whan Torrtcalll discovered tha vacuus which ii

produced at tba top of a column of mercury Whan a long tuba aaalad

AC ona and la filled with Bcrcury and inverted in a trough

containing Bg.

Tha pioneer period A vacuum techniques continue* up to tha

invention of the electric leap. In this period important theoretical

and experimental scientific progress is achieved In tha fundamental*

of gas laws (Boyle-Maxlotte, Charles-Gar Lusac, Bernoulli;' Avogadro, Maxwell, Bolt*mann,etc). The first progress in the practical use of vacuus m s connected to the mechanical effect* which can be achieved

by using the pressure difference between vacuum and atmosphere. Tha

classic experiment of Guerieke (1654) showing that the two hemispheres of an 119 cm "evacuated" ball cannot be separated by pulling with

2 x 1 horses, demonstrated the atmospheric forces.

The application of this knowledge, to drive railway cars (Dublin) was used only e few years, but the pneumatic-vacuum transport systems

begun in 1850 - 1860 in London and Patio are still in use {slighthy modernised!).

The development of the incandescent lamp (Edison, 1879) was also a consequence of the pumping system Invented during previous yeers

(loepler, Sprengel see Table 1.5). The He Leod gauge (1874) gave for the first time the possibility of measuring low presaures. The

Incandescent lamp has shown the ussfulness of low molecular dsnsitlea

(removel of the active etmoapherlc constituents), the cathode ray tubs of Crookes (1879) was the first Application, of the Increased mean free path, while the Dewar flask (1B93) constitutea the firat application of vacuum thermal insulation.

The invention of the vacuum diodes (1902) and trlode (1907), and of tha tungsten filament (1909), bsgln the development of the electron tubes, sad brought that of the Incandescent lamps to a maturity

- 15 -

(Langmuir, 1315). The "quality" of the vacuus used in the production

of the incandescent lamps revealed to be insufficient in the new

field of electron tubes, which brought to research and development

work cm pumping and measurement.

The Piranl Gauge (1906) t Gaede (1915) and Langmuir (1916);

diffusion pumps, and the hoc cathode ionization gauge (1916), opened

the possibilities of the high vacuus technology. The development of

high vacuum technology continued up to the second world war, in the

years 1935 - 1936 receiving three new items: the gas ballast pumps,

tbo oil diffusion pump, and the Penning cold cathode ionization gauge,

items which together with the Pirani gauge remained up toaow.tne-

usual components of most vacuums systems.

After 1940 vacuum technology had a very large development in

the direction of equipment for nuclear research (cyclotron, isotope

separation, etc,), vacuum metallurgy, vacuum coating, freeze? drying,

etc.

Up to 1950 the usual vacuum range extended to 10 - 10 Torr,

Perhaps lower pressures were obtained also before-, but no possibility

existed for measuring lower pressures. The Bayard-Alpert gaug* Q&50)

opened the way to measure lower pressures, in the range called later

ultra-high vacuum. The ion-pumps produced after 1953, permitted to

obtain very low pressures, and the so called " clean vacuum".

In the last decade, the space research gave a new quantitative'

jump to vacuum techniques, by tie numerous vacuum problems which bad to be solved for space missions.

- 16 -

Table 1.5. - Stages in the history of vacuum techniques.

Tnr Author Work (Discovery)

1643 Evangelise* lorricelli Vacuus in the 760 am aarcur column

1650 Blaise Pascal Variation of Hg column with altitude

1654 Otto von Guerlck* Vacuum plato-pumpe; Magdeburg hemispheres

1662 1679

lobart Boyle M a s Kariotte

Pressure-volume law of idecl gasu

1775 A.t. Lavoisier Atmospheric air: * mlxtttrs of nitrogen and oxygen

1783 Danial Bernoulli Kinetic theory of gases

1802 J.A, Charles J. -Gay-Lussac

Volume temperature lav of gaass

1810 Kedhurst Propoas first vacuus post lines

1811 Amedeo Avogadro Constant molecular density f gases

1843 Clagg and Saauda First vacuusi railways (Dublin)

1850 Gelsslar and Toepler Mercury column vacuusi pump

1859 J.K. Maxwell Gas nolecul* velocity laws

1865 Sprengal Mercury drop vacuum pump

1874 H. HcLaod Compression, vacuum gsugs

1879 T.A. Edison 'Carbon filament, incandescent lamp

1879 W. Crookaa Cathode ray tube

- 17 -

Table 1.5 (continued)

] 1881 J. Van der Waala Equation of state of reel gases

1893 Janes Dewar Vacuum insulated flask

1895 Wilhelm Roentgen X-raya

1902 A. Fleming Vacuum diode

1904 Arthur Wehnelt Oxyde-coated cathode

1905 Wolfgang Gaede Rotary vacuum pump

1906 Maixello FIrani Thermal conductivity vacuum gauge

1907 Lae de Forest Vacuum triode

1909 W.D. Coolidge Powder metallurgy of tungsten Tungsten filament lamp

1909 M. Knudsen Molecular lo? of gaaes

1913 M. Gaede Molecular vacuum pump

L915 W.D. Coolidge x-ray tube

1915 W, Gaede Diffusion pump

1915 Irving Langmilr Gas filled incandescent lamp

1915 Saul Dushuan The kenotron

1916 Irving Langmuir Condensation pump

1916 O.E. Buckley Hat cathode ionisation gauge

1923 F. Holwack Molecular pump

1935 W. Gaede Gas-ballast pump

1936 Kenneth Hickman Oil diffusion pump

1937 P.M. Penning Cold cathode ionisation gauge

1950 R.T, Bayard and D. Alpart

Ultra-high vacuum gauge

1953 H.J. Schwartz, R.G. Herb, etal

Ion pumps

- 18 -

1.4. friforaturfc sources.

Vacuum Technology is baaed today on a very extensive literature

of books, journals and conference transaction dealing exclusively with the various aspects of the subject. The list vhich follows gives the names of the most inoortant literature sources currently- used in

recent yean.

The list dees not include the books appeared between 1920-19+0,

which have no aore practical interest, their content bain? republished

in the nor? recent works listed.

?or an historical interest, it must he mentioned that the first

back published on vacuum was in latin :

Ottonis de Suericke: Experienta Nova Magdeturgica de Vacuo Spatio,

J. Jansson, Amsterdam, 1672

which was republished in German, by VDI - Verlag, Dfisseldorf in 1968.

As regarding the journal miblications, besides the journals listed which are exclusively dedicated to vacuum urobleqis, a large number of

papers on vacuum techniques were and are published also in: British

Journal of Applied Physics, Experimentelle Technik der Physik, Japan

Journal of Applied Physicsr Journal of Applied Physics (USA)Journal of Scientific Instruments* Materials Evaluation, Nuclear Instruments and

Methods, Review of Scientific Instruments, Research and Development*

SQL Review ant1 Solid State Technology.

Abstracts of rewires published on subjects of vacuum technology are currently listed in HASA - Scientific and Technical Aerospace

Seporta, a miblicstion *Mch anpeara twice a month.

- 19 -

Publications dedicated exclusively to

Vacuum Techniques

1 Jc Strong, Procedures in Experimental Physics, Prentice-Ball, New York, 1936, p.93-187,

2. CH.Bachman, Techniques in Experimental Electronics, J. Wiley, New York, 1948, p. 1-67, 89-140,

3. A. Guthrie and R.K.Wakerling, Vacuum Equipment and Techniques, Mc Graw-Hill, New York, 1949*

4. E. Jaekel, Kleinste Dracke, Ifare Measung und Erzeugung, Springer, Berlin, 1950, 302 p.

5. H. Auwartar, Ergebnisae der Hocbvakuumtechnik und der Phya$k dunner Schichten, Wisserschaftliche Verl, Stuttgart 1957, 282p

6. fi. CimmpeiXi- ulementa de Technique du Vide, Dunod, Paria, 1958, 214p=

7. K. yorand, Traite Pratitme de Technique du Vide, Soc. G.B.P., Paris," 1958, 347p.

6. R.F. Buns hah, Vacuum Metallurgy, Eeinhold, New York, 1958, 472p.

9. 3.C. MBnch, Neues und Bewahrtes ana der HochvakuuiatechniJc, VEB Knapp, Halle, 1959-

lO.W.H.Kohl, Materiala and Techniques for Electron Tubes, Ksinhold, New York, I960, 638p.

l l . J .V. Cable, Vacuum Proceasing in Ifetalworking, teinhold, Hew Tork, I960, 202p.

- 20 -

12. L. Holland, Vacuus Dtpoaition of Thin Pilao, Chapaan 4 Ball* London, I960, 542p.

13. H. Pirani and J . Tarvood, Principles of Vacuum Englneerinj?, Chapman A Hall, London, 1961, 578p.

14. J . Dalafoese and G. Bongodin, Les Calculs de la Technique du Vide, La Vide, 1961, 107p.

15* AJI. Turnbull, R.S. Barton and J.C. Riviere, An Introduction to Vacuua Technique, G. lennea, London, 1962, 19Pp.

16. S. Dosnaen, Scientif ic Foundations of Vacuum Technique, J . Wiley, HewTork 2nd >d.,1962, 806p.

17. H.L Bscnbach, Piaktikum der Hochvakuumtechnik, Akadeaiache Verlag, Leipzig, 1962, 243p.

IB. 3 . Eucb, Einfannmg in die Ailgeaeine Vakuuiitechnilc, Viasenschaftlicbe Verlag, Stuttgart, 1962, 207p.

19. G.A. Boutry, Physique Appliqnee aux Industries du Vide et de 1' Electronique, Kaason, Paris, 1962,388p.

20. A.B, Barrington, High Vacuus Engineering, Frantlce-Hall, Bnglewuod Cl i f fs , N.J.,1963.212p.

21. H.A. Steinherz, Handbook of HiA. Vacuum Engineering, Heinhold, Bav York, I965,358p.

22. K.tf. Hoberts and T.A. Vanierslice, Dltra-high Vacuum and i t s Applications, Prentice-Hall, Enfflewood Cl i f fs , H.J., 1963.

23. J2,A, Trendelenburg, Dltrahoenvakuum, Verl. Braun, KarlBruhe, 19

- 21

26. S.V. Spiuks, Vacuum Technology, Chapman 4 Hal l , London, 1963.

27. J.H. Leek, Pressure Measurement in vacuum Systems, 2nd Ed, Chapman ft Hall, London, 1964.

28. V. Pupr>, Vakuumtachnit, I . Grundlagen(l962)lC9D, EE. Anirendungen (I964),3l2p. Verlag K. Thiemig, Wlnchen.

29- G. Lewin, fundamentals of Vacuum Science and Technology, He Graw-Hill, New York, 1965, 248p.

30. P. Roaebury, Handbook of Electron Tube and Vacuum Techniques, Addison-Wesley, Heading USA, 1965,597n.

31. V . F , Brunner and T.H. Batzer, Prac t ica l Vacuum Techniauea, fieinhold, New York, 1965,197D.

32. K. Wutz, Theoiie und Praxis der Vakuumtechnik, P. Vieweg 4 Sohn, Braunschweig, 1965.439D.

33. CM, Van Atta, Vacuum Science and Engineering. Kc Graw-Hill, Hew York, 1 9 6 5 . 4 5 9 D .

34. B.D. Power, High. Vacuum Punning Equipment, Chapman ft Hall, London, 1966,412p.

35. E. Diels and R.J. Jaeckel , Leybold Vacuum Handbook, Pergamon Press, Oxford, 1966,360p,

36. A. Both, Vacuum Sealing Techniques, Pergamon Press, Oxford, 1966,845n.

37. D.J. Santeler , e t a l , Vacuum Technology and Space Simulation, NASA, Washington, 1966,305p.

38. J* Yarwood, High Vacuum Technique, 4th Ed, Chapman 4 Hal l , London, 1967.274p.

39. L. Ward and J . p . Bunn, Introduotion. to the Theory and Practice of High Vacuum Technology. Butterwortho, London, 1967,216p.

- 22 -

40. V.B. Kohl, Handbook of Materials and Techniques for Vacuum Devices. Keinhold, leu Tork, 1967,623D.

41. A.E. Beck (Editor}, Handbook of Vacuum Physics. Tol. I . Bases and Vacua

- 23 -

I I I . Conferegoq Trspaactions

1. Vacuum Bymposxuoi Transactions) of the Conferences held hy the American Vacuum Society, Volumes Edited each yeex between 1954-1963, 10 volumes, Pergaacn Press, Oxford.

2. Advances in Vacuum Science and Technology, Proceeding? of the Fi rs t International Congress on Vacuum Technology, held Samur (Belgium) 10-13 June 1958. 2 volumes, Pergsmon Preea, Oxford,824D.

3 . Transactions of the Second International Congress on Vacuum Science and Technology, held Washington, 16-19 Oct. 196*1 # 2 volumes, Pergamon Press, Oxford, 1351n.

4-. Advances in Vacuum Science and Technology, Proceedings of the Third Internat ional Congress on Vacuum Techniques, held S tu t tgar t , 28 June-2 July 1965, 4 volumes, Pergaaon Press, Oiford, 929D.

5 . Proceedings of the Fourth Internat ional Vacuum. Congress, held Hanchester, 17-20 Anr.1968, 2 volumes, Inst , of Physics, London, 827*.

6. Transactions of the Vacuum Metallurgy Conferences, Edited by the American Vacuum Society, each year between 1962-1968, 7 voluoes.

7. Internat ional SymD. on Hesidual Gases in Electron Tubes and Related Vacuum Systems, held Rome, 14-17 March 1967, Suopl. to Huovo Cimento, Bologna ( I ta ly) 2 volumes, 619p,

8. Vacuum Microbalance Techniques, Proceedings of Conferences held each year between 1960-1966, 6 volumes, Plenum Press, NBW Tork.

9. DeurLeme Colloque International sur lea Amplications das Techniques du Vide a 1'Industrie des Seaiconducteura, Pa r i s , 5-8 O^t. 1966., 151p.

10, Colloque Internat ional aur l'TJltra-Vide, Par i s , 28-30 Jun, 1967il95p.

11. Congrea Internat ional sur lea Applications des Techniques du Vide a la Ketallurgie, Strasbourg, 13-17 HOT.,1967, 280p.

- 24 -

12. I* ftelmologi* d l'Bltra-Vide at das SasaM Praaaioas, YersalllaB, 20-23 May, 1969.307p.

15. Colloatte International Vide et Froid, Grenoble, 1-5 Dec. 19S9,226p.

14. Congrea International sur les Couches Mincea, Cannea, 5-10 Oct. 1970, 664p.

- 25 -

2 . RARFJIEU) GAS THEORT FOR VACUUM IECHHOLOCY

C o m o n l y used symbols . -A re* c

p s p e c i f i c beat at constant pressure c s p e c i f i c heat at constant volume D d i m e t e r of aperture or tube E energy e charge of the e l ec t ron F force h height (of a column of l iquid) k Boltrmann constant K heat conductivity L length

a mass of molecule H molecular weight n number of molecules per unit volume N t o t a l ninber of molecules

\ number of molecules per s o l e P pressure

q gas flow (molecules per second) r radius R general gas constant R 0 gas constant per mole t time T absolute temperature V volume V v e l o c i t y w s p e c i f i c mass (per s e c , per cm )

(alpha) - accomodation c o e f f i c i e n t ( t o u ) - ra t io C /C

P v

- 26 -

it (eta) - vlacoalty l (laabda) - Man f raa path A (lambda) - f n t solacular beat conductivity C (xi) - molecular diaaetar p (rfao) - density, maaa par unit voltaM T (tau) - (tlaw] period 4 Cpbi) - Molecular incidence rate.

- 27 -

2.1. Physical states of matter

A collection of molecules can occur either In tbe solid, liquid

or gaseous Btate, depending on the strength of the lntermolecular

forces and the average kinetic energy pec iulecule (temperature).

The state in which molecules axe most independent f r o each

other Is called an ideal or perfect gas. This is a theoretical concept

which corresponds to the assumptions that: a) the molecules are minute

spheres; b) their volume la very small compared with that actually

occupied by the gas; c) the molecules do not exert forces upon each

other; d) they travel along rectilinear paths in a perfectly random

cushion; e) the molecules make perfectly elastic collisions.

Some real gases, such as hydrogen, nitrogen, oxygen, argon, helium,

krypton, neon, xenon, approximate closely at atmospheric pressures the

behavior assumed for ideal gases. At lover pressures (vacuum) many

more gases approach the ideal gases.

Real gaseB, unlike ideal ones, have internelecular forces. At

pressures and temperatures where the molecules of the gas are brought

close to each other they will begin to form new structures, which

will have properties very different from those of the gas. When

these new structures begin to form, the gas is aaid to be liquifying.

Figure 2.1 shows a plot of pressure versus volume for different

temperatures of a raal gas (e.g. carbon dioxide). Curves A and B ,

fox which the temperatures are high, are hyperbolas conforming to

Boyle's law, describing a behavior assumed for ideal gasea. At

temperature T_ , curve C is no longer completely hyperbolic.

A small hump has formed at point P. At still lower temperatures*

curves D and E show complete departure from the hyperbola of ideal

gases; a flat plateau appears. When the system has the pressure and

volume associated with points L or H , the material (CO.) is in

the gaseous state. Along the plateau N-0 the temperature and pressure

- 28 -

Tig,2,1. - Variation of pressure with volume in a real gas at various temperatures. T, > T > T, > T A > T c

of tb system axe both constant while the volume changes. At N the

material ia in a gaseous atate, while at 0 it la a liquid. At K

a fraction of the system is liquid. It is important to note that each

curve (Fig,2.1) has only one plateau, that is, there is only one

pressure for a given temperature, et which the gas will liquefy. At

temperatures higher than that of curve C , there is no pressure at

which the gas can be liquefied. Point P ou curve C la called the

critical point. Table 2.1 lists these values for some gaaes.

From Fig-2.1 it is clear that at higher pressures the liquefaction

process takes place at higher temperatures. The temperature at which

a gas liqueflea ia called the boiling point and depends on the pressure

of Che syscen. For example to boll at 20"C, water r*quire* tbmc the pressure of Che surrounding be 17.5A Torr, mercury requires 1.2 x 10 Torr, while C0 requ i res 42959 Torr (56.5 At) .

Xable 2.1 -SOME PHYSICAL PROPERTIES OF SUBSTANCES AT LOW T E M P H R A T U R E S

J W I A ^ I W C rt^K*. C t i'ubttancr r

"aal'

fud i l c ? s

lfa pressure exerted by the molecules on Che surrounding atmosphere

and liquid Is celled the vapour pressure. The vapour pressure depends

oa the temperature of the material.

Ilu boiling point of a liquid is that teaperature at which the

Tapour pressure of the liquid is equal to the surrounding pressure.

If the vapour pressure is plotted vs. the temperaturek curves as that

in Fig.2.2 are obtained. At the right side (below) of these

Fif. 2.2, ~ TI i e vapour - pressure curve for water.

curves vapour exists, while at the left side {above) the curve,

liquid exists. Table 2.2 lists the vapour pressures of water and

mercury ac various temperatures*

If (Fig.2.1) the liquid is conpressed below point Q , a second plateau appears (Fig.2.3); it is here chat the liquid undergoes, a change of phase, Into a solid.

Table J.2 VAFtlUK PRISNUKfi I1F W * l l K (((1 ) MI Ml KCVRY (lO(T>

IH3 1.4*10-" U S : I O - 3 ; / JO 31.82 2.8 v | 0 - =

150 7 . 4 - M O 1 " ' 40 55.32 fi.1^10-3

MO 2.9- ' 10->" Ml 92.51 1.27 1 0 - =

-- 130 fc.8 - 1 0 - ' J | 6( 149.3 2 . 5 2 * 1 0 - -

- 121) 1.1.1:- 10 J ; 233.7 4.82 M O - :

- no 1.25 * t 0 - s no 3iS.I B.Sif *.-(- =

mo 1 . 1 : 1 0 - 2.39 111- " w 525.7 1.58- 10" '

. w 7 .45v 1 0 " , too 760 2.72 V 1 0 - '

-BO 4.1 x 10 2 . 3 8 V I O - " 150 .i570.4 2.80

-70 1 . 9 8 x 1 0 - * 1.6H:-IO- ! 200 11 650 17.28

- 6 0 8.1 x l O " 1 9 . 8 9 ~ - ' [ 0 - ' I 250 29 8 ( 7 74.17

-SO 2 . 9 x 1 0 - 2 4 . 9 4 x 1 0 - ' ' 500 64 432 146.8

- 4 0 9 . 7 x l O " ! 2.51 X 1 0 - ' r - - . 1 8 . 9 T )

400

J -

1574 0

- 3 0 2.9 v 1 0 - ' 4.78 x 1 0 - * I 500 -

7691

- 2 0 7 . 8 x 1 0 - ' I . B l w I O - ' 600 -

22.B a tin

- 1 0 1.95 6 . 0 6 X 1 0 - 1 700 - 52.5 aim

0 4.S8 1.85 v 1 0 - ' J 800 ~ 103.3 otiti

10 9.2 4 . 9 v l 0 - 900 " 180.9 aim

20 17.54 l . l x l f l - * 1000 ' 7W.S

Pig.2 .3 . - Liquid-to-solld phase change represented by the plateau AB .

The temperature corresponding to the l iquid-solid phase change it ataospuerle pressure Is called the freezing^ or melting point.

Tin* sol id- l iquid transition point (freezing i t various pressures) varied according to curves an tliouc shown on Fig.2.4 t and their slope i s negative or pos i t ive , depending if the substanca expands on freezing (e .g . water) or contracts on freezing (*$. Mercury)* The known experiment of the ice cut by the wire under load, shows that as Che pressure i Increased, th* "freezing point" i s lowered.

Fig .2 .4 . - Liquid-solid transition curves: e) for substances which expand upon freezing; b) for substances which contract upon freezing.

At all points on the vapour pressure curves (Fig.2.2* ths liquid

snd vspour coexist la equilibrium, and at all points on ths "frssiioj point" curves (Flg.2.4) the solid and liquid coexist. At the

Intersection of these two curves (Fig.2.5) all three phases coexist.

The point is called the triple point, of the substance. Values of the

pressure and temperature corresponding to the triple point of various

substances, are listed In Table 2.1.

Fig.2.5. - Dolling, freezing and sublimation curves a) for substances which expand upon freezing,and b) substances vhlch contract upon freezing. Points A and B refer to the respective triple points.

At pressures and temperatures below the triple point substances

ar changing fro* the solid to the vapour phase without passing through

the liquid phase. This process la known as sublimation, and ths U n a

representing pressure - temperatures at which a solid and Its vapour

coexist, la the sublimation curve (Fig.2.5).

Any equation of state which describes the changes In a thermodynamic

system must be a function of three variables: pressure, volume snd

temperature, and such an equation can be represented by a three -

dimensional P - V - T surface (Fig.2.6). The equations of this surface

will be discusssd In the following chapterers (2.2, 2.3, 2.4, etc).

- 34

Fig.2 .6 . - Ths P - V - T surface for water end I t s projections on the P - V and P - T planes.

2.2. Perfect and real tas laws 2.21. Boyle's law

By an ideal or perfect gas we nean one which obeys Boyle's law at a l l teajpersturea. The relationships established by Boyle (1662) sod Harlots (1679) Is valid for esses over those ranges of pressures snd teaperaturas for which the forces between the olecules ol eh* gas can be considered nef l l j lb la , Rsferlng to Table 2 .1 , at teaperatures higher than the cr i t i ca l point any gu bshaves as a perfect {** The hyperbolas A and 1 on Fl f .2 .1 represent the Boyle's law;

P.V - const (2.1)

Considering two different point* on s hyperbola the relationship between then 1> written

p v p v 11 V2 (2.2)

describing tin isothermal coaprcuuion.

If the apparatus shown In Fl.2.7a, La considered, it can be

seen that for any position of die aercury colum, the pressure P of

the enclosed gas is equal to tne .itnospheric pressure P alaus the

Fig.2.7.- a) lioylo's law apparatus; b) KcLeod gauge.

gauge pressure caused tiy the column of mercury of height h . The

products of the pressure I* and volume V, renalns a constant.

This principle was used by McLeod (1874) in his high vacuum

gauge, which remained until now the reference gauge in calibrating

other vacuum gauges. The essential elements of a HcLeod gauge are

thoun in Fig,2,7 b, and consist of a glass bulh with a capillary tube

extension on the top, a side arm connecting to the vacuum ayste*, and

some means of raising and lowering the mercury level within the gauge.

when the mercury level in the gauge t(t lowered below the branch point A.

tlM bulb of volume V ia connected to tha ayatem. through alda arat B .

Tha ga in tha bulb ia than at tha same praaaura F aa that In tha

system (vacuimO. Whan the mercury lavel ia ralaed, the bulb la cut off from tha aide a m and the aample of (as coapreaaed into tha capillary C.. The capillary C, Is in parallel uith a section of

the side a n B and has the same bore as C .

Since the surface tension or capillary effect in C. and C,

re the law, the difference in level of the mercury is due to the

pressure difference resulting froai compression of the gas sample from

the large volume V into tha small volume of C above the mercury

level. The pressure of the compressed gas in the closed capillary la

proportional to P + (h.-b,)-

Aceordlng to Boyle'a law:

IP + (h 2-h x)] x A(h o-h 3) - PV

t and V preaaur* ttd voluat t O'C. The extrapolation of these expranaleas to P - V - 0 , b u shown that thle would theoretically happen at t - -273"C. On this basis th* ebsolute tenoeracure icala was established, vbera the xaro point of the scale was set at t - -273.16*C exactly, ao that the teaperatur* T In *K (degrees Kelvin) la given by

X - t + 273

By Introducing thia last relation in cqa.2.7 and 2.8 It rcaults

that:

P T - ^ r I (2.9)

soy fas occupies a voluac of 22415 ca (22,4 Hear). Values of

olccular weights of same gascti ace listed in Table 2.3.

For one ole of gas, Che expression

PV (2.14)

was written, where R fit an universal constant

tu l i le J . 3 JloLKCii_m UiauilTa c

(; PunuuLi ^lolttculw weight, g/malB He Stt Ar K r X.-

11, s s

i 1*1,

H4I H,S

NO* N0 X H ,

CO CO, ( H 4 ' fH , I j l l ,

4.003 20.18 39.044

Sfau A n ; i

He Stt Ar K r X.-

11, s s

i 1*1,

H4I H,S

NO* N0 X H ,

CO CO, ( H 4 ' fH , I j l l ,

4.003 20.18 39.044

V-nun

He Stt Ar K r X.-

11, s s

i 1*1,

H4I H,S

NO* N0 X H ,

CO CO, ( H 4 ' fH , I j l l ,

131.30

2.01

He Stt Ar K r X.-

11, s s

i 1*1,

H4I H,S

NO* N0 X H ,

CO CO, ( H 4 ' fH , I j l l ,

131.30

2.01

He Stt Ar K r X.-

11, s s

i 1*1,

H4I H,S

NO* N0 X H ,

CO CO, ( H 4 ' fH , I j l l ,

131.30

2.01

O Teen

He Stt Ar K r X.-

11, s s

i 1*1,

H4I H,S

NO* N0 X H ,

CO CO, ( H 4 ' fH , I j l l ,

32.000 70.t>l 28.98 (moan)

36.4? 34.fW 94.08 30.01 44.03 17.011

28.01 44.01 IB.Ov 98.04 SH.0S

OiJurintf

He Stt Ar K r X.-

11, s s

i 1*1,

H4I H,S

NO* N0 X H ,

CO CO, ( H 4 ' fH , I j l l ,

32.000 70.t>l 28.98 (moan)

36.4? 34.fW 94.08 30.01 44.03 17.011

28.01 44.01 IB.Ov 98.04 SH.0S

A r

He Stt Ar K r X.-

11, s s

i 1*1,

H4I H,S

NO* N0 X H ,

CO CO, ( H 4 ' fH , I j l l ,

32.000 70.t>l 28.98 (moan)

36.4? 34.fW 94.08 30.01 44.03 17.011

28.01 44.01 IB.Ov 98.04 SH.0S

J|y.ta>Ki-n ch lor ide , . .

He Stt Ar K r X.-

11, s s

i 1*1,

H4I H,S

NO* N0 X H ,

CO CO, ( H 4 ' fH , I j l l ,

32.000 70.t>l 28.98 (moan)

36.4? 34.fW 94.08 30.01 44.03 17.011

28.01 44.01 IB.Ov 98.04 SH.0S

CVrboa fnanaai i l i ' .

He Stt Ar K r X.-

11, s s

i 1*1,

H4I H,S

NO* N0 X H ,

CO CO, ( H 4 ' fH , I j l l ,

32.000 70.t>l 28.98 (moan)

36.4? 34.fW 94.08 30.01 44.03 17.011

28.01 44.01 IB.Ov 98.04 SH.0S

He Stt Ar K r X.-

11, s s

i 1*1,

H4I H,S

NO* N0 X H ,

CO CO, ( H 4 ' fH , I j l l ,

32.000 70.t>l 28.98 (moan)

36.4? 34.fW 94.08 30.01 44.03 17.011

28.01 44.01 IB.Ov 98.04 SH.0S W l i y t o w

He Stt Ar K r X.-

11, s s

i 1*1,

H4I H,S

NO* N0 X H ,

CO CO, ( H 4 ' fH , I j l l ,

32.000 70.t>l 28.98 (moan)

36.4? 34.fW 94.08 30.01 44.03 17.011

28.01 44.01 IB.Ov 98.04 SH.0S

* Houreo: Hat\ilUink of iHirminirn and i'Uimim (Chemical Rubber PublMiiBg ,>., (%vf1id. IMS), 44rli l.

Th nuBcricsl value of R depends upon the units nf pressure,

voluae and temperature unci. IT the pressure i s measured In Torr,

the volww lo l i t e r s and the temperature In degrees Kelvin, than

undsr standard conditions where P - 760 Torr, V - 22.415 litara

and T - 273.1CX the value of T! Is:

The syaliol R

of Gay-Lusaac.

refers to 11.V. KngnaulC (1610-1878) successor

o T 273.16

By expressing pressure and volume In C.G.S. u n i t s , 1 a t a -

1.0133 x 10 6 dynes/ca 2 , and

1.0133 10 6 x 2.24 x 10 4 fl , . . , f t 7 . t w . .

R Q 273716 " 8 ' 3 1 * x 1 0 ergs/*K.ole.

since 1 cal - 4.186 x 10 ergs (see Appendix), R % 2 cal/*K.Bole.

Table 2.4 l i s t s numerical values of R for various systems of u n i t s .

-tuble 2.4 XUMEBICAL VALUES OF Rt GAS COSSTAKT FEB BIOLE FOX Vinous

I' r T *. i lyn^/cui* m> J K 8 . 3 U x 1 0 ' y g . / * K IWWtOIw/ni* m J - K 8,31* joules/*K torr cut 3 C K 62,364 torr ea^l*K torr lite pa - K 62.36* ton- liurs/'K UHlt cm* -K 82.03T tin cm*7'K pdi ft3 ' K 1,5*3 Ibft/'R

* In engineering units, 1 lb rooki of g u occupie* 359 ft* *t 32*K art *troo-l>horio itruMiiru (14.67 pui). The Ran kino baoluto temperature acM M bwj upon ilu* Fahn-nhuit ucalu for which abnoluto WJTO temporal uro ia 431.61'F. ThiwT-u r u F i - - i c a . a o j l u , t M T * K - T " C + m-ie.

f .Suiirot-ii: \V. E. Forty 11 m, SmWttoixian PAyjixJ 3*oUu (Smithsonian. IrMti-tution. Wudiinjiion. D.C.. 111.14. fitli rov. od.: T. Buunciner (od.). MvW Mtt/iaiticat EngittUT** Handbook (5leCnw-Hill Book Company, Now York. 195UJ, Oth rd.

For a fi*i aa*pl of TMB S VI , O ( I g having a Molecular weight

M , the general gas lav is written;

(2.15)

2.2*. Molecular dMritr

Awydro (Mi l ) concluded that equal volusas of a l l t u n under thai saw.* condition* of temperature and u r t i i u w contain am"i " ' * " of nolecolss*

Tha number of molecules in on* mole la defined as Avogadro's Msabanc. JL .. By X-ray techniques that accurately determine the interatomic spacing of sol id crystals, the mass of the hydrogen atoa la known to be 1.67 x 10~ g. Tha molecular weight of H, (mole of hydrogen) being 2.016 g, i t results that:

u 2.016 2 x 1.67 x 10 r M

6.023 x 10 molec/mol*.

The Avogadro number also remits from the precise measurement of the Faraday* F - 96,488 coulomb, defined as the electrical charge necessary to deposit a wile of s substance in electrolysis . Tha charge of sn electron being e 1.602 :

H. - 7 _ 96488 A t w i t w

In equation 2.15 W/H denotes the number of moles, thus

i (2.16) 1* tht flyi^*** "* ol.cul. pr unit VOIUM. From aquation! 2.15 and 2.16, i t rMulti that

\ ? o

thus If P Is expressed In Torr, and S la Torr em /'It t the

n l B f (2.18)

At normal pressure (P - 760 Torx) and temperature (T - 273.16' t ) , ion 2.18 glv<

Loschnidt number*,

Prom the no:

rasutls that the mass of a molecule, m (In grans), i s

m - - - 1.66035 x 10~2 4M (2.19) "A

The distances between molecules can be visualized by using a

model In which all the molecules are steady and at same distances to

each other. In this case* the distance L (cm) between molecules is

given by using eq.2.18, and is

L - n ~ 1 / 3 * 4.6 K 10" 7 ||| (cm) (2.20)

which gives at T = 273K

10 Torr.

It should he mentioned that these distances are (much) smaller than the mean free path (Bee Chapter 2.4), but are (very) large compared to the molecular diameters (see Chapters 2,4, and 2.5). Equation 2.17 can also be written

^ T - nkT (2.21) KA

She value of the Boltzunn constant i s

'A *PL - 1.3805 x lO"16 g/'K

* Sometimes the Avogadro number H. , is also rafat*d to as Loschmidt

nunbar, since this latter calculated It In 1865.

- 44 -

The molecular w i g h t of gas mixtures , i t es tabl ished by using eq .2 .15 . The p a r t i a l pressure of th various g u u being P . , P^, P . . t h e i r u n a W' I L . . . H , and t h e i r molecular weights 1 > M 2 - . - M , aquation 2.15 bacomaa

(2,22)

If the average molecular weight of the mixture is M , than

EW P.V R T - ^ R T (2.23)

M M

M - f- (2.24)

2.25. Equation of atata of real Rases Tha ganaral gas lav (eq.2.14, 2.15) is valid for tha region above

the critical point (Fig.2.6) where the ntattar ia In a atata of gaa. as we hava seen In Cfaaptar 2.1, tha P - V curva of real gases* ahows a flat plateau, corresponding to the liquid-gas transition. Near tha critical point tha bahsvior of real gaaaa can be described vary satisfactorily by a modified font of eq.2.14, deduced by Van Jar Waals ( 1 M 0 ) J

[p + ^ ] (V - b) - * o T (2.25)

In this aquation, tha tarsi A/v take* account of tha fact that the attractive f orcea between molecules will bring them closer together and will thus hava tha same effect ea an additional pressure governed by the constant 4 . This "pressure" snist be the stronger, the closer the

2 molecules axe together, hence A is devidad by V

The correction b reduces the to t a l volume, fa representing that par t of i t which i s occupied by the molecules themselves. The volume which i s excluded, wu established to be for each molecule four time Lhat of the molecule i t se l f , thus

b - 4.N,. ~ (2.26)

is the molecular dianeter.

Fig.2.9. - Isotherms corresponding to Van der Weals'equation of:tate.

The plot of eq.2.25 appears in Fig.2,9. Exclusiv of the

region inside the dashed curves (region of liquid-vapour equilibrium), Fig.2.9 agrees with Fig.2.1 (experimental data); point P correspond* to the critical point on Fig,2.1. The dashed portions of the curves

which show the pressure and volume both decreasing simultaneously,

such as RS, are physically untenable. However in the region where

Vandex tfaals equation fails to agree with experimental results, the

plataau can bs inserted so that the areas of the two lobe* I and tl

- 46 -

are aqual (Hg.2.9). With this understanding, Van der Waala' equation can be need u fair approximation of the behavior of real gatee.

attempt* have bttn Bad* to explain the portion* ST and OR of th*

curves, by assarting that they rater to tit* states of supercooled

| u u cod superheated liquids. Th* values A and b in q.2,25 v a n determined by writing

that at the critical point th* thr* rooti where the curve cuta

the horizontal (Fig.2.9) are equal. Eqiutlon 2.25 can be written

V 3 - (*+--) V 2 + | v - ^ - o (2,27)

whila th cubic equation with three roots at the critical voluaa

c '

(V - V ) 3 - V 3 - 3V V*+3V2V~VZ-Q (2.28) C C C C

Comparing the coefficients of eq.2.28 with those of eq.2.27t It

raaulta that th* constants are

h - - | ^ and A - 2? b 2 ? c (2.29) c

The values of the constants for various gates are U s tad in'tkBto%2J5.

2 .3 . Motion of molecules in rarefied Bases

2 .31. Kinetic anrxfty of molecules Iha kinet ic theory of gases rests anon the fundamental aaauuptioaa

that the matter i s made up of molecules, and that the mdleculee of a gas are in constant notion, Intimately related to the temperature of the gaa.

During their motion the molecules suffer col l l s iona between tbeswalvee, and alao impinge on the va l la of the confining venial .

Table 2.5 CHITICAI. CONSTANTS. VAN UEH WAALS' CONSTANTS. MOLECUIAA DIAHETEU, AND MEAN FHEH PATHS COMFUTEU mux THE CONSTANT t

( l u FoimuU *c 1'!

A* (E3n3/inute)'

em*/mol) Urn

P " Itorr T = . O'C

X 10-

Ha Kc Ar Kr X .

H, N , O, C), H

HCI H t O H^S SO, NO N,U NH,

CO CO, CK. C.M, e , t i . cs .

-J07.9 -J3B.7 -\Si. -6S.0

18.1

- M M - 147.1 11S.1

144.0 >I60D

374.0 100.4 1W.S

- W . 0 3S.S

132.4

-139.0 * 31.1

>16S0 36.0

9.1 271.0

iS.9 4B.G 04.0

es.a

!*. 33.5 49.7 70.1

>*oo

217.7J U8.I 77.7 65.0 71.7

l l l .S

35.0 73.0

>aoo 02.0 HJ.9 7B.0

0.03413 0.2107 1.3IS 318 4.194

0.S4S 1.310 1.3(0 0.493 UL093

3.0*7 S.494 4.411 0.714 1.340 P.7I2 4.170

1.483 3.593 S.263 4.390 4.471

11.01

S3.M 17.01 33.11 39.71 M M

M i l SMS 31.13 W.M iro 40.11 30.49 4S.B1 60.3B 37.89 44.1 B 37.07

sto 43.87 42.76 SI.4 7.14 73.9

ZJ i H I X.M 3LM 3.13

*. 3.14 3.93 1 1 1 S.3S

9.11 2.19 3.*4 3.5* 3.31 3.27 3.W

3d 3.2S 3.24 3.44 3.56 3.04

Ha Kc Ar Kr X .

H, N , O, C), H



-J07.9 -J3B.7 -\Si. -6S.0

18.1

- M M - 147.1 11S.1

144.0 >I60D

374.0 100.4 1W.S

- W . 0 3S.S

132.4

-139.0 * 31.1

>16S0 36.0

9.1 271.0

iS.9 4B.G 04.0

es.a

!*. 33.5 49.7 70.1

>*oo

217.7J U8.I 77.7 65.0 71.7

l l l .S

35.0 73.0

>aoo 02.0 HJ.9 7B.0

0.03413 0.2107 1.3IS 318 4.194

0.S4S 1.310 1.3(0 0.493 UL093

3.0*7 S.494 4.411 0.714 1.340 P.7I2 4.170

1.483 3.593 S.263 4.390 4.471

11.01

S3.M 17.01 33.11 39.71 M M


sto 43.87 42.76 SI.4 7.14 73.9


*. 3.14 3.93 1 1 1 S.3S

9.11 2.19 3.*4 3.5* 3.31 3.27 3.W

3d 3.2S 3.24 3.44 3.56 3.04

Ha Kc Ar Kr X .

H, N , O, C), H



-J07.9 -J3B.7 -\Si. -6S.0

18.1

- M M - 147.1 11S.1

144.0 >I60D

374.0 100.4 1W.S

- W . 0 3S.S

132.4

-139.0 * 31.1

>16S0 36.0

9.1 271.0

iS.9 4B.G 04.0

es.a

!*. 33.5 49.7 70.1

>*oo

217.7J U8.I 77.7 65.0 71.7

l l l .S

35.0 73.0

>aoo 02.0 HJ.9 7B.0

0.03413 0.2107 1.3IS 318 4.194

0.S4S 1.310 1.3(0 0.493 UL093

3.0*7 S.494 4.411 0.714 1.340 P.7I2 4.170

1.483 3.593 S.263 4.390 4.471

11.01

S3.M 17.01 33.11 39.71 M M


sto 43.87 42.76 SI.4 7.14 73.9


*. 3.14 3.93 1 1 1 S.3S

9.11 2.19 3.*4 3.5* 3.31 3.27 3.W

3d 3.2S 3.24 3.44 3.56 3.04

Ha Kc Ar Kr X .

H, N , O, C), H



-J07.9 -J3B.7 -\Si. -6S.0

18.1

- M M - 147.1 11S.1

144.0 >I60D

374.0 100.4 1W.S

- W . 0 3S.S

132.4

-139.0 * 31.1

>16S0 36.0

9.1 271.0

iS.9 4B.G 04.0

es.a

!*. 33.5 49.7 70.1

>*oo

217.7J U8.I 77.7 65.0 71.7

l l l .S

35.0 73.0

>aoo 02.0 HJ.9 7B.0

0.03413 0.2107 1.3IS 318 4.194

0.S4S 1.310 1.3(0 0.493 UL093

3.0*7 S.494 4.411 0.714 1.340 P.7I2 4.170

1.483 3.593 S.263 4.390 4.471

11.01

S3.M 17.01 33.11 39.71 M M


sto 43.87 42.76 SI.4 7.14 73.9


*. 3.14 3.93 1 1 1 S.3S

9.11 2.19 3.*4 3.5* 3.31 3.27 3.W

3d 3.2S 3.24 3.44 3.56 3.04

Ha Kc Ar Kr X .

H, N , O, C), H



-J07.9 -J3B.7 -\Si. -6S.0

18.1

- M M - 147.1 11S.1

144.0 >I60D

374.0 100.4 1W.S

- W . 0 3S.S

132.4

-139.0 * 31.1

>16S0 36.0

9.1 271.0

iS.9 4B.G 04.0

es.a

!*. 33.5 49.7 70.1

>*oo

217.7J U8.I 77.7 65.0 71.7

l l l .S

35.0 73.0

>aoo 02.0 HJ.9 7B.0

0.03413 0.2107 1.3IS 318 4.194

0.S4S 1.310 1.3(0 0.493 UL093

3.0*7 S.494 4.411 0.714 1.340 P.7I2 4.170

1.483 3.593 S.263 4.390 4.471

11.01

S3.M 17.01 33.11 39.71 M M


sto 43.87 42.76 SI.4 7.14 73.9


*. 3.14 3.93 1 1 1 S.3S

9.11 2.19 3.*4 3.5* 3.31 3.27 3.W

3d 3.2S 3.24 3.44 3.56 3.04

Ha Kc Ar Kr X .

H, N , O, C), H



-J07.9 -J3B.7 -\Si. -6S.0

18.1

- M M - 147.1 11S.1

144.0 >I60D

374.0 100.4 1W.S

- W . 0 3S.S

132.4

-139.0 * 31.1

>16S0 36.0

9.1 271.0

iS.9 4B.G 04.0

es.a

!*. 33.5 49.7 70.1

>*oo

217.7J U8.I 77.7 65.0 71.7

l l l .S

35.0 73.0

>aoo 02.0 HJ.9 7B.0

0.03413 0.2107 1.3IS 318 4.194

0.S4S 1.310 1.3(0 0.493 UL093

3.0*7 S.494 4.411 0.714 1.340 P.7I2 4.170

1.483 3.593 S.263 4.390 4.471

11.01

S3.M 17.01 33.11 39.71 M M


sto 43.87 42.76 SI.4 7.14 73.9


*. 3.14 3.93 1 1 1 S.3S

9.11 2.19 3.*4 3.5* 3.31 3.27 3.W

3d 3.2S 3.24 3.44 3.56 3.04

Ha Kc Ar Kr X .

H, N , O, C), H



-J07.9 -J3B.7 -\Si. -6S.0

18.1

- M M - 147.1 11S.1

144.0 >I60D

374.0 100.4 1W.S

- W . 0 3S.S

132.4

-139.0 * 31.1

>16S0 36.0

9.1 271.0

iS.9 4B.G 04.0

es.a

!*. 33.5 49.7 70.1

>*oo

217.7J U8.I 77.7 65.0 71.7

l l l .S

35.0 73.0

>aoo 02.0 HJ.9 7B.0

0.03413 0.2107 1.3IS 318 4.194

0.S4S 1.310 1.3(0 0.493 UL093

3.0*7 S.494 4.411 0.714 1.340 P.7I2 4.170

1.483 3.593 S.263 4.390 4.471

11.01

S3.M 17.01 33.11 39.71 M M


sto 43.87 42.76 SI.4 7.14 73.9


*. 3.14 3.93 1 1 1 S.3S

9.11 2.19 3.*4 3.5* 3.31 3.27 3.W

3d 3.2S 3.24 3.44 3.56 3.04

Ha Kc Ar Kr X .

H, N , O, C), H



-J07.9 -J3B.7 -\Si. -6S.0

18.1

- M M - 147.1 11S.1

144.0 >I60D

374.0 100.4 1W.S

- W . 0 3S.S

132.4

-139.0 * 31.1

>16S0 36.0

9.1 271.0

iS.9 4B.G 04.0

es.a

!*. 33.5 49.7 70.1

>*oo

217.7J U8.I 77.7 65.0 71.7

l l l .S

35.0 73.0

>aoo 02.0 HJ.9 7B.0

0.03413 0.2107 1.3IS 318 4.194

0.S4S 1.310 1.3(0 0.493 UL093

3.0*7 S.494 4.411 0.714 1.340 P.7I2 4.170

1.483 3.593 S.263 4.390 4.471

11.01

S3.M 17.01 33.11 39.71 M M


sto 43.87 42.76 SI.4 7.14 73.9


*. 3.14 3.93 1 1 1 S.3S

9.11 2.19 3.*4 3.5* 3.31 3.27 3.W

3d 3.2S 3.24 3.44 3.56 3.04

Ha Kc Ar Kr X .

H, N , O, C), H



-J07.9 -J3B.7 -\Si. -6S.0

18.1

- M M - 147.1 11S.1

144.0 >I60D

374.0 100.4 1W.S

- W . 0 3S.S

132.4

-139.0 * 31.1

>16S0 36.0

9.1 271.0

iS.9 4B.G 04.0

es.a

!*. 33.5 49.7 70.1

>*oo

217.7J U8.I 77.7 65.0 71.7

l l l .S

35.0 73.0

>aoo 02.0 HJ.9 7B.0

0.03413 0.2107 1.3IS 318 4.194

0.S4S 1.310 1.3(0 0.493 UL093

3.0*7 S.494 4.411 0.714 1.340 P.7I2 4.170

1.483 3.593 S.263 4.390 4.471

11.01

S3.M 17.01 33.11 39.71 M M


sto 43.87 42.76 SI.4 7.14 73.9


*. 3.14 3.93 1 1 1 S.3S

9.11 2.19 3.*4 3.5* 3.31 3.27 3.W

3d 3.2S 3.24 3.44 3.56 3.04

Ha Kc Ar Kr X .

H, N , O, C), H



-J07.9 -J3B.7 -\Si. -6S.0

18.1

- M M - 147.1 11S.1

144.0 >I60D

374.0 100.4 1W.S

- W . 0 3S.S

132.4

-139.0 * 31.1

>16S0 36.0

9.1 271.0

iS.9 4B.G 04.0

es.a

!*. 33.5 49.7 70.1

>*oo

217.7J U8.I 77.7 65.0 71.7

l l l .S

35.0 73.0

>aoo 02.0 HJ.9 7B.0

0.03413 0.2107 1.3IS 318 4.194

0.S4S 1.310 1.3(0 0.493 UL093

3.0*7 S.494 4.411 0.714 1.340 P.7I2 4.170

1.483 3.593 S.263 4.390 4.471

11.01

S3.M 17.01 33.11 39.71 M M


sto 43.87 42.76 SI.4 7.14 73.9


*. 3.14 3.93 1 1 1 S.3S

9.11 2.19 3.*4 3.5* 3.31 3.27 3.W

3d 3.2S 3.24 3.44 3.56 3.04

HyUrojjoneJilorids. Hydrogun tulfido...

Ha Kc Ar Kr X .

H, N , O, C), H



-J07.9 -J3B.7 -\Si. -6S.0

18.1

- M M - 147.1 11S.1

144.0 >I60D

374.0 100.4 1W.S

- W . 0 3S.S

132.4

-139.0 * 31.1

>16S0 36.0

9.1 271.0

iS.9 4B.G 04.0

es.a

!*. 33.5 49.7 70.1

>*oo

217.7J U8.I 77.7 65.0 71.7

l l l .S

35.0 73.0

>aoo 02.0 HJ.9 7B.0

0.03413 0.2107 1.3IS 318 4.194

0.S4S 1.310 1.3(0 0.493 UL093

3.0*7 S.494 4.411 0.714 1.340 P.7I2 4.170

1.483 3.593 S.263 4.390 4.471

11.01

S3.M 17.01 33.11 39.71 M M


sto 43.87 42.76 SI.4 7.14 73.9


*. 3.14 3.93 1 1 1 S.3S

9.11 2.19 3.*4 3.5* 3.31 3.27 3.W

3d 3.2S 3.24 3.44 3.56 3.04

7.91 0.07 8.03 a,w SJ4J

Crlxjii manovid* . . RMIKHI diuiidn . . . .

Ha Kc Ar Kr X .

H, N , O, C), H



-J07.9 -J3B.7 -\Si. -6S.0

18.1

- M M - 147.1 11S.1

144.0 >I60D

374.0 100.4 1W.S

- W . 0 3S.S

132.4

-139.0 * 31.1

>16S0 36.0

9.1 271.0

iS.9 4B.G 04.0

es.a

!*. 33.5 49.7 70.1

>*oo

217.7J U8.I 77.7 65.0 71.7

l l l .S

35.0 73.0

>aoo 02.0 HJ.9 7B.0

0.03413 0.2107 1.3IS 318 4.194

0.S4S 1.310 1.3(0 0.493 UL093

3.0*7 S.494 4.411 0.714 1.340 P.7I2 4.170

1.483 3.593 S.263 4.390 4.471

11.01

S3.M 17.01 33.11 39.71 M M


sto 43.87 42.76 SI.4 7.14 73.9


*. 3.14 3.93 1 1 1 S.3S

9.11 2.19 3.*4 3.5* 3.31 3.27 3.W

3d 3.2S 3.24 3.44 3.56 3.04

1.J8 (.13

Ha Kc Ar Kr X .

H, N , O, C), H



-J07.9 -J3B.7 -\Si. -6S.0

18.1

- M M - 147.1 11S.1

144.0 >I60D

374.0 100.4 1W.S

- W . 0 3S.S

132.4

-139.0 * 31.1

>16S0 36.0

9.1 271.0

iS.9 4B.G 04.0

es.a

!*. 33.5 49.7 70.1

>*oo

217.7J U8.I 77.7 65.0 71.7

l l l .S

35.0 73.0

>aoo 02.0 HJ.9 7B.0

0.03413 0.2107 1.3IS 318 4.194

0.S4S 1.310 1.3(0 0.493 UL093

3.0*7 S.494 4.411 0.714 1.340 P.7I2 4.170

1.483 3.593 S.263 4.390 4.471

11.01

S3.M 17.01 33.11 39.71 M M


sto 43.87 42.76 SI.4 7.14 73.9


*. 3.14 3.93 1 1 1 S.3S

9.11 2.19 3.*4 3.5* 3.31 3.27 3.W

3d 3.2S 3.24 3.44 3.56 3.04

Ha Kc Ar Kr X .

H, N , O, C), H



-J07.9 -J3B.7 -\Si. -6S.0

18.1

- M M - 147.1 11S.1

144.0 >I60D

374.0 100.4 1W.S

- W . 0 3S.S

132.4

-139.0 * 31.1

>16S0 36.0

9.1 271.0

iS.9 4B.G 04.0

es.a

!*. 33.5 49.7 70.1

>*oo

217.7J U8.I 77.7 65.0 71.7

l l l .S

35.0 73.0

>aoo 02.0 HJ.9 7B.0

0.03413 0.2107 1.3IS 318 4.194

0.S4S 1.310 1.3(0 0.493 UL093

3.0*7 S.494 4.411 0.714 1.340 P.7I2 4.170

1.483 3.593 S.263 4.390 4.471

11.01

S3.M 17.01 33.11 39.71 M M


sto 43.87 42.76 SI.4 7.14 73.9


*. 3.14 3.93 1 1 1 S.3S

9.11 2.19 3.*4 3.5* 3.31 3.27 3.W

3d 3.2S 3.24 3.44 3.56 3.04 CAAKUI duulBilo . . .

Ha Kc Ar Kr X .

H, N , O, C), H



-J07.9 -J3B.7 -\Si. -6S.0

18.1

- M M - 147.1 11S.1

144.0 >I60D

374.0 100.4 1W.S

- W . 0 3S.S

132.4

-139.0 * 31.1

>16S0 36.0

9.1 271.0

iS.9 4B.G 04.0

es.a

!*. 33.5 49.7 70.1

>*oo

217.7J U8.I 77.7 65.0 71.7

l l l .S

35.0 73.0

>aoo 02.0 HJ.9 7B.0

0.03413 0.2107 1.3IS 318 4.194

0.S4S 1.310 1.3(0 0.493 UL093

3.0*7 S.494 4.411 0.714 1.340 P.7I2 4.170

1.483 3.593 S.263 4.390 4.471

11.01

S3.M 17.01 33.11 39.71 M M


sto 43.87 42.76 SI.4 7.14 73.9


*. 3.14 3.93 1 1 1 S.3S

9.11 2.19 3.*4 3.5* 3.31 3.27 3.W

3d 3.2S 3.24 3.44 3.56 3.04 4.11

Source*: Amtrimn Innitvto of Fkyka Hindboat iMcGrw-Hill Book Company, Nw York, 1W3), Jndcd.i Hcnulboo* of I'hysic* ant Chtmutry {Ctionucal Rubber Publiil ng Co ClmUnd, JWJ3J, MUted.

The noaentun transfer fron the molecules to the vails of the vessel results In the pressure P , which appears In previous chapters, thus the pressure can be related to the kinetic energy of the molecules.

Consider the collision of just one particle (molecule) of mass *, traveling with the velocity v in the x direction of a box of length L (in the x direction)

t with a vails of area A perpendicular to the x .direction. The tine between successive collisions with

the wall A is it - 2L/v . The change of momentum A(v) of the

particle in each collision is

A(nv) - nv - ni

Kewton's second law defines the force F at the rate of change of momentum with reapect to time, thui

2 , ._... 2mv_ rav

' - ^ - i r f r - T -

one concludes that

2 mv

2

3kT 2

(2.35)

i.e. the average kinetic energy of the molecules is the sane for all aeses, and ia proportional to the absolute temperature.

2.32. Molecular velocities The constant occurence of collisions produces a wide distribution

of velocities. IF a collision of two aolecules with velocities v. and v. , the total kinetic energy is preserved, thus the quantity

m(v_ + v 2 J

is the sane before and after the collision, even if v. and v* oust change.

Maxwell and Boltzmann expressed the distribution of the velocities fay the law

n dV* f v--J^T72 l2kfj v f t ( 2 , 3 6 )

where f is the fractional nunber of molecules in the velocity rang* between v and v + dv , per unit of velocity range.

The value of f la zero for v 0 , and v > and has V

its iiaxiaum at . value

ffl 1/2 (2.37)

OJ u 0.7 i >\ 0 i ! l \ 03 i \

t. 04 OJ / &

*i* \ 02 / *" 01 i.i,.. > > - . . 0 02 M OS M 10 12 I* ! 18 20 22 24 26 23 30

Fig.2.10. - Kaxuell-BoltzHann olecular velocity distribution curve.

given by differentiating f with respect to v and setting the result equal to zero:

dfv t> L s _ | 3 / 2 |, S- ,.3L"2kT . n

^m IzkfJ | 2 v ET v | e - Figure 2.10 shows equation 2.36, plotted versus v/v . The

V

have this velocity then any other value of the: velocity. The v value, is different from the arithaetlc averaRe value v , which results Cram

/ vvv v o T 2 f2kT] 1 / Z , 128 v (2.38)

The ncan square velocity v is obtained from

v 2 U 2 - 3 ^ m n

/ V v (2.39)

and i t th same as obtained in e q . 2 . 3 4 . The root-mean-aquare v e l o c i t y i s therefore

v r " M " I 3 IT] " 1 - 2 2 5 v p < 2 - 4 0 )

Which of these velocities is of interest as representing the average behavior of a gas depnds upon the process under consideration. When the molecules directly influence the process by their velocity, (e.g. flov of gases), the arithmetic average is used, while when the kinetic energy of the molecule influences the process the root-mean-square should be used.

Based on eqs.2.19 and 2.21

. R -' (2.41)

4 h i 1 ' 2 1.45 x 10 cm/s (2.42)

it results that the average air molecule (M - 29) at T m 300 *K , A

has a velocity of about 4.6 x 10 cm/sec.

2.33. Molecular incidence rate In a similar way Co eq.2.36 the distribution function fv of

the velocities of molecules in the x direction was written as:

The number of molecules striking an element of surface (perpendicular to the x direction), per unit time is given by

[ v x dn x (2.44)

iy lMrodaclng da x f r a .q .2 .43 into 2.44 and integrating. I t m u l t , that:

lc /eW.a (2.45) 2 ( 2 t t l1 / 2

tmd by using aq.2.38, 2.42 and 2.17 it also results

- i nv - 3.513 x 1 0 2 2 975- le/ea Z.i (2.46)

where ? is la Torr.

Table 1.1 lists SOBS values of . If a hoi* of ara A is cut in the thin wall of th vassal

beyoend which the gas density is cero, the rate at which Molecules of gas leave the vessel is

1 3 ( T \ U Z q * +A - j m A - 3.64 x 1ST jjj nA molec/sec (2.47)

The volae* of aaa at the pressure in the vessel escaping each second 1* obtained by dividing the flow q by the density n. thus

f - J . 3.64, 10' (I] A c 3 / . (2.48)

bleb for ill at 20*C would b.

b.x* k If In a'

dt

2

(2.49)

Th. aaa H of gM aacaplng, can ba found by cofd>lnlng aqa.2.46 I 2.19, tfcua

O-'P(M) 1/2

V - 5.83 x 10 * P f g / a . c . (2.50)

- 53 -

2 . 4 . Pressure and M M free path

2 .41 . item free path During the ir notion the molecules suffer c o l l i s i o n s between

themselves. The distance traversed by a nolacule between success ive c o l l i s i o n s , i s i t s free path. Since, the magnitude of t h i s distance i s * function of the v e l o c i t i e s of the molecules, the conception of mean free path X i s used. This i s defined as the average distance traversed by a l l the molecules between successive c o l l i s i o n to each other, or as the average of the distances traversed between success ive c o l l i s i o n s by the same molecule, in a Riven time.

A molecule having a diameter and a veLocity v moves a distance v6fc in the time fit . The molecule suffers a. c o l l i s i o n with another molecule i f anywhere i t s center i s within the distance of the center of another molecule, therefore sweeps out without c o l l i s i o n a cyl inder of diamet

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