Vacuum Engineering Calculations and Applications

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Vacuum Engineering Calculations and Applications

Vacuum Engineering Calculations and Applications
Armand Berman
National Physical Laboratory of Israel
Hebrew University Givat Ram
Jerusalem
271 pages

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Vacuum is now required for many scientific and industrial purposes, particularly those associated with semiconductors, lighting bulbs, and material-coating industries. The need to manufacture in highly characterized and controlled vacuum brings continual progress in the design, operation, and maintenance of vacuum systems, challenging the people involved in these activities. To many of these people, the use and application of vacuum engineering formulas rather than vacuum's theoretical basis are prime objectives.

TOC

1 . Ideal Gases 1
1.1 The Ideal Gas Law 1
1.2 Boyle's Law 1
1.3 Charles's Law 1
1.4 Gay-Lussac's Law 1
1.5 Mole Amount 2
1.6 Dalton's Law 2
1.7 The Mean Molar Mass of a Mixture of Gases 2
1.8 The Number Density n of Particles (Molecules, Atoms, etc.) 3
1.9 Standard Conditions for Gases (STP, Standard Temperature and Pressure) 6
1.10 Avogadro's Number 6
1.11 The Mass per Molecule 7
1.12 The Molar Volume 7
1.13 The Equation of State 7
1.13.1 Single Species of Gas 7
1.13.2 Mixture of Gases 7
1.14 Boltzmann's Constant 8
1.15 The Gas Density 8
1.16 Gas Pressure 9

2 . Real Gases 29
2.1 The van der Waals Equation of State 29

3 . Kinetic Theory of Gases 35
3.1 Molecular Velocities 35
3.1.1 The Most Probable Velocity v 35
3.1.2 The Arithmetic Average Velocity va 35
3.1.3 The Mean-Square Velocity vT 36
3.1.4 The Root-Mean-Square Velocity vr 37
3.2 Relationships between Molecular Velocities 38
3.3 Th e Maxwell-Boltzmann Law of Distribution of Molecular Velocities 38
3.4 Kinetic Energy of Molecules 39
3.4-1 The Average Translational Energy £ per Molecule in Random Motion 39
3.4-2 The Total Translational Energy E of Molecules in Random Motion 39
3.5 Quantitative Relationships between Molecules and Areas 40
3.5.1 The Rate ф at Which Molecules at Steady State Strike a Unit Area per Unit Time 40
3.5.2 The Mass of Gas G Incident on Unit Area per Unit Time 42
3.5.3 Effusion Rate of Molecules
3.15.2 Energy Transferred by Molecules Ev in the Viscous Range 57
3.15.3 Energy Transferred by Molecules Em in the Molecular Range 58
3.16 Thermomolecular Flow 59
3.16.1 Thermal Transpiration 59

4 Gas Flow in Components and Vacuum Systems 76
4.1 Quantity of Gas 76
4.2 Molar Flow Rate of Gas 77
4.2.1 Single Species of Gas 77
4.2.2 Mixture of Gases 77
4.3 Conversion of Molar Flow Rates to Molecular or Mass Flow Rates 77
4.4 Throughput 78
4.5 Conversion of Throughputs 78
4.6 Gas Flow Regimes 80
4-6.1 Quantifying Criteria of Gas Flow 80
4-7 Impedance to Gas Flow 82
4.8 Conductance to Gas Flow 83
4.9 Comparison between Electrical and Vacuum Circuits 84
4.10 Impedance and Conductance of Interconnected Vacuum Components 84
4-10.1 Vacuum Components Connected in Series 85
4.10.2 Vacuum Components Connected in Parallel 86
4.11 Conversion of Conductances for Cylindrical Pipes of Uniform Cross Section 86
4.11.1 Conversion for Laminar Flow 86
4.11.2 Conversion for Molecular Flow 86
4.12 Pumping Speed—Volume Rate of Flow—Permanent Regime 86
4.12.1 Pumping Speed of a Vacuum Component or a Vacuum Pump 86 4.12.2 Pumping Speed of an Orifice 87
4-12.3 Pumping Speed of an Assembly Vacuum Pump—Vacuum Component 88
4.13 Basic Considerations in the Design of a Vacuum System 89

5. Steady Flow of Gas in the Viscous Range 104
5.1 Turbulent Flow 104
5.2 Laminar Flow through an Aperture 104
5.2.1 Laminar Nonchocked Throughput 104
5.2.2 Laminar Nonchocked Conductance 106
5.2.3 Laminar Chocked Conductance 106
5.2.4 Laminar Chocked Throughput 107
5.3 Laminar Flow through Long Pipes 107
5.3.1 Poiseuille's Law 107
5.3.2 Laminar Volume Flow Rate of Gas through a Pipe 111
5.3.3 Pressure-Drop Formula 112
5.3.4 Correction to Poiseuille's Law owing to Surface Slip 112
5.3.5 Laminar Conductance of a Circular Annulus 113
5.4 Laminar Flow through Long Channels 113
5.4.1 Laminar Conductance of Channels of Elliptical Cross Section 114
5.4-2 Laminar Conductance of Channels of Rectangular Cross Section 114
5.4-3 Laminar Conductance of Channels of Triangular (Equilateral) Cross Section 114
5.5 Laminar Flow through Short Pipes of Uniform Circular Cross Section 114

6 . Stead y Flow o f Gas in th e Molecular Range 127
6.1 Molecular Flow through an Apertur e 127
6.1.1 Molecular Throughput of an Aperture 127
6.1.2 Molecular Conductance of an Aperture 128
6.1.3 Molecular Pumping Speed of an Aperture 128
6.2 Molecular Flow through a Diaphragm—Diaphragm Effect 130
6.2.1 Molecular Conductance of a Diaphragm 130
6.2.2 Molecular Pumping Speed of a Diaphragm 131
6.3 Molecular Flow through Long Pipes 131
6.3.1 Molecular Throughput of a Pipe of Varying Cross Section and Perimeter 1 31
6.3.2 Molecular Conductance of a Pipe of Varying Cross Section and Perimeter 1 31
6.3.3 Molecular Conductance of a Pipe of Uniform Cross Section 132
6.3.4 Molecular Conductance of a Tapered (Conical) Pipe of Circular Cross Section 133
6.3.5 Molecular Conductance of a Circular Annulus 133
6.4 Molecular Flow through Long Channels 134
6.4.1 Molecular Conductance of Channels of Uniform Elliptical Cross Section 1 34
6.4.2 Molecular Conductance of Channels of Rectangular Cross Section 134
6.43 Molecular Conductance of Slit-Like Channels 135
6.4-4 Molecular Conductance of Channels of Triangular (Equilateral) Cross Section 135
6.5 Molecular Flow through Short Pipes 136
6.5.1 Molecular Conductance of a Pipe of Circular Cross Section 136
6.6 Molecular Flow through Short Channels 138
6.6.1 Molecular Conductance of Rectangular Slits 138
6.7 Molecular Flow through Vacuum Components of Simple and Complex Geometries 139
6.7.1 Molecular Conductance of Vacuum Components in Series 145

7 . Steady Flow of Gas in the Transition Range 171
7.1 Conductance of Long Cylindrical Pipes in the Transition Range 171
7.2 Transition Pressure in Long Cylindrical Pipes 173
7.3 Maximum and Minimum Pressures of the Transition Range 173
7.4 Maximum and Minimum Mean Free Path in the Transition Range 173

8. Gas Load 176
8.1 Sources of Gas in Vacuum Systems 176
8.2 Evaluation of the Gas Load 176
8.2.1 Outgassing (Surface) 177
8.2.2 Evaporation 181
8.2.3 Leakage 188
8.2.4 Permeation 196

9. Vacuum Pumps 20 2
9.1 Survey of Various Types of Vacuum Pumps 202
9.2 Positive-Displacement Pumps 202
9.2.1 Compression Ratio 202
9.2.2 Simultaneous Pumping of Gas and Vapor 202
9.3 Diffusion Pumps 207
9.4 Pumping by Dilution 208

10. Pumpdown Transient 211
10.1 Constant-Speed Case, Gas Load Disregarded 211
10.1.1 Evacuation Rate 211
10.1.2 Pressure Decay with Time 211
10.1.3 Time Required to Reach a Certain Pressure 212
10.1.4 Time Required to Reduce Pressure to a Specified Value 213
10.2 Constant-Speed Case, Gas Load Considered 213
10.2.1 Evacuation Rate 213
10.2.2 Pressure Decay with Time 214
10.2.3 Time Required to Reach a Certain Pressure 214
10.3 Variable-Speed Case, Gas Load Disregarded 215
10.3.1 Time Required to Reduce Pressure to a Certain Value 216
10.4 Constant-Throughput Case 217
10.4.1 Time Required to Reach a Certain Pressure 217
10.5 Pumpdown Transient in the Viscous Range 217
10.5.1 Time Required to Reach a Certain Pressure in the Viscous Range 217
10.6 Pumpdown Transient in the Molecular Range 218
10.6.1 Time Required to Reach a Certain Pressure in the Molecular Range 218

11. Pumping Steady State 235
11.1 Pumping Steady State with Localized Gas Load 235
11.1.1 Ultimate Pressure of a Vacuum System 235
11.2 Pumping Steady State with Distributed Gas Load 235