Chapter 1. Ultra High Vacuum and Sample Preparation Kinetic theory of gases Vacuum concept Pressure measurement Vacuum pumps UHV hardwares Sample preparations Kinetic Theory of Gases Number density of gases: ρ ρ = number of molecules/volume = p/kT = 9.66 x10 18 p (torr)/T (molecules/cm 3 ) eg) p=10 -10 torr ρ = 3x10 6 molecules/cm 3 Pressure unit 1 Pa =1N/m 2 , 1bar = 10 5 Pa 1 atm = 1.013 bar = 760 mmHg = 760 torr = 101,325 Pa Collision frequency Z per molecule d L Length of cylinder L= <v>t The cross section area of the cylinder σ= πd 2 Total chamber volume = V The number of collisions of a molecule in a chmaber V = Nx(number of molecules in a cylinder)/V = N x(πd 2 <v>t)/V = (N/V)( πd 2 ) <v>t = ρσ<v>t The collision frequency = # of collisions per second Z= √2ρσ<v> <v> =(8kT/πM) 1/2 σ=πd 2
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Chapter 1. Ultra High Vacuum and Sample Preparation
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Chapter 1. Ultra High Vacuum and Sample Preparation
Kinetic theory of gases Vacuum concept Pressure measurement Vacuum pumps UHV hardwares Sample preparations
Kinetic Theory of Gases
Number density of gases: ρ
ρ = number of molecules/volume = p/kT = 9.66 x1018 p (torr)/T (molecules/cm3)
eg) p=10 -10torr ρ = 3x106 molecules/cm 3
Pressure unit
1 Pa =1N/m2 , 1bar = 105 Pa 1 atm = 1.013 bar = 760 mmHg = 760 torr = 101,325 Pa
Collision frequency Z per molecule
d
L
Length of cylinder L= <v>t
The cross section area of the cylinder σ= πd2
Total chamber volume = V The number of collisions of a molecule in a chmaber V = Nx(number of molecules in a cylinder)/V = N x(πd2<v>t)/V = (N/V)( πd2) <v>t = ρσ<v>t The collision frequency = # of collisions per second
Z= √2ρσ<v> <v> =(8kT/πM)1/2
σ=πd2
Mean free path The average distance travelled by a molecucle between collision λ = <v>/Z =1/√2ρσ = kT/2pσ = ~ 1/p
eg) at 10-10 torr λ = 106 m Molecular flux on the surface F
The number of molecules striking the surface per unit area per unit time [molecules/m2sec]
F = (1/4) ρ <v> =(1/4)(p/kT)( 8kT/πM)1/2
= p/ mkTπ2
eg) F of O2 molecules at 298K and 10-6 torr F = 1.333x10-4Pa/(2πx(32g/mol/6.0x1023)x1.38x10-23J/Kx298K) = 6.4x1018 molecules/m2sec = 6.4x1014 molecules/cm2 sec
F ~1015 molecules/ cm2 sec
The number of surface atoms per unit area for the cubic crystal
(a = 3.0A) The unit cell has one atom, area = (3x10-8cm)2= 9x10-16cm2 ~10-15 cm2
Number of atoms per unit area (cm2) = 1cm2/10-15cm2 =1015atoms
Degree of Vacuum Pressure Range (Pa) : 1 Pa = 7.5x10-3 Torr
Low Vacuum (LV) 3.3x103 < P < 105 Medium Vacuum 10-1 < P < 3.3x103
High Vacuum (HV) 10-4 < P < 10-1 Very High Vacuum 10-7 < P < 10-4
Ultrahigh Vacuum (UHV) 10-10 < P < 10-7 Extremely High Vacuum (XHV) P < 10-10
Gas density is still high even in UHV conditions !!
Collision free conditions: mfp > diameter of chamber
θ =
P <10-4 torr Conditions to keep clean surfaces : time to reach 1ML contamination >> exp. Time
P< 10-9 torr !!
Vacuum Concept Gas flow
Viscous flow : mfp < dim. of chamber Molecular flow : mfp >> dim. of chamber In the molecular flow, momentum transfer occurs between molecules and the wall of a container, but molecules seldom encounter one another Pumping speed: S [m3/sec, l/sec]
The volumetric rate at which a gas is transported across a plane S = Q/P
Throughput: Q [Pa m3/sec, J/sec, W]
The volume of gas at a known pressure and temperature that passes
a plane in a known time
Q = Energy per unit time crossing a plane
= mass flow rate at constant T
Conductance [m3/sec]
C = Q/∆P = Q/(P1-P2), P1 > P2
[compare with electrical conductivity σ = 1/R = I/V]