L04-Gas_Kinetics

# L04-Gas_Kinetics - Gas Kinetics Introduction Most...

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Gas Kinetics

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Introduction Most deposition techniques rely on gas flow in a vacuum. We need a model for understanding; the speed and energy of the gas molecules as a function of temperature and pressure, how these molecules interact with each other and their surroundings, and how mass, heat and momentum is transported by these molecules.
The Size of a Molecule (a very rough calculation) Take water (liquid H 2 O) as an example. Oxygen has 8 protons and 8 neutrons for a total of 16 nucleons and Hydrogen has 1 proton. So water has 16+1+1=18 nucleons g mm NP 24 10 66 . 1 ± u| | g N OH 23 10 99 . 2 18 2 ± u g molecules mN / 10 35 . 3 1 22 2 2 3 / 00 . 1 2 cm g U molecule cm N V / 10 99 . 2 1 3 23 2 2 2 ± cm V d 8 3 10 64 . 5 4 3 2 2 2 ± u d 2

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The Distance Between Molecules in a Gas Now take water vapor (gaseous H 2 O). OH l 2 3 3 / 10 8 . 0 2 cm g ± u U molecule cm N V / 10 73 . 3 1 3 20 2 2 2 ± cm Vl 7 3 10 34 . 3 2 2 ± dl 2 2 6 |
Molecular Velocities Basic assumptions: We’ll assume an ideal gas where the gas molecules interact elastically (collisions are similar to the collisions of hard billiard balls). The distance between molecules are large compared to their sizes. There are no attractive or repulsive forces between the molecules and each molecule moves independently of the others.

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Maxwell-Boltzmann Distribution Under these assumptions, the molecules of a gas have velocities that are distributed according to: ¸ ¸ ¹ · ¨ ¨ © § ± RT Mv RT M v dv dn n vf 2 exp 2 4 1 )( 2 2 S where f is the fractional number of molecules, v is the velocity, M is the molecular weight, T is the temperature and R is the universal gas constant.
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L04-Gas_Kinetics - Gas Kinetics Introduction Most...

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