By A. M. Howatson (Auth.)
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26) If the electrons have a temperature Te much higher than that of the ions, then DJße > A/ft o r so that A f t > A/*c ft ^Te A = /),-=—e. 27) are commonly used, although both are only approximate and suffer from the weakness of eqn. 24) applied to electrons. However, they serve to show that Da increases with Te, that is with random electron energy, and that if the electrons are at the same temperature as the gas, Da is of the same order as A> s o t n a t t n e electrons are slowed much more than the positive ions are accelerated.
This is the Schottky effect; it can be calculated by classical methods in terms of the force on an electron. At room temperatures the total emission is still low for ordinary field strengths. If, however, the electric field is in the order of 106 volts/cm an electron current flows which is appreciably greater than the calculated thermionic value. The reason for this can be properly explained only in terms of quantum mechanics, but in essence the field serves to pull electrons through the potential barrier represented by the work function, however small their thermal energy.
6. DIFFUSION It is well known that a gas which initially has a non-uniform concentration ultimately assumes a uniform distribution within its container if there is no appreciable field of force acting (in many laboratory applications the gravitational field of force may be ignored). In the same way, two initially separate gases become uniformly mixed. The process by which the condition of equilibrium is reached is diffusion. 1. The Diffusion Process Consider the concentration n of a simple gas in a container to vary, for any reason, in the x-direction only at some instant; there is then a net transfer of particles across any plane normal to x.
An Introduction to Gas Discharges by A. M. Howatson (Auth.)