Abstracts of Technical Articles from Bell System Sources (01 July 1934)

Is a critical correlation of the slope and intercept of experimental Richardson lines with the quantities appearing in theoretical equationsbased on thermodynamic and statistical reasoning. The equation for experimental Richardson lines is log i -- 2 log T = log A -- bj2.3 T; A and b are constants characteristic of the surface, i is the electron emission current in amp./cm. 2 , T is the temperature in degrees K, log A is the intercept and -- b/2.3 is the slope of experimental lines. Statistical theory based on the Fermi-Dirac distribution of electron velocities in the metal shows that i should be given by log i -- 2 log T = log £7(1 -- r) -- w/2.3 T, where U is a universal constant which has the value 120 amp./cm. 2 °K 2 , r is the reflection coefficient, and w is the work junction. 

A correlation of the experimental and theoretical equations shows t h a t b = w -- Tdwjdt, and log A = log U{ 1 -- r) -- (1/2.3)dw/dT. Only when r is 0 and the work function is independent of the temperature, is it correct to say t h a t the slope is --w/2.3 and t h a t the intercept has the universal value log U. But even when w is a function of T, it follows from a thermodynamic argument that the slope is given by --h/2.3, where the heat function h is defined by h = ( L p / R ) -- (5/2)7", L p is the heat of vaporization per mol at constant pressure. T h e heat function is related to the work function by the equation h = w -- Tdw/dT. From experimental and theoretical arguments it is deduced that the reflection coefficient is probably negligibly small.