THERMIONIC ELECTRON EMISSION 461 



remained practically constant during the last 700 hours. This decrease 

 is ascribed to the formation of new crystal facets, which produce more 

 nearly equal work functions for the two surfaces. That different 

 crystal planes have different work functions also follows from the 

 photoelectric work of Nitzsche ^^ on single crystals of zinc. The work 

 function for a surface normal to the hexagonal axis was found to be 

 3.28 volts while that for a surface parallel to this axis was 3.09 volts. 

 These observed differences in work function of different surfaces of 

 single crystals are quite large enough to account for the deviations 

 from the Schottky law for clean surfaces. 



Still another prediction of the patch theory is verified by experiment. 

 In connection with Fig. 15 it was pointed out that at low applied fields 

 something more than half the area is effective in emitting electrons; as 

 the field is increased the effective area decreases until the log i vs. V F 

 curves approach the Schottky line when the effective area attains a 

 constant value whose order of magnitude is 0.1. From this it follows 

 that if Richardson lines are obtained for a series of applied potentials, 

 the intercepts or values of log A should decrease as V increases, but 

 should approach a constant value for sufficiently large values of V. 

 Experimental values of log A vs. V are given in Fig. 14 of Brattain and 

 Becker's ^^ article on thorium on tungsten. They show the predicted 

 trend. Furthermore, the change in log A with V should be most 

 pronounced for large values of m- It was shown above that the 

 largest values of /x occur in the neighborhood of / = 0.6 while near 

 / = 1.0, M is comparatively small. The experimental curves show the 

 largest dependence of log A on V for / = 0.6 and only a small de- 

 pendence for / = 1. In this respect too, experiment confirms the 

 theory. 



Non-uniformities on the cathode affect the shape of the retarding 

 potential curves as was explained in a previous section. Here too, 

 there is at least qualitative agreement between theory and experiment. 



In connection with the analysis of log i vs. yj F curves we have, in 

 the course of the last five or six years, developed a number of simple 

 methods for computing approximate values of b and /jl. We have also 

 proved a number of useful theorems. If and when the interest in 

 this subject warrants it, we intend to publish these methods and 

 theorems. 



Checkerboard with Uniform Charge Distribution 



While the agreement between experimental log ivs.yjF curves with 

 theoretical curves based on a hill and valley charge distribution over a 

 checkerboard array is quite good, it is probable that even better 



