THERMIONIC ELECTRON EMISSION 



469 



from equation (80) will only be approximate. The approximation is 

 about the same as computing Pje from equation (78) or (79). Equa- 

 tion (80) has the advantage that Pje is given by a single function. 



20 



0.01 



0.02 0.03 0.040.05 



0.1 



0.2 0.3 0.4 0.5 



1.0 



(&-) 



Fig. 23 — Correlation of P with atomic properties. 



Chittum ^^ has related the work function to the bulk modulus of 

 compressibility in a different manner than that used by Bomke. His 

 computed values of the work function deviate from the experimental 

 values by about the same amount as do the values computed from 

 equations (77) and (80). 



From the fact that metals with large atomic spacing have a low P 

 while those with small atomic spacing have a high P, it might be 

 expected that P would depend on the spacing of the atoms in the 

 surface layer and that different faces of a single crystal would have 

 different work functions. In fact, Farnsworth and Rose ^^ have shown 

 that the contact potential for different faces of a single crystal of Cu 

 varies by about 0.4 volt; and Nitzsche ^^ finds the photoelectric work 

 function of two planes of a single crystal of zinc different by about 0.2 

 volt. Now the values of {DjM) or of the cubic compressibility used 

 in the above calculations do not take into consideration any dependence 

 on the crystal face exposed and, therefore, we would not expect P to be 

 a single-valued function of these properties. This fact may explain 

 the failure to correlate exactly the body properties of the metal with 

 P or the work function. It is quite likely that a better correlation 

 exists between the work function or P and the atomic spacing which 

 prevails on the crystal faces which develop when a metal is heated in a 

 vacuum. 



