796 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 



ments of this type were done at Bell Telephone Laboratories by L. H. 

 Germer; they do not fall within the scope of this article, but we may be 

 sure that Davisson was interested in them. 



Davisson also studied the refraction of electrons at the surface of nickel, 

 and this is work which in my opinion has never received the attention that 

 it merits. Let us consider its importance. 



I have already spoken of the work which an electron must do in order to 

 quit a metal, and have mentioned two ways employed by Davisson (and 

 by others) to ascertain its value — the measurement of the constant b which 

 figures in Richardson's equation, and the measurement of the quantity 

 by the calorimetric method. It is customary to ascribe this work of egress 

 to the presence of a "surface potential-barrier," usually imagined as an 

 infinitely sudden potential-drop occurring at the surface of the metal: the 

 potential immediately outside the metal is supposed to be less than the 

 potential immediately inside by a non-zero amount, which I will denote by 

 X. One is tempted to identify X with and with kb/e\ but this is an over- 

 simplification. By the classical theory there is a difference which is small 

 but not quite negligible. By the new theory there is a difference which is 

 neither small nor by any means negligible. By the new theory, in fact, X 

 is greater than <^ by an amount which is equal to the so-called "Fermi 

 energy" — the kinetic energy of the electrons which, if the metal were at the 

 absolute zero of temperature, would be the fastest-moving electrons in the 

 metal. Now, this last amount is of the order of half-a-dozen electron-volts 

 for the metals of major interest in thermionic experiments, and so also is 

 the value of 0. Thus, if there were a method for determining the height of 

 the surface potential-barrier, this would be expected to yield a value of the 

 order of six volts if the old theory were right and a value of the order of 

 twelve volts if the new theory were correct. 



Well, there is such a method, and it consists precisely in observing and 

 measuring the refraction of the electron-waves as they pass through the sur- 

 face of the metal. This refraction has a deceptive effect; it alters the orient- 

 ations of the diffraction-beams as though the crystal were contracted in the 

 direction normal to its surface. Once this is comprehended, the refractive 

 index may be calculated from the observations, and from the refractive 

 index the value of X the surface potential drop. This was done by Davisson 

 and Germer for nickel, and published in the Proceedings of the National 

 Academy of Sciences for 1928. The value which they found for the surface 

 potential-drop was 18 volts — three times as great as the value prescribed 

 by the old theory, half again as great as the value afforded by the new. 

 Thus the experiments speak for the new theory over the old, yet not with 

 unambiguous support of the new. This has been described to me, by a dis- 



