THERMIONIC ELECTRON EMISSION 427 



etch facets which are oriented at various angles with respect to a mean 

 surface plane. The appearance of the surface is to be compared with 

 an airplane view of a city whose gabled roofs have various designs and 

 various angles. The size and shape of the etch facets depend on the 

 material of the cathode, the crystal size, the orientation of the crystal 

 with respect to the mean surface, the degree of heat treatment and 

 presumably some unknown factors. Theoretically it is possible to 

 deduce values of S, the ratio of the true surface area to the apparent 

 surface area, for certain simple cases. Thus, Tonks ^"^ has computed 

 the following average values of S: For cubic facets or 100 planes, 

 1.500; for dodecahedral facets or 110 planes, 1.225; for 100 and 110 

 planes, 1.129. Some of the assumptions on which these values are 

 based are: (1) The surface is covered with pyramids whose sides are 

 crystal planes; (2) the orientation of crystal axes with respect to the 

 surface is random ; (3) for a given type of etch plane or planes, the 

 facets occur in such a way as to give a minimum surface area. No 

 one has made a thorough investigation to test these assumptions by 

 experiment. Some microscopic pictures of etched surfaces which I 

 have seen showed truncated pyramids in contrast with the first 

 assumption ; they also showed sub-facets, thus violating the third 

 assumption. 



Values of 5 have been obtained from experiments on adsorption of 

 gases on solid and liquid surfaces. Particularly significant experi- 

 ments are those of Bowden and Rideal ^^ on the adsorption of hydrogen 

 ions deposited on metal surfaces by electrolysis of a solution of sulphuric 

 acid. The potential of these surfaces was determined against a 

 calomel electrode. They found that when the electrolytic current 

 exceeded a minimum value, the surface potential increased linearly 

 with the quantity of electricity until it reached a new steady value. 

 For a mercury surface as well as for a thin film of platinum on mercury 

 the potential increased by one volt for 6 X 10~® coulomb/cm. ^ The 

 direction of the potential change and its amount are such as to be 

 expected if hydrogen ions are adsorbed on the surface. For surfaces 

 other than mercury the charge per cm.^ required to change the po- 

 tential by one volt was S times 6 X 10~^ They obtained the fol- 

 lowing values for S: smooth platinum, 2.0; platinum black, 2000; 

 sandpapered nickel, 10; oxidized and reduced nickel, 50. They inter- 

 pret this S as the ratio of the true area to apparent area. Their 

 values are considerably greater than those expected from Tonks' 

 theoretical calculations. 



As a result of this it is my opinion that a considerable amount of 

 careful work must be done before reliable values of S are obtained for 



