THERMIONIC ELECTRON EMISSION 465 



temperature is lowered, — ." The theory predicts this as shown by 

 Fig. 18. There may, however, be another reason: As T increases jx 

 may decrease. If there are differences in concentration between 

 neighboring crystals, and if the temperature is high enough for migra- 

 tion to occur, Boltzmann's law would require that the difference in 

 concentration should decrease as T increases. 



About the third feature they say: "These results indicate that with 

 nearly complete thoriation of the surface (/ = 0.91) and with a bare 

 surface (/ = 0.00) the approach to the Schottky curve is fairly close, 

 but relatively large departures occur with incomplete thoriation." 

 This fact which is abundantly confirmed by my experience not only 

 with thorium on tungsten but also with cesium on tungsten, cesium on 

 oxygen on tungsten, and barium on tungsten means that as/ increases, 

 jLi increases at first, rises to a maximum and then decreases. Such a 

 variation of ju with / is to be expected from the shape of the log i vs. f 

 or (p vs. f curve which will be discussed more fully later on. As / 

 increases, cp decreases rapidly at first, then more and more slowly until 

 it passes through a minimum when/ = 1 ; beyond this point <p increases 

 again. It is natural to expect that A/, the difference between/ for the 

 black and the white squares, should increase with /; A/ is probably 

 nearly proportional to /. From this and the shape of the cp — f curve 

 it follows that A^p, the difference in tp between black and white squares, 

 is small when /is small; as/ increases A(^ increases at first but later on it 

 decreases; when /approaches 1.0, A(p approaches and the surface has a 

 uniform work function. Since /x and Acp are proportional, m should 

 vary in the same way. Hence this feature of Compton and Lang- 

 muir's curves as well as the first two is entirely in agreement with the 

 predictions based on the checkerboard theory. 



Whether the uniform charge distribution or the hill and valley 

 distribution gives better agreement with experiment has not been 

 decided. This, however, is not very important or very pressing. In 

 an experimental filament the distribution is probably neither one nor 

 the other but something in between. Furthermore, it should be 

 emphasized that in an experimental cathode the patches are not all of 

 the same size nor is the contact potential between two neighboring 

 patches a constant; both of these quantities fluctuate about a mean 

 value. Nevertheless I believe that a sufficiently good case has been 

 made out to show that non-uniformities play an important role in 

 many thermionic experiments, and that the checkerboard theory can 

 be used as a powerful tool in the study of adsorption phenomena, where 

 non-uniformities almost always occur. 



This analysis of the effect of non-uniformities has brought out that 



