382 PHENOMENA, ATOMS, AND MOLECULES 



equation to be at least roughly applicable to surface diffusion. Putting 

 ■^ = I33> <?! = 3-56 X lo^^ and T = 500 (the mean temperature) we find 

 from Eq. (65) 



logio T = - 13.4 + o^z^/T. (66) 



The values of T2 calculated from this equation by putting 0.43& = 1000 

 are of roughly the same magnitude as those by Eq. (64) . A change of about 

 10 percent in the assumed value of the coefficient of i/T would bring the 

 two equations into agreement at a given temperature. 



The values of T2 calculated from Eq. (64) are given in the 4th column 

 of Table VI, and D2 calculated from these by Eq. (57) taking 



02 = 5.3X10-8 (67) 



is given in the 6th column while the time of transit 0^2/^2 is given in the 

 5th column. 



The last column of Table VI gives the evaporation life of adatoms in 

 the 2nd layer as calculated from Eq. (49). Comparing t with T2 and ^2/^2 

 we see that at T = 300 each adatom in the 2nd layer moves through about 

 10^^ elementary spaces before evaporating and even at 700° it moves 

 through 10^ spaces during its life. This fact affords a simple explanation 

 of the high values of a. 



Surface random flux 



A very useful concept ^^ in the study of electric discharges in gases is 

 that of random current density Ig- If n is the number of electrons per 

 unit volume in a uniform plasma and v is their average velocity, then across 

 any imaginary plane there is a current density Ig ={i/4)nve of electrons 

 which pass across the plane from one side to the other and an equal current 

 of electrons passing back in the opposite direction. 



Similarly for the motions of adatoms on any surface in a steady state 

 we may define the random flux density qp as the number of atoms per unit 

 length which cross any imaginary line in the surface from one side to the 

 other (while an equal flux passes in the opposite direction). 



If the adatoms move in random directions parallel to the plane of the 

 surface with the average velocity v, then one-half the atoms on one side of 

 the line are approaching the line with an average velocity (2/k)v. Thus we 

 find 



^={1/Tr)av = (<ri/T)ev. (68) 



^^ I. Langmuir and H. Mott-Smith, G. E. Rev., zj, 449 (1924) ; I. Langmuir and 

 K. T. Compton, Rev. Mod. Phys., 3,221 (1931) 



