3 80 PHENOMENA, ATOMS, AND MOLECULES 



When the time of transit a/v is not negligible, Eq. (56) needs to be 

 modified merely by adding a/v to t so that 



p = aV4(T+aA2), (57) 



where v^ the average velocity parallel to the plane of the surface (2-dimen- 

 sional velocity) is given in cm sec."-^ by 



v, = {rkTllni)'^ = nAlKTIM)\ (58) 



M being the molecular or atomic weight. 



If T is negligible compared to afv^, this reduces to 



D = (l/4)ay2. (59) 



In the elementary kinetic theory of gases it is shown ^^ that the co- 

 efficient of self-dififusion of a gas is Z) = (i/3)A37;3 where Vz is the average 

 (3-dimensional) molecular velocity and X3 is the 3-dimensional free path. 

 A similar calculation for the 2-dimensional case of surface diffusion leads to 



Z)= (l/2)>.2Z^2, (60) 



where \i is now the length of the projection of the free path on the plane 

 of the surface. If we identify Xo with a, this equation is the same as Eq. (59) 

 except for the numerical factor. This difference is due to the fact that in 

 deriving Eq. (60) it was assumed that all directions of motion in the plane 

 are equally probable, while for Eq. (59) the motions were taken to be 

 parallel to the two axes of the square lattice. 



Measurements of the surface diffusion coefficient D\ for Cs adatoms on 

 tungsten for an average value of Q of about 0.03 have given,^^ for the 

 temperature range from 650 to 812° K., 



logio Z)i = — 0.70 — 3060/r. (61) 



Since the number of tungsten atoms per cm^ on a tungsten surface is 

 1.425 X 10^^ we must take this to be the number of elementary spaces and 

 thus get 



ax = 2.64 X 10"^ cm. (62) 



Using this value of ai a;nd the value of V2 from Eq. (58) we calculate Ti 

 at various temperatures in the range from 650 to 812° and find that they 

 are represented by 



logio Ti = - 15.09 + 3082/r. (63) 



^^ See for example Dynamical Theory of Gases, J. H. Jeans, p. 326, Cambridge, 

 2nd Edition. 



