EVAPORATION OF ATOMS 



383 



If the adatoms, instead of moving with uniform velocity, hop from 

 space to space as postulated in the derivation of Eqs. (54), (55) and (57), 

 we obtain 



^ = aaid{\-e)/'i{T-\-a/v2) = {(TiD/a)e{l-0). 



(69) 



Rate of interchange of atoms between the first and second adsorbed layers 

 Consider that the first layer in a square surface lattice is nearly com- 

 pletely filled by adatoms as indicated in Fig. 28, so that the Oi(i —61) 



|o|o |o]oyete|o| 



-\az\^ 



Fig. 28. First layer in a square surface lattice nearly completely filled by adatoms, 

 denoted by circles. Available spaces in the second layer are indicated by crosses. 



vacant spaces per unit area are separated from one another. The available 

 elementary spaces in the second layer are indicated in the figure by crosses. 

 Each vacant space in the first layer causes a decrease of four in the number 

 of available spaces in the second layer ; this number per unit of filament 

 surface is therefore ai[i — 4(1 — ^1)], which for values of di close to 

 unity agrees with Oi^i^ as deduced previously. 



Any adatom in the second layer which migrates across the dotted line 

 in Fig. 28, which has a perimeter 800, evidently falls into the vacant space 

 in the first layer. Thus the rate p at which atoms pass from the second to 

 the first layer, expressed in atoms cm"^ sec."^, is 



P = 6«2<,?2criil —tf[J. 



(70) 



Under equilibruim conditions this must be balanced by the passage of 

 an equal number of atoms from the ist and the 2nd layers. Thus p may be- 

 termed the rate of interchange between the 2 layers. If this rate is very 

 high compared to the rates of evaporation v or condensation \i from or to 

 the surface, the relative numbers of adatoms in the two layers a^Oi and 

 aiOoOi'^ will be the same whether or not the adsorbed films are in equilibrium 

 with the vapor phase. Therefore the conditions for which the surface phase 

 postulate will be fulfilled are p/v»i, and p/n»i. 



