372 PHENOMENA, ATOMS, AND MOLECULES 



distributed over the ideal surface plane (i.e., distributed with uniform 

 probability per unit area). 



Since the adatoms are held by strong forces originating from the under- 

 lying tungsten atoms which are arranged in a definite surface lattice, there 

 must be a strong tendency for the adatoms to occupy definite positions 

 (elementary spaces) on the surface. Experiments on the mobility of 

 caesium adatoms on tungsten ^^ have shown that the activation energy 

 needed to cause an adatom to hop from one elementary space to an adjacent 

 one is about 0.6 electron-volts. Introducing this value into the exponent of 

 Eq. (46) we find that at T = 1000° the probability per unit volume for 

 the occurrence of an atom (i.e., its nucleus) in the potential depression near 

 the center of an elementary space is 1050 times as great as the correspond- 

 ing probability for a position at the potential barrier which separates the 

 elementary spaces. 



Thus the adatoms are normally oscillating about equilibrium positions 

 corresponding to the elementary spaces, with amplitudes which are rather 

 small compared to the distance between elementary spaces, and only rarely 

 hop from one position to another. 



Evaporation of adatoms from dilute films 



With the foregoing concept of elementary spaces, it might seem reason- 

 able to postulate that most of the evaporating adatoms pass from their 

 normal positions directly into the vapor phase as emergent atoms. If we 

 think of the reverse process, however, we recognize that since the flight 

 termini must be uniformly distributed over the surface, the incident atoms 

 cannot in general have paths which lead them directly to the normal equi- 

 librium positions. A large portion of the incident atoms must make their 

 first contact with the surface in positions close to the potential barriers, and 

 if a = I all of these must then move to their final normal positions by a 

 series of hops. Conversely, we must reason, by the reversibility principle, 

 that a large fraction of the emergent atoms have flight origins near the 

 potential barriers in spite of the low concentration of adatoms in these 

 regions. 



A little closer consideration shows that although at the barrier the con- 

 centration is only i/ioooth of that at the normal positions, this difference 

 is counterbalanced by the fact that the probability of evaporation of any 

 atom at the barrier is 1000 times as great as for an atom in a normal 

 position. Thus the evaporation is essentially uniform over the surface, 

 althousfh the distribution of adatoms is nearlv discontinuous. 



It is thus evident, if a = i, that hopping paths must be enormously 

 more numerous than emergent paths. Surface mobility is an essential part 

 of the mechanism of evaporation. 



