56 PHENOMENA, ATOMS, AND MOLECULES 



in increasing the electron emission. It has been possible to develop this 

 relationship between Va and Ve into a quantitative theory. 



A single caesium adatom on a tungsten surface may be regarded as an 

 ion held to the metal by its image force. The image and the ion thus 

 constitute a dipole, having an electric moment M, oriented with its axis 

 perpendicular to the surface. Because of the strong electric fields close to 

 the ion when it is adsorbed on the surface, we should expect the conduction 

 electrons in the metal to be drawn towards the ion so that the dipole 

 moment should be considerably less than we would calculate for a caesium 

 ion at a distance from an ideal metal surface equal to its radius. The ex- 

 perimental values of M have actually been found to be 16.2 X lO"^^, 

 whereas we calculate 25 X io~^^ for a spherical caesium ion in contact 

 with an ideal conducting plane. 



The force f between two such adion dipoles is given by 



f = (3/2)MVr^, (21) 



where r is the distance between the adions. 



We may now work out the equation of state of the adsorbed caesium 

 films in terms of these forces by means of Clausius' virial equation whic^^ 

 for surfaces takes the form 



F = okT + {i/4)o2{Tl), (22) 



where the summation is to extend over all adatoms which act on any one 

 adatom. The forces f are of two kinds : first, the long range forces which 

 correspond to the dipole repulsion given by Eq. (21), and second, the 

 short range forces acting between atoms in contact which prevent any two 

 from occupying a single elementary space at the same time. These short 

 range forces may be taken into account by dividing the second member of 

 Eq. (6) by (i — 0), as has already been done in Eq. (7). In this way 

 by an integration process it has been possible to derive the general equation 

 of state for adsorbed atoms which repel as dipoles. This equation is 



F = akT/(l - Q) + 3.34 a^'^M2 + 1.53 X lo-sa^T'^M^'^I, (23) 



where I is an integral whose numerical value can never exceed 0.89 and 

 which can be obtained from tables and curves from the value of M, 

 and Oi. 



The spreading force F calculated in this way cannot be measured 

 directly for a solid surface but it can be related to the rate of evaporation Va 

 by means of Gibbs' equation 



-^ = akT. (24) 



d In Va 



