52 PHENOMENA, ATOMS, AND MOLECULES 



is very high, we might expect these atoms to evaporate before finding places 

 in the first layer. On this basis, therefore, instead of Eq. (i6), the ex- 

 pression for the rate of arrival of atoms in the first layer should be 



a^ = ajl~ ©")«. (i8) 



Some experiments were made to test the reasonableness of these con- 

 clusions. The bottom of a tray was covered with steel balls (^ inch 

 diameter) closely packed into a square lattice and cemented into position. 

 This surface thus possessed many of the features of a homogeneous crystal 

 surface, the steel balls corresponding to the individual atoms. When other 

 balls of the same size were thrown on to the surface, they occupied definite 

 elementary spaces, each being in contact with four underlying balls. The 

 number of such elementary spaces (except for an edge correction) was the 

 same as the number of balls which were cemented into place (zero layer). 

 A large number of balls, sufficient to cover the fraction of the available 

 spaces, was placed in the tray (in first layer) and the tray was shaken to 

 give a random distribution. A small number of additional balls was then 

 dropped at random from a height of 5 cm. to the surface, and the number 

 of these which went into the second layer was counted. It was found that 

 the probability P that a given incident ball would occupy a position in the 

 second layer was quite accurately given by 



The fraction of the incident balls finding positions in the first layer was 

 thus 1—0^-^. A comparison of this with Eq. (18) gives a value of n=4.5. 

 The reason that n is greater than 4, the number of underlying atoms, is 

 probably that the kinetic energy of the balls causes some of them to roll 

 from their positions of first contact. 



Applying these results to adsorption, we should expect that, until is 

 very close to unity, all atoms incident on the surface should reach positions 

 in the first layer without any opportunity of evaporation or reflection, even 

 if the evaporation rate in the second layer is very high. 



Effect of Forces Acting betzveen Adatoins (28). The fact that 2 

 adatoms cannot occupy the same elementary space at the same time must 

 mean that they exert repulsive forces on one another. This will manifest 

 itself in the equation of state of the adsorbed atoms by a factor such as the 

 1—0 in the denominator of the first term of the second member of Eq. (7). 

 This means that the spreading force tends to rise indefinitely as ap- 

 proaches the value unity. Combining this equation of state with Gibbs' 

 equation, and assuming a = i, we obtain for an adsorption isotherm the 

 equation 



In (v/0) = In [1/(1 - 0)] + 1/(1 - 0) + const. (20) 



