932 ADVENTURES IN RADIOISOTOPE RESEARCH 



these measurements made possible the determination of diffusion coef- 

 ficients as small as 10~^^ cm^ per day. 



Our measurements led to the result that, while the diffusion coef- 

 ficient of gold in lead is found to be 5 • 10""^ cm^ day~i at 165°, the coef- 

 ficient of self-diffusion in lead at the same temperature is only 10~^ cm^ 

 day~i, the difference rapidly increasing with decreasing temperature. 

 The change of the value of the coefficient of self-diffusion, D, in lead 

 foils and single crystals is represented by the equation 



-1 



D = 5.76. 10%-2'''°°^'^cm2 day 



Making use of this formula, we can show that, at room temperature, 

 the atoms will change their places in a piece of lead on the average 

 only once in 10 days. 



From the change of the coefficient of self-diffusion with temperature, 

 the heat of activation of the diffusion process, the heat of loosening 

 of the lead lattice, can be calculated. The value obtained and, for pur- 

 poses of comparison, other thermal data are given in Table 1. 



Table 1. — Thermal Data fob. Solid Lead 



kcal. per g. atom 



Heat of melting 



Energy content at the melting point 



Heat of lattice-loosening 



Heat of evaporation 



1.1 



3.5 



27.9 



36.2 



Roberts-Austin measured the diffusion rate of gold in solid lead. 

 His measurements gave the first quantitative determination of diffusion 

 rates in solids. The high values he obtained, shown in Fig. 1 (13), led 

 his contemporaries to consider diffusion in solid metals a comparatively 

 rapid process. The introduction of the conception of self-diffusion and 

 the subsequent development led to a very different view and also to 

 the elucidation of the remarkable nature of the gold-lead system in- 

 vestigated by that pioneer metallurgist. 



The methods outlined above were also applied to determine the self- 

 diffusion rate of Pb"''"'' in solid lead chloride and lead iodide. ^^"^ The 

 variation of the self-diffusion rates with temperature can be expressed 

 by the equations 



D = 1.06 . 10" e-38i2o/«T ^j^j D = 3.43 • 104 g-3oooo/OT^ 



respectively. As first shown by Nernst, the ionic mobilities in an elec- 

 trolyte solution, and hence the conductivity of the solution, can be 

 calculated if the diffusion rates of the ions are known. We can apply 

 the same ideas to solid electrolytes^^*^ and calculate, for example, the 



