NUCLEAR-DEBRIS FORMATION 1: favored by small particles and rapidly diffusing molecules. Einstein’: equation i-— 2 ~ 2Di> provides a helpful rule of thumb in this regard. This equation relate: the time t required for the mean-square displacement ¢? to the coefficient of interdiffusion D,,. To estimate the time required to approacl a Significant degree of equilibrium, we can calculate the time required for & to equal one-tenth of a particle diameter. The degree achieved in this time will be appreciable as shown in the section en- titled “Particle Diffusion.” Thus, for D,, equal to 5 x 107’ cm’/see, : 100-y-diameter particle would be well on the way to equilibrium ir about a second, Interdiffusion coefficients for fission products ir fused silicates are scarce. Figure 7 shows some cases that have beer measured, together with some for elements that reasonably approxi- mate fission products. Thus the curves for Rb* and Cs* in Na,O*Ca0O : 4SiO, would probably be similar to, but below, that for Na*, with Cs’ being lowest. Similar relations would be expected among Sr’*, Ba’*, and Ca’*, To determine the validity of the thermodynamic equilibrium treat- ment under different conditions, one must compare the diffusion times with the cooling rate. The cooling rate is easily calculated by com- bining Hillendahl’s equations,'® ~0.34 T(°K) = 7000 W(kt)-°-°" («| fmax and 49 t tmax(Sec) = 0.037 W(kt)” to eliminate t;,,,, (the time of the final maximum) and differentiating the result. The cooling rate, in terms of either time or temperature, is then given by AT _ p7gyyt-10 pots at _ = 30w -~029 T (rans) 3.94 \" =3x 107! w-?-3 74 The last equation was used to prepare Fig. 8, which shows cooling rate as a function of temperature for a wide range of total yields. We can now see what would happen during the 1-sec equilibration time referred