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