PLENTIFUL ENERGY

Constant activity coefficients are a good enough assumption as long as the
reactants are present in concentrations where they remain dissolved—that is, for
unsaturated conditions. This comes up in a case important to the cadmium cathode.
Calculations are simplified by the assumption of constant activity coefficients, as
activities are then directly proportional to concentration, from zero to its value at
saturation in cadmium where precipitation of the intermetallic compound begins.
An example of great interest to our process is the degree of enrichment of the Pu
to U ratio in the cathode possible from a given ratio of PuCl 3 /UCl 3 in the
electrolyte. The measured ratio in the electrolyte to the ratio in the cadmium
cathode is given as 1.88 for Pu/U, for example, from the Ackerman and Johnson
results. [3] This says that at equilibrium, the ratio of plutonium to uranium in our
cathode will be only 1/1.88 of the ratio in the electrolyte. The corollary is that for
reasonable enrichments of the material in the cathode—our input fuel material—the
ratio of uranium to plutonium in the electrolyte must be far lower than the ratio
commonly used for uranium deposition.
As we will discuss in some detail in a later section, effects of actinide saturation
of the liquid cadmium cathode have importance in determining its composition at
the end of the run. After saturation of the plutonium in the cadmium, metallic
PuCd 6 can be deposited for a time and will act to increase the Pu/U product ratio.
But increasing the PuCl 3 /UCl 3 ratio from the ratio used for uranium deposition
before using the cadmium cathode at all is an absolute necessity. The maximum
attainable PuCl 3 /UCl 3 ratio is determined by the solid cathode process—we only
run the solid cathode until plutonium impurity in the solid cathode uranium product
becomes excessive. The minimum PuCl 3 /UCl 3 ratio that is usable comes when more
U than is acceptable begins to deposit in the Cd cathode. The PuCl 3 /UCl 3 ratio must
be high enough to make the product ratio adequate for its subsequent use in fuel
enrichment.
We want to establish as well as we can the systematics of the ratios of plutonium
(and other actinide) concentrations to the uranium concentration in the cadmium
cathode product as a function of their ratio as chlorides in the electrolyte. Our final
product can be no more plutonium rich than whatever the ratio of plutonium to
uranium in the cadmium turns out to be. After that, we can further dilute the
product with uranium where we need to in fuel fabrication, but there are no more
steps in the process that could enrich it further.
The equilibrium distributions of plutonium and uranium between the electrolyte
and the cadmium cathode can be calculated from Equation 4 below. This expression
looks complicated, but all it amounts to is equating the two different ways of
writing the equilibrium coefficient, one in terms of in terms of free energy change
(the exponential) and the other in terms of activities ( concentrations multiplied by
their appropriate activity coefficients).
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