Toward Modeling Charge-Defect Reactions at the Atomistic Level

Defect reactions involving charged species are commonplace in nuclear fuels fabrication and burn-up. Even the simplest of these fuels, uranium dioxide (UO2), typically involves the nominal charge states of +3, +4, and +5 or +6 in U and -1 and -2 states in O. Simulations that attempt to model evolutionary processes in the fuels require tracking changes among these charge states. At the atomistic level, modeling defect reactions poses a particularly vexing problem. Typical potential energy surfaces do not have this type of physical phenomena built into them. Those models that do attempt to model charge-defect reactions do not have especially strong physical bases for the models. For instance, most do not obey established limits of charge behavior at dissociation or lack internal consistency. This work presents substantial generalizations to earlier work of Perdew et al. No matter the size of the system, total system hamiltonians can be decomposed into subsystem or site hamiltonians and coulombic interactions. Site hamiltonians can be evaluated in a spectral representation, once an integer number of electrons are assigned. For both pair and individual site hamiltonians a dilemma emerges in that many sites are better understood as possessing a fractional charge. The dilemma is how to weight the site integer-charge states in a physically consistent manner. One approach to solving the dilemma results in two distinct charge-dependent energy contributions emerge, arising from intra- and inter-subsystem charge transfer. Further analysis results in a model of the intra-subsystem charge-transfer that can accommodate the mixed valence states of either U or O in nuclear fuels. Mixed valence properties add complications to the model that originate in the phenomenological fact that it typically requires different amounts of energy to increase or decrease charge. As a result of the inherent complexity one has the option of using multiple charges, a concept with strong ties to shell models, or modeling parameters not directly related to charge as functions of charge. This latter approach is illustrated by invoking a minimization principle that does preserve the important dissociation limits of Perdew et al., in order to complete the model.