Atomistic modeling of the U-Zr system

Simulation of the behaviour of multicomponent alloy systems under high temperature and neutron flux conditions is of interest to recent activities related to science based advanced modelling and simulation of nuclear fuels. In particular, multicomponent U-Z, U-Pu-Zr, and U-TRU-Zr fuels are of interest to advanced fast reactor systems. Issues related to the performance of those fuels, such as constituent redistribution and fuel cladding chemical interaction, are the focus of some of the advanced simulation activities. The activities aim at replacing empirical relations that describe those phenomena with mechanistic models that are based on fundamental understanding at different scales ranging from the atomistic level to the macroscopic level. Presented in this paper are atomistic level simulations of the two phenomena in relation to the U-Zr based fuels. The simulation is based on the BFS method which is a quantum approximate method that allows for straightforward atom-by-atom analysis of multicomponent systems without limitations on the number of elements considered. The method, based on perturbation theory and the equivalent crystal theory, is founded on the assumption that the energy of a system can be computed as a sum of individual contributions from each atom in the system. In turn, such contributions can be partitioned between strain (structural) and chemical (composition) effects via corresponding virtual processes that simulate the actual process of alloy formation by changes in the electron density in the overlap region between a given atom and its environment. Due to this formulation the method is free of limitations on the number and type of elements. It provides equal accuracy for simple binary systems or multicomponent systems allowing for the simulation of complex systems such as those resulting from the interaction between a multicomponent fuel and its cladding. The methodology has been applied previously to modelling and simulations of the interaction of UMo-based fuels with Al cladding in low enrichment test reactors. Here, the methodology is applied to the U-Zr fuel system. First,the fundamentals of the methodology are discussed. Its first principles-based parameterization of the U-Zr system is presented,in addition to validation and verification of the parameters via comparison to the experimental phase diagram and properties of the U-Zr solid solution. For example, using results from large scale simulations, the concentration dependence of the lattice parameter as a function of temperature is estimated, as shown in Fig. 1. Other properties used for validation include the coefficient of thermal expansion. Fig. 2 shows preliminary results for Fe interdiffusion (red spheres) in U-10 wt%Zr (blue-yellow) with increasing temperature. Similar results are also presented for the U-Pu-Zr system for the characteristic range of concentrations considered for such fuels. This provides insight into the changes in composition and concentration associated with this interdiffusion phenomenon that is fundamental to the understanding of fuel cladding chemical interaction in this fuel type. Finally, the well-known constituent redistribution due to temperature gradient in the fuel is dealt with by means of a finite temperature BFS-based algorithm. The algorithm is designed to determine the concentration profiles for arbitrary changes in temperature distribution in the fuel. Validation of these results will be done with available experimental data of concentrations profiles in U-Zr and U-Zr-Pu fuels