Mesoscale Simulations of Microstructure Evolution in a Temperature Gradient
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Mesoscale Simulations of Microstructure Evolution in a Temperature Gradient Bala Radhakrishan and Gorti Sarma Computer Science and Mathematics Division, Oak Ridge National Laboratory Oak Ridge, TN 37831-6164, U.S.A. ABSTRACT The evolution of pore and grain structure in a nuclear fuel environment is strongly influenced by the local temperature, and the temperature gradient. The evolution of pore and grain structure in an externally imposed temperature gradient is simulated for a hypothetical material using a Potts model approach that allows for porosity migration by mechanisms similar to surface, grain boundary and volume diffusion, as well as the interaction of migrating pores with stationary grain boundaries. First, the migration of a single pore in a single crystal in the presence of the temperature gradient is simulated. Next, the interaction of a pore moving in a temperature gradient with a grain boundary that is perpendicular to the pore migration direction is simulated in order to capture the force exerted by the pore on the grain boundary. The simulations reproduce the expected variation of pore velocity with pore size as well as the variation of the grain boundary force with pore size. INTRODUCTION Fuel pellets of oxide fuels are fabricated by solid state sintering processes that invariably result in the presence of pores in the sintered microstructure. The fresh fuel often undergoes restructuring due to the presence of a temperature gradient that develops because of the internal heat sources generated by nuclear fission. Pores migrate against the temperature gradient either by surface or volume diffusion mechanisms and eventually form a central hole in the fuel [1]. The migrating pores also interact with grain boundaries that offer a drag to their free motion in a single crystal. The overall kinetics of the pore and grain structure evolution are tightly coupled because of this interaction. This initial stage of the reactor operation is quite critical because of the dynamic changes in the fuel thermal conductivity that accompanies fuel restructuring, which in turn determines the instantaneous temperature of the fuel as well as the temperature gradient. The objective of the present simulations is to assess the applicability of the Potts model to simulate the temporal evolution of the microstructure in a fuel environment characterized by the presence of a temperature gradient. The present simulations represent the initial phase of a larger mesoscale simulation program whose objective is to extend the Potts model capabilities to a real fuel material by incorporating lower length scale physics into the model either through experimental data or data derived from atomistic models. THEORY In mesoscale Monte Carlo (MC) simulations, the microstructure is mapped to a two- or three-dimensional regular grid. In mesoscale simulations, the size of each grid point is significantly larger than that of an atom, and the geometry of the MC grid is not related to the crystal geometry. Obtaining material-specific r
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