Introduction

Fundamental understanding of nuclear fuel materials has of major interest in order to predict fuel performance. One major area of work is the study of diffusion of defects, as these can affect the mechanical properties of the fuel elements. Conventional methods and fuel performance codes have relied mostly on chemical rate theories and experimental data to model fuel performance. More recently, as computational power has evolved, modeling work of nuclear fuel materials at the atomic level has been carried out. However, this subject remains a big challenge today, due to the unavailability of reliable interatomic atomic potentials. These potentials can be used to predict multiple mechanical and thermodynamic properties, defect chemistry and defect transport phenomena, but because of the way they are derived (often by fitting parameters to experimental data, or from first principles calculations), they are often unable to accurately predict multiple material properties simultaneously. For example, using a potential derived by fitting parameters to experimentally determined lattice constants in an atomic scale simulation might very accurately reproduce measured lattice constants for different systems, but might fail to accurately reproduce the measured specific heat for the same systems. When attempting to simulation defect diffusion, it therefore critical that the interatomic potential used be validated before it is used to predict results.

The goal of this study is to develop a generalized kinetic Monte Carlo (KMC) code to simulate defect diffusion that can be used both as a validation tool and as a predictive tool. This code uses migration energies that depend on the migrating particle's local atomic environment. These migration energies are calculated in advance, using Molecular Dynamics (MD) simulations with the desired interatomic potential. As a validation tool, the code would be run using migrations energies generated from the desired interatomic potential and the results would be compared to experimental data. As a predictive tool, the code would be run using migration energies generated from a validated interatomic potential in order to predict data that has not yet been obtained experimentally.

Uranium oxide (UO$_2$) is the primary fuel used in most nuclear power plants in the United States today. However, because it is radioactive, there are many practical difficulties involved with studying it experimentally. Cerium oxide (CeO$_2$) has attracted a lot of attention as a surrogate for uranium oxide because it exhibits many of the same material properties, but is not radioactive. Thus, but studying defect transport and interactions in cerium oxide, similar insight can be gained into defect transport and interactions in uranium oxide. To demonstrate this code as a validation tool, the effect of dopant concentration on oxygen diffusivity in lanthanum-doped cerium oxide is calculated using three different interatomic potentials and compared to experimental data. Lanthanum was chosen as the dopant species mainly because lanthanum is a common fission product created by nuclear fission, so understanding the effects of lanthanum in cerium oxide helps in the understanding of the effects of lanthanum in uranium oxide fuel, and also because, as will be explained later, lanthanum introduces a controllable level of oxygen vacancies, which can help clarify the hypostoichiometric effects in cerium oxide and uranium oxide.