UO2核燃料中Xe气泡演化的相场模型与分析

Abstract

在UO2核燃料中, 由于空位和Xe气体原子形成能较大, 导致其在核燃料基体中的热平衡浓度极低, 因此通 过传统相场方法难以定量地研究UO2中气泡的演化过程. 本文针对这一问题, 提出了一个定量的相场模型. 根据 热力学理论以及KKS模型推导出系统的自由能密度方程. 利用该相场模型可以研究极低空位和Xe气体原子浓度 下纳米尺度气泡生长演化过程. 本文分别研究了空位和Xe气体原子产生速率以及温度和温度梯度对气泡演化的 影响. 研究发现在高温和高的空位以及Xe气体原子产生速率下气泡生长较快. 纳米尺度的气泡在向高温区移动 过程中沿温度梯度方向被拉长. 同时模拟结果也证实了核燃料中心空洞的形成. 基于本模型的模拟结果与经典速 率理论以及实验观察一致. Owing to the large formation energy of vacancies and inert gas atoms (Xe and Kr) in nuclear fuel (UO2), the thermodynamic equilibrium concentrations of these species are extremely low in the UO2 matrix, which makes it extremely difficult to conduct quantitative study of gas bubbles evolution by phase-field method (PFM). In this study, a more physics based quantitative phase-field model has been proposed. The free energy density of the system was derived according to the principles of thermodynamics and KKS model, the UO2 tri-vacancy, Xe gas atoms and gas bubbles were considered in the system. This model enables one to study the gas bubble growth with extremely low concentrations of vacancy and Xe gas atom in the UO2 matrix. The influence of temperature, vacancy and Xe gas atom generation rates on single and multi-gas bubbles evolution were studied. At high temperature and with high generation rates of vacancies and Xe gas atoms, the gas bubbles had higher growth rate. In addition, the effect of temperature gradient on gas bubble migration was also studied by adding a temperature gradient term in the Cahn-Hillard equations. The gas bubble preferred to migrate to high temperature area. Their shape changed from initial circular shape to a prolate shape along the direction of temperature gradient, which is consistent with the experimental results. The simulation results confirmed the formation of center cavity in the nuclear fuel pellet. The simulation results are consistent with the classical rate theory and experimental observations.