Abstract Due to the large formation energy of vacancies and noble gas atoms at interstitial and/or substitutional sites in nuclear fuel (UO2), the thermodynamic equilibrium concentrations of these species are very low in the nuclear fuel matrix even at very high temperature, which imposes difficulties upon the quantitative study of bubble evolution via the phase-field method. In this study, a quantitative phase-field model is proposed to deal with this problem. The free energy density of the system is derived according to the principles of thermodynamics, with consideration of the elastic interaction and internal pressure of each gas bubble, and with the use of material parameters from experiments. The model enables one to study the kinetics of gas bubble growth with very dilute concentrations of vacancy and gas atoms in the matrix. With this model, the growth of a single bubble and multiple bubbles were simulated under different concentrations of vacancy and gas atoms and at different temperatures. The effect of elastic interaction energy and the generation rate of vacancies and gas atoms on bubble growth are analyzed.

中文翻译：

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UO2中气泡演化的定量相场模型

摘要 由于空位和惰性气体原子在核燃料 (UO2) 的间隙和/或取代位点的形成能很大，即使在非常高的温度下，这些物质在核燃料基质中的热力学平衡浓度也非常低，这对相场法定量研究气泡演化的难点。在这项研究中，提出了一个定量相场模型来解决这个问题。该系统的自由能密度是根据热力学原理，考虑到每个气泡的弹性相互作用和内部压力，并使用实验中的材料参数推导出来的。该模型使人们能够研究基质中空位和气体原子浓度非常稀薄的气泡生长动力学。使用该模型，模拟了在不同空位和气体原子浓度以及不同温度下的单个气泡和多个气泡的生长。分析了弹性相互作用能以及空位和气体原子的产生率对气泡生长的影响。