A formal asymptotic analysis of two classes of phase field models for void growth and coarsening in irradiated solids has been performed to assess their sharp-interface kinetics. It was found that the sharp interface limit of type B models, which include only point defect concentrations as order parameters governed by Cahn-Hilliard equations, captures diffusion-controlled kinetics. It was also found that a type B model reduces to a generalized one-sided classical Stefan problem in the case of a high driving thermodynamic force associated with the void growth stage, while it reduces to a generalized one-sided Mullins-Sekerka problem when the driving force is low in the case of void coarsening. The latter case corresponds to the famous rate theory description of void growth. Type C models, which include point defect concentrations and a non-conserved order parameter to distinguish between the void and solid phases and employ coupled Cahn-Hilliard and Allen-Cahn equations, are shown to represent mixed diffusion and interfacial kinetics. In particular, the Allen-Cahn equation of model C reduces to an interfacial constitutive law representing the attachment and emission kinetics of point defects at the void surface. In the limit of a high driving force associated with the void growth stage, a type C model reduces to a generalized one-sided Stefan problem with kinetic drag. In the limit of low driving forces characterizing the void coarsening stage, however, the model reduces to a generalized one-sided Mullins-Sekerka problem with kinetic drag. The analysis presented here paves the way for constructing quantitative phase field models for the irradiation-driven nucleation and growth of voids in crystalline solids by matching these models to a recently developed sharp interface theory.

中文翻译：

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两种类型的相场模型的分析，这些相场模型是辐照结晶固体中的空隙生长和粗化的

进行了两类相场模型的正式渐近分析，以评估受辐照固体中的空隙生长和粗化作用，以评估其尖锐的界面动力学。已经发现，B型模型的尖锐边界限制（仅包括点缺陷浓度作为由Cahn-Hilliard方程控制的阶次参数）捕获了扩散控制的动力学。我们还发现，在与空洞生长阶段相关的驱动热动力很高的情况下，B型模型可以简化为广义单侧经典Stefan问题，而当B型模型可以简化为广义单向Mullins-Sekerka问题时在空隙变粗的情况下，驱动力较低。后一种情况对应于空隙率增长的著名速率理论描述。C型模型 其中包括点缺陷浓度和区分空穴相和固相的非保守阶数参数，并采用耦合的Cahn-Hilliard和Allen-Cahn方程，它们代表混合扩散和界面动力学。尤其是，模型C的Allen-Cahn方程简化为一个界面本构律，代表了缺陷表面处点缺陷的附着和发射动力学。在与空隙生长阶段相关的高驱动力的限制下，C型模型简化为带有动阻力的广义单侧Stefan问题。然而，在表征空隙粗化阶段的低驱动力的极限下，该模型简化为具有动阻力的广义单面Mullins-Sekerka问题。