A quantitative phase field formalism for void evolution in irradiated crystalline solids

Abstract

Existing phase field (diffuse interface) models for void evolution in solids are not quantitative, in the sense that they do not capture the physics of the sharp interface counterpart. In this work, we introduce a thermodynamically consistent, quantitative phase field model for void evolution in crystalline solids under irradiation. This model considers both vacancies and self-interstitials in the description of void evolution. Unique to this model is fixing the evolution of the non-conserved order parameter describing void surface dynamics by two contributions associated with the interactions of vacancies and interstitials with the void surface by incorporating two mobility parameters in the corresponding Allen–Cahn equation. Asymptotic matching of the phase field model with the sharp-interface theory fixed the two Allen–Cahn mobility parameters in terms of the kinetics of the point defect-surface reactions. The Landau and the gradient coefficients in the free energy construction of the system in its diffuse-interface description are fixed using thermodynamic arguments in terms of the interfacial energy and diffuse interface width. With all the parameters in the phase model clearly expressed in terms of the sharp interface counterparts, we have a novel, quantitative phase field formalism for void evolution in the presence of point defects. To validate this new formalism, several simple test cases were carried out showing the void evolution under simple defect supersaturation scenarios.