An analysis of two classes of phase field models for void growth and coarsening in irradiated crystalline solids

Materials Theory

A. El-Azab²  K. Ahmed³ 

[1] M University, College Station, USA;Present address: Department of Nuclear Engineering, Texas A&School of Nuclear Engineering, Purdue University, West Lafayette, USA

关键词: Phase field models;    Voids;    Irradiated solids;    Asymptotic analysis;   

DOI  :  10.1186/s41313-017-0008-y

学科分类：凝聚态物理

来源: Springer

【 摘 要 】

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.

【 授权许可】

CC BY