Modeling of the Simultaneous Evolution of Vacancy and Interstitial Dislocation Loops in hcp Metals Under Irradiation

Abstract

We present a model of the homogeneous nucleation and growth of vacancy and interstitial loops in irradiated hcp metals, which allows one to find the size distribution function, the dose dependence of the mean parameters of the dislocation system, and to describe effects due to temperature, material parameters, and initial microstructure. The model is based on a hierarchy of coupled ordinary differential equations. The first two equations are the rate equations for vacancy and interstitial concentrations. Other equations describe random walks of interstitial and vacancy clusters in a size space, i.e., the time dependence of loop densities. As an input, the model contains the capture efficiencies of point defects by loops, which depend self-consistently on the loop size and dislocation density. We have considered two possible scenarios depending on the point defect dilatation volume ratio: (i) dislocation bias for interstitial atoms and (ii) dislocation bias for vacancies. The model results are qualitatively consistent with experimental observations of a coexistence of interstitial and vacancy dislocation loops on the same habit planes in Zr and other hcp metals. The temperature dependence of the resulting loop size distributions depends strongly on the material properties and the initial microstructure.