Thermal effects on interaction of solute atmosphere with a spherical void in three-dimensional elastic solid: Statistical mechanics description with Monte Carlo simulation

Abstract

The distribution of solute atoms around defects is a hot research topic in the solid theory with long-term importance. In the present work, the interaction of solute atmosphere with a spherical void in a spherical elastic solid is studied based on the elastic and statistical mechanics description of solute atmosphere. The rationality of further modeling a solute atom as a point dilatation to obtain the image stress fields is demonstrated. Based on this point dilatation model, a three-dimensional boundary value problem in the framework of elasticity is formulated and solved. The displacement, strain and stress fields due to a point dilatation in a spherical elastic solid containing a spherical void are derived. The statistical mechanics framework is extended to the three-dimensional case of solute atmosphere. Configurational forces on both the solute atoms and spherical void are defined through the gradient of enthalpy and the well-established surface-independent integrals, respectively. Based on the elastic and statistical description of solute atmosphere, Monte Carlo (MC) method is employed to investigate the effects of initial solute distribution and temperature on the solute atom distribution. Carrying out a great number of MC simulations in a wide range of temperature with different total numbers of solute atoms, a metastable equilibrium state is found, which results from the synergistic effects of low temperature and initial solute distribution. It is shown that there are three stages of variations of the enthalpy with the temperature, from which two transition temperatures have been identified.