On modeling global grain boundary energy functions

TL;DR

This paper investigates the modeling of grain boundary energy functions, emphasizing the importance of stability conditions and structural multiplicity, and proposes a method to construct continuous, stable energy functions.

Contribution

It introduces a natural procedure for constructing stable, continuous grain boundary energy functions that account for metastable states and satisfy interface stability conditions.

Findings

Violations of Herring's stability condition are demonstrated.

A method for constructing stable energy functions from data is proposed.

Application to simulated data illustrates the approach.

Abstract

Grain boundaries affect properties of polycrystalline materials. The influence of a boundary is largely determined by its energy. Grain boundary energy is often portrayed as a function of macroscopic boundary parameters representing grain misorientation and boundary plane inclination. In grain boundary simulation and modeling, many studies neglect structural multiplicity of boundaries, i.e., existence of metastable states, and focus on minimum energy. The minimum energy function restricted to constant misorientation should satisfy Herring's condition for interface stability. This requirement has been ignored in recent works on grain boundary energy functions. Example violations of the stability condition are shown. Moreover, a simple and natural procedure for constructing a continuous function satisfying the condition is described. Cusps in the energy as a function of boundary plane inclinations arise because of the imposition of the stability condition, and their locations and shapes result from properties of input data. An example of applying the procedure to simulated data is presented.