On modeling global grain boundary energy functions

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.