Computational Method of Grain Boundary Energy Consistent for Different Orientations and Applications to Double Gyroid Beyond Twinning

Abstract

We develop the method for computing grain boundary (GB) energy consistent for different grain orientations for phase-field type models. The computation is carried out in a parallelepiped domain such that public periodicity is attained along two edges parallel to the dividing plane of two grains. The width of the normal direction is carefully chosen such that the part of each grain in the computational domain can be reassembled into several unit cells. In this way, the bulk energy per volume in the computational domain is identical to the energy density of a unit cell, so that GB energy of different orientations can be obtained in a unified standard. We apply this method to the study of four double-gyroid (DG) GBs with different orientations numerically using the Landau–Brazovskii free energy, including the (422) twin boundary studied recently, a network switching GB, and two tilt GBs. Topological variations and geometric deformations are investigated. It is found that deviations in strut lengths and dihedral angles from the bulk DG substantially exceed changes in strut angles and nodal coplanarity. We also examine the spectra along the contact plane of two grains and utilize them to evaluate the GB widths. Of the four GBs we study, the network switching GB changes to the least extent topologically and geometrically, meanwhile has the lowest energy and the smallest GB width.