| A multi-phase field method is presented both in two and three dimensions to model grain boundary migration and to study the effect of anisotropy in boundary energy on populations during grain growth. The misorientation-dependent distribution of boundaries is correlated to the anisotropy in boundary energy, which scales with the sum of surface energies for grains on either side. These surface energies are inclination-dependent in the crystal frame of reference. The steady-state morphology of isolated grains, shrinking with time, is different for varying anisotropic conditions. For a given anisotropy of boundary energy, it is shown that the evolution of grain boundary character is different in the case of isolated shrinking grains when compared to that of polycrystalline grain growth. The effect of different boundary conditions imposed at junctions is found to be the key factor influencing the development of anisotropic grain boundary character in polycrystalline systems. In the later half of the present work grain boundary energies for arbitrary boundary types are estimated through use of appropriate interpolation methods and distance metrics. The anisotropy in boundary populations is correlated to the anisotropy in interpolated energies to demonstrate that for an initial random texture, an inverse relation between boundary energy and population holds true across the entire grain boundary space. |
