Evaluating anisotropic surface energies using the capillarity vector reconstruction method

By measuring the geometry and crystallography of the three interfaces that meet at grain boundary thermal grooves, it is possible to determine the anisotropy of the surface free energy. Previously, the surface energy of MgO at 1400 deg C in air was approximated by a truncated double Fourier series with coefficients that were determined by fitting the observations to Herring's condition for local equilibrium at a triple junction. The purpose of this paper is to describe an alternative analysis of the same data set that is not limited by an assumed functional form of the surface energy. In this case, the space of surface characters is discretized and each orientation is associated with a capillarity vector (according to the Cahn-Hoffmann definition). The set of capillarity vectors that most closely satisfies the condition for local equilibrium at each triple junction is then determined by an iterative method. The relative surface free energies derived from this analysis are more anisotropic than those derived from the series fit and more consistent with the observed faceting of MgO in air at 1400 deg C. The relative surface energies of the low index planes are gamma sub 110 / gamma sub 100 = 1.07 plus/minus 0.04 and gamma sub 111 / gamma sub 100 = 1.17 plus/minus 0.04.