Thermal grain-boundary grooving in bicrystal thin solid films having strong anisotropic surface Gibbs free energy represented by the modified cycloid-curtate function

The variational non-equilibrium thermodynamic method is further extended to give full coverage for the tilted grain-boundary (GB) configuration with respect to the sidewalls of a bicrystal thin solid film having strong anisotropic specific surface Gibbs free energy associated with the singular directions (faceting, vicinal planes). A set of critical computer simulation experiments supported by the generalized longitudinal force diagrams is performed on the asymmetrically disposed (inclination) bicrystal thin metallic films having four- and six-fold anisotropic specific surface Gibbs free energy to demonstrate the various GB-groove root topologies caused by the grain-boundary grooving under the surface drift-diffusion driven by the capillarity forces (thermal grooving). In the computer simulations, the strongly anisotropic surface-specific Gibbs free energy associated with the cusp regions is represented by the modified cycloid-curtate function (MCCF) as a basis (generator) for the Dirac delta distribution function on the Wulff construction, which involves not only the Wulff surface roughness (WSR) parameter (anisotropy constant) but also the Wulff surface topography (WST) index (shape parameter) that may be used as a metric for the temperature roughening phenomenon. A special computer run is also designed using the realistic structural and physicochemical properties in order to simulate the thermal groove profiles of cube-textured pure nickel tape {Ni—99.99 wt%} annealed four hours in vacuum at 800 °C, and observed by the atomic force microcopy (AFM). The experimental line width fitting procedure applied to the simulation profile subjected to the self-similarity transformation, which resulted in almost perfect replication of the experimental digitized AFM photography, has yielded a mean surface (mass) diffusivity of nickel about 5.7×10 −13 m 2/s (800 °C), which is in excellent quantitative agreement with the diffusivity relationship at T⩾1300 K reported in the literature on relatively contaminated surfaces, and obtained by high-precision profilometry measurements of the decay of capillary modes associated with the wide surface scratches.