Abstract
Previous numerical methods that calculate equilibrium particle shape to study thermodynamic and kinetic processes depend on interfacial (surface) free energy functions γ(\(\skew7\hat{n}\)) that have cubic symmetry and thus produce Wulff shapes W of cubic symmetry. This work introduces a construction yielding the minimal surface energy density γconvex(W) that can be determined for any W. Each γ(\(\skew7\hat{n}\)) that belongs to the equivalence class γ(W) bounded by γconvex(W) can be used in an energy-minimizing calculation that depends only on W. For practical numerical calculations, this work gives two methods taking directional distance from specified orientation minima as a parameter to produce analytic forms of γ(\(\skew7\hat{n}\)) giving W as the equilibrium shape for (an otherwise unconstrained) fixed volume. Included are several two- and three-dimensional examples that demonstrate the application and utility of the model γ(\(\skew7\hat{n}\)) functions.
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Siem, E.J., Carter, W.C. Orientation-dependent surface tension functions for surface energy minimizing calculations. J Mater Sci 40, 3107–3113 (2005). https://doi.org/10.1007/s10853-005-2671-7
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DOI: https://doi.org/10.1007/s10853-005-2671-7