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The Interfacial Energy of a Phase Boundary via a Lattice-Cell Average Approach

The calculation of the discrete atomistic energy of a crystal near the continuum limit encounters difficulties caused by the geometric discrepancy between the continuum region occupied by the body, and the discrete collection of lattice points contained in it. This results in ambiguities in the asymptotic expansion of the energy for small values of the lattice parameter, that are traced back to the lattice point problem of number theory. The lattice-cell average of the discrete energy is introduced and is shown to eliminate this ambiguity in various circumstances. It is used to find explicit continuum expressions for surface energies and interfacial energies of coherent phase boundaries in deformed crystals in terms of the interatomic potential.