Physics – Mathematical Physics
Scientific paper
2008-04-09
Physics
Mathematical Physics
28 pages, 3 figures; removed a worng comment in page 8, removed irrelevant references, longer title
Scientific paper
In this paper we present two atomistic models for the energy of a one-dimensional elastic crystal. We assume that the macroscopic displacement equals the microscopic one. The energy of the first model is given by a two-body interaction potential, and we assume that the atoms follow a continuous and piecewise smooth macroscopic (continuum) deformation. We calculate the first terms of the Taylor expansion (with respect to the parameter representing the interatomic distance) of the atomistic energy, and obtain that the coefficients of that Taylor expansion represent, respectively, an elastic energy, a sharp-interface energy, and a smooth-interface energy. The second atomistic model is a variant of the first one, and its Taylor expansion predicts, in addition, a new term that accounts for the repulsion force between two sharp interfaces.
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