  We investigate connections between the continuum and atomistic descriptions
of deformable crystals, using certain interesting results from number theory.
The energy of a deformed crystal is calculated in the context of a lattice
model with general binary interactions in two dimensions. A new bond counting
approach is used, which reduces the problem to the lattice point problem of
number theory. The main contribution is an explicit formula for the surface
energy density as a function of the deformation gradient and boundary normal.
The result is valid for a large class of domains, including faceted (polygonal)
shapes and regions with piecewise smooth boundaries.
