Surface energies in atomistic systems

Some of the most striking effects that dominate the behaviour of microscopic systems are caused by interfacial energies. One example are surface-relaxation patterns. For a simplistic atomistic model based on pair-potentials which describes the elastic behavior of a monatomic crystal it can be proven that the first correction term of the total energy can be written as a surface integral. The integrand is implicitly defined by a family of algebraic equations that determine the relaxation pattern. Numerical computations suggest that the associated Frank-diagram is differentiable only for irrational surface normals.