Boundary correlation functions and interface formation in two-dimensional solids

Abstract

Two-point correlation functions at the rectilinear boundary of a two-dimensional crystal half-space on a reference lattice are studied for the case of free boundary conditions. We show that the power of the decay law of the positional correlation function at the surface satisfies η surf = 2η bulk, within the approximation that dislocation pair correlations are taken into account. Dislocations at the boundary form a quasi-one-dimensional plasma for T ≠ 0 and this may lead to a dynamic roughening of the surface. Formation of dynamic interfaces in grain boundaries and near free boundaries is discussed in terms of 1-dimensional charged gas models with long-range interaction. Melting of boundary layers at T surf c< T bulk c is suggested to be possible only if topological effects of moving dislocations on the reference lattice are taken into account.