Surface steps as interacting fermions: An approach to the disordering of surfaces with sublattices

Abstract

The problem of thermal structural disordering of the fee (110) crystal surface is formulated in terms of a system of interacting domain walls, representing the elementary defects ((111) steps) of the flat surface. The method is quite general and may be extended to other systems, such as the fee (111) surfaces. The theory makes use of the known (approximate) mapping of the two-dimensional statistical mechanics problem on a one-dimensional fermionic hamiltonian, but here two fermionic bands, multiple-hopping and short-range finite interactions must also be included. The phase diagram of a recently proposed extended body-centred solid-on-solid (BCSOS) model of noble-metal fee (110) surfaces is derived by means of a mean-field calculation for the ground state energy of the quantum hamiltonian which has the advantage of reproducing the exact classical ground state structure. Good agreement with results previously obtained by Monte Carlo simulation on the BCSOS model is obtained, indicating that the present treatment is qualitatively, as well as semiquantitatively, correct as far as the phase structure is concerned. Deconstruction, pre-roughening and roughening transitions are detected and the criteria for the occurrence of these disordering phenomena are recast in terms of microscopic step-step interaction parameters.