Site correlation and the determination of interactions between atoms situated on a 2-d triangular lattice

Site correlations are very sensitive to atomic interactions, especially for weak interactions far from the onset of long-range order. Therefore, they are especially suited for the determination of atomic interactions from STM measurements. In this paper, site correlations are given for dominant repulsive interaction between nearest and arbitrary (repulsive or attractive) interactions between next-nearest neighbors on a 2-d triangular lattice. This scheme simulates a fcc(111) or hexagonal (0001) surface: adatoms in atop sites, constituents of a substitutional alloy segregating or atoms forming a surface alloy there. Interactions considered are limited: J, the interaction between nearest neighbors, to |J/kT|<1 and R, the ratio of next-nearest to nearest neighbor interactions, to |R|<1. Based on a Monte-Carlo calculation, graphs are given for various fixed surface concentrations ranging from 0.15 to 0.50, displaying J/kT and R as functions of the correlations between nearest and next nearest neighbors, pnn/c and pnnn/c. The graphs shown are normalized so as to permit a simple interpolation between them.