Adsorption patterns and adsorbate–adsorbate interactions up to third neighbors on fcc(1 1 0) surfaces

Low temperature adsorption of particles on a semi-infinite fcc(1 1 0) surface is studied at thermal equilibrium. The chemical system is not specified, neither the atoms comprising the surface, nor the particles in the gas phase. No a priori assumptions are made as to whether forces are attractive or repulsive, or as to their relative strength. The phases and transitions between phases are obtained from the largest eigenvalue of a matrix, constructed recursively in terms of the width M of the surface. Numerical results fit exact analytic expressions in M and the Fibonacci sequence. Extrapolation to the infinite two-dimensional surface exhibits phases at 1/4, 1/2 and 3/4 coverage. Agreement with the following specific systems is discussed: H and CN on Rh(1 1 0), Cl, S and O on Ni(1 1 0), S and Co on Cu(1 1 0), and Br on Pt(1 1 0). Experiments are suggested to determine adsorbate–adsorbate interaction energies.