Order–disorder phenomena in adsorbed layers described by a lattice gas model

Abstract

Order–disorder transitions in adsorbed phases on single crystalsurfaces manifest themselves by variations of the low energy electron diffraction(LEED)patterns. The present paper contains a theoretical treatment of the statistical properties of the simplest structure within this framework, namely a layer which may be described by a square lattice gas model with repulsive interactions between nearest neighbors and giving rise to a c2×2‐LEED pattern on the (100) surface of a fcc or bcc crystal. At a coverage ϑ=1/2 the relative intensities of the half‐order LEED spots are, within the kinematic approximation, shown to be identical to the expectation value of the spin‐correlation function of the two‐dimensional Ising model, averaged over an area corresponding to the coherence width of the electron beam. For ϑ<1/2 no analytic solutions are available, but the problem may be treated by means of the Monte Carlo technique, the results of which for ϑ=1/2 agree quite well with those from the analytic solution. The order–disorder transition temperature is predicted to decrease strongly with decreasing coverage. Below ϑ=0.25 the distinction between ordered and disordered phases becomes more or less irrelevant, a fact made evident by a crude determination of the configurational entropies. The configurational energy, the specific heat of the adsorbate layer and some parameters characterizing short‐range order are evaluated as further quantities. The latter data may be of some importance for the kinetics of ad‐ and de‐sorption. Quantitative comparison with experimental results is so far only possible with the LEED data for the system H/W (100) where the agreement is rather good. In a series of other cases, at least the qualitative features of the present treatment are applicable.