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

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Order–disorder transitions in adsorbed phases on single crystal surfaces 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 =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 <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 =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 =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. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.