Relationship between disordered c(2 × 2) structure and diffracted intensity: The 5-site filling model and the hard-square lattice GAS

Abstract

The relationship between the size of disordered c(2 × 2) domains on a square lattice, and the associated diffracted intensity, is investigated for two specific models. The hard-square model describes an equilibrium lattice gas with infinitely repulsive nearest-neighbor (NN) interactions. A transition from short-range to long-range c(2 × 2) order occurs at θ c = 0.368 monolayers mimicking Cl/Ag(100) behavior. Here the singular ( 1 2 , 1 2 )-beam diffracted intensity behavior matches that of the average size (number of atoms) and radius of gyration of suitably defined c(2 × 2) domains. In the non-equilibrium 5-site filling model, empty sites fill irreversibly, at random, provided that all four NN sites are empty. A saturation state occurs at θ s = 0.364 monolayers modelling metastable disordered c(2 × 2) O/Fe(001). Here the ( 1 2 , 1 2 )-beam behavior does not match rapid increases in average domain size and radius of gyration near θ s, but correlates better with domain chord length behavior. This difference between equilibrium and non-equilibrium behavior is a general phenomenum.