Tiling model for glass formation with incremental domain-size kinetics

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Abstract
The equilibrium and kinetic properties of the square-tiling model proposed by Stillinger and Weber had been studied previously by Monte Carlo simulation using a set of kinetic transition-rate rules which allowed only those aggregation and fragmentation processes which involved a minimal number of square arrays of square tiles. In the present work a new set of transition-rate rules is studied which allows fragmentation and aggregation to occur at the boundary by the shedding or addition of L-shaped arrays of unit squares. The equilibrium properties of the model at temperatures above the condensation point are found to be in excellent agreement with those found using the minimal-aggregation transition-rate rules. The kinetic properties are found to differ significantly. The current model is found to relax substantially more rapidly and to produce a somewhat different texture of tiles in the low-temperature glass. The relaxation of the potential autocorrelation function (as before) is found to be nonexponential and can be described by the Kohlrausch-Williams-Watts equation with a temperature-dependent fractional exponent. In addition the system still exhibits non-Arrhenius temperature dependence of the average relaxation rate.