A statistical-mechanics model of ordering in aluminosilicate solid solutions

A statistical-thermodynamic approximation for order-disorder phase transitions in aluminosilicate solid solutions is presented. The approximation involves estimating the number of configurations with long range order parameter Q and short range order parameter sigma, using an approximation to the probability that a configuration with the correct amount of long range order will also have the correct amount of short range order. This estimate is then used to give a free energy F(Q, sigma, x, T), where x is the concentration of Al in the structure, and hence quantities such as T-c(x) are estimated. The predictions of the model for T-c(x) and the critical concentration x(c) at which T-c falls to zero are shown to be in good agreement with the results of Monte Carlo simulations.