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Abstract

Thermodynamic modelling of a solid solution requires a description of the mixing functions, of the Gibbs free energy, enthalpy, volume, vibrational and configurational entropy. The enthalpy of mixing, volume and the vibrational entropy of silicate solid solutions can be measured directly. For example, the vibrational entropy can be determined from calorimetric experiments through integration of the heat capacity. The same method does not work for the configurational entropy, however. Due to the slow kinetics of cationic order/disorder in silicates, the configurational degrees of freedom of atoms remain unchanged in the calorimetric experiments and do not contribute to the heat capacity. Therefore, the configurational entropy can only be determined from indirect experimental data. There are two approaches to this problem. The first one is to use the classical thermodynamic relationship ΔGmix = ΔHmixTΔSmix + PΔVmix, where ΔSmix = ΔSmix,conf + ΔSmix, vib. when the ΔGmix term is constrained by phase equilibrium experiments and the ΔHmix, ΔSmix,vib and ΔVmix terms are known from calorimetric and X-ray diffraction measurements, ΔSmix,conf can be calculated. The second approach is to calculate the configurational entropy using its statistical-thermodynamic definition, by counting the number of available configurational states. To do this one needs to know which configurational states are available. Such information can be obtained from diffraction and spectroscopic data.

The configurational entropy can be described with a variety of models with different levels of accuracy and simplicity. The choice of a model depends largely on the availability of experimental data.

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