Configurational entropy of binary silicate solid solutions
Published:January 01, 2001
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 = ΔHmix − TΔSmix + 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.
Figures & Tables
Solid Solutions in Silicate and Oxide Systems
The EMU book series or notes, as they are called, were introduced to provide university teachers with up-to-date reviews in important, rapidly evolving areas of mineralogy, petrology and geochemistry. They are also meant to introduce scientists into special and often interdisciplinary fields of research. In this regard, a volume on solid solutions is current and sorely needed. The solid Earth, as well as many meteorites and the other solid planets, consists for the most part of mineral solid solutions. Research on solid solutions is extremely broad encompassing work in physics and chemistry, metallurgy, materials science and, last but not least, mineralogy and petrology. Hence, because the theme is so strongly interdisciplinary in nature, the workshop was organised to include solid state physicists, physical chemists, crystallographers, mineralogists and petrologists. The various chapters reflect some of this diversity and show what mineralogy has become. Experimental investigations in mineralogy now routinely include different types of spectroscopies along with more traditional phase equilibrium, X-ray diffraction, calorimetry, and TEM methods. There have also been new and impressive developments in theory and computation. Many computational approaches relating to the study of solid solutions, for example, the Cluster Variation Method or Monte Carlo simulations, have been brought in from materials science, chemistry and physics. It can be concluded that the traditional or historical, and perhaps artificial, boundaries between the various disciplines are disappearing. Many current research efforts in mineralogy are similar to those in chemistry, materials science and physics.