The influence of elastic strain heterogeneities in silicate solid solutions
Published:January 01, 2001
Michael A. Carpenter, Tiziana Boffa Ballaran, 2001. "The influence of elastic strain heterogeneities in silicate solid solutions", Solid Solutions in Silicate and Oxide Systems, Charles A. Geiger
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A convenient and widely used model for analysing the thermodynamic changes which accompany mixing and ordering processes in mineral solid solutions is based on pairwise interactions between atoms which occupy nearest neighbour structural sites. The simplest of such models reduces to a single parameter, the sum z[wAB – ½(wAA + wBB)], where z is the coordination number for A cations around Β cations (and vice versa) and wAB, wAA, wBB are interaction energies for A-B, A-A and B-B pairs. In the regular solution model, this sum is expressed as-WH and gives rise to an enthalpy of mixing, ΔHmix = WH XA XB, for a binary solid solution; XA and XB are the mole fractions of end-member components containing A and Β cations. This leads to the prediction of a symmetrical solvus with its crest at a temperature, Tc, given by Tc =WH/2nR; is the number of cation sites per formula unit on which mixing occurs and R is the gas constant. If A-B interactions are energetically favoured relative to A-A and B-B interactions, the sum of interaction energies, expressed as WBW in the Bragg-Williams model, favours ordering. A structure with AB stoichiometry would be expected to order below a critical temperature, Tc, given by Tc = WBW/2R.
During the 1970’s and 1980’s, the enthalpies of mixing of many important rockforming silicate solid solutions were measured by solution calorimetry (reviewed by Geiger, 2001). The regular solution model, modified to allow for asymmetry in the mixing, has continued to provide an effective phenomenological description of mixing properties.
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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.