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Thermodynamics of mixing and ordering in pyrope–grossular solid solution

V. L. Vinograd^1,4,*, M. H. F. Sluiter², B. Winkler¹, A. Putnis³, U. Hålenius⁴, J. D. Gale^5, and U. Becker⁶

¹ Institute of Mineralogy, University of Frankfurt, Senckenberganlage 30, 60054 Frankfurt/Main, Germany
² Institute for Materials Research, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan
³ Institute of Mineralogy, University of Muenster, Correnstrasse 24, 49149, Muenster, Germany
⁴ Department of Mineralogy, Swedish Museum of Natural History, Frescativägen 40, SE-10405, Stockholm, Sweden
⁵ Department of Chemistry, Imperial College of Science, Technology and Medicine, London SW7 2AZ, UK
⁶ Department of Geological Sciences, University of Michigan, 2534 C.C. Little Building, 425 E. University Ave., Ann Arbor, MI 48109-1063, USA

^* E-mail: vinogra{at}uni-muenster.de

Static lattice energy calculations have been combined with cluster expansion formalism to predict pairwise ordering interactions in the pyrope–grossular solid solution. The ordering interactions, the Js, have been then used to calculate the activity-composition relations over a wide temperature range with the help of the Cluster Variation Method. It is shown that short-range ordering in the system is driven by size mismatch. The prediction of the right signs and magnitudes of the ordering interaction energies requires separation of the mixing enthalpy into the configuration-dependent (chemical) and the configuration-independent (elastic) components. The study predicts the existence of a miscibility gap below 500°C.

KEYWORDS: interatomic potentials, pyrope–grossular, activity-composition relations

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