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Thermodynamics of mixing and ordering in pyrope — grossular solid solution

Published online by Cambridge University Press:  05 July 2018

V. L. Vinograd*
Affiliation:
Institute of Mineralogy, University of Frankfurt, Senckenberganlage 30, 60054 Frankfurt/Main, Germany Department of Mineralogy, Swedish Museum of Natural History, Frescativägen 40, SE-10405, Stockholm, Sweden
M. H. F. Sluiter
Affiliation:
Institute for Materials Research, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan
B. Winkler
Affiliation:
Institute of Mineralogy, University of Frankfurt, Senckenberganlage 30, 60054 Frankfurt/Main, Germany
A. Putnis
Affiliation:
Institute of Mineralogy, University of Muenster, Correnstrasse 24, 49149, Muenster, Germany
U. Hålenius
Affiliation:
Department of Mineralogy, Swedish Museum of Natural History, Frescativägen 40, SE-10405, Stockholm, Sweden
J. D. Gale
Affiliation:
Department of Chemistry, Imperial College of Science, Technology and Medicine, London SW7 2AZ, UK
U. Becker
Affiliation:
Department of Geological Sciences, University of Michigan, 2534 C.C. Little Building, 425 E. University Ave., Ann Arbor, MI 48109-1063, USA

Abstract

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.

Type
Research Article
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 2004

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Footnotes

present address: Nanochemistry Research Institute, Curtin University of Technology, U1987, Perth 6845, Western Australia

References

Bass, J.D. (1995) Elasticity of minerals, glasses, and melt s. Pp.4563 in: Mineral Phy sic s and Cryst al logra phy. A Hand book of Phys ical Constants(Ahrens, Th., editor). AGU Reference Shelf, 2. American Geophysical Union.CrossRefGoogle Scholar
Becker, U. and Pollok, K. (2002) Molecular simulations of interfacial and thermodynamic mixing properties of the grossular-andradite garnets. Physics and Chemistry of Minerals, 29, 5264.CrossRefGoogle Scholar
Becker, U., Fernandez-Gon zalez, A., Prieto, M., Harrison, R. and Putnis, A. (2000) Direct calculation of thermodynamic properties of the barite/celestite solid solution from molecular principles. Physics and Chemistry of Minerals, 27, 291300.CrossRefGoogle Scholar
Berman, R.G. and Aranovich, L.Ya. (1996) Optimized standard state and solution properties of minerals. I. Model calibration for olivine, orthopyroxene, cordierite, garnet, and ilmenite in the system FeO-MgOCaO- Al2O3-TiO2-SiO2 . Contributions to Mineralogy and Petrology, 126, 124.CrossRefGoogle Scholar
Bosenick, A., Geiger, C.A., Schaller, T. and Sebald, A. (1995) A 29Si MAS NMR and IR spectroscopic investigation of synthetic pyrope-grossular garnet solid solutio ns. American Mineralogist, 80, 691704.CrossRefGoogle Scholar
Bosenick, A., Geiger, C.A. and Phillips, B.L. (1999) Local Ca-Mg distribution of Mg-rich pyropegrossular garnets synthesized at different temperatures revealed by 29Si MAS NMR spectroscopy. American Mineralogist, 84, 14221432.CrossRefGoogle Scholar
Bosenick, A., Dove, M.T. and Geiger, C.A. (2000) Simulation studies of pyrope-grossular solid solutions. Physics and Chemistry of Minerals, 27, 398418.CrossRefGoogle Scholar
Bosenick, A., Dove, M.T., Heine, V. and Geiger, C.A. (2001) Scaling of thermodynamic mixing properties in garnet solid solutions. Physics and Chemistry of Minerals, 28, 117187.CrossRefGoogle Scholar
Bosenick, A., Dove, M.T., Myers, E.R., Palin, E.J., Sainz-Diaz, C.I., Guiton, B.S., Warren, M.C. and Craig, M.S. (2001) Computational methods for the study of energies of cation distributions: applications to cation-ordering phase transitions and solid solutions. Mineralogical Magazine, 65, 193219.CrossRefGoogle Scholar
Carpenter, M.A. and Boffa Ballaran, T. (2001) The influence of elastic strain heterogeneities in silicate solid solutions. Pp. 155178 in: Solid Solutions in Silicate and Oxide Systems of Geological Importance (Geiger, Ch., editor). EMU Notes in Mineralogy, 3. Eötvö s University Press, Budapest.Google Scholar
Connolly, J.W.D., and Williams, A.R. (1983) Density functional theory applied to phase transformations in transition-metal alloys. Physics Review B, 27, 51695172.CrossRefGoogle Scholar
Dove, M.T. (1993) Introduction to Lattice Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Dove, M.T. (1999) Order/disorder phenomena in minerals: Ordering phase transitions and solid solutions. Pp. 451475 in: Microscopic Properties and Processes in Minerals. (Wright, K. and Catlow, R., editors). NATO Science Series, C543. Kluwer Academic Publishers, Dordrecht, The Netherlands.CrossRefGoogle Scholar
Dove, M.T. (2001) Computer simulations of solid solutions. Pp. 225249 in: Solid Solutions in Silicate and Oxide Systems of Geological Importance (Geiger, Ch., editor). EMU Notes in Mineralogy, 3. Eötvös University Press, Budapest.Google Scholar
Dove, M.T., Thayaparam, S., Heine, V. and Hammonds, K.D. (1996) The phenomenon of low Al-Si ordering temperatures in aluminosilicate framework structures. American Mineralogist, 81, 349362.CrossRefGoogle Scholar
Ferreira, L.G., Mbaye, A.A. and Zunger, A. (1988) Chemical and elastic effects on isostructural phase diagrams: The e-G approach. Physics Review B, 37, 1054710570.CrossRefGoogle Scholar
Gale, J.D. (1996) Empirical derivation of interatomic potentia ls for ionic materia ls. Philosop hical Magazine B, 73, 319.CrossRefGoogle Scholar
Gale, J.D. (1997) GULP–a computer program for the symmetry adapted simulation of solids. Journal of the Chemical Society: Faraday Transactions, 93, 629637.Google Scholar
Ganguly, J., Cheng, W. and O’Neil, H.St.C. (1993) Syntheses, volume, and structural changes of garnets in the pyrope-grossular join: Implications for stability and mixing properties Amer ican Mineralogist, 78, 583593.Google Scholar
Ganguly, J., Cheng, W. and Tirone, M. (1996) Thermodynamics of aluminosilicate garnet solid solution: new experimental data, an optimized model, and thermometric applications. Contributions to Mineralogy and Petrology, 126, 137151.CrossRefGoogle Scholar
Geiger, C.A. (1999) Thermo dynamics of (Fe2+,Mg2+,Mn,Ca)3Al2Si3O12 garnet: a review and analysis. Mineralogy and Petrology, 66, 271299.CrossRefGoogle Scholar
Geiger, C.A. and Armbruster, T. (1997) Mn3Al2Si3O12 spessartine and Ca3Al2Si3O12 grossular garnet: Structural dynamics and thermodynamic properties. American Mineralogist, 82, 740747.CrossRefGoogle Scholar
Guggenheim, E.A. (1952) Mixtures. Clarendon Press, Oxford, UK.Google Scholar
Haselton, H.T. Jr. and Newton, R.C. (1980) Thermodynamic properties of pyrope-grossular garnets and their stabilities at high temperatures and high pressures. Journal of Geophysical Research, 85, 69736982.CrossRefGoogle Scholar
Haselton, H.T., Jr. and Westrum, E.F., Jr. (1980) Lowtemperature heat capacities of synthetic pyrope, grossular, and pyrope60grossular40. Geochimica et Cosmochimica Acta, 44, 701709.CrossRefGoogle Scholar
Holland, T.J.B. and Powell, R. (1998) An internally consistent thermodynamic data set for phases of petrological interest. Journal of Metamorphic Geology, 16, 309343.CrossRefGoogle Scholar
Kolesnik, Y.N., Nogteva, V.V., Arkhipenko, D.K., Ore khov, B.A. and Paukov, I.Y. (1979) Thermodynamics of pyrope-grossular solid solutions and the specific heat of grossular at 13–300 K. Geochemistry International, 16, 5764.Google Scholar
Myers, E., Heine, V. and Dove, M.T. (1998) Some consequences of Al/Al avoidance in the ordering of Al/Sitetrahedral framework structures. Physics and Chemistry of Minerals, 25, 457464.CrossRefGoogle Scholar
Mukhopadhyay, B., Holdaway, M.J. and Koziol, A.M. (1997) A statistical model of the thermodynamic mixing properties of Ca-Mg-Fe2+ garnets. American Mineralogist, 82, 165181.CrossRefGoogle Scholar
Newton, R.C., Charlu, T.V. and Kleppa, O.J. (1977) Thermochemistry of high pressure garnets and clinopyroxenes in the system CaO-MgO-Al2O3-SiO2 . Geochimica et Cosmochimica Acta, 41, 369377.CrossRefGoogle Scholar
Patel, A., Price, G.D. and Mendelsson, M.J. (1991) A computer-simulation approach to modeling the structure, thermodynamics and oxygen isotope equilibria of silicates. Physics and Chemistry of Minerals, 17, 690699.CrossRefGoogle Scholar
Pavese, A., Artioli, G. and Prencipe, M. (1995) X-ray single-crystal diffraction study of pyrope in the temperature range American Mineralogist, 80, 457464.CrossRefGoogle Scholar
Sanchez, J.M. and de Fontaine, D. (1978) The fcc Ising model in the cluster variation approximation. Physics Review B, 17, 29262936.CrossRefGoogle Scholar
Sanders, M.J., Leslie, M. and Catlow, C.R. (1984) Interatomic potentials for SiO2 . Journal of the Chemical Society, Chemical Communications, 19, 12711273.CrossRefGoogle Scholar
Shannon, R.D. and Rossman, G.R. (1992) Dielectric constants of silicate garnets and the oxide additivity rule. American Mineralogist, 77, 94100.Google Scholar
Urusov, V.S. (2001) The phenomenological theory of solid solutions. Pp. 121153 in: Solid Solutions in Silicate and Oxide Systems of Geological Importance (Geiger, Ch., editor). EMU Notes in Mineralogy, 3. Eötvös University Press, Budapest.Google Scholar
Vinograd, V.L. (2001) Configurational entropy of binary silicate solid solutions. Pp. 303346 in: Solid Solutions in Silicate and Oxide Systems of Geological Importance (Geiger, Ch., editor). EMU Notes in Mineralogy, 3. Eötvös University Press, Budapest.Google Scholar
Vinograd, V.L. (2002) Thermodynamics of mixing and ordering in the diopside–jadeite system: I. A CVM model. Mineralogical Magazine, 66, 513536.CrossRefGoogle Scholar
Vinograd, V.L. and Putnis, A. (1999) The description of Al,Si ordering in aluminosilicates using the cluster variation method. American Mineralogist, 84, 311324.CrossRefGoogle Scholar
Vinograd, V.L., Becker, U. and Putnis, A. (2000) Maximisation of cluster entropy via an irreversible algorithm: Application to the cluster variation method. Pp. 249260 in Properties of Complex Inorganic Solids 2 (Meike, A., Gonis, A., Turchi, P.E.A. and Rajan, K., editors). Kluwer Academic/ Plenum Publishers, Dordrecht, The Netherlands.CrossRefGoogle Scholar
Wang, L., Essene, E.J. and Zhang, Y. (2000) Direct observation of immiscibility in pyrope-almandinegrossular garnet. American Mineralogist, 85, 4146.CrossRefGoogle Scholar
Warren, M.C., Dove, M.T. and Redfern, S.A.T. (2000) Disordering of MgAl2O4 spinel from. rst principles. Mineralogical Magazine, 64, 311318.CrossRefGoogle Scholar
Warren, M.C., Dove, M.T., Myers, E.R., Bosenick, A., Palin, E.J., Sainz-Diaz, C.I. and Guiton, B.S. (2001) Monte Carlo methods for the study of cation ordering in minerals. Mineralogical Magazine, 65, 221248.CrossRefGoogle Scholar
Westrum, E.F. Jr., Essene, E.J. and Perkins D., III (1979) Thermophysical properties of garnet, grossular: Ca3Al2Si3O12 . Journ al of Chemical Thermophysics, 11, 5766.CrossRefGoogle Scholar
Winkler, B., Dove, M.T. and Leslie, M. (1991) Static lattice energy minimization and lattice dynamics calculations on aluminosilicate minerals. American Mineralogist, 76, 313331.Google Scholar
Zunger, A. (1994) First-principles statistical mechanics of semiconductor alloys and intermetallic compounds. Pp. 361–419 in: Statics and Dynamics of Alloy Phase Transformations (Turchi, P.E.A. and Gonis, A., editors). Plenum Press, New York.Google Scholar