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Thermodynamics of mixing and ordering in the diopside–jadeite system: I. A CVM model

Published online by Cambridge University Press:  05 July 2018

V. L. Vinograd*
Affiliation:
Institut für Mineralogie, J. W. Goethe Universität, Senckenberganlage 30, 60054 Frankfurt, Germany Institut für Mineralogie, Universität Münster, Corrensstrasse 24, D-48149 Münster, Germany

Abstract

Solution calorimetry and phase equilibrium data for the diopside–jadeite system are assessed using a combination of the cluster variation method (CVM) and Redlich-Kister (RK) polynomial expansion. The CVM is used to model part of the free energy of mixing which depends on short-range order (SRO) and long-range order (LRO) effects. The SRO/LRO independent part of the free energy is modelled using an RK polynomial. The parameters of the RK and CVM models are obtained through the fit to the experimental data. The best-fit parameters are used to calculate activity-composition relations and a temperature-composition phase diagram of the diopside–jadeite system.

Type
Research Article
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 2002

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References

Aranovich, L.Ya. and Perchuk, A.L. (1989) Experimental study of clinopyroxene + quartz + albite equilibrium in the system Na2O-CaO-FeO-Al2O3-SiO2 at 900–1100°C and 14–25 kbar. Doklady Academii Nauk USSR, 307, 155236.Google Scholar
Asta, M., McCormack, R. and de Fontaine, D. (1993) Theoretical study of alloy phase stability in the Cd-Mg system. Physical Review B, 48, 747766.CrossRefGoogle ScholarPubMed
Becker, U., Fernandez-Gonzalez, 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
Boffa Ballaran, T., Carpenter, M.A., Domeneghetti, M.C. and Tazzoli, V. (1998) Structural mechanisms of solid solution and cation ordering in augite-jadeite pyroxenes: I. A macroscopic perspective. American Mineralogist, 83, 419433.CrossRefGoogle Scholar
Bosenick, A., Dove, M.T., Myers, E.R., Palin, E.J., Sainz-Diaz, C.I., Guiton, B.S., Warren, M.C., Craig, M.S. and Redfern, S.A.T. (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
Brenker, F.E. (1998) Mikrogefügethermochronometrie für Eklogite. Dissertation, Johan Wolfgang Goehte – Universität, Frankfurt am Main, Germany.Google Scholar
Burton, B.P. and Davidson, P.M. (1988 a) Order-disorder in omphacitic pyroxenes: A model for coupled substitution in the point approximation – Reply. American Mineralogist, 73, 916918.Google Scholar
Burton, B.P. and Davidson, P.M. (1988 b) Short-range order and frustration in omphacite: Comparison of three CVM approximations. Physics and Chemistry of Minerals, 15, 570578.CrossRefGoogle Scholar
Burton, B.P., Dupin, N., Fries, S.G., Grimvall, G., Fernandez Guilermet, A., Miodownik, P., Oates, W.A. and Vinograd, V.L. (2001) Using ab initio calculations in the CALPHAD environment. Zeitschrift für Metallkunde, 92, 514525.Google Scholar
Carpenter, M.A. (1980) Mechanisms of exsolution in sodic pyroxenes. Contributions to Mineralogy and Petrology, 71, 289300.CrossRefGoogle Scholar
Carpenter, M.A. (1981 a) Time-Temperature-Transformation (TTT) analysis of cation disordering in omphacite. Contributions to Mineralogy and Petrology, 78, 433440.CrossRefGoogle Scholar
Carpenter, M.A. (1981 b) Omphacite microstructures as time-tempera ture indicators of blueschist- and eclogite-facies metamorphism. Contributions to Mineralogy and Petrology, 78, 441451.CrossRefGoogle Scholar
Carpenter, M.A. (1983) Microstructures in sodic pyroxenes: implications and applications. Periodica Mineralogica, 52, 271301.Google Scholar
Carpenter, M.A., Domeneghetti, M.C. and Tazzoli, V. (1990) Application of Landau theory to cation ordering in omphacite I: Equilibrium behaviour. European Journal of Mineralogy, 2, 718.CrossRefGoogle Scholar
Carpenter, M.A. and Boffa Ballaran, T. (2001) The influence of elastic strain heterogeneties 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. Eötvös University Press, Budapest.Google Scholar
Champness, P.E. (1973) Speculation on an order-disorder transformation in omphacite. American Mineralogist, 58, 540542.Google Scholar
Clark, J.R. and Papike, J.J. (1968) Crystal-chemical characterisation of omphacites. American Mineralogist, 53, 840868.Google Scholar
Clark, J.R., Appelman, D.E. and Papike, J.J. (1969) Crystal-chemical characterisation of clinopyroxenes based on eight new structure refinements. Mineralogical Society of America Special Paper, 2, 3150.Google Scholar
Cohen, R.E. (1986 a) Configurational thermodynamics of aluminous pyroxenes: A generalized pair approximation. Physics and Chemistry of Minerals, 13, 183197.CrossRefGoogle Scholar
Cohen, R.E. (1986 b) Thermodynamic solution properties of aluminous clinopyroxenes: Nonlinear least squares refinements. Geochimica et Cosmochimica Acta, 50, 563575.CrossRefGoogle Scholar
Cohen, R.E. (1988) Order-disorder in omphacitic pyroxenes: A model for coupled substitution in the point approximat ion – Discussion. American Mineralogist, 73, 910915.Google Scholar
Cohen, R.E. and Burnham, C.W. (1985) Energetics of ordering in aluminous pyroxenes. American Mineralogist, 70, 559567.Google Scholar
Colinet, C. and Pasturel, A. (1998) Theoretical calculation of the Cu-Ni, Ag-Ni and Au-Ni miscibility gaps. Zeitschrift für Metallkunde, 89, 863867.Google Scholar
Davidson, P.M. and Burton, B.P. (1987) Order-disorder in omphacitic pyroxenes: A model for coupled substitution in the point approximation. American Mineralogist, 72, 337344.Google Scholar
Dove, M.T. (2001) Computer simulations of solid solutions. Pp. 225250 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. (1987) Effect of chemical and elastic interactions on phase diagrams of isostructural solids. Physical Review, B, 35, 64756478.CrossRefGoogle ScholarPubMed
Ferreira, L.G., Mbaye, A.A. and Zunger, A. (1988) Chemical and elastic effects on isostructural phase diagrams: The ε-G approach. Physical Review, B, 37, 1054710570.CrossRefGoogle ScholarPubMed
Fleet, M.E., Herzberg, C.T., Bancroft, G.M. and Aldridge, L.P. (1978) Omphacite studies. I: The P2/nC2/c transformation. American Mineralogist, 63, 11001106.Google Scholar
Ganguly, J. (1973) Activity-composition relation of jadeite in omphacite pyroxene: Theoretical deductions. Earth and Planetary Science Letters, 19, 145153.CrossRefGoogle Scholar
Gasparik, T. (1985) Experimentally determined compositions of diopside-jadeite pyroxene in equilibrium with albite and quartz at 1200–1350°C and 15–34 kbar. Geochimica et Cosmochimica Acta, 49, 865870.CrossRefGoogle Scholar
Glauber, R.J. (1963) Time-dependent statistics of the Ising model. Journal of Mathematical Physics, 4, 294307.CrossRefGoogle Scholar
Guggenheim, E.A. (1952) Mixtures. Oxford University Press, Oxford, UK.Google Scholar
Haselton, H.T. and Westrum, E.F. Jr. (1980) Low-temperature heat capacities of synthetic pyrope, grossular, and pyrope60grossular40 . Geochimica et Cosmochimica Acta, 44, 701710.CrossRefGoogle Scholar
Haselton, H.T., Hovis, G.L., Hemingway, B.S. and Robie, R.A. (1983) Calorimetric investigation of the excess entropy of mixing in analbite-sanidine solid solutions: lack of evidence for Na,K short-range order and implications for two-feldspar thermometry. American Mineralogist, 86, 398413.Google Scholar
Holland, T.J.B. (1980) The reaction albite = jadeite + quartz determined experimentally in the range of 600–1200°C. American Mineralogist, 65, 129134.Google Scholar
Holland, T.J.B. (1983) The experimental determination of activities in disordered and short-range ordered jadeitic pyroxenes. Contributions to Mineralogy and Petrology, 82, 214220.CrossRefGoogle Scholar
Holland, T.J.B. (1990) Activities of components in omphacitic solid solutions. An application of Landau theory to mixtures. Contributions to Mineralogy and Petrology, 105, 446453.CrossRefGoogle Scholar
Holland, T.J.B. and Powell, R. (1996) Thermodynamics of order-disorder in minerals: II. Symmetric formalism applied to solid solutions. American Mineralogist, 81, 14251437.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
Kikuchi, R.A. (1951) Theory of cooperative phenomena. Physical Review, 81, 9881003.CrossRefGoogle Scholar
Kikuchi, R.A. (1974) Superposition approximation and natural iteration calculation in cluster-variation method. Journal of Chemical Physics, 60, 10711080.CrossRefGoogle Scholar
Kurepin, V.A. (1983) A thermodynamic model for a heterovalent solid solution with equilibrium deviation from local electrical neutrality. Geochemistry International, 20, 147157.Google Scholar
Kushiro, I. (1969) Clinopyroxene solid solutions formed by reactions between diopside and plagioclase at high pressures. Minereralogical Society of America Special Paper, 2, 179191.Google Scholar
Matsumoto, T., Tokonami, M. and Morimoto, N. (1975) The crystal structure of omphacite. American Mineralogist, 60, 634641.Google Scholar
Meyre, C., de Capitani, C. and Partzsch, J.H. (1997) A ternary solid solution model for omphacite and its application to geothermobarometry of eclogites from the Middle Adula nappe (Central Alps, Switzerland). Journal of Metamorphic Geology, 15, 687700.CrossRefGoogle Scholar
Nakamura, D. and Banno, S. (1997) Thermodynamic modelling of sodic pyroxene solid-solution and its application in a garnet-omphacite-kyanite-coesite geothermobarometer for UHP metamorphic rocks. Contributions to Mineralogy and Petrology, 130, 93102.CrossRefGoogle Scholar
Ozolins, V., Wolverton, C. and Zunger, A. (1998) Cu-Au, Ag-Cu, and Ni-Au intermetallics: First-principles study of temperature-composition phase diagrams and structures. Physical Review B, 57, 64276443.CrossRefGoogle Scholar
Perchuk, A.L. and Aranovich, L.Ya. (1991) Thermodynamics of jadeite –diopside–hedenbergite solid solutions. Geochemistry Internationl, 28, 7886.Google Scholar
Phakey, P.P. and Ghose, S. (1973) Direct observation of ant iphase domain structure in omphacite. Contributions to Mineralogy and Petrology, 39, 239245.CrossRefGoogle Scholar
Putnis, A. (1992) Introduction to Mineral Sciences. Cambridge University Press, Cambridge, UK.CrossRefGoogle Scholar
Ross, C.R. II (1988) Statistical mechanical modeling of the kinetics of order-disorder in omphacitic pyroxenes. Physics and Chemistry of Minerals, 15, 274282.CrossRefGoogle Scholar
Ross, C.R. II (1991) Ising model and geological applications. Pp. 5190 in: Diffusion, Atomic Ordering, and Mass Transport. (Ganguly, J., editor). Advances in Physical Geochemistry 8, Springer-Verlag, New York.CrossRefGoogle Scholar
Rossi, G., Smith, D.C., Ungaretti, L. and Domeneghetti, M.C. (1983) Crystal-chemistry and cation ordering in the system diopside-jadeite: A detailed study by crystal structure refinement. Contributions to Mineralogy and Petrology, 83, 247258.CrossRefGoogle Scholar
Sanchez, J.M. and de Fontaine, D. (1978) The fcc Ising model in the cluster variation approximation. Physical Review B, 17, 29262936.CrossRefGoogle Scholar
Schlijper, A.G. and Westerhoff, J. (1987) Improved cluster variation approximations by extension of local thermodynamic states. Physical Review B, 36, 54585465.CrossRefGoogle ScholarPubMed
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. 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., Saxena, S.K. and Putnis, A. (1997) Calculation of the probability distribution of basic clusters involved in cluster variation approximations to the Ising model. Physical Review B, 56, 1149311502.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 (Meike, A., Gonis, A., Turchi, P.E.A. and Rajan, K., editors), 2. Kluwer Academic/Plenum Publishers, Dordrecht, The Netherlands.CrossRefGoogle Scholar
Vinograd, V.L., Putnis, A. and Kroll, H. (2001) Structural discontinuities in plagioclase and constraints on mixing properties of the low series: a computational study. Mineralogical Magazine, 65, 131.CrossRefGoogle Scholar
Warren, M.C., Dove, M.T. and Redfern, S.A.T. (2000) Disordering of MgAl2O4 spinel from first 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., Guiton, B.S. and Redfern, S.A.T. (2001) Monte Carlo methods for the study of cation ordering in minerals. Mineralogical Magazine, 65, 221248.CrossRefGoogle Scholar
Wood, B.J., Holland, T.J.B., Newton, R.C. and Kleppa, O.J. (1980) Thermochemistry of jadeite-diopside pyroxenes. Geochimica et Cosmochimica Acta, 44, 13631371.CrossRefGoogle Scholar