Thermodynamics of pyrope–majorite, Mg₃Al₂Si₃O₁₂–Mg₄Si₄O₁₂, solid solution from atomistic model calculations

References

• Fiquet , G. 2001 . Mineral phases of the Earth's mantle . Z. Kristallogr. , 216 : 248
   Google Scholar
• Gasparik , T. 2003 . Phase Diagrams for Geoscientists. An Atlas of the Earth's Interior , Berlin, Heidelberg : Springer-Verlag .
   Google Scholar
• Fabrichnaya , O.B. , Saxena , S.K. , Richet , P. and Westrum , E.F. 2004 . Thermodynamic Data, Models and Phase Diagrams in Multicomponent Oxide Systems , Berlin : Springer-Verlag .
   Google Scholar
• Akaogi , M. , Navrotsky , A. , Yagi , T. and Akimoto , S. 1987 . “ Pyroxene–garnet transformation: thermochemistry and elasticity of garnet solid solutions, and applications to a pyrolite mantle ” . In High-Pressure Research in Mineral Physics , Edited by: Manghnani , M.H. and Syono , Y. 251 – 260 . Washington, DC : Am. Geophys. Union .
   Google Scholar
• Yusa , H. , Akaogi , M. and Ito , E. 1993 . Calorimetric study of MgSiO3 garnet and pyroxene: heat capacities, transition enthalpies, and equilibrium phase relations in MgSiO3 at high pressures and temperatures . J. Geophys. Res. , 48 : 6453
   Google Scholar
• Akaogi , M. and Akimoto , S. 1977 . Pyroxene–garnet solid solution equilibria in the systems Mg4Si4O4–Mg3Al2Si3O12 and Fe4Si4O4–Fe3Al2Si3O12 at high pressures and temperatures . Phys. Earth Planet. Interiors , 15 : 90
   Web of Science ®Google Scholar
• Kanzaki , M. 1987 . Ultrahigh-pressure phase relations in the system . Phys. Earth Planet. Interiors , 49 : 168
   Google Scholar
• Kato , T. and Kumazawa , M. 1985 . Garnet phase of MgSiO3 filling the pyroxene–ilmenite gap at very high temperatures . Nature , : 316
   PubMedGoogle Scholar
• Angel , R.J. , Finger , L.W. , Hasen , R.M. , Kanzaki , M. , Weidner , D.L. , Liebermann , R.C. and Veblen , D.R. 1989 . Structure and twinning of single crystal MgSiO3 garnet synthesized at 17 GPa and 1800°C . Am. Mineral. , 74 : 509
   Web of Science ®Google Scholar
• Phillips , B.L. , Howell , D.A. , Kirkpatrick , R.J. and Gasparik , T. 1992 . Investigation of cation order in MgSiO3-rich garnet using 29Si and 27Al MAS NMR spectroscopy . Am. Mineral. , 77 : 704
   Google Scholar
• Heinemann , S. , Sharp , T. , Seifert , F. and Rubie , D.C. 1997 . The cubic–tetragonal phase transition in the system majorite (Mg4Si4O12)–pyrope (Mg3Al2Si3O12), and garnet symmetry in the Earth's transition zone . Phys. Chem. Minerals , 24 : 206
   Google Scholar
• Hatch , D.M. and Ghose , S. 1989 . Symmetry analysis of the phase transition and twinning in MgSiO3 garnet: implications to mantle mineralogy . Am. Mineral. , 74 : 1221
   Web of Science ®Google Scholar
• Wang , Y. , Gasparik , T. and Liebermann , R.C. 1993 . Modulated microstructure in synthetic majorite . Am. Mineral. , 78 : 1165
   Google Scholar
• Gasparik , T. 1990 . Phase relations in the transition zone . J. Geophys. Res. , 95 : 15751
   Web of Science ®Google Scholar
• Tomioka , N. , Fujino , K. , Ito , E. , Katsura , T. , Sharp , T. and Kato , T. 2002 . Microstructures and structural phase transition in (Mg,Fe)SiO3 majorite . Eur. J. Mineral. , 14 : 7
   Google Scholar
• Harrison , R.J. , Redfern , S.A.T. and Smith , J. 2003 . The effect of transformation twins on the seismic frequency mechanical properties of polycrystalline Ca1 − xSrxTiO3 perovskite . Am. Mineral. , 88 : 574
   Web of Science ®Google Scholar
• Carpenter , M.A. and McConnell , J.D.C. 1984 . Experimental delineation of the transformation in intermediate plagioclase feldspars . Am. Mineral. , 69 : 112
   Web of Science ®Google Scholar
• Myers , E.R. , Heine , V. and Dove , M.T. 1998 . Some consequences of Al/Al avoidance in the ordering of Al/Si tetrahedral framework structures . Phys. Chem. Minerals , 25 : 457
   Google Scholar
• Dove , M.T. 2001 . “ Computer simulations of solid solutions ” . In Solid Solutions in Silicate and Oxide Systems of Geological Importance. EMU Notes in Mineralogy , Edited by: Geiger , Ch. Vol. 3 , 245 – 249 . Budapest : Eötvös University Press .
   Google 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 . Mineral. Mag. , 65 : 193
   Google Scholar
• Warren , M.S. , Dove , M.T. , Myers , E.R. , Bosenick , A. , Palin , E.J. , Sainz-Diaz , C.I. , Guiton , B.S. , Craig , M.C. and Redfern , S.A.T. 2001 . Monte–Carlo methods for the study of cation ordering in minerals . Mineral. Mag. , 65 : 221
   Google Scholar
• Becker , U. , Fernandez-Gonzales , A. , Prieto , M. , Harrison , R. and Putnis , A. 2000 . Direct calculation of thermodynamic properties of the barite/celestite solid solution from molecular principles . Phys. Chem. Minerals , 27 : 291
   Google Scholar
• Becker , U. and Pollock , K. 2002 . Molecular simulations of interfacial and thermodynamic mixing properties of the grossular–andradite garnets . Phys. Chem. Minerals , 29 : 52
   Google Scholar
• Vinograd , V.L. , Sluiter , M.H.F. , Winkler , B. , Putnis , A. , HÅlenius , U. , Gale , J.D. and Becker , U. 2004 . Thermodynamics of mixing and ordering in the pyrope–grossular solid solution . Mineral. Mag. , 68 : 101
   Google Scholar
• Gale , J.D. 1996 . Empirical potential derivation for ionic materials . Phil. Mag. B , 73 : 3
   Web of Science ®Google Scholar
• Gale , J.D. 1997 . GULP—a computer program for symmetry adapted simulations of solids . J. Chem. Soc. Faraday Trans. , 93 : 629
   Google Scholar
• Sanders , M.J. , Leslie , M. and Catlow , C.R. 1984 . Interatomic potentials for SiO2 . J. Chem. Soc., Chem. Commun. , 19 : 1271
   Google Scholar
• Patel , A. , Price , G.D. and Mendelsson , M.J. 1991 . A computer-simulation approach to modelling the structure, thermodynamics and oxygen isotope equilibria of silicates . Phys. Chem. Minerals , 17 : 690
   Google Scholar
• Winkler , B. , Dove , M.T. and Leslie , M. 1991 . Static lattice energy minimization and lattice dynamics calculations on aluminosilicate minerals . Am. Mineral. , 76 : 313
   Google Scholar
• Vinograd , V.L. , Sluiter , M.H.F. , Winkler , B. , Putnis , A. and Gale , J.D. 2004 . “ Thermodynamics of mixing and ordering in silicates and oxides from static lattice energy and ab initio calculations ” . In First-Principles Simulations: Perspectives and Challenges in Mineral Sciences. Deutsche Gesellschaft für Kristallographie. Berichte aus Arbeitskreisen der DFK Edited by: Warren , M. , Oganov , A. and Winkler , B. Vol. 14 , 143 – 151 .
   Google Scholar
• Bass , J.D. 1995 . “ Elasticity of Minerals, Glasses, and Melts ” . In Mineral Physics & Crystallography. A Handbook of Physical Constants. Am. Geophys. Union, AGU Reference Shelf Ser., 2 Edited by: Ahrens , Th.J. 45 – 63 .
   Google Scholar
• Downs , R.T. and Hall-Wallace , M. 2003 . The American mineralogist crystal structure database . Am. Mineral. , 88 : 247
   Web of Science ®Google Scholar
• Pacalo , R.E.G. and Weidner , D.L. 1997 . Elasticity of majorite MgSiO3 tetragonal garnet . Phys. Earth. Planet. Interiors , 99 : 145
   Web of Science ®Google Scholar
• Sinogeikin , S.V. and Bass , J.D. 2002 . Elasticity of majorite and majorite–pyrope solid solution to high pressure: Implications for the transition zone . Geophys. Res. Lett. , 29 ( 2 ) : 4-1
   Google Scholar
• Hohenberg , P. and Kohn , W. 1964 . Inhomogeneous electron gas . Phys. Rev. , 136 : B864
   Web of Science ®Google Scholar
• Kohn , W. and Sham , L.J. 1965 . Self-consistent equations including exchange and correlation effects . Phys. Rev. , 140 : A1133
   Web of Science ®Google Scholar
• Parr , R.G. and Yang , W. 1989 . Density-functional theory of atoms and molecules , Oxford : Oxford University Press .
   Google Scholar
• Kryachko , E.S. and Ludena , E.V. 1990 . “ Energy density functional theory of many-electron systems ” . In Understanding Chemical Reactivity , Vol. 4 , Dordrecht : Kluwer Academic Publishers .
   Google Scholar
• Jones , R.O. and Gunnarsson , O. 1989 . The density functional formalism, its applications and prospects . Rev. Mod. Phys. , 61 : 689
   Web of Science ®Google Scholar
• Perdew , J.P. , Burke , K. and Ernzerhof , M. 1996 . Generalized gradient approximation made simple . Phys. Rev. Lett. , 77 : 3865
   PubMed Web of Science ®Google Scholar
• Leung , T.C. , Chan , C.T. and Harmon , B.N. 1991 . Ground-state properties of Fe, Co, Ni and their monoxides: results of the generalized gradient approximation . Phys. Rev. , B44 : 2923
   Google Scholar
• Goniakowski , J. , Holdender , J.M. , Kantarovich , L.N. , Gillan , M.J. and White , J.A. 1996 . Influence of gradient corrections on the bulk and surface properties of TiO2 and SnO2 . Phys. Rev. , B53 : 957
   Google Scholar
• Hamman , D.R. 1996 . Generalized gradient theory for silica phase transitions . Phys. Rev. Lett. , 76 : 660
   PubMedGoogle Scholar
• Vanderbilt , D. 1990 . Soft self-consistent pseudopotentials in a generalized eigenvalue formalism . Phys. Rev. , B41 : 7894
   Google Scholar
• Kresse , G. and Hafner , J. 1994 . Norm-conserving and ultrasoft pseudopotentials for first-row and transition elements . J. Phys.: Condens. Matter , 6 : 8245
   Web of Science ®Google Scholar
• McCommon , C.A. and Ross , N.L. 2003 . Crystal chemistry of ferric iron in (Mg,Fe)(Si,Al)O3 majorite with implications for the transition zone . Phys. Chem. Minerals , 30 : 206
   Google Scholar
• Vinograd , V.L. 2001 . “ Configurational entropy of binary silicate solid solutions ” . In Solid Solutions in Silicate and Oxide Systems of Geological Importance. EMU Notes in Mineralogy Edited by: Geiger , Ch. Vol. 3 , 245 – 249 .
   Google Scholar
• Fleming , S.D. and Rohl , A.L. 2005 . GDIS: A visualization program for molecular and periodic systems . Z. Kristallogr. , 220 : 580
   Google Scholar
• Vinograd , V.L. and Putnis , A. 1999 . The description of Al, Si ordering in aluminosilicates using the cluster variation method . Am. Mineral. , 84 : 311
   Google Scholar
• E.R. Myers. Al/Si ordering in silicate minerals. PhD thesis, Univ. of Cambridge (1999).
   Google Scholar
• Carpenter , M.A. and Putnis , A. 1985 . “ Cation order and disorder during crystal growth: some implications for natural mineral assemblages ” . In Advances in Physical Geochemistry , Edited by: Thompson , A.B. and Rubie , D.C. Vol. 4 , Berlin : Springer-Verlag .
   Google Scholar
• Carpenter , M.A. 1991 . Mechanisms and kinetics of Al–Si ordering in anorthite: I. Incommensurate structure and domain coarsening . Am. Mineral. , 76 : 1110
   Web of Science ®Google Scholar
• Kroll , H. and Müller , W.F. 1980 . X-ray and electron-optical investigation of synthetic high-temperature plagioclases . Phys. Chem. Minerals , 5 : 255
   Web of Science ®Google Scholar
• Smith , J.V. and Brown , W.L. 1988 . Feldspar minerals. 1. Crystal structures, physical, chemical and microtextural properties , Berlin, Heidelberg : Springer-Verlag .
   Google Scholar
• Putnis , A. 1980 . The distortion index in anhydrous Mg-cordierite . Contrib. Mineral. Petrol. , 74 : 135
   Google Scholar
• Putnis , A. and Bish , D.L. 1983 . The mechanism and kinetics of Al, Si ordering in Mg-cordierite . Am. Mineral. , 68 : 60
   Google Scholar
• Putnis , A. , Fyfe , C.A. and Gobbi , G.C. 1985 . Al,Si ordering in cordierite using “magic angle spinning” NMR spectroscopy. I: 29Si spectra of synthetic cordierites . Phys. Chem Minerals , 12 : 211
   Google Scholar
• Putnis , A. , Salje , E.S. , Redfern , S.A.T. , Fyfe , C.A. and Strobl , H. 1987 . Structural states of Mg-cordierite I: Order parameters from synchrotron X-ray and NMR data . Phys. Chem. Minerals , 14 : 446
   Web of Science ®Google Scholar
• Sundman , B. , Jansson , B. and Andersson , J-O. 1985 . The Thermo-Calc databank system . Calphad , 9 : 153
   Web of Science ®Google Scholar