Contributions to Mineralogy and Petrology

, Volume 165, Issue 1, pp 25–43 | Cite as

The molar volume of FeO–MgO–Fe2O3–Cr2O3–Al2O3–TiO2 spinels

  • Emily A. Hamecher
  • Paula M. Antoshechkina
  • Mark S. Ghiorso
  • Paul D. Asimow
Original Paper

Abstract

We define and calibrate a new model of molar volume as a function of pressure, temperature, ordering state, and composition for spinels in the supersystem (Mg, Fe2+)(Al, Cr, Fe3+)2O4 − (Mg, Fe2+)2TiO4. We use 832 X-ray and neutron diffraction measurements performed on spinels at ambient and in situ high-P, T conditions to calibrate end-member equations of state and an excess volume model for this system. The effect on molar volume of cation ordering over the octahedral and tetrahedral sites is captured with linear dependence on Mg2+, Al3+, and Fe3+ site occupancy terms. We allow standard-state volumes and coefficients of thermal expansion of the end members to vary within their uncertainties during extraction of the mixing properties, in order to achieve the best fit. Published equations of state of the various spinel end members are analyzed to obtain optimal values of the bulk modulus and its pressure derivative, for each explicit end member. For any spinel composition in the supersystem, the model molar volume is obtained by adding excess volume and cation order-dependent terms to a linear combination of the five end-member volumes, estimated at pressure and temperature using the high-T Vinet equation of state. The preferred model has a total of 9 excess volume and order-dependent parameters and fits nearly all experiments to within 0.02 J/bar/mol, or better than 0.5 % in volume. The model is compared to the current MELTS spinel model with a demonstration of the impact of the model difference on the estimated spinel-garnet lherzolite transition pressure.

Keywords

Spinel Molar volume Thermodynamic modeling MELTS 

Notes

Acknowledgments

We wish to thank Peter Luffi for identifying the garnet solid solution error in the original MELTS code, Ashley Nagle for pointing out the anomalously low spinel–garnet transition pressures obtained when the corrected garnet model is used, and Aaron Wolf for helpful discussions regarding statistical analysis. Comments by Associate Editor Jon Blundy are greatly appreciated, as are the reviews of two anonymous reviewers. This work was supported by the National Science Foundation and the American Recovery and Reinvestment Act through award 0838244.

Supplementary material

410_2012_790_MOESM1_ESM.pdf (34 kb)
Supplementary material 1 (PDF 34 kb)
410_2012_790_MOESM2_ESM.xls (276 kb)
Supplementary material 2 (XLS 275 kb)
410_2012_790_MOESM3_ESM.pdf (154 kb)
Supplementary material 3 (PDF 154 kb)
410_2012_790_MOESM4_ESM.pdf (36 kb)
Supplementary material 4 (PDF 35 kb)
410_2012_790_MOESM5_ESM.pdf (38 kb)
Supplementary material 5 (PDF 38 kb)
410_2012_790_MOESM6_ESM.pdf (218 kb)
Supplementary material 6 (PDF 217 kb)

References

  1. Akimoto S (1954) Thermo-magnetic study of ferromagnetic minerals contained in igneous rocks. J Geomagn Geoelectr 6:1–14CrossRefGoogle Scholar
  2. Andreozzi GB, Lucchesi S (2002) Intersite distribution of Fe2+ and Mg in the spinel (sensu stricto)-hercynite series by single-crystal X-ray diffraction. Am Mineral 87:1113Google Scholar
  3. Andreozzi GB, Princivalle F (2002) Kinetics of cation ordering in synthetic MgAl2O4 spinel. Am Mineral 87:838–844Google Scholar
  4. Andreozzi GB, Princivalle F, Skogby H, Della Giusta A (2000) Cation ordering and structural variations with temperature in MgAl2O4 spinel: an X-ray single-crystal study. Am Mineral 85:1164–1171Google Scholar
  5. Andreozzi GB, Lucchesi S, Skogby H, Della Giusta A (2001) Compositional dependence of cation distribution in some synthetic (Mg, Zn)(Al, Fe3+)2O4 spinels. Eur J Mineral 13:391–402CrossRefGoogle Scholar
  6. Antao SM, Hassan I, Parise JB (2005a) Cation ordering in magnesioferrite, MgFe2O4, to 982 °C using in situ synchrotron X-ray powder diffraction. Am Mineral 90:219–228CrossRefGoogle Scholar
  7. Antao SM, Hassan I, Crichton WA, Parise JB (2005b) Effects of high pressure and high temperature on cation ordering in magnesioferrite, MgFe2O4, using in situ synchrotron X- ray powder diffraction up to 1430 K and 6 GPa. Am Mineral 90:1500–1505CrossRefGoogle Scholar
  8. Asimow PD, Dixon JE, Langmuir CH (2004) A hydrous melting and fractionation model for mid-ocean ridge basalts: application to the Mid-Atlantic Ridge near the Azores. Geochem Geophys Geosyst 5. doi: 10.1029/2003GC000568
  9. Barnes SJ, Roeder PL (2001) The range of spinel compositions in terrestrial mafic and ultramafic rocks. J Petrol 42:2279–2302CrossRefGoogle Scholar
  10. Berman RG (1988) Internally-consistent thermodynamic data for minerals in the system Na2O-K2O-CaO-MgO-FeO-Fe2O3-Al2O3-SiO2-TiO2-H2O-CO2. J Petrol 89:168–183Google Scholar
  11. Berman RG, Koziol AM (1991) Ternary excess properties of grossular-pyrope-almandine garnet and their influence in geothermobarometry. Am Mineral 76:1223–1231Google Scholar
  12. Bhagavantam S (1955) Elastic properties of single crystals and polycrystalline aggregates. Proc Math Sci 41:72–90Google Scholar
  13. Bosi F, Hålenius U, Andreozzi GB, Skogby H, Lucchesi S (2007) Structural refinement and crystal chemistry of Mn-doped spinel: a case for tetrahedrally coordinated Mn3+ in an oxygen-based structure. Am Mineral 92:27–33CrossRefGoogle Scholar
  14. Bosi F, Hålenius U, Skogby H (2009) Crystal chemistry of the magnetite-ulvöspinel series. Am Mineral 94:181–189CrossRefGoogle Scholar
  15. Bragg W (1915) The structure of magnetite and the spinels. Nature 95:561CrossRefGoogle Scholar
  16. Brey GP, Doroshev AM, Girnis AV, Turkin AI (1999) Garnet-spinel-olivine-orthopyroxene equilibria in the FeO-MgO-Al2O3-SiO2-Cr2O3 system: I. Composition and molar volumes of minerals. Eur J Mineral 11:599–617Google Scholar
  17. Buddington AF, Lindsley DH (1964) Iron-titanium oxide minerals and synthetic equivalents. J Petrol 5:310–357CrossRefGoogle Scholar
  18. Callen HB, Harrison SE, Kriessman CJ (1956) Cation distributions in ferrospinels. Theoretical Phys Rev 103:851–856Google Scholar
  19. Carbonin S, Russo U, Della Giusta A (1996) Cation distribution in some natural spinels from X-ray diffraction and Mössbauer spectroscopy. Mineral Mag 60:355–368CrossRefGoogle Scholar
  20. Carbonin S, Martignago F, Menegazzo G, Dal Negro A (2002) X-ray single-crystal study of spinels: in situ heating. Phys Chem Miner 29:503–514CrossRefGoogle Scholar
  21. Carraro A (2003) Crystal chemistry of Cr-spinels from a suite of spinel peridotite mantle xenoliths from the Predazzo Area (Dolomites, Northern Italy). Eur J Mineral 15:681–688CrossRefGoogle Scholar
  22. Connolly JAD (2009) The geodynamic equation of state: What and how. Geochem Geophys Geosys 10. doi: 10.1029/2009GC002540
  23. Della Giusta A, Carbonin S, Ottonello G (1996) Temperature-dependent disorder in a natural Mg-Al-Fe2 + -Fe3 + -spinel. Mineral Mag 60:603–616CrossRefGoogle Scholar
  24. Dick HJB, Bullen T (1984) Chromian spinel as a petrogenetic indicator in abyssal and alpine- type peridotites and spatially associated lavas. Contrib Mineral Petrol 86:54–76CrossRefGoogle Scholar
  25. Doraiswami MS (1947) Elastic constants of magnetite, pyrite and chromite. Proc Math Sci 25:413–416Google Scholar
  26. Doroshev AM, Brey GP, Girnis AV, Turkin AI, Kogarko LN (1997) Pyrope-knorringite garnets in the Earth’s mantle: experiments in the MgO-Al2O3-SiO2-Cr2O3 system. Russ Geol Geophys 38:559–586Google Scholar
  27. Downs RT, Hall-Wallace M (2003) The American Mineralogist crystal structure database. Am Mineral 88:247–250Google Scholar
  28. Dunitz J, Orgel L (1957) Electronic properties of transition-metal oxides-II: cation distribution amongst octahedral and tetrahedral sites. J Phys Chem Solids 3:318–323CrossRefGoogle Scholar
  29. Efron B (1982) The jackknife, the bootstrap, and other resampling plans. Soc Ind Appl Math, PhiladelphiaCrossRefGoogle Scholar
  30. Fan D, Zhou W, Liu C, Liu Y, Jiang X, Wan F, Liu J, Li X, Xie H (2008) Thermal equation of state of natural chromium spinel up to 26.8 GPa and 628 K. J Mater Sci 43:5546–5550CrossRefGoogle Scholar
  31. Finger LW, Hazen RM, Hofmeister AM (1986) High-pressure crystal chemistry of spinel (MgAl2O4) and magnetite (Fe3O4): comparisons with silicate spinels. Phys Chem Miner 13:215–220CrossRefGoogle Scholar
  32. Fleet ME (1981) The structure of magnetite. Acta Crystallogr B37:917–920Google Scholar
  33. Fleet ME (1984) The structure of magnetite: two annealed natural magnetites, Fe3.005O4 and Fe2.96Mg0.04O4. Acta Crystallogr C40:1491–1493Google Scholar
  34. Gatta G, Kantor I, Boffa Ballaran T, Dubrovinsky L, McCammon C (2007) Effect of non-hydrostatic conditions on the elastic behaviour of magnetite: an in situ single-crystal X-ray diffraction study. Phys Chem Miner 34:627–635CrossRefGoogle Scholar
  35. Ghiorso MS (1990) Thermodynamic properties of hematite-ilmenite-geikielite solid solutions. Contrib Mineral Petrol 104:645–667CrossRefGoogle Scholar
  36. Ghiorso MS (2004a) An equation of state for silicate melts. I. Formulation of a general model. Am J Sci 304:637–678CrossRefGoogle Scholar
  37. Ghiorso MS (2004b) An equation of state for silicate melts. III. Analysis of stoichiometric liquids at elevated pressure: shock compression data, molecular dynamics simulations, and mineral fusion curves. Am J Sci 304:752–810CrossRefGoogle Scholar
  38. Ghiorso MS (2004c) An equation of state for silicate melts. IV. Calibration of a multicomponent mixing model to 40 GPa. Am J Sci 304:811–838CrossRefGoogle Scholar
  39. Ghiorso MS, Evans BW (2008) Thermodynamics of rhombohedral oxide solid solutions and a revision of the Fe-Ti two-oxide geothermometer and oxygen- barometer. Am J Sci 308:957–1039CrossRefGoogle Scholar
  40. Ghiorso MS, Kress VC (2004) An equation of state for silicate melts. II. Calibration of volumetric properties at 105 Pa. Am J Sci 304:679–751CrossRefGoogle Scholar
  41. Ghiorso MS, Sack RO (1991) Fe-Ti oxide geothermometry: thermodynamic formulation and the estimation of intensive variables in silicic magmas. Contrib Mineral Petrol 108:485–510CrossRefGoogle Scholar
  42. Ghiorso MS, Sack RO (1995) Chemical mass transfer in magmatic processes IV. A revised and internally consistent thermodynamic model for the interpolation and extrapolation of liquid-solid equilibria in magmatic systems at elevated temperatures and pressures. Contrib Mineral Petrol 119:197–212CrossRefGoogle Scholar
  43. Ghiorso MS, Hirschmann MM, Reiners PW, Kress III VC (2002) The pMELTS: a revision of MELTS for improved calculation of phase relations and major element partitioning related to partial melting of the mantle to 3 GPa. Geochem Geophys Geosyst 3. doi: 10.1029/2001GC000217
  44. Ghiorso, MS, Hirschmann, MM, Grove, TL (2007) xMELTS: A thermodynamic model for the estimation of magmatic phase relations over the pressure range 0–30 GPa and at temperatures up to 2500 °C. Eos Trans Am Geophys Union 88(52), Fall Meet Suppl Abstr V31C-0608Google Scholar
  45. Girnis A, Brey G, Doroshev A, Turkin A, Simon N (2003) The system MgO-Al2O3-Cr2O3 revisited: reanalysis of Doroshev et al’.s (1997) experiments and new experiments. Eur J Mineral 15:953–964CrossRefGoogle Scholar
  46. Golla-Schindler U, O’Neill HStC, Putnis A (2005) Direct observation of spinodal decomposition in the magnetite-hercynite system by susceptibility measurements and transmission electron microscopy. Am Mineral 90:1278–1283Google Scholar
  47. Haavik C, Stølen S, Fjellvåg H, Hanfland M, Häusermann D (2000) Equation of state of magnetite and its high-pressure modification: thermodynamics of the Fe-O system at high pressure. Am Mineral 85:514–523Google Scholar
  48. Haggerty S (1971) Compositional variations in lunar spinels. Nat Phys Sci 233:156–160Google Scholar
  49. Hamecher EA, Antoshechkina PM, Ghiorso MS, Asimow PD (2009) Thermodynamic calibration of Cr-Al exchange equilibria for garnet and spinel. Eos Trans Am Geophys Union 90(52), Fall Meet Suppl Abstr V31D-2056Google Scholar
  50. Harrison RJ, Redfern SAT, O’Neill HStC (1998) The temperature dependence of the cation distribution in synthetic hercynite (FeAl~2O~4) from in situ neutron structure refinements. Am Mineral 83:1092–1099Google Scholar
  51. Hazen RM, Navrotsky A (1996) Effects of pressure on order-disorder reactions. Am Mineral 81:1021–1035Google Scholar
  52. Hill RJ (1984) X-ray powder diffraction profile refinement of synthetic hercynite. Am Mineral 69:937–942Google Scholar
  53. Hirschmann MM, Ghiorso MS, Davis FA, Gordon SM, Mukherjee S, Grove TL, Krawczynski M, Medard E, Till CB (2008) Library of experimental phase relations (LEPR): a database and web portal for experimental magmatic phase equilibria data. Geochem Geophys Geosyst 9. doi: 10.1029/2007GC001894
  54. Holland TJB, Powell R (1990) An enlarged and updated internally consistent thermodynamic dataset with uncertainties and correlations: the system K2O–Na2O–CaO–MgO–MnO– FeO–Fe2O3–Al2O3–TiO2–SiO2–C–H2–O2. J Metamorph Geol 8:89–124CrossRefGoogle Scholar
  55. Holland TJB, Powell R (1998) An internally consistent thermodynamic data set for phases of petrological interest. J Metamorph Geol 16:309–343CrossRefGoogle Scholar
  56. Holland TJB, Powell R (2011) An improved and extended internally consistent thermodynamic dataset for phases of petrological interest, involving a new equation of state for solids. J Metamorph Geol 29:333–383CrossRefGoogle Scholar
  57. Irifune T, Ohtani E, Kumazawa M (1982) Stability field of knorringite Mg3Cr2Si3O12 at high pressure and its implication to the occurrence of Cr-rich pyrope in the upper mantle. Phys Earth Planet Inter 27:263–272CrossRefGoogle Scholar
  58. Ishii M, Nakahira M, Yamanaka T (1972) Infrared absorption spectra and cation distributions in (Mn, Fe)3O4. Solid State Commun 11:209–212CrossRefGoogle Scholar
  59. Ishii M, Hiraishi J, Yamanaka T (1982) Structure and lattice vibrations of Mg-Al spinel solid solution. Phys Chem Miner 8:64–68CrossRefGoogle Scholar
  60. Kessel R, Beckett JR, Stolper EM (2003) Experimental determination of the activity of chromite in multicomponent spinels. Geochim Cosmochim Acta 67:3033–3044CrossRefGoogle Scholar
  61. Klemme S (2004) The influence of Cr on the garnet–spinel transition in the Earth’s mantle: experiments in the system MgO–Cr2O3–SiO2 and thermodynamic modelling. Lithos 77:639–646CrossRefGoogle Scholar
  62. Klemme S, Ivanic TJ, Connolly JAD, Harte B (2009) Thermodynamic modelling of Cr-bearing garnets with implications for diamond inclusions and peridotite xenoliths. Lithos 112:986–991CrossRefGoogle Scholar
  63. Larsson L, O’Neill HStC, Annersten H (1994) Crystal chemistry of synthetic hercynite (FeAl2O4) from XRD structural refinements and Mössbauer spectroscopy. Eur J Mineral 6:39–51Google Scholar
  64. Lavina B, Koneva A, Della Giusta A (2003) Cation distribution and cooling rates of Cr- substituted Mg-Al spinel from the Olkhon metamorphic complex, Russia. Eur J Mineral 15:435–441Google Scholar
  65. Lavina B, Princivalle F, Della Giusta A (2005) Controlled time-temperature oxidation reaction in a synthetic Mg-hercynite. Phys Chem Miner 32:83–88CrossRefGoogle Scholar
  66. Lavina B, Cesare B, Alvarez-Valero AM, Uchida H, Downs RT, Koneva A, Dera P (2009) Closure temperatures of intracrystalline ordering in anatectic and metamorphic hercynite, Fe2+Al2O4. Am Mineral 94:657–665CrossRefGoogle Scholar
  67. Lenaz D, Princivalle F (2005) The crystal chemistry of detrital chromian spinel from the southeastern Alps and outer Dinarides: the discrimination of supplies from areas of similar tectonic setting? Can Mineral 43:1305–1314CrossRefGoogle Scholar
  68. Lenaz D, Skogby H, Princivalle F, Hålenius U (2004) Structural changes and valence states in the MgCr2O4-FeCr2O4 solid solution series. Phys Chem Miner 31:633–642CrossRefGoogle Scholar
  69. Lenaz D, Braidotti R, Princivalle F, Garuti G, Zaccarini F (2007) Crystal chemistry and structural refinement of chromites from different chromitite layers and xenoliths of the Bushveld Complex. Eur J Mineral 19:599–609CrossRefGoogle Scholar
  70. Lenaz D, Logvinova AM, Princivalle F, Sobolev NV (2009) Structural parameters of chromite included in diamond and kimberlites from Siberia: a new tool for discriminating ultramafic source. Am Mineral 94:1067–1070CrossRefGoogle Scholar
  71. Levy D, Artioli G (1998) Thermal expansion of chromites and zinc spinels. Mater Sci Forum 278–281:390–395CrossRefGoogle Scholar
  72. Levy D, Pavese A, Hanfland M (2003) Synthetic MgAl2O4 (spinel) at high-pressure conditions (0.0001–30 GPa): a synchrotron X-ray powder diffraction study. Am Mineral 88:93–98Google Scholar
  73. Levy D, Diella V, Dapiaggi M, Sani A, Gemmi M, Pavese A (2004) Equation of state, structural behaviour and phase diagram of synthetic MgFe2O4, as a function of pressure and temperature. Phys Chem Miner 31:122–129CrossRefGoogle Scholar
  74. Lindsley DH (1965) Iron-titanium oxides. Carnegie Inst Year B 64:144–148Google Scholar
  75. Lucchesi S, Amoriello M, Della Giusta A (1998) Crystal chemistry of spinels from xenoliths of the Alban Hills volcanic region. Eur J Mineral 10:473–482Google Scholar
  76. Martignago F, Dal Negro A, Carbonin S (2003) How Cr3+ and Fe3+ affect Mg–Al order–disorder transformation at high temperature in natural spinels. Phys Chem Miner 30:401–408CrossRefGoogle Scholar
  77. Martignago F, Andreozzi G, Dal Negro A (2006) Thermodynamics and kinetics of cation ordering in natural and synthetic Mg(Al, Fe3+)2O4 spinels from in situ high-temperature X-ray diffraction. Am Mineral 91:306–312CrossRefGoogle Scholar
  78. Mattioli GS, Wood BJ, Carmichael ISE (1987) Ternary-spinel volumes in the system MgAl2O4–Fe3O4–γFe8/3O4: implications for the effect of P on intrinsic fo2 measurements of mantle- xenolith spinels. Am Mineral 72:468–480Google Scholar
  79. Méducin F, Redfern SAT, Le Godec Y, Stone HJ, Tucker MG, Dove MT, Marshall WG (2004) Study of cation order-disorder in MgAl2O4 spinel by in situ neutron diffraction up to 1600 K and 3.2 GPa. Am Mineral 89:981–986Google Scholar
  80. Menegazzo G, Carbonin S (1998) Oxidation mechanisms in Al-Mg-Fe spinels. A second stage: α-Fe2O3 exsolution. Phys Chem Miner 25:541–547CrossRefGoogle Scholar
  81. Millard RL, Peterson RC, Hunter BK (1995) Study of the cubic to tetragonal transition in Mg2TiO4 and Zn2TiO4 spinels by 17O MAS NMR and Rietveld refinement of X-ray diffraction data. Am Mineral 80:885–896Google Scholar
  82. Muan A, Hauck J, Löfall T (1972) Equilibrium studies with a bearing on lunar rocks. In: Proceedings of the Third Lunar Science Conference (Suppl 3). Geochim Cosmochim Acta 1:185–196Google Scholar
  83. Nakagiri N, Manghnani MH, Ming LC, Kimura S (1986) Crystal structure of magnetite under pressure. Phys Chem Miner 13:238–244CrossRefGoogle Scholar
  84. Nakatsuka A, Ueno H, Nakayama N, Mizota T, Maekawa H (2004) Single-crystal X-ray diffraction study of cation distribution in MgAl2O4–MgFe2O4 spinel solid solution. Phys Chem Miner 31:278–287CrossRefGoogle Scholar
  85. Nell J, Wood BJ (1989) Thermodynamic properties in a multicomponent solid solution involving cation disorder: Fe3O4–MgFe2O4–FeAl2O4–MgAl2O4 spinels. Am Mineral 74:1000–1015Google Scholar
  86. Nestola F, Ballaran T, Balic-Zunic T, Princivalle F, Secco L, Dal Negro A (2007) Comparative compressibility and structural behavior of spinel MgAl2O4 at high pressures: the independency on the degree of cation order. Am Mineral 92:1838–1843CrossRefGoogle Scholar
  87. O’Neill HStC, Navrotsky A (1983) Simple spinels: crystallographic parameters, cation radii, lattice energies, and cation distribution. Am Mineral 68:181–194Google Scholar
  88. O’Neill HStC, Navrotsky A (1984) Cations distributions and thermodynamic properties of binary spinel solid solutions. Am Mineral 69:733–753Google Scholar
  89. Oka Y, Steinke P, Chatterjee ND (1984) Thermodynamic mixing properties of Mg(Al, Cr)2O4 spinel crystalline solution at high temperatures and pressures. Contrib Mineral Petrol 87:196–204CrossRefGoogle Scholar
  90. O’Neill HStC, Dollase WA (1994) Crystal structures and cation distributions in simple spinels from powder XRD structural refinements: MgCr2O4, ZnCr2O4, Fe3O4, and the temperature dependence of the cation distribution in ZnAl2O4. Phys Chem Miner 20:541–555Google Scholar
  91. O’Neill HStC, Annersten H, Virgo D (1992) The temperature dependence of the cation distribution in magnesioferrite (MgFe2O4) from powder XRD structural refinements and Mössbauer spectroscopy. Am Mineral 77:725–740Google Scholar
  92. O’Neill HStC, Redfern S, Kesson S, Short S (2003) An in situ neutron diffraction study of cation disordering in synthetic qandilite Mg2TiO4 at high temperatures. Am Mineral 88:860–865Google Scholar
  93. Pascal ML, Fonteilles M, Boudouma O, Principe C (2011) Qandilite from Vesuvius skarn ejecta: conditions of formation and miscibility gap in the ternary spinel—qandilite—magnesioferrite. Can Mineral 49:459–485CrossRefGoogle Scholar
  94. Passerini L (1930) Richerche sugli spinelli. II. I composti. CuAl2O4, MgAl2O4, MgFe2O4, ZnAl2O4, ZnCr2O4, ZnFe2O4, MnFe2O4. Gazz Chim Ital 60:389–399Google Scholar
  95. Peterson RC, Lager GA, Hitterman RL (1991) A time-of-flight neutron powder diffraction study of MgAl2O4 at temperatures up to 1273 K. Am Mineral 76:1455–1458Google Scholar
  96. Powell R, Holland TJB (1985) An internally consistent thermodynamic dataset with uncertainties and correlations: 1. Methods and a worked example. J Metamorph Geol 3:327–342CrossRefGoogle Scholar
  97. Powell R, Holland TJB, Worley B (1998) Calculating phase diagrams involving solid solutions via non-linear equations, with examples using THERMOCALC. J Metamorph Geol 16:577–588CrossRefGoogle Scholar
  98. Princivalle F, Della Giusta A, De Min A, Piccirillo E (1999) Crystal chemistry and significance of cation ordering in Mg-Al rich spinels from high-grade hornfels (Predazzo-Monzoni, NE Italy). Mineral Mag 63:257–262Google Scholar
  99. Princivalle F, Martignago F, Del Negro A (2006) Kinetics of cation ordering in natural Mg(Al, Cr3+)2O4 spinels. Am Mineral 91:313–318CrossRefGoogle Scholar
  100. Redfern SAT, Harrison RJ, O’Neill HStC, Wood DRR (1999) Thermodynamics and kinetics of cation ordering in MgAl2O4 spinel up to 1600 °C from in situ neutron diffraction. Am Mineral 84:299–310Google Scholar
  101. Reichmann HJ, Jacobsen SD (2004) High-pressure elasticity of a natural magnetite crystal. Am Mineral 89:1061–1066Google Scholar
  102. Robbins M, Wertheim GK, Sherwood RC, Buchanan DNE (1971) Magnetic properties and site distributions in the system FeCr2O4–Fe3O4 (Fe2+Cr2 – xFex3+O4). J Phys Chem Solids 32:717–729CrossRefGoogle Scholar
  103. Robie RA, Hemingway BS, Fisher JR (1979) Thermodynamic properties of minerals and related substances at 298.15 K and 1 bar (1e5 Pa) pressures and at higher temperatures. US Geol Surv Bull 1452:1–456Google Scholar
  104. Sack RO (1982) Spinels as petrogenetic indicators: activity-composition relations at low pressures. Contrib Mineral Petrol 79:169–186CrossRefGoogle Scholar
  105. Sack RO, Ghiorso MS (1991a) An internally consistent model for the thermodynamic properties of Fe-Mg-titanomagnetite-aluminate spinels. Contrib Mineral Petrol 106:474–505CrossRefGoogle Scholar
  106. Sack RO, Ghiorso MS (1991b) Chromian spinels as petrogenetic indicators: thermodynamics and petrological applications. Am Mineral 76:827–847Google Scholar
  107. Sack RO, Ghiorso MS (1994a) Thermodynamics of multi component pyroxenes: iI. Phase relations in the quadrilateral. Contrib Mineral Petrol 116:287–300CrossRefGoogle Scholar
  108. Sack RO, Ghiorso MS (1994b) Thermodynamics of multicomponent pyroxenes: III. Calibration of Fe2+(Mg)-1, TiAl2(MgSi2)-1, TiFe2 3+(MgSi2)-1, AlFe3+(MgSi)-1, NaAl(CaMg)-1, Al2(MgSi)-1 and Ca(Mg)-1 exchange reactions between pyroxenes and silicate melts. Contrib Mineral Petrol 118:271–296CrossRefGoogle Scholar
  109. Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6:461–464CrossRefGoogle Scholar
  110. Sedler IK, Feenstra A, Peters T (1994) An X-ray powder diffraction study of synthetic (Fe, Mn)2TiO4 spinel. Eur J Mineral 6:873–885Google Scholar
  111. Smith PM, Asimow PD (2005) Adiabat_1ph: a new public front-end to the MELTS, pMELTS, and pHMELTS models. Geochem Geophys Geosyst 6. doi: 10.1029/2004GC000816
  112. Stout M, Bayliss P (1980) Crystal structure of two ferrian ulvöspinels from British Columbia. Can Mineral 18:339–341Google Scholar
  113. Taberna PL, Mitra S, Poizot P, Simon P, Tarascon J-M (2006) High rate capabilities Fe3O4- based Cu nano-architectured electrodes for lithium-ion battery applications. Nat Mater 5:567–573CrossRefGoogle Scholar
  114. Tabira Y, Withers RL (1999) Cation ordering in NiAl2O4 spinel by a 111 systematic row CBED technique. Phys Chem Miner 27:112–118CrossRefGoogle Scholar
  115. Verwey E, Heilmann E (1947) Physical properties and cation arrangement of oxides with spinel structures I. Cation arrangement in spinels. J Chem Phys 15:174–180CrossRefGoogle Scholar
  116. Waerenborgh JC, Figueiredo MO, Cabral JMP, Pereira LCJ (1994) Powder XRD structure refinements and 57Fe Mössbauer effect study of synthetic Zn1-xFexAl2O4 (0 < x ≤ 1) spinels annealed at different temperatures. Phys Chem Miner 21:460–468CrossRefGoogle Scholar
  117. Wang H, Simmons G (1972) Elasticity of some mantle crystal structures 1. Pleonaste and hercynite spinel. J Geophys Res 77:4379–4392CrossRefGoogle Scholar
  118. Wechsler BA, Von Dreele RB (1989) Structure refinements of Mg2TiO4, MgTiO3 and MgTi2O5 by time-of-flight neutron powder diffraction. Acta Crystallogr B45:542–549Google Scholar
  119. Wechsler BA, Lindsley D, Prewitt C (1984) Crystal structure and cation distribution in titanomagnetites (Fe3-xTixO4). Am Mineral 69:754–770Google Scholar
  120. Woodland AB, Bauer M, Ballaran TB, Hanrahan M (2009) Crystal chemistry of Fe3 2+Cr2Si3O12 – Fe3 2+Fe2 3+Si3O12 garnet solid solutions and related spinels. Am Mineral 94:359–366CrossRefGoogle Scholar
  121. Workman RK, Hart SR (2005) Major and trace element composition of the depleted MORB mantle (DMM). Earth Planet Sci Lett 231:53–72CrossRefGoogle Scholar
  122. Yamanaka T, Shimazu H, Ota K (2001) Electric conductivity of Fe2SiO4–Fe3O4 spinel solid solutions. Phys Chem Miner 28:110–118CrossRefGoogle Scholar
  123. Yang Z, Xia G-G, Li X-H, Stevenson JW (2007) (Mn, Co)3O4 spinel coatings on ferritic stainless steels for SOFC interconnect applications. Int J Hydrogen Energy 32:3648–3654CrossRefGoogle Scholar
  124. Zhao Y, Zhang Y, Bi C, Guo L (1998) The discovery of magnesioferrite from Au(Fe, Cu) magnesian skarn deposits and study of the magnesioferrite-magnesiomagnetite series. Acta Geol Sin 74:382–391Google Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Emily A. Hamecher
    • 1
  • Paula M. Antoshechkina
    • 1
  • Mark S. Ghiorso
    • 2
  • Paul D. Asimow
    • 1
  1. 1.Division of Geological and Planetary SciencesCalifornia Institute of TechnologyPasadenaUSA
  2. 2.OFM ResearchSeattleUSA

Personalised recommendations