Contributions to Mineralogy and Petrology

, Volume 102, Issue 1, pp 41–68 | Cite as

Importance of considerations of mixing properties in establishing an internally consistent thermodynamic database: thermochemistry of minerals in the system Mg2SiO4-Fe2SiO4-SiO2

  • Richard O. Sack
  • Mark S. Ghiorso


A thermodynamic solution model is developed for minerals whose compositions lie in the two binary systems Mg2SiO4-Fe2SiO4 and Mg2Si2O6-Fe2Si2O6. The formulation makes explicit provision for nonconvergent ordering of Fe2+ and Mg2+ between M1 and M2 sites in orthopyroxenes and non-zero Gibbs energies of reciprocal ordering reactions in both olivine and orthopyroxene. The calibration is consistent with (1) constraints provided by available experimental and natural data on the Fe-Mg exchange reaction between olivine and orthopyroxene ± quartz, (2) site occupancy data on orthopyroxenes including both crystallographic refinements and Mössbauer spectroscopy, (3) enthalpy of solution data on olivines and orthopyroxenes and enthalpy of disordering data on orthopyroxene, (4) available data on the temperature and ordering dependence of the excess volume of orthopyroxene solid solutions, and (5) direct activity-composition determinations of orthopyroxene and olivine solid solutions at elevated temperatures. Our analysis suggests that the entropies of the exchange [Mg(M2)Fe(M1)⇔Fe(M2)Mg(M1)] and reciprocal ordering reactions [Mg(M2)Mg(M1)+ Fe(M2)Fe(M1)⇔Fe(M2)Mg(M1)+Mg(M2)Fe(M1)] cannot differ significantly (± 1 cal/K) from zero over the temperature range of calibration (400°–1300° C). Consideration of the mixing properties of olivine-orthopyroxene solid solutions places tight constraints on the standard state thermodynamic quantities describing Fe-Mg exchange reactions involving olivine, orthopyroxene, pyralspite garnets, aluminate spinels, ferrite spinels and biotite. These constraints are entirely consistent with the standard state properties for the phasesα-quartz,β-quartz, orthoenstatite, clinoenstatite, protoenstatite, fayalite, ferrosilite and forsterite which were deduced by Berman (1988) from an independent analysis of phase equilibria and calorimetric data. In conjunction with these standard state properties, the solution model presented in this paper provides a means of evaluating an internally consistent set of Gibbs energies of mineral solid solutions in the system Mg2SiO4-Fe2SiO4-SiO2 over the temperature range 0–1300° C and pressure interval 0.001–50 kbars. As a consequence of our analysis, we find that the excess Gibbs energies associated with mixing of Fe and Mg in (Fe, Mg)2SiO4 olivines, (Fe, Mg)3Al2Si3O12 garnets, (Fe, Mg)Al2O4 and (Fe, Mg)Fe2O4 spinels, and K(Mg, Fe)3AlSi3O10(OH)2 biotites may be satisfactory described, on a macroscopic basis, with symmetric regular solution type parameters having values of 4.86±0.12 (olivine), 3.85±0.09 (garnet), 1.96±0.13 (spinel), and 3.21±0.29 kcals/gfw (biotite). Applications of the proposed solution model demonstrate the sensitivity of petrologic modeling to activity-composition relations of olivine-orthopyroxene solutions. We explore the consequences of estimating the activity of silica in melts forming in the mantle and we develop a graphical geothermometer/geobarometer for metamorphic assemblages of olivine+orthopyroxene+quartz. Quantitative evaluation of these results suggests that accurate and realistic estimates of silica activity in melts derived from mantle source regions,P-T paths of metamorphism and other intensive variables of petrologic interest await further refinements involving the addition of “trace” elements (Al3+ and Fe3+) to the thermodynamic formulation for orthopyroxenes.


Olivine Forsterite Fayalite Aluminate Spinel Clinoenstatite 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Adams GE, Bishop FC (1986) The olivine-clinopyroxene geobarometer: experimental results in the CaO-FeO-MgO-SiO2 system. Contrib Mineral Petrol 94:230–237Google Scholar
  2. Akimoto S, Fujisawa, H (1968) Olivine-spinel solid solution equilibria in the system Mg2SiO4-Fe2SiO4. J Geophys Res 73:1467–1479Google Scholar
  3. Annersten H, Olesch M, Seifert FA (1978) Ferric iron in orthopyroxene: A Mössbauer spectroscopic study. Lithos 11:301–310Google Scholar
  4. Annersten H, Siefert F (1981) Stability of the assemblage orthopyroxene-sillimanite-quartz in the system MgO-FeO-Fe2O3-Al2O3-SiO2-H2O. Contrib Mineral Petrol 77:158–165Google Scholar
  5. Anovitz LM, Essene EJ, Dunham WR (1988) Order-disorder experiments on orthopyroxenes: Implications for the orthopyroxene speedometer. Am Mineral 73:1060–1073Google Scholar
  6. Berg JH (1977) Regional geobarometry in the contact aureoles of the anorthositic Nain complex, Labrador. J Petrol 18:399–430Google Scholar
  7. Berg JH, Weibe RA (1985) Petrology of a xenolith of ferro-aluminous gneiss from the Nain complex. Contrib Mineral Petrol 90:226–235Google Scholar
  8. 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 29:445–522Google Scholar
  9. Berman RG, Brown TH (1985) Heat capacity of minerals in the system Na2O-FeO-Fe2O3-Al2O3-SiO2-TiO2-H2O-CO2: representation, estimation, and high temperature extrapolation. Contrib Mineral Petrol 89:168–183Google Scholar
  10. Berman RG, Brown TH, Perkins EH (1987) GEO-CALC: software for calculation and display of pressure-temperature-composition phase diagrams. Am Mineral 72:861–862Google Scholar
  11. Berman RG, Engi M, Greenwood HJ, Brown TH (1986) Derivation of internally-consistent thermodynamic data by the technique of mathematical programming, a review with application to the system MgO-SiO2-H2O. J Petrol 27:1331–1364Google Scholar
  12. Besancon JR (1981) Rate of cation disordering in orthopyroxenes. Am Mineral 66:965–973Google Scholar
  13. Bohlen SR, Essene EJ (1979) A critical evaluation of two-pyroxene thermometry in Adirondack granulites. Lithos 12:335–345Google Scholar
  14. Bohlen SR, Boettcher AL, Dollase WA, Essene EJ (1980c) The effect of manganese on olivine-quartz-orthopyroxene stability. Earth Planet Sci Lett 47:11–20Google Scholar
  15. Bohlen SR, Essene EJ, Boettcher AL (1980a) Reinvestigation and application of olivine-quartz-orthopyroxene barometry. Earth Planet Sci Lett 47:1–10Google Scholar
  16. Bohlen SR, Essene EJ, Hoffman KS (1980b) Evaluation of coexisting garnet-biotite, garnet clinopyroxene and other Fe-Mg exchange thermometers in Adirondack granulites. Geol Soc Am Bull 91 Part II:685–719Google Scholar
  17. Bohlen SR, Boettcher AL (1981) Experimental investigations and geological applications of orthopyroxene geothermometry. Am Mineral 66:951–964Google Scholar
  18. Bonnichsen B (1969) Metamorphic pyroxenes and amphiboles in the Biwabik Iron Formation, Dunka River area, Minnesota. Mineral Soc Am S Paper 2:217–239Google Scholar
  19. Boyd FR (1973) A pyroxene geotherm. Geochim Cosmochim Acta 37:2533–2546Google Scholar
  20. Bragg WL, Williams EJ (1934) The effect of thermal agitation on atomic arrangement in alloys. Proc R Soc London A 145:699–730Google Scholar
  21. Bragg WL, Williams EJ (1935) The effect of thermal agitation on atomic arrangement in alloys. Proc R Soc London A 151:540–566Google Scholar
  22. Brousse C, Newton RC, Kleppa OJ (1984) Enthalpy of formation of forsterite, enstatite, akermanite, monticellite and merwinite at 1073 K determined by alkali borate solution calorimetry. Geochim Cosmochim Acta 48:1081–1088Google Scholar
  23. Carswell DA (1968) Picrite magma-residual dunite relationships in garnet peridotite at Kalskaret near Tafjord, South Norway. Contrib Mineral Petrol 19:97–124Google Scholar
  24. Carswell DA, Gibb FGF (1980) Geothermometry of garnet lherzolite nodules with special reference to those from the kimberlites of northern Lesotho. Contrib Mineral Petrol 74:403–416Google Scholar
  25. Charlu TV, Newton RC, Kleppa OJ (1975) Enthalpies of formation at 970 K of compounds in the system MgO-Al2O3-SiO2 by high temperature solution calorimetry. Geochim Cosmochim Acta 39:1487–1497Google Scholar
  26. Chatillon-Colinet C, Newton RC, Perkins D III, Kleppa OJ (1983) Thermochemistry of (Fe2+, Mg)SiO3 orthopyroxene. Geochim Cosmochim Acta 47:1597–1603Google Scholar
  27. Davidson PM, Lindsley DH (1985) Thermodynamic analysis of quadrilateral pyroxenes. Part II: Model calibration from experiments and applications to geothermometry. Contrib Mineral Petrol 91:390–404Google Scholar
  28. Davidson PM, Lindsley DH (1989) Thermodynamic analysis of pyroxene-olivine-quartz equilibria in the system CaO-MgO-FeO-SiO2. Am Mineral 74:18–30Google Scholar
  29. Davidson PM, Mukhopadhay DK (1984) Ca-Fe-Mg olivines: phase relations and a solution model. Contrib Mineral Petrol 86:256–263Google Scholar
  30. Deer WA, Howie RA, Zussman J (1966) An introduction to the rock-forming minerals. Wiley, New YorkGoogle Scholar
  31. Ferry JM (1980) A comparative study of geothermometers and geobarometers in pelitic schists from south-central Maine. Am Mineral 65:720–732Google Scholar
  32. Ferry JM (1984) A biotite isograd in south-central Maine, USA: mineral reactions, fluid transfer, and heat transfer. J Petrol 25:871–893Google Scholar
  33. Ferry JM, Spear FS (1978) Experimental calibration of the partitioning of Fe and Mg between biotite and garnet. Contrib Mineral Petrol 66:113–117Google Scholar
  34. Finnerty AA, Boyd FR (1984) Evaluation of thermobarometers for garnet peridotites. Geochim Cosmochim Acta 48:15–27Google Scholar
  35. Fisher GW, Medaris LG (1969) Cell dimensions and X-ray determinative curve for synthetic Mg-Fe olivines. Am Mineral 54:741–753Google Scholar
  36. Frisch T, Bridgewater D (1976) Iron- and manganese-rich minor intrusions emplaced under late-orogenic conditions in the Proterozoic of South Greenland. Contrib Mineral Petrol 57:25–48Google Scholar
  37. Fujii T, Scarfe CM (1982) Petrology of ultramafic nodules from West Kettle River, near Kelowna, Southern British Columbia. Contrib Mineral Petrol 80:297–306Google Scholar
  38. Ganguly J, Saxena SK (1984) Mixing properties of aluminosilicate garnets: constraints from natural and experimental data, and applications to geothermo-barometry. Am Mineral 69:88–97Google Scholar
  39. Gaskell DR (1981) The thermodynamic properties and structures of slags. In: Tien JK, Elliot JF (eds) Metallurgical treatises. Metallurgical Soc AIME, Warrendale, pp 59–77Google Scholar
  40. Gee LL, Sack RO (1988) Experimental petrology of melilite nephelinites. J Petrol (in press)Google Scholar
  41. Geiger CA, Newton RC, Kleppa OJ (1987) Enthalpy of mixing of synthetic almandine-grossular and almandine-pyrope garnets from high-temperature solution calorimetry. Geochim Cosmochim Acta 51:1755–1763Google Scholar
  42. Ghiorso MS (1987) Modeling magmatic systems: thermodynamic relations. In: Carmichael ISE, Eugster HP (eds) Thermodynamic modeling of geological materials: minerals fluids and melts. Mineral Soc Am Short Course Notes 12:443–465Google Scholar
  43. Ghiorso MS, Carmichael ISE (1987) Modeling magmatic systems: petrologic applications. In: Carmichael ISE, Eugster HP (eds) Thermodynamic modeling of geological materials: minerals, fluids and melts. Mineral Soc Am Short Course Notes 12:467–499Google Scholar
  44. Ghiorso MS, Carmichael ISE, Rivers ML, Sack RO (1983) The Gibbs free energy of mixing of natural silicate liquids; an expanded regular solution model for the calculation of magmatic intensive variables. Contrib Mineral Petrol 84:107–145Google Scholar
  45. Goldman DS, Albee AL (1977) Correlation of Mg/Fe partitioning between garnet and biotite with O18/O16 partitioning between quartz and magnetite. Am J Sci 277:750–761Google Scholar
  46. Gole MJ, Klein C (1981) High-grade metamorphic Archaen banded iron-formations, Western Australia: assemblages with coexisting pyroxenes±fayalite. Am Mineral 66:87–99Google Scholar
  47. Grover JE, Orville PM (1969) The partitioning of cations between coexisting single- and multi-site phases: application to the assemblages orthopyroxene-clinopyroxene and orthopyroxene-olivine. Geochim Cosmochim Acta 33:205–226Google Scholar
  48. Hackler RT, Wood BJ (1989) Experimental determination of Fe and Mg exchange between garnet and olivine and estimation of Fe-Mg garnet mixing properties. Am Mineral (in press)Google Scholar
  49. Harley SL (1984a) The solubility of alumina in orthopyroxene coexisting with garnet in FeO-MgO-Al2O3-SiO2 and CaO-FeO-MgO-Al2O3-SiO2. J Petrol 25:665–696Google Scholar
  50. Harley SL (1984b) Comparison of the garnet-orthopyroxene geobarometer with the recent experimental studies, and applications to natural assemblages. J Petrol 25:697–712Google Scholar
  51. Hill RL, Sack RO (1987) Thermodynamic properties of Fe-Mg titaniferous magnetite spinels. Can Mineral 25:443–464Google Scholar
  52. Jamieson HC, Roeder PL (1984) The distribution of Mg-Fe2+ between olivine and spinel at 1300° C. Am Mineral 69:283–291Google Scholar
  53. Johnson CA, Essene EJ (1982) The formation of garnet in olivine-bearing metagabbros from the Adirondacks. Contrib Mineral Petrol 81:240–251Google Scholar
  54. Kawasaki T, Matsui Y (1977) Partitioning of Fe+2 and Mg+2 between olivine and garnet. Earth Planet Sci Lett 37:159–166Google Scholar
  55. Kawasaki T, Matsui Y (1983) Thermodynamic analyses of equilibria involving olivine, orthopyroxene and garnet. Geochim Cosmochim Acta 47:1661–1679Google Scholar
  56. Kitayama K, Katsura T (1968) Activity measurements in orthosilicate and metasilicate solid solutions: I. Mg2SiO4-Fe2SiO4 and MgSiO3-FeSiO3 at 1204° C. Bull Chem Soc Japan 41:1146–1151Google Scholar
  57. Krupka KM, Robie RA, Hemingway BS, Kerrick DM, Ito J (1985a) Low-temperature heat capacities and derived thermodynamic properties of anthophyllite, diopside, enstatite, bronzite, and wollastonite. Am Mineral 70:249–260Google Scholar
  58. Krupka KM, Robie RA, Hemingway BS, Kerrick DM, Ito J (1985b) High-temperature heat capacities and derived thermodynamic properties of anthophyllite, diopside, dolomite, enstatite, bronzite, talc, tremolite, and wollastonite. Am Mineral 70:261–271Google Scholar
  59. Lange RA, Carmichael ISE (1987) Densities of Na2O-K2O-CaO-MgO-FeO-Fe2O3-Al2O3-TiO2-SiO2 liquids: New measurements and derived partial molar properties. Geochim Cosmochim Acta 51:2931–2946Google Scholar
  60. Larimer JW (1968) Experimental studies on the system Fe-MgO-SiO2-O2, and their bearing on the petrology of chondritic meteorites. Geochim Cosmochim Acta 32:1187–1207Google Scholar
  61. Lehmann J, Roux J (1986) Experimental and theoretical study of (Fe2+, Mg)(Al, Fe3+)2O4 spinels: Activity-composition relationships, miscibility gaps, vacancy contents. Geochim Cosmochim Acta 50:1765–1783Google Scholar
  62. MacGregor ID (1974) The system MgO-Al2O3-SiO2: solubility of Al2O3 in enstatite for spinel and garnet peridotite compositions. Am Mineral 59:110–119Google Scholar
  63. Matsui Y, Nishizawa O (1974) Iron(II)-magnesium exchange equilibrium between olivine and calcium-free pyroxene over a temperature range 800° C to 1300° C. Bull Soc Franc Mineral Cristallog 97:122–130Google Scholar
  64. Matsui Y, Syono Y, Akimoto S-iti, Kitayama K (1968) Unit cell dimensions of some synthetic orthopyroxene group solid solutions. Geochem J 2:61–70Google Scholar
  65. Miyano T, Klein C (1986) Fluid behavior and phase relations in the system Fe-Mg-Si-C-O-H. Application to high grade metamorphism of iron formations. Am J Sci 286:540–575Google Scholar
  66. Mori T, Banno S (1973) Petrology of peridotite and garnet clinopyroxenite of the Mt Higasi-Akaisi Mass, Central Sikoku, Japan — subsolidus relation of anhydrous phases. Contrib Mineral Petrol 41:301–323Google Scholar
  67. Nafziger RH, Muan A (1967) Equilibrium phase compositions and thermodynamic properties of olivines and pyroxenes in the system MgO-“FeO”-SiO2. Am Mineral 52:1364–1385Google Scholar
  68. O'Hara MJ, Mercy ELP (1963) Petrology and petrogenesis of some garnetiferous peridotites. Trans R Soc Edinburgh 65:251–314Google Scholar
  69. O'Neill HStC, Navrotsky A (1984) Cation distributions and thermodynamic properties of binary spinel solid solutions. Am Mineral 69:733–753Google Scholar
  70. Orr RL (1953) High temperature heat contents of magnesium orthosilicate and ferrous orthosilicate. J Am Chem Soc 75:528–529Google Scholar
  71. Perkins D, Newton RC (1980) Compositions of coexisting pyroxenes and garnets in the system CaO-MgO-Al2O3-SiO2 at 900–1100° C and high pressures. Contrib Mineral Petrol 75:291–300Google Scholar
  72. Peters T (1968) Distribution of Mg, Fe, Al, Ca and Na in coexisting olivine, orthopyroxene and clinopyroxene in the Totalp serpentinite (Davos, Switzerland) and in the alpine metamorphosed Malenco serpentinite (N Italy). Contrib Mineral Petrol 18:65–75Google Scholar
  73. Ramberg H, DeVore G (1951) The distribution of Fe2+ and Mg2+ in coexisting olivines and pyroxenes. J Geol 59:193–216Google Scholar
  74. Richet P, Bottinga Y, Denielou L, Petitet JP, Tequi C (1982) Thermodynamic properties of quartz, cristobalite and amorphous SiO2: Drop calorimetry measurements between 1000 and 1800 K and a review from 0 to 2000 K. Geochim Cosmochim Acta 46:2639–2658Google Scholar
  75. Robie RA, Bethke PM, Beardsley KM (1967) Selected X-ray crystallographic data, molar volumes, and densities of minerals and related substances. US Geol Surv Bull 1248Google Scholar
  76. Robie RA, Hemingway BS, Takei H (1982) Heat capacities and entropies of Mg2SiO4, Mn2SiO4, and Co2SiO4 between 5 and 380 K. Am Mineral 67:470–482Google Scholar
  77. Sack RO (1979) Studies of mafic granulites. PhD thesis, Harvard University, Cambridge, MasachusettsGoogle Scholar
  78. Sack RO (1980) Some constraints on the thermodynamic mixing properties of Fe-Mg orthopyroxenes and olivines. Contrib Mineral Petrol 71:257–269Google Scholar
  79. Sack RO (1982a) Spinels as petrogenetic indicators: Activity-composition relations at low pressures. Contrib Mineral Petrol 79:169–182Google Scholar
  80. Sack RO (1982b) Reaction skarns between quartz-bearing and olivine-bearing rocks. Am J Sci 282:970–1011Google Scholar
  81. Sack RO, Carmichael ISE (1984) Fe2+⇔Mg2+ and TiAl2⇔MgSi2 exchange reactions between clinopyroxenes and silicate melts. Contrib Mineral Petrol 85:103–115Google Scholar
  82. Sack RO, Ebel DS, O'Leary MJ (1987a) Tennahedrite thermochemistry and metal zoning. In: Helgeson HC (ed) Chemical transport in metasomatic processes. Reidel, Dordrecht Boston, pp 701–731Google Scholar
  83. Sack RO, Walker D, Carmichael ISE (1987b) Experimental petrology of alkalic lavas: constraints on cotectics of multiple saturation in natural basic liquids. Contrib Mineral Petrol 96:1–23Google Scholar
  84. Sahama ThG (1962) Order-disorder in natural nepheline solid solutions. J Petrol 3:65–81Google Scholar
  85. Sahama ThG, Torgeson DR (1949) Some examples of the application of thermochemistry to petrology. J Geol 57:255–262Google Scholar
  86. Saxena SL, Ghose S (1971) Mg2+-Fe2+ order-disorder and the thermodynamics of the orthopyroxene-crystalline solution. Am Mineral 56:532–559Google Scholar
  87. Sharma KC, Agrawal KC, Kapoor ML (1987) Determination of thermodynamic properties of (Fe, Mg)-pyroxenes at 1000 K by the EMF method. Earth Planet Sci Lett 85:302–310Google Scholar
  88. Shieh YN (1974) Mobility of oxygen isotopes during metamorphism. In: Hofmann AW, Giletti BJ, Yoder HS, Yund RA (eds) Geochemical Transport and Kinetics. Carnegie Inst Wash, pp 325–335Google Scholar
  89. Shieh YN, Taylor HP (1969) Oxygen and hydrogen isotope studies of contact metamorphism in the Santa Rosa Range, Nevada and other areas. Contrib Mineral Petrol 20:306–356Google Scholar
  90. Smith D (1971) Stability of the assemblage iron-rich orthopyroxene-olivine-quartz. Am J Sci 271:370–382Google Scholar
  91. Spear FS (1988) The Gibbs method and Duhem's theorem: the quantitative relationships among P, T, chemical potential, phase composition and reaction progress in igneous and metamorphic systems. Contrib Mineral Petrol 99:249–256Google Scholar
  92. Springer RK (1974) Contact metamorphosed ultramafic rocks in the Western Sierra Nevada foothills, California. J Petrol 15:160–195Google Scholar
  93. Thierry P, Chatillon-Colinet C, Mathieu JC, Regnard JR, Amosse J (1980) Thermodynamic properties of the forsterite-fayalite (Mg2SiO4-Fe2SiO4) solid solution. Determination of heat of formation. Phys Chem Mineral 7:43–46Google Scholar
  94. Thompson JB Jr (1967) Thermodynamic properties of simple solutions. In: Abelson PH (ed) Res geochem 2:340–361Google Scholar
  95. Thompson JB Jr (1969) Chemical reactions in crystals. Am Mineral 54:341–375Google Scholar
  96. Thompson JB Jr (1970) Chemical reactions in crystals: corrections and clarification. Am Mineral 55:528–532Google Scholar
  97. Trinel-Dufour MC, Perot P (1977) Etude thermodynamique des solutions solides dans le système Fe-Mg-O. Ann Chim 2:309–318Google Scholar
  98. Turnock AC, Lindsley DH, Grover JE (1973) Synthesis and unit cell parameters of Ca-Mg-Fe pyroxenes. Am Mineral 58:50–59Google Scholar
  99. Vaniman DT, Papike JJ, Labotka T (1980) Contact-metamorphic effects of the Stillwater Complex, Montana: the concordant iron-formation. Am Mineral 65:1087–1102Google Scholar
  100. Virgo D, Hafner SS (1969) Fe2+, Mg order-disorder in heated orthopyroxenes. Mineral Soc Am Spec Paper 2:67–81Google Scholar
  101. Walther JV, Orville PM (1982) Volatile production and transport in regional metamorphism. Contrib Mineral Petrol 79:252–257Google Scholar
  102. Wood BJ (1987) Thermodynamics of multicomponent systems containing several solid solutions. In: Carmichael ISE, Eugster HP (eds) Thermodynamic modeling in geological materials: minerals, fluids and melts. Mineral Soc Am Short Course Notes 12:71–95Google Scholar
  103. Wood BJ, Graham CM (1986) Infiltration of aqueous fluid and high fluid: rock ratios during greenschist facies metamorphism: a discussion. J Petrol 27:751–761Google Scholar
  104. Wood BJ, Kleppa OJ (1981) Thermochemistry of forsterite-fayalite olivine solutions. Geochim Cosmochim Acta 45:529–534Google Scholar
  105. Zyrianov VN, Perchuk LL, Podlesskii KK (1978) Nepheline-alkali feldspar equilibria: I. Experimental data and thermodynamic calculations. J Petrol 19:1–44Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Richard O. Sack
    • 1
  • Mark S. Ghiorso
    • 2
  1. 1.Department of Earth and Atmospheric SciencesPurdue UniversityWest LafayetteUSA
  2. 2.Department of Geological Sciences, AJ-20University of WashingtonSeattleUSA

Personalised recommendations