Abstract
Systematic thermodynamic analysis reveals that an essential condition for the thermodynamically valid chemographic projections proposed by Greenwood is completely excessive. In other words, the phases or components from which the projection is made need not be pure, nor have their chemical potentials fixed over the whole chemographic diagram. To facilitate the analysis of phase assemblages in multicomponent systems, all phases and components in the system are divided into internal and external ones in terms of their thermodynamic features and roles, where the external phases are those common to all assemblages in the system, and the external components include excess components and the components whose chemical potentials (or relevant intensive properties of components) are used to define the thermodynamic conditions of the system. This general classification overcomes the difficulties and defects in the previous classifications, and is easier to use than the previous ones. According to the above classification, the phase rule is transformed into a new form. This leads to two findings: (1) the degree of freedom of the system under the given conditions is only determined by the internal components and phases; (2) different external phases can be identified conveniently according to the conditions of the system before knowing the real phase relations. Based on the above results, a simple but general approach is proposed for the treatment of phases and components: all external phases and components can be eliminated from the system without affecting the phase relations, where the external components can be eliminated by appropriate chemographic projections. The projections have no restriction on the states of the phases or the chemical potentials of components from which the projections are made. The present work can give a unified explanation of the previous treatments of phases and components in the analysis of phase assemblages under various specific conditions. It helps to avoid potential misunderstandings or errors in the topological analysis of phase relations.
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References
Korzhinskii D S. Physicochemical Basis of the Analysis of the Paragenesis of Minerals. New York: Consultants Bureau Inc, 1959
Thompson J B J. The graphical analysis of mineral assemblages of pelitic schists. Amer Mineral, 1957, 42: 842–858
Greenwood H J. Thermodynamically valid projections of extensive phase relations. Amer Mineral, 1975, 60: 1–8
Fitzsimons I C W. Metapelitic migmatites from Brattstrand Bluffs, east Antarctica—Metamorphism, melting, and exhumation of the mid-crust. J Petrol, 1996, 37: 395–414
Longhi J. Comparative liquidus equilibria of hypersthene-normative basalts at low pressure. Amer Mineral, 1991, 76: 785–800
Thompson J B J. Local equilibrium in metasomatic processes. In: Abelson P H, ed. Researches in Geochemistry. New York: John Wiley and Sons, 1959. 427–457
Zen E A. Components, phases, and criteria of chemical equilibrium in rocks. Amer J Sci, 1963, 261: 929–942
Thompson J B J. Geochemical reaction and open systems. Geochim Cosmochim Acta, 1970, 34: 529–551
Rumble III D. The role of perfectly mobile components in metamorphism. Ann Rev Earth Planet Sci, 1982, 109: 221–233
Weill D F, Fyfe W S. A discussion of the Korzhinskii and Thompson treatment of thermodynamic equilibrium in open systems. Geochim Cosmochim Acta, 1964, 28: 565–576
Korzhinskii D S. On thermodynamics of open systems and the phase rule (A reply to D. F. Weill and W. S. Fyfe). Geochim Cosmochim Acta, 1966, 30: 829–835
Weill D F, Fyfe W S. On equilibrium thermodynamics of open systems and the phase rule (A reply to D. S. Korzhinskii). Geochim Cosmochim Acta, 1967, 31: 1167–1176
Korzhinskii D S. On thermodynamics of open systems and the phase rule (A reply to the second critical paper of D. F. Weill and W. S. Fyfe). Geochim Cosmochim Acta, 1967, 31: 1177–1180
Burt D M. Multisystem analysis of beryllium mineral stabilities: The system BeO-Al2O3-SiO2-H2O. Amer Mineral, 1978, 63: 664–676
Liu J Z, Qiang X K, Liu X S, et al. Dynamics and genetic grids of sapphirine-brearing spinel gneiss in Daqing Mountain in orogen zone, Inner Mongolia. Acta Petrol Sin, 2000, 16: 245–255
Abbott R N J. Muscovite-bearing granites in the AFM liquidus projection. Can Mineral, 1985, 23: 553–561
Abbott R N J. A petrogenetic grid for medium and high grade metabasites. Amer Mineral, 1982, 67: 865–876
Thompson J B J, Algor J R. Model systems for anatexis of pelitic rocks. I. Theory of melting reactions in the system KAlO2-NaAlO2-Al2O3-SiO2-H2O. Contrib Mineral Petrol, 1977, 63: 247–269
Bromiley G D, Pawley A R. The stability of antigorite in the systems MgO-SiO2-H2O (MSH) and MgO-Al2O3-SiO2-H2O (MASH): The effects of Al3+ substitution on high-pressure stability. Amer Mineral, 2003, 88: 99–108
Carman J H. Synthetic sodium phlogopite and its two hydrates: Stabilities, properties and mineralogic implications. Amer Mineral, 1974, 59: 261–273
Fleming P D, Fawcett F J. Upper stability of chlorite+quartz in the system MgO-FeO-Al2O3-SiO2-H2O at 2 kbar water pressure. Amer Mineral, 1976, 61: 1175–1193
Molina J F, Poli S. Singular equilibria in paragonite blueschists, amphibolites and eclogites. J Petrol, 1998, 39: 1325–1346
Wei C J, Powell R, Clarke G L. Calculated phase equilibria for low- and medium-pressure metapelites in the KFMASH and KMnFMASH systems. J Metamorph Geol, 2004, 22: 495–508
Yang J J, Powell R. Calculated phase relations in the system Na2O-CaO-K2O-FeO-MgO-Al2O3-SiO2-H2O with applications to UHP eclogites and whiteschists. J Petrol, 2006, 47: 2047–2071
Das K, Dasgupta S, Miura H. Stability of osumilite coexisting with spinel solid solution in metapelitic granulites at high oxygen fugacity. Amer Mineral, 2001, 86: 1423–1434
Das K, Dasgupta S, Miura H. An experimentally constrained petrogenetic grid in the silica-saturated portion of the system KFMASH at high temperatures and pressures. J Petrol, 2003, 44: 1055–1075
Greenfield J E, Clarke G L, White R W. A sequence of partial melting reactions at Mt Stafford, central Australia. J Metamorph Geol, 1998, 16: 363–378
Yang J J, Powell R. Ultrahigh-pressure garnet peridotites from the devolatilization of sea-floor hydrated ultramafic rocks. J Metamorph Geol, 2008, 26: 695–716
Wei C, Powell R. Phase relations in high-pressure metapelites in the system KFMASH (K2O-FeO-MgO-Al2O3-SiO2-H2O) with application to natural rocks. Contrib Mineral Petrol, 2003, 145: 301–315
Wei C, Powell R. Calculated phase relations in the system NCKFMASH (Na2O-CaO-K2O-FeO-MgO-Al2O3-SiO2-H2O) for high-pressure metapelites. J Petrol, 2006, 47: 385–408
Wei C, Wang W, Clarke G L, et al. Metamorphism of high/ultrahigh-pressure pelitic-felsic schist in the southTianshan orogen, NW China: Phase equilibria and P-T path. J Petrol, 2009, 50: 1973–1991
Ranson W A. Margarite-corundum phyllites from the Appalachian orogen of South Carolina: Mineralogy and metamorphic history. Amer Mineral, 2000, 85: 1617–1624
Burt D M. Some phase equilibria in the system Ca-Fe-Si-C-O. Carnegie Institution of Washington Year Book, 1971, 70: 178–184
London D, Burt D M. Chemical models for lithium aluminosilicate stabilities in pegmatites and granites. Amer Mineral, 1982, 67: 494–509
Guo Q, Wang S. The stability of laihunite—A thermodynamic re-analysis. Sci Sin Ser B, 1988, 31: 1515–1528
Chen Y, Ye K, Liu J B, et al. Quantitative P-T-X constraints on orthopyroxene-bearing high-pressure granulites in felsic-metapelitic rocks: evidence from the Huangtuling granulite, Dabieshan Orogen. J Metamorph Geol, 2008, 26: 1–15
Rice J M. Petrology of clintonite-bearing marbles in the Boulder aureole, Montana. Amer Mineral, 1979, 64: 519–526
Burt D M. Multisystem analysis of the relative stabilities of babingtonite and ilvaite. Carnegie Institution of Washington Year Book, 1971, 70: 189–197
Burt D M. Beryllium mineral stabilities in the model system CaO-BeO-SiO2-P2O5-F2O-1 and the breakdown of beryl. Econ Geol, 1975, 70: 1279–1292
Ferry J M. A map of chemical potential differences within an outcrop. Amer Mineral, 1979, 64: 966–985
White R W, Powell R, Baldwin J A. Calculated phase equilibria involving chemical potentials to investigate the textural evolution of metamorphic rocks. J Metamorph Geol, 2008, 26: 181–198
Sang S H, Peng J. (Solid + liquid) equilibria in the quinary system Na+, Mg2+, K+//SO 2−4 , B4O 7−4 -H2O at 288 K. CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry, 2010. 64–67
Huang X L, Song P S, Chen L J, et al. Liquid-solid equilibria in quinary system Na+, Mg2+/Cl−, SO 2−4 , NO3/−-H2O at 298.15 K. CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry, 2008. 188–194
Song P, Yao Y. Thermodynamics and phase diagram of the salt lake brine system at 298.15 K: V. Model for the system Li+, Na+, K+, Mg2+/Cl−, SO 2−4 -H2O and its applications. CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry, 2003. 343–352
Sang S H, Yin H A, Tang M L, et al. (Liquid + Solid) Phase equilibria in quaternary system Na2CO3+K2B4O7+K2CO3+Na2B4O7+H2O at 288 K. J Chem Eng Data, 2004, 49: 1775–1777
Niu Z, Cheng F, Li B, et al. The Phase Diagrams of Salt-water Systems and Their Applications (in Chinese). Tianjin: Tianjin University Press, 2002
Thompson J B J. The thermodynamic basis for the mineral facies concept. Amer J Sci, 1955, 253: 65–103
Zen E A. Mineralogy and petrology of the system Al2O3-SiO2-H2O in some pyrophyllite deposits of North Carolina. Amer Mineral, 1961, 46: 52–66
Harvie C E, Weare J H. The prediction of mineral solubilities in natural waters: the Na-K-Mg-Ca-Cl-SO4-H2O system from zero to high concentration at 25°C. Geochim Cosmochim Acta, 1980, 44: 981–997
Ellis D E, Wyllie P J. Phase relations and their petrological implications in the system MgO-SiO2-H2O-CO2 at pressures up to100 kbar. Amer Mineral, 1980, 65: 540–556
Ferry J M, Baumgartner L. Thermodynamic models of molecular fluids at the elevated pressures and temperatures of crustal metamorphism. Rev Mineral, 1987, 17: 323–365
Yardley B W D, Barber J P. Melting reactions in the Connemara schists: The role of water infiltration in the formation of amphibolite facies migmatites. Amer Mineral, 1991, 76: 848–856
Baldwin J A, Powell R, Brown M, et al. Modeling of mineral equilibria in ultrahigh-temperature metamorphic rocks from the Anapolis-Itaucu Complex, central Brazil. J Metamorph Geol, 2005, 23: 511–531
Johnson T E, Hudson N F C, Droop G T R. Partial melting in the Inzie Head gneisses: The role of water and a petrogenetic grid in KFMASH applicable to anatectic pelitic migmatites. J Metamorph Geol, 2001, 19: 99–118
Chatterjee N D. Margarite stability and compatibility relations in the system CaO-Al2O3-SiO2-H2O as a pressure-temperature indicator. Amer Mineral, 1976, 61: 699–709
Worley B, Powell R. Singularities in NCKFMASH (Na2O-CaO-K2O-FeO-MgO-Al2O3-SiO2-H2O). J Metamorph Geol, 1998, 16: 169–188
Barton M D. Phase equilibria and thermodynamic properties of minerals in the BeO-Al2O3-SiO2-H2O (BASH) system with petrologic application. Amer Mineral, 1986, 71: 277–300
Hu J W, Mao S D, Du G Q, et al. A new thermodynamic analysis of the intergrowth of hedenbergite and magnetite with Ca-Fe-rich olivine. Amer Mineral, 2011, 96: 599–608
Lindsley D H, Speidel D H, Nafziger R H. P-T-f(O2) relations for the system Fe-O-SiO2. Amer J Sci, 1968, 266: 342–360
Ehlers E G. The Interpretation of Geological Phase Diagrams, San Francisco: W. H. Freeman and Company, 1972
Andrievskaya E R, Lopato L M. Phase equilibria during the solidification of alloys of the ternary system HfO2-Y2O3-La2O3. Powder Metall Metal Ceramics, 2002, 41: 609–619
Andrievskaya E R, Lopato L M. Approximating the liquidus surface of the ZrO2-Y2O3-La2O3 phase equilibrium diagram with reduced polynomials. Powder Metall Metal Ceramics, 2000, 39: 444–450
Linnen R L, Williams-Jones A E. The evolution of pegmatite-hosted Sn-W mineralization at Nong Sua, Thailand: Evidence from fluid inclusions and stable isotopes. Geochim Cosmochim Acta, 1994, 58: 735–747
Grapes R. Anthropogenic Pyrometamorphism Pyrometamorphism. Chapter 6. Berlin: Springer-Verlag Berlin Heidelberg, 2006. 191–218
Grant J A. Quartz-phlogopite-liquid equilibria and origins of charnockites. Amer Mineral, 1986, 71: 1071–1075
Lee W J, Wyllie P J, Rossman G R. CO2-rich glass, round calcite crystals, and no liquid immiscibility in the system CaO-SiO2-CO2 at 2.5 GPa. Amer Mineral, 1994, 79: 1135–1144
Huang W L, Wyllie P J, Nehru C E. Subsolidus and liquidus phase relationships in the system CaO-SiO2-CO2 to 30 kbar with geological applications. Amer Mineral, 1980, 65: 285–301
Hu J W, Yin H A, Tang M L. A simple, universal theory and method for computer-plotting of phase diagrams of a multisystem—SFM method. Sci China Ser B-Chem, 2000, 43: 219–224
Hillert M. Phase Equilibria, Phase Diagrams and Phase Transformations—Their Thermodynamic Basis. Cambridge: Cambridge University Press, 2008
McDade P, Harley S L. A petrological grid for aluminous granulite facies metapelites in the KFMASH system. J Metamorph Geol, 2001, 19: 45–59
Thompson J B J. Composition space: An algebraic and geometric approach. In: Ferry J M, ed. Characterization of Metamorphism through Mineral Equilibria. Rev Mineral, 1982, 10: 1–31
Brown T H, Berman R G. PTA-SYSTEM: A Ge0-Calc software package for the calculation and display of activity-temperature-pressure phase diagrams. Amer Mineral, 1989, 74: 485–487
Krot A N, Petaev M I, Zolensky M E, et al. Secondary calcium-iron-rich minerals in the Bali-like and Allende-like oxidized CV3 chondrites and Allende dark inclusions. Meteor Planet Sci, 1998, 33: 623–645
Bowers T S, Burns R G. Activity diagrams for clinoptilolite: Susceptibility of this zeolite to further diagenetic reactions. Amer Mineral, 1990, 75: 601–619
Bowers T S. Equilibrium Activity Diagrams: For Coexisting Mineral and Aqueous Solutions at Pressures and Temperatures to 5 kb and 600°C, New York: Springer-Verlag, 1984
Burt D M. Vectors, components, and minerals. Amer Mineral, 1991, 76: 1033–1037
Greenwood H J. The N-dimensional tie-line problem. Geochim Cosmochim Acta, 1967, 31: 465–490
Spear F S. Thermodynamic projection and extrapolation of high-variance mineral assemblages. Contrib Miner Petrol, 1988, 98: 346–351
Harvie C E, Eugster H P, Weare J H. Mineral equilibria in the six-component seawater system, Na-K-Mg-Ca-SO4-Cl-H2O at 25°C. II. Comparisons of the saturated solutions. Geochim Cosmochim Acta, 1982, 46: 1603–1618
Thompson J B J. Reaction space: An algebraic and geometric approach. In: Ferry J M, ed. Characterization of Metamorphism Through Mineral Equilibria. Rev Mineral, 1982, 10: 33–52
Schreinemakers F A H. In-, mono-, and divariant equilibria I. In: Proceedings of Koninklijke Akademie van Wetentschappen te Amsterdam. Amsterdam, 1915. 116–126
Zen E A. Construction of pressure-temperature diagrams for multicomponent systems after the method of Schreinemakers: A geometric approach. US Geol Sur Bull, 1966, 1225: 1–56
Yin H A, Hu J W, Tang M L, et al. The Phase Diagrams of Multisystems (in Chinese). Beijing: Peking University Press, 2002
Hu J, Yin H, Duan Z. A new method for the derivation of the closed nets in the phase diagram space of multisystem. I. The absent phase substitution method. J Metamorph Geol, 2004, 22: 413–425
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Hu, J. A general thermodynamic analysis and treatment of phases and components in the analysis of phase assemblages in multicomponent systems. Sci. China Earth Sci. 55, 1371–1382 (2012). https://doi.org/10.1007/s11430-011-4340-9
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DOI: https://doi.org/10.1007/s11430-011-4340-9