Thermodynamic Procedures for Treating the Monoclinic/Triclinic Inversion as a High-Order Phase Transition in Equations of State for Binary Analbite-Sanidine Feldspars

  • G. A. Merkel
  • J. G. Blencoe
Part of the Advances in Physical Geochemistry book series (PHYSICAL GEOCHE, volume 2)


Many solid-state phase transitions (transformations) can be classified thermo-dynamically according to their order (Ehrenfest, 1933): an wth-order phase transition is characterized by discontinuities in the nth and all higher-order derivatives of G with respect to an intensive variable—e.g., pressure, temperature, or composition—while lower-order derivatives are continuous.1 Therefore, a first-order phase transition produces discontinuities in V, H, and μ i , because these properties are related to the first derivatives ∂G/∂P, ∂G/∂T, and ∂G/∂X i , respectively, and properties related to higher-order derivatives of G—e.g., C p=-T(∂2 G/∂T 2), α= (1/V)(2 G/∂PT), and β=-(1/V) (∂2 G/∂P 2)—also exhibit discontinuities. On the other hand, for a second-order phase transition, V, H, and μ i , are all continuous at the point of phase change, so Δ V and ΔH of transition are zero, but, C p α, and β are discontinuous. Finally, at a third-order phase transition all properties related to the first and second derivatives of G are continuous, and only third- and higher-order derivatives of G are discontinuous. In this chapter, transitions that fit into this classification scheme and whose order is greater than one will be referred to as high-order transitions.


Phase Relation Alkali Feldspar Tricritical Point Thermal Maximum Metastable Extension 
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. Allen, S. M., and Cahn, J. W. (1975) Coherent and incoherent equilibria in iron-rich iron-aluminum alloys, Ada Metall. 23, 1017–1026.CrossRefGoogle Scholar
  2. Allen, S. M., and Cahn, J. W. (1976a) On tricritical points resulting from the intersection of lines of higher-order transitions with spinodals, Scr. Metall. 10, 451–454.CrossRefGoogle Scholar
  3. Allen, S. M., and Cahn, J. W. (1976b) Mechanisms of phase transformations within the miscibility gap of Fe-rich Fe-Al alloys, Acta Metall. 24, 425–437.CrossRefGoogle Scholar
  4. Blencoe, J. G. (1977) Computation of thermodynamic mixing parameters for isostructural, binary crystalline solutions using solvus experimental data, Comput. Geosci. 3, 1–18.CrossRefGoogle Scholar
  5. Blencoe, J. G. (1979a) The use of thermodynamic excess functions in the Nernst distribution law: discussion. Amer. Mineral. 64, 1122–1128.Google Scholar
  6. Blencoe, J. G. (1979b) An ion-exchange method for evaluating Δμ°1 and Δμ2 for nonisostructural binary crystalline solutions, Amer. Geophys. Union Trans. 60, 404–405.Google Scholar
  7. Carpenter, M. A. (1980) Mechanisms of exsolution in sodic pyroxenes, Contrib. Mineral. Petrol 71, 289–300.CrossRefGoogle Scholar
  8. Carpenter, M. A. (1981) A “conditional spinodal” within the peristerite miscibility gap of plagioclase feldspars, Amer. Mineral. 66, 553–560.Google Scholar
  9. Donnay, G., and Donnay, J. D. H. (1952) The symmetry change in the high-temperature alkali-feldspar series, Amer. J. Sci. 250A, 115–132.Google Scholar
  10. Ehrenfest, P. (1933) Phasenumwandlunsen im ueblichen und erweiterten sinn, klassifiziert nach den entsprechenden singularitaeten des thermodynamischen potentiales, Proc. Acad. Sci. Amsterdam 36, 153.Google Scholar
  11. Epstein, P. S. (1937) Textbook of Thermodynamics. Wiley, New York.Google Scholar
  12. Goldsmith, J. R. (1972) Cadmium dolomite and the system CdCO3-MgCO3, J. Geology 80, 611–626.CrossRefGoogle Scholar
  13. Goldsmith, J. R., and Heard, H. C. (1961) Subsolidus relations in the system CaCO3-MgCO3. J. Geology 69, 45–74.CrossRefGoogle Scholar
  14. Goldsmith, J. R., and Newton, R. C. (1974) An experimental determination of the alkali feldspar solvus, in The Feldspars, edited by W. S. MacKenzie and J. Zussman, Proc. NATO Adv. Study Inst., pp. 337–359. Manchester University Press, Manchester, England.Google Scholar
  15. Gordon, P. (1968) Principles of Phase Diagrams in Material Systems. McGraw-Hill, New York.Google Scholar
  16. Hazen, R. M. (1976) Sanidine: predicted and observed monoclinic-to-triclinic reversible transformations at high pressure, Science 194, 105–107.CrossRefGoogle Scholar
  17. Hazen, R. M., and Finger, L. W. (1979) Polyhedral tilting: A common type of pure displacive phase transition and its relationship to analcite at high pressure, Phase Transitions 1, 1–22.CrossRefGoogle Scholar
  18. Henderson, M. B. (1979) An elevated temperature X-ray study of synthetic disordered Na-K alkali feldspars, Contrib. Mineral. Petrol. 70, 71–79.CrossRefGoogle Scholar
  19. Henderson, C. M. and Roux, J. (1979) Inversions in subpotassic nephelines, Contrib. Mineral. Petrol. 61, 279–298.CrossRefGoogle Scholar
  20. Henderson, C. M. and Thompson, A. B. (1980) The low-temperature inversion in subpotassic nephelines, Amer. Mineral. 65, 970–980.Google Scholar
  21. Hovis, G. L. (1980) Angular relations of alkali feldspar series and the triclinic-monoclinic displacive transformation, Amer. Mineral. 65, 770–778.Google Scholar
  22. Hovis, G. L., and Waldbaum, D. L. (1977) A solution calorimetric investigation of K-Na mixing in a sanidine-analbite ion-exchange series, Amer. Mineral 62, 680–686.Google Scholar
  23. Kroll, H. (1971) Feldspäte im System KAlSi3O8-NaAlSi3O8-CaAl2Si2O8: Al, Si-Verteilung und Gitterparameter, Phasen-Transformationen und Chemismus. Dissertation, Westf Wilhems-Universität, Munster, Germany.Google Scholar
  24. Kroll, H., Bambauer, H. U., and Schirmer, U. (1980) The high albite-monalbite and analbite-monalbite transitions, Amer. Mineral. 65, 1192–1211.Google Scholar
  25. Lagache, M., and Weisbrod, A. (1977) The system: two alkali feldspars-KCl-NaCl-H2O at moderate to high temperatures and low pressures, Contrib. Mineral. Petrol. 62, 77–101.CrossRefGoogle Scholar
  26. Laves, F. (1952) Phase relations of the alkali feldspars. II. The stable and pseudo-stable phase relations in the alkali feldspar system, J. Geology 60, 549–574.CrossRefGoogle Scholar
  27. Lindsley, D. H., Davidson, P. M., and Grover, J. E. (1980) Ca-Mg pyroxenes: a solution model that permits coexisting Enss + Pig + Diss, Geol. Soc. Amer., Abstr. Progs. 12, 472.Google Scholar
  28. Lindsley, D. H., Grover, J. E., and Davidson, P. M. (1981) The thermodynamics of the Mg2Si2O6-CaMgSi2O6 join: a review and a new model, in Advances in Physical Geochemistry, edited by R. C. Newton, A. Navrotsky, and B. J. Wood, Vol. 1, Springer-Verlag, New York.Google Scholar
  29. Luth, W. C, and Fenn, P. M. (1973) Calculation of binary solvi with special reference to the sanidine-high albite solvus, Amer. Mineral. 58, 1009–1015.Google Scholar
  30. Luth, W. C, Martin, R. F., and Fenn, P. M. (1974) Peralkaline alkali feldspar solvi, in The Feldspars, edited by W. S. MacKenzie and J. Zussman, Proc NATO Adv. Study Inst., pp. 297–312. Manchester University Press, Manchester, England.Google Scholar
  31. Luth, W. C, and Querol-Suné, F. (1970) An alkali feldspar series, Contrib. Mineral. Petrol 25, 25–40.CrossRefGoogle Scholar
  32. Luth, W. C, and Tuttle, O. F. (1966) The alkali feldspar solvus in the system Na2O-K2O-Al2O3-SiO2-H2O, Amer. Mineral. 51, 1359–1373.Google Scholar
  33. MacKenzie, W. S. (1952) The effect of temperature on the symmetry of high-temperature soda-rich feldspars, Amer. J. Sci. 252A, 319–342.Google Scholar
  34. Merkel, G. A., and Blencoe, J. G. (1978) Calculated activity coefficients and thermodynamic excess properties for high albite-sanidine feldspars at 2 kbar pressure, 600–700°C, Amer. Geophys. Union Trans. 59, 395.Google Scholar
  35. Merkel, G. A., and Blencoe, J. G. (in preparation) Thermodynamic mixing properties of binary analbite-sanidine feldspars.Google Scholar
  36. Müller, G. (1971) Der einfluss der Al, Si-Verteilung auf die mischungslücke der alkali-feldspäte, Contrib. Mineral. Petrol 34, 73–79.CrossRefGoogle Scholar
  37. Nukui, A., Nakazawa, H., and Akao, M. (1978) Thermal changes in monoclinic tridymite, Amer. Mineral. 63, 1252–1259.Google Scholar
  38. Okamura, F. P., and Ghose, S. (1975) Analbite-monalbite transition in a heat treated twinned Amelia albite, Contrib. Mineral Petrol 50, 211–216.CrossRefGoogle Scholar
  39. Orville, P. M. (1963) Alkali ion exchange between vapor and feldspar phases, Amer. J. Sci. 261, 201–237.CrossRefGoogle Scholar
  40. Orville, P. M. (1967) Unit-cell parameters of the microcline-low albite and the sanidine-high albite solid solution series. Amer. Mineral 52, 55–86.Google Scholar
  41. Parsons, I. (1978) Alkali feldspars: which solvus? Phys. Chem. Minerals 2, 199–213.CrossRefGoogle Scholar
  42. Perchuk, L. L., and Ryabchikov, I. D. (1968) Mineral equilibria in the system nepheline-alkali feldspar-plagioclase and their petrological significance, J. Petrology 9, 123–167.Google Scholar
  43. Pippard, A. B. (1966) Elements of Classical Thermodynamics. Cambridge University Press, Cambridge.Google Scholar
  44. Rao, N. R., and Rao, K. J. (1978) Phase Transitions in Solids. McGraw-Hill, New York.Google Scholar
  45. Seck, H. A. (1972) The influence of pressure on the alkali feldspar solvus from peraluminous and persilicic materials, Fortschr. Mineral. 49, 31–49.Google Scholar
  46. Smith, P., and Parsons, I. (1974) The alkali-feldspar solvus at 1 kilobar water-vapour pressure, Mineral. Mag. 39, 747–767.CrossRefGoogle Scholar
  47. Thompson, A. B. and Perkins, E. H. (1981) Lambda transitions in minerals, in Advances in Physical Geochemistry, edited by R. C. Newton, A. Navrotsky, and B. J. Wood, Vol. 1. Springer-Verlag, New York.Google Scholar
  48. Thompson, and Wennemer, M. (1979) Heat capacities and inversions in tridymite, cristobalite, and tridymite-cristobalite mixed phases, Amer. Mineral. 64, 1018–1026.Google Scholar
  49. Thompson, J. Jr., and Hovis, G. L. (1979a) Entropy of mixing in sanidine, Amer. Mineral. 64, 57–65.Google Scholar
  50. Thompson, J. Jr., and Hovis, G. L. (1979b) Structural-thermodynamic relations of the alkali feldspars, Trans. Amer. Crystallogr. Assoc. 15, 1–26.Google Scholar
  51. Thompson, J. Jr., and Waldbaum, D. R. (1968) Mixing properties of sanidine crystalline solutions: I. Calculations based on ion-exchange data, Amer. Mineral. 53, 1965–1999.Google Scholar
  52. Thompson, J. Jr., and Waldbaum, D. R. (1969) Mixing properties of sanidine crystalline solutions: III. Calculations based on two-phase data, Amer. Mineral. 54, 811–838.Google Scholar
  53. Traetteberg, A., and Flood, H. (1972) Alkali ion exchange equilibria between feldspar phases and molten mixtures of potassium and sodium chloride, Trans. Roy. Inst. Technol. Stockholm 296, 608–618.Google Scholar
  54. Willaime, C, Brown, W. L., and Perucaud, M. C. (1974) On the orientation of the thermal and compositional stain ellipsoids in feldspars, Amer. Mineral. 59, 457–464.Google Scholar
  55. Winter, J. K., Okamura, F. P., and Ghose, S. (1979) A high-temperature structural study of high albite, monalbite, and the analbite → monalbite phase transition, Amer. Mineral. 64, 409–423.Google Scholar
  56. Wood, B. J. (1977) Experimental determination of the mixing properties of solid solutions with particular reference to garnet and clinopyroxene solutions, in Thermodynamics in Geology, edited by D. G. Fraser, pp. 11–27. Reidel, Dordrecht, The Netherlands.Google Scholar
  57. Wright, T. L., and Stewart, D. B. (1968) X-ray and optical study of alkali feldspar. I. Determination of composition and structural state from refined unit-cell parameters and 2V, Amer. Mineral. 53, 38–87.Google Scholar
  58. Zyrianov, V. N., Perchuk, L. L., and Podlesski, K. K. (1978) Nepheline-alkali feldspar equilibria: I. Experimental data and thermodynamic calculations, J. Petrology 19, 1–44.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1982

Authors and Affiliations

  • G. A. Merkel
  • J. G. Blencoe

There are no affiliations available

Personalised recommendations