A Structure Energy Model for C2/c Pyroxenes in the System Na-Mg-Ca-Mn-Fe-Al-Cr-Ti-Si-O

  • G. Ottonello
  • A. Della Giusta
  • A. Dal Negro
  • F. Baccarin
Part of the Advances in Physical Geochemistry book series (PHYSICAL GEOCHE, volume 10)


Pyroxenes, like feldspars, occupy a position that is “chemically central to the composition realm of rocks” (Robinson, 1980) and occur ubiquitously in most part of igneous and metamorphic terrains. Understanding their crystal-chemical and thermodynamic properties is thus of primary importance in the earth sciences. Due to their importance in earth sciences, pyroxenes have been the object of various petrologic and thermodynamic investigations. Most published experimental data concern the pyroxene quadrilateral and have been restricted to the binary joins. The work of modeling multicomponent pyroxene mixtures using the binary solution data has begun only recently, and we wish to contribute to its development by presenting a series of structure-energy calculation procedures for the various phases of interest. This first work concerns the structural class C2/c that is the most representative of pyroxenes in nature and for which most crystal-chemical and thermodynamic data are available.


Gibbs Free Energy Energy Model Lattice Energy Hardness Factor Interionic Distance 
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  1. Akimoto, S. (1972). The system MgO-FeO-SiO2 at high pressures and temperatures. Phase equilibria and elastic properties. Tectonophys 13, 161–187.CrossRefGoogle Scholar
  2. Baerlocher, C., Hepp, A., and Meier, W.M. (1977). DLS-76. A program for the Simulation of Crystal Structures by Geometric Refinement. Institute of Crystallography and Petrography, ETH Zurich, Switzerland.Google Scholar
  3. Berman, R.G. (1988). Internally-consistent thermodynamic data for minerals in the system Na2O-K2O-CaO-MgO-FeO-Fe2O3-A12O3-SiO2-TiO2-H2O-CO2. J. Petrol., 29, 445–522.Google Scholar
  4. Birch, F. (1966). Compressibility; elastic constants, Geology Society American Mem., Vol. 97, pp. 97–174.Google Scholar
  5. Bokreta, M. and Ottonello, G. (1987). Enthalpy of formation of end-member garnets. EOS 68, 448.Google Scholar
  6. Bruno, E., Carbonin, S., and Molin, G.M. (1982). Crystal structures of Ca-rich clino-pyroxenes on the CaMgSi2O6-Mg2Si2O6 join. Tsch. Min. Petr. Mitt. 29, 223–240.CrossRefGoogle Scholar
  7. Burnham, C.W., Clark, J.R., Papike, J.J., and Prewitt, C.T. (1967). A proposed crystallo-graphic nomenclature for clinopyroxene structures. Zeit. Krist. 125, 1–6.CrossRefGoogle Scholar
  8. Cameron, M. and Papike, J.J. (1980). Crystal chemistry of silicate pyroxenes. Rev. Mineral. 7, 5–87.Google Scholar
  9. Carbonin, S., Dal Negro, A., Ganeo, S., and Piccirillo, E.M. (1991). Influence of magma composition and oxygen fugacity on the crystal structure of C2/c clinopyroxenes from a basalt-pantellerite suite. Contrib. Mineral. Petrol. 108, 34–42.CrossRefGoogle Scholar
  10. Catti, M. (1981a). The lattice energy of forsterite. Charge distribution and formation enthalpy of the SiO4- 4ion. Phys. Chem. Mineral 7, 20–25.CrossRefGoogle Scholar
  11. Catti, M. (1981b). A generalized Born-Mayer parametrization of the lattice energy in orthorombic ionic crystals. Acta Cryst. A37, 72–76.Google Scholar
  12. Chatterjee, N. (1989). An internally consistent thermodynamic data base on minerals: Applications to the earth’s crust and upper mantle. Ph.D. Thesis, City University, New York.Google Scholar
  13. Clark, S.P., Jr., Schairer, J.F., and De Neufville, J. (1962). Phase relations in the system CaMgSi2O6-CaAl2SiO6-SiO2 at low and high pressure. Carnegie Inst. Wash. Yearbook 61, 59–68.Google Scholar
  14. Clark, J.R., Appleman, D.E., and Papike, J.J. (1969). Crystal-chemical characterization of clinopyroxenes based on eight new structure refinements. Miner. Soc. Amer. Spec. Papers 3, 31–50.Google Scholar
  15. Cohen, R.E. (1986). Thermodynamic solution properties of aluminous clinopyroxenes: nonlinear least squares refinements. Geochim. Cosmochim. Acta. 50, 563–575.CrossRefGoogle Scholar
  16. Dal Negro, A., Carbonin, S., Molin, G.M., Cundari, A., and Piccirillo, E.M. (1982). Intracrystalline cation distribution in natural clinopyroxenes of tholeiitic, transitional and alkaline basaltic rocks. Adv. Physical Geochem. 2, 117–150.Google Scholar
  17. Davidson, P.M. and Lindsley, D.H. (1989). Thermodynamic analysis of pyroxene-olivine-quartz equilibria in the system CaO-MgO-FeO-SiO2. Amer. Mineral 74, 18–30.Google Scholar
  18. Delia Giusta, A., Ottonello, G., and Secco, L. (1990). Precision estimates of interatomic distances using site occupancies, ionization potentials and polarizability in Pbnm silicate olivines. Acta Cryst. B46, 160–165.Google Scholar
  19. Doroshev, A.M., Malinovskaya, Ye. K., Surkov, N.V., and Bulakov, V.K. (1987). Synthesis and unit cell parameters of CaMgSi2O6-CaAl2SiO6 clinopyroxenes. Geochem. Internat. 16, 83–92.Google Scholar
  20. Dunitz, J.D. and Orgel, L.E. (1957). Electronic properties of transition metal oxides. II. Cation distribution among octahedral and tetrahedral sites. J. Phys. Chem. Solids 3, 318–323.CrossRefGoogle Scholar
  21. Ganguly, J. (1973). Activity-composition relation of jadeite in omphacite pyroxene: Theoretical deductions. Earth Planet. Sci. Lett. 19, 145–153.CrossRefGoogle Scholar
  22. Ganguly, J. and Saxena, S.K. (1987). Mixtures and Mineral Reactions. Springer-Verlag, Berlin-Heidelberg-New York.Google Scholar
  23. Gasparik, T. (1985). Experimentally determined composition of diopside-jadeite pyroxenes in equilibrium with albite and quartz at 1200–1350°C and 15–34 Kbar. Geochim. Cosmochim. Acta 49, 865–870.CrossRefGoogle Scholar
  24. Gasparik, T. and Lindsley, D.H. (1980). Phase equilibria at high pressure of pyroxenes containing monovalent and trivalent ions, in Reviews in Mineralogy, C.T. Prewitt, ed., Vol. 7, Mineralogy Society of America Washington, D.C.Google Scholar
  25. Gilbert, T.L. (1968). Soft sphere model for closed-shell atoms and ions. J. Chem. Phys. 49, 2640–2642.CrossRefGoogle Scholar
  26. Haselton, H.T., Jr., Hemingway, B.S., and Robie, R.A. (1984). Low-temperatute heat capacities of CaAl2SiO6 glass and pyroxene and thermal expansion of CaAl2SiO6. Amer. Mineral. 69, 481–489.Google Scholar
  27. Heitler, W. and London, F. (1927). Wechselwirkung neutraler Atome und homöopolare Bindung nach der Quantenmechanik. B. Physik. 44, 455–472.CrossRefGoogle Scholar
  28. Helgeson, H.C., Delany, J.M., Nesbitt, H.W., and Bird, D.K. (1978). Summary and critique of thermodynamic properties of rock-forming minerals. Amer. J. Sci. 278A, 1–229.Google Scholar
  29. Hemingway, B.S., Krupka, K.M., and Robie, R.A. (1981). Heat capacities of the alkali feldspars between 350 and 1000 K from differential scanning calorimetry, the thermodynamic functions of alkali feldspars from 298.15 to 1400 K, and the reaction quartz + jadeite = albite. Amer. Mineral. 66, 1202–1215.Google Scholar
  30. Holland, T.J.B. (1983). The experimental determination of activities in disordered and short-range ordered jadeitic pyroxenes. Contrib. Mineral. Petrol. 82, 214–220.CrossRefGoogle Scholar
  31. Holland, T.J.B., Navrotsky, A., and Newton, R.C. (1979). Thermodynamic parameters of CaMgSi2O6-Mg2Si2O6 pyroxenes based on regular solution and cooperative disordering models. Contrib. Mineral. Petrol 69, 337–344.CrossRefGoogle Scholar
  32. IUPAC (1979). Manual of symbols and therminology for physicochemical quantities and units. Pure & Appl. Chem. 51, 1–41.CrossRefGoogle Scholar
  33. James, F. and Roos, M. (1977). MINUIT. A system for function minimization and analysis of the parameter errors and correlations. CERN Computer Ctr., Geneva, Switzerland.Google Scholar
  34. Lindsley, D.H. (1981). The formation of pigeonite on the join hedembergite-ferrosilite at 11.5 and 15 Kbar: Experiments and a solution model. Am. Mineral 66, 1175–1182.Google Scholar
  35. Lindsley, D.H., Munoz, J.L., and Finger, L.W. (1969). Unit-cell parameters of clinopyroxenes along the join hedenbergite-ferrosilite. Carnegie Inst. Wash. Yearbook 67, 91–92.Google Scholar
  36. 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, R.C. Newton, A., Navrotsky, B.J. and Wood, eds., Springer-Verlag, Berlin-Heidelberg-New York, Vol. 1, pp. 149–175.Google Scholar
  37. Meier, W.M. and Villiger, H. (1969). Die Methode der Abstandsverfeinerung zur Bestim-mung der Atomkoordinaten idealisierter Gerustsruckturen Zeits. Kristallogr. 129, 411–423.CrossRefGoogle Scholar
  38. Miyamoto, M., Takeda, H., Fujino, K., and Takeuchi, Y. (1982). The ionic compressibilities and radii estimates for some transition metals in olivine structures. Aim. J. 11, 172–179.Google Scholar
  39. Naumov, G.B., Ryzhenko, B., and Khodakovsky, I.L. (1971). Handbook of Thermodynamic Data. Atomizdat, Moscow.Google Scholar
  40. Newton, R.C., Charlu, T.V., and Kleppa, O.J. (1977). Thermochemistry of high pressure garnets and clinopyroxenes in the system CaO-MgO-Al2O3-SiO2. Geochim. Cosmo-chim. Acta 41, 369–377.CrossRefGoogle Scholar
  41. Newton, R.C., Charlu, T.V., Anderson, P.A.M., and Kleppa, O.J. (1979). Thermochemistry of synthetic clinopyroxenes on the join CaMgSi2O6-Mg2Si2O6. Geochim. Cosmochim. Acta 42, 55–60.CrossRefGoogle Scholar
  42. Newton, W. and McCready, N. (1948). Thermodynamic properties of sodium silicates. C. Phys. Coll. Chem. 52, 1277–1283.CrossRefGoogle Scholar
  43. Nickel, K.G. and Brey, G. (1984). Subsolidus orthopyroxene-clinopyroxene systematics in the system CaO-MgO-SiO2 to 60 Kbar: A re-evaluation of the regular solution model. Contrib. Mineral. Petrol 87, 35–42.CrossRefGoogle Scholar
  44. Ottonello, G. (1987). Energies and interactions in binary (Pbnm) orthosilicates: A Born parametrization. Geochim. Cosmochim. Acta 51, 3119–3135.CrossRefGoogle Scholar
  45. Ottonello, G., Delia Giusta, A., and Molin, G.M. (1989). Cation ordering in Ni-Mg olivines. Amer. Mineral. 74, 411–421.Google Scholar
  46. Ottonello, G., Princivalle, F., and Delia Giusta, A. (1990). Temperature, composition and f o2 effects on intersite distribution of Mg and Fe2+ in olivines. Phys. Chem. Miner. 17, 301–312.CrossRefGoogle Scholar
  47. Pauling, L. (1960). The Nature of the Chemical Bond, 3rd ed. Cornell University Press, Ithaca, New York.Google Scholar
  48. Popp, R.K. and Gilbert, M.C. (1972). Stability of acmite-jadeite pyroxenes at low pressures. Amer. Mineral. 57, 1210–1231.Google Scholar
  49. Robie, R.A., Hemingway, B.S., and Fisher, J.R. (1978). Thermodynamic properties of minerals and related substances at 298.15 K and 1 bar (105 Pascals) pressure and at higher temperatures. U.S. Geol. Surv. Bull. 1452, pp. 1–452.Google Scholar
  50. Robinson, P. (1980). The composition space of terrestrial pyroxenes-internal and expernal limits. Rev. Mineral. 7, 419–494.Google Scholar
  51. Sack, R.O. (1980). Some constraints on the thermodynamic mixing properties of Fe-Mg orthopyroxenes and olivines. Contrib. Mineral. Petrol. 71, 257–269.CrossRefGoogle Scholar
  52. Saxena, S.K. (1981). Fictive component model of pyroxenes and multicomponent phase equilibria. Contrib. Mineral Petrol 78, 245–251.Google Scholar
  53. Saxena, S.K. (1983). Exsolution and Fe2+-Mg order-disorder in pyroxenes, in Advances in Physical Geochemistry, S.K. Saxena, ed., Springer-Verlag, Berlin-Heidelberg-New York, Vol. 2, pp. 61–80.Google Scholar
  54. Saxena, S.K. (1990). Programs INSP and THERMO and corresponding data-base (unpublished).Google Scholar
  55. Saxena, S.K. and Chatterjee, N. (1986). Thermochemical data on mineral phases. I. The system CaO-MgO-Al2O3-SiO2. J. Petrol 27, 827–842.Google Scholar
  56. Saxena, S.K. and Eriksson, G.E. (1983). High temperature phase equilibria in a solar-composition gas. Geochim. Cosmochim. Acta 47, 1865–1874.CrossRefGoogle Scholar
  57. Saxena, S.K., Sykes, J., and Eriksson G. (1986). Phase equilibria in the pyroxene quadrilateral. J. Petrol, 27, 843–852.Google Scholar
  58. Shannon, R.D. (1976). Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Cryst. A32, 751–767.Google Scholar
  59. Skinner, B.J. (1966). Thermal expansion, in Handbook of Physical Constants, S.P. Clark, Jr., ed., Geology Society of Amer. Mem. Vol. 97, pp. 75–95.Google Scholar
  60. Smith, J.V. (1959). The crystal structure of proto-enstatite. Acta Cryst. 12, 515–519.CrossRefGoogle Scholar
  61. Steele, I.M. (1975). Mineralogy of lunar norite 78235; second lunar occurrence of P21Ca pyroxene from Apollo 17 soils. Amer. Mineral 60, 1086–1091.Google Scholar
  62. Stull, D.R. and Prophet, H. (1971). JANAF Thermochemical Tables. Data Series, Washington, D.C., Vol. 37, pp. 1–1141.Google Scholar
  63. Syono, Y., Akimoto, S., and Matsui, Y. (1971). High pressure transformations in zinc silicates. Solid State Chem. 3, 369–380.CrossRefGoogle Scholar
  64. Tosi, M. (1964). Cohesion of ionic solids in the Born model. Solid State Phys. 16, 1–120.CrossRefGoogle Scholar
  65. Tosi, M. and Fumi, F.G. (1964). Ionic sizes and Born repulsive parameters in the NaCl-type alkali halides-II. Phys. Chem. Solids. 25, 45–52.CrossRefGoogle Scholar
  66. Turnock, A.C., Lindsley, D.H., and Grover, J.E. (1973). Synthesis and unit cell parameters of Ca-Mg-Fe pyroxenes. Amer. Mineral 58, 50–59.Google Scholar
  67. Vieillard, P. (1982). Modele de calcul des energies de formation des mineraux, bati sur la connaissance affinee des structures cristallines. C.N.R.S. Mem. 69, 1–206.Google Scholar
  68. Wagman, D.D., Evans, W.H., Parker, V.B., Halow, I., Bailey, S.M., and Schumm, R.H. (1981). Selected values of chemical thermodynamic properties. Nbs Tech. Note, 270–8, pp. 1–134.Google Scholar
  69. Wood, B.J., Holland, T.J.B., Newton, R.C. and Kleppa, O.J. (1980). Thermochemistry of jadeite-diopside pyroxenes. Geochim. Cosmochim. Acta 44, 1363–1371.CrossRefGoogle Scholar
  70. Zener, C. (1931). Interchange of translational, rotational and vibrational energy in molecular collisions. Phys. Rev. 37, 556–569.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1992

Authors and Affiliations

  • G. Ottonello
    • 1
  • A. Della Giusta
    • 2
  • A. Dal Negro
    • 2
  • F. Baccarin
    • 3
  1. 1.Dipartimento di Scienze della TerraUniversita di CagliariCagliariItaly
  2. 2.Dipartimento di Mineralogia e PetrologiaUniversita di PadovaPadovaItaly
  3. 3.E.N.E.L., Unita Nazionale GeotermicaPisaItaly

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