Physics and Chemistry of Minerals

, Volume 23, Issue 6, pp 345–353 | Cite as

Molecular dynamics study of the structures and bulk moduli of crystals in the system CaO-MgO-Al2O3-SiO2

  • Masanori Matsui
Original Paper


Molecular dynamics (MD) simulations have been used to calculate the structures and bulk moduli of crystals in the system CaO-MgO-Al2O3-SiO2 (CMAS) using an interatomic potential model (CMAS94), which is composed of pairwise additive Coulomb, van der Waals, and repulsive interactions. The crystals studied, total of 27, include oxides, Mg meta- and ortho-silicates, Al garnets, and various Ca or Al bearing silicates, with the coordination number of cations ranging 6 to 12 for Ca, 4 to 12 for Mg, 4 to 6 for Al, and 4 and 6 for Si. In spite of the simplicity of the CMAS94 potential and the diversity of the structural types treated, MD simulations are quite satisfactory in reproducing well the observed structural data, including the crystal symmetries, lattice parameters, and average and individual nearest neighbour Ca-O, Mg-O, Al-O, and Si-O distances. In addition MD simulated bulk moduli of crystals in the CMAS system compare well with the observed values.


Silicate Molecular Dynamic Molecular Dynamic Simulation Coordination Number Structural Type 
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.


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  1. Anderson OL, Schreiber E, Liebermann RC, Soga N (1968) Some elastic constant data on minerals relevant to geophysics. Rev Geophys 6:491–524Google Scholar
  2. Angel RJ, Hugh-Jones DA (1994) Equations of state and thermodynamic properties of enstatite pyroxenes. J Geophys Res 99:19777–19783Google Scholar
  3. Angel RJ, Finger LW, Hazen RM, Kanzaki M, Weidner DJ, Liebermann RC, Veblen DR (1989) Structure and twinning of single-crystal MgSiO3 garnet synthesized at 17 GPa and 1800 °C. Am Mineral 74:509–512Google Scholar
  4. Brace WF, Scholz CH, La Mori PN (1969) Isothermal compressibility of kyanite, andalusite, and sillimanite from synthetic aggregates. J Geophys Res 74: 2089–2098Google Scholar
  5. Burnham CW (1990) The ionic model: Perceptions and realities in mineralogy. Am Mineral 75:443–463Google Scholar
  6. Catlow CRA, Price GD (1990) Computer modelling of solid-state inorganic materials. Nature 347:243–248Google Scholar
  7. Catti M, Valerio G, Dovesi R, Causà M (1994) Quantum-mechanical calculation of the solid-state equilibrium MgO+α-Al2O3⇄MgAl2O4 (spinel) versus pressure. Phys Rev B49:14179–14187Google Scholar
  8. Cohen RE (1992) Origin of ferroelectricity in perovskite oxides. Nature 358:136–138Google Scholar
  9. Czaya R (1971) Refinement of the structure of γ-Ca2SiO4. Acta Crystallogr B 27:848–849Google Scholar
  10. Dovesi R, Roetti C, Freyria-Fava C, Aprà E, Saunders VR, Harrison NM (1992) Ab initio Hartree Fock treatment of ionic and semi-ionic compounds. State of the art. Phil Trans R Soc Lond A341:203–210Google Scholar
  11. Finger LW, Hazen RM, Hofmeister AM (1986) High-pressure crystal chemistry of spinel (MgAl2O4) and magnetite (Fe3O4): comparison with silicate spinels. Phys Chem Minerals 13:215–220Google Scholar
  12. Fujino K, Sasaki S, Takéuchi Y, Sadanaga R (1981) X-ray determination of electron distributions in forsterite, fayalite and tephroite. Acta Crystallogr B37:513–518Google Scholar
  13. Goto T, Anderson OL, Ohno I, Yamamoto S (1989) Elastic constants of corundum up to 1825 K. J Geophys Res 94:7588–7602Google Scholar
  14. Hazen RM, Finger LW (1978) Crystal structures and compressibilities of pyrope and grossular to 60 kbar. Am Mineral 63:297–303Google Scholar
  15. Hill RJ, Newton MD, Gibbs GV (1983) A crystal chemical study of stishovite. J Solid State Chem 47:185–200Google Scholar
  16. Horiuchi H, Sawamoto H (1981) β-Mg2SiO4: single-crystal X-ray diffraction study. Am Mineral 66:568–575Google Scholar
  17. Horiuchi H, Hirano M, Ito E, Matsui Y (1982) MgSiO3 (ilmenite-type): single crystal X-ray diffraction study. Am Mineral 67:788–793Google Scholar
  18. Horiuchi H, Ito E, Weidner DJ (1987) Perovskite-type MgSiO3: single-crystal X-ray diffraction study. Am Mineral 72:357–360Google Scholar
  19. Isaak DG, Anderson OL, Goto T (1989a) Measured elastic moduli of single-crystal MgO up to 1800 K. Phys Chem Minerals 16:704–713Google Scholar
  20. Isaak DG, Anderson OL, Goto T, Suzuki I (1989b) Elasticity of single-crystal forsterite measured to 1700 K. J Geophys Res 94:5895–5906Google Scholar
  21. Isaak DG, Anderson OL, Oda H (1992) High-temperature thermal expansion and elasticity of calcium-rich garnets. Phys Chem Minerals 19:106–120Google Scholar
  22. Ishizawa N, Miyata T, Minato I, Marumo F, Iwai S (1980) A structural investigation of α-Al2O3 at 2170 K. Acta Crystallogr B36:228–230Google Scholar
  23. Knittle E, Jeanloz R (1987) Synthesis and equation of state of (Mg, Fe)SiO3 perovskite to over 100 gigapascals. Science 235:668–670Google Scholar
  24. Lager GA, Meagher EP (1978) High-temperature structural study of six olivines. Am Mineral 63:365–377Google Scholar
  25. Leinenweber K, Navrotsky A (1988) A transferable interatomic potential for crystalline phases in the system MgO-SiO2. Phys Chem Minerals 15:588–596Google Scholar
  26. Levien L, Prewitt CT (1981a) High-pressure structural study of diopside. Am Mineral 66:315–323Google Scholar
  27. Levien L, Prewitt CT (1981b) High-pressure crystal structure and compressibility of coesite. Am Mineral 66:324–333Google Scholar
  28. Levien L, Prewitt CT, Weidner DJ (1980) Structure and elastic properties of quartz at pressure. Am Mineral 65:920–930Google Scholar
  29. Liebermann RC, Ringwood AE (1976) Elastic properties of anorthite and the nature of the lunar crust. Earth Planet Sci Lett 31:69–74Google Scholar
  30. Mao HK, Chen LC, Hemley RJ, Jephcoat AP, Wu Y (1989) Stability and equation of state of CaSiO3-perovskite to 134 GPa. J Geophys Res 94: 17889–17894Google Scholar
  31. Matsui M (1988) Molecular dynamics study of MgSiO3 perovskite. Phys Chem Minerals 16:234–238Google Scholar
  32. Matsui M (1989) Molecular dynamics study of the structural and thermodynamic properties of MgO crystal with quantum correction. J Chem Phys 91:489–494Google Scholar
  33. Matsui M (1994) A transferable interatomic potential model for crystals and melts in the system CaO-MgO-Al2O3-SiO2. Mineral Mag 58A:571–572Google Scholar
  34. Matsui M, Price GD (1991) Simulation of the pre-melting behaviour of MgSiO3 perovskite at high pressures and temperatures. Nature 351:735–737Google Scholar
  35. Matsui M, Price GD (1992) Computer simulation of the MgSiO3 polymorphs. Phys Chem Minerals 18:365–372Google Scholar
  36. Matsui M, Price GD, Patel A (1994) Comparison between the lattice dynamics and molecular dynamics methods: calculation results for MgSiO3 perovskite. Geophys Res Lett 21:1659–1662Google Scholar
  37. Oda H, Anderson OL, Isaak DG, Suzuki I (1992) Measurement of elastic properties of single-crystal CaO up to 1200 K. Phys Chem Minerals 19:96–105Google Scholar
  38. Ohashi Y (1984) Polysynthetically-twinned structures of enstatite and wollastonite. Phys Chem Minerals 10:217–229Google Scholar
  39. Ohashi Y, Finger LW (1976) The effect of Ca substitution on the structure of clinoenstatite. Carnegie Inst Washington, Year Book 75:743–746Google Scholar
  40. Parker SC, Titiloye JO, Watson GW (1993) Molecular modelling of carbonate minerals: studies of growth and morphology. Phil Trans R Soc Lond A344:37–48Google Scholar
  41. Patel A, Price GD, Mendelssohn MJ (1991) A computer simulation approach to modelling the structure, thermodynamics and oxygen isotope equilibria of silicates. Phys Chem Minerals 17:690–699Google Scholar
  42. Peacor DR (1973) High-temperature single-crystal study of the cristobalite inversion. Z Kristallogr 138:274–298Google Scholar
  43. Sasaki S, Prewitt CT, Sato Y, Ito E (1982a) Single-crystal X ray study of γ Mg2SiO4. J Geophys Res 87:7829–7832Google Scholar
  44. Sasaki S, Takéuchi Y, Fujino K, Akimoto S (1982b) Electron-density distributions of three orthopyroxenes, Mg2Si2O6, Co2Si2O6, and Fe2Si2O6. Z Kristallogr 158:279–297Google Scholar
  45. Sawamoto H, Weidner DJ, Sasaki S, Kumazawa M (1984) Single-crystal elastic properties of the modified spinel (beta) phase of magnesium orthosilicate. Science 224:749–751Google Scholar
  46. Sharp ZD, Hazen RM, Finger LW (1987) High-pressure crystal chemistry of monticellite, CaMgSiO4. Am Mineral 72:748–755Google Scholar
  47. Stixrude L, Cohen RE (1995) High-pressure elasticity of iron and anisotropy of earth's inner core. Science 267:1972–1975Google Scholar
  48. Suzuki I, Anderson OL (1983) Elasticity and thermal expansion of a natural garnet up to 1000 K. J phys Earth 31:125–138Google Scholar
  49. Takéuchi Y, Yamanaka T, Haga N, Hirano M (1984) High-temperature crystallography of olivines and spinels. In: Sunagawa I (ed) Materials Science of the Earth's Interior. TERRAPUB, Tokyo, pp 191–231Google Scholar
  50. Tsuneyuki S, Tsukada M, Aoki H, Matsui Y (1988) First-principles interatomic potential of silica applied to molecular dynamics. Phys Rev Lett 61: 869–872Google Scholar
  51. Vaughan MT, Weidner DJ (1978) The relationship of elasticity and crystal structure in andalusite and sillimanite. Phys Chem Minerals 3:133–144Google Scholar
  52. Wainwright JE, Starkey J (1971) A refinement of the structure of anorthite. Z Kristallogr 133:75–84Google Scholar
  53. Weidner DJ, Ito E (1985) Elasticity of MgSiO3 in the ilmenite phase. Phys Earth Planet Inter 40:65–70Google Scholar
  54. Weidner DJ, Wang H, Ito J (1978) Elasticity of orthoenstatite. Phys Earth Planet Inter 17:P7-P13Google Scholar
  55. Weidner DJ, Bass JD, Ringwood AE, Sinclair W (1982) The single-crystal elastic moduli of stishovite. J Geophys Res 87:4740–4746Google Scholar
  56. Weidner DJ, Sawamoto H, Sasaki S, Kumazawa M (1984) Single-crystal elastic properties of the spinel phase of Mg2SiO4. J Geophys Res 89:7852–7860Google Scholar
  57. Wentzcovitch RM, Martins JL, Price GD (1993) Ab initio molecular dynamics with variable cell shape: application to MgSiO3. Phys Rev Lett 70:3947–3950Google Scholar
  58. Winkler B, Dove MT (1992) Thermodynamic properties of MgSiO3 perovskite derived from large scale molecular dynamics simulations. Phys Chem Minerals 18:407–415Google Scholar
  59. Winkler B, Dove MT, Leslie M (1991) Static lattice energy minimization and lattice dynamics calculations on aluminosilicate minerals. Am Mineral 76:313–331Google Scholar
  60. Winter JK, Ghose S (1979) Thermal expansion and high-temperature crystal chemistry of the Al2SiO3 polymorphs. Am Mineral 64:573–586Google Scholar
  61. Yagi T, Uchiyama Y, Akaogi M, Ito E (1992) Isothermal compression curve of MgSiO3 tetragonal garnet. Phys Earth Planet Inter 74:1–7Google Scholar
  62. Yeganeh-Haeri A, Weidner DJ, Parise JB (1992) Elasticity of α-cristobalite: a silicon dioxide with a negative Poison's ratio. Science 257:650–652Google Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Masanori Matsui
    • 1
  1. 1.Department of Earth and Planetary Sciences, Faculty of ScienceKyushu UniversityFukuokaJapan

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