Skip to main content
SpringerLink
Log in

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

  • Original Paper
  • Published:
Physics and Chemistry of Minerals Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Anderson OL, Schreiber E, Liebermann RC, Soga N (1968) Some elastic constant data on minerals relevant to geophysics. Rev Geophys 6:491–524

    Google Scholar 

  • Angel RJ, Hugh-Jones DA (1994) Equations of state and thermodynamic properties of enstatite pyroxenes. J Geophys Res 99:19777–19783

    Google Scholar 

  • 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 74:509–512

    Google Scholar 

  • Brace WF, Scholz CH, La Mori PN (1969) Isothermal compressibility of kyanite, andalusite, and sillimanite from synthetic aggregates. J Geophys Res 74: 2089–2098

    Google Scholar 

  • Burnham CW (1990) The ionic model: Perceptions and realities in mineralogy. Am Mineral 75:443–463

    Google Scholar 

  • Catlow CRA, Price GD (1990) Computer modelling of solid-state inorganic materials. Nature 347:243–248

    Google Scholar 

  • 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 B49:14179–14187

    Google Scholar 

  • Cohen RE (1992) Origin of ferroelectricity in perovskite oxides. Nature 358:136–138

    Google Scholar 

  • Czaya R (1971) Refinement of the structure of γ-Ca2SiO4. Acta Crystallogr B 27:848–849

    Google Scholar 

  • 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 A341:203–210

    Google Scholar 

  • Finger LW, Hazen RM, Hofmeister AM (1986) High-pressure crystal chemistry of spinel (MgAl2O4) and magnetite (Fe3O4): comparison with silicate spinels. Phys Chem Minerals 13:215–220

    Google Scholar 

  • Fujino K, Sasaki S, Takéuchi Y, Sadanaga R (1981) X-ray determination of electron distributions in forsterite, fayalite and tephroite. Acta Crystallogr B37:513–518

    Google Scholar 

  • Goto T, Anderson OL, Ohno I, Yamamoto S (1989) Elastic constants of corundum up to 1825 K. J Geophys Res 94:7588–7602

    Google Scholar 

  • Hazen RM, Finger LW (1978) Crystal structures and compressibilities of pyrope and grossular to 60 kbar. Am Mineral 63:297–303

    Google Scholar 

  • Hill RJ, Newton MD, Gibbs GV (1983) A crystal chemical study of stishovite. J Solid State Chem 47:185–200

    Google Scholar 

  • Horiuchi H, Sawamoto H (1981) β-Mg2SiO4: single-crystal X-ray diffraction study. Am Mineral 66:568–575

    Google Scholar 

  • Horiuchi H, Hirano M, Ito E, Matsui Y (1982) MgSiO3 (ilmenite-type): single crystal X-ray diffraction study. Am Mineral 67:788–793

    Google Scholar 

  • Horiuchi H, Ito E, Weidner DJ (1987) Perovskite-type MgSiO3: single-crystal X-ray diffraction study. Am Mineral 72:357–360

    Google Scholar 

  • Isaak DG, Anderson OL, Goto T (1989a) Measured elastic moduli of single-crystal MgO up to 1800 K. Phys Chem Minerals 16:704–713

    Google Scholar 

  • Isaak DG, Anderson OL, Goto T, Suzuki I (1989b) Elasticity of single-crystal forsterite measured to 1700 K. J Geophys Res 94:5895–5906

    Google Scholar 

  • Isaak DG, Anderson OL, Oda H (1992) High-temperature thermal expansion and elasticity of calcium-rich garnets. Phys Chem Minerals 19:106–120

    Google Scholar 

  • Ishizawa N, Miyata T, Minato I, Marumo F, Iwai S (1980) A structural investigation of α-Al2O3 at 2170 K. Acta Crystallogr B36:228–230

    Google Scholar 

  • Knittle E, Jeanloz R (1987) Synthesis and equation of state of (Mg, Fe)SiO3 perovskite to over 100 gigapascals. Science 235:668–670

    Google Scholar 

  • Lager GA, Meagher EP (1978) High-temperature structural study of six olivines. Am Mineral 63:365–377

    Google Scholar 

  • Leinenweber K, Navrotsky A (1988) A transferable interatomic potential for crystalline phases in the system MgO-SiO2. Phys Chem Minerals 15:588–596

    Google Scholar 

  • Levien L, Prewitt CT (1981a) High-pressure structural study of diopside. Am Mineral 66:315–323

    Google Scholar 

  • Levien L, Prewitt CT (1981b) High-pressure crystal structure and compressibility of coesite. Am Mineral 66:324–333

    Google Scholar 

  • Levien L, Prewitt CT, Weidner DJ (1980) Structure and elastic properties of quartz at pressure. Am Mineral 65:920–930

    Google Scholar 

  • Liebermann RC, Ringwood AE (1976) Elastic properties of anorthite and the nature of the lunar crust. Earth Planet Sci Lett 31:69–74

    Google Scholar 

  • 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: 17889–17894

    Google Scholar 

  • Matsui M (1988) Molecular dynamics study of MgSiO3 perovskite. Phys Chem Minerals 16:234–238

    Google Scholar 

  • Matsui M (1989) Molecular dynamics study of the structural and thermodynamic properties of MgO crystal with quantum correction. J Chem Phys 91:489–494

    Google Scholar 

  • Matsui M (1994) A transferable interatomic potential model for crystals and melts in the system CaO-MgO-Al2O3-SiO2. Mineral Mag 58A:571–572

    Google Scholar 

  • Matsui M, Price GD (1991) Simulation of the pre-melting behaviour of MgSiO3 perovskite at high pressures and temperatures. Nature 351:735–737

    Google Scholar 

  • Matsui M, Price GD (1992) Computer simulation of the MgSiO3 polymorphs. Phys Chem Minerals 18:365–372

    Google Scholar 

  • Matsui M, Price GD, Patel A (1994) Comparison between the lattice dynamics and molecular dynamics methods: calculation results for MgSiO3 perovskite. Geophys Res Lett 21:1659–1662

    Google Scholar 

  • Oda H, Anderson OL, Isaak DG, Suzuki I (1992) Measurement of elastic properties of single-crystal CaO up to 1200 K. Phys Chem Minerals 19:96–105

    Google Scholar 

  • Ohashi Y (1984) Polysynthetically-twinned structures of enstatite and wollastonite. Phys Chem Minerals 10:217–229

    Google Scholar 

  • Ohashi Y, Finger LW (1976) The effect of Ca substitution on the structure of clinoenstatite. Carnegie Inst Washington, Year Book 75:743–746

    Google Scholar 

  • Parker SC, Titiloye JO, Watson GW (1993) Molecular modelling of carbonate minerals: studies of growth and morphology. Phil Trans R Soc Lond A344:37–48

    Google Scholar 

  • 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 17:690–699

    Google Scholar 

  • Peacor DR (1973) High-temperature single-crystal study of the cristobalite inversion. Z Kristallogr 138:274–298

    Google Scholar 

  • Sasaki S, Prewitt CT, Sato Y, Ito E (1982a) Single-crystal X ray study of γ Mg2SiO4. J Geophys Res 87:7829–7832

    Google Scholar 

  • Sasaki S, Takéuchi Y, Fujino K, Akimoto S (1982b) Electron-density distributions of three orthopyroxenes, Mg2Si2O6, Co2Si2O6, and Fe2Si2O6. Z Kristallogr 158:279–297

    Google Scholar 

  • Sawamoto H, Weidner DJ, Sasaki S, Kumazawa M (1984) Single-crystal elastic properties of the modified spinel (beta) phase of magnesium orthosilicate. Science 224:749–751

    Google Scholar 

  • Sharp ZD, Hazen RM, Finger LW (1987) High-pressure crystal chemistry of monticellite, CaMgSiO4. Am Mineral 72:748–755

    Google Scholar 

  • Stixrude L, Cohen RE (1995) High-pressure elasticity of iron and anisotropy of earth's inner core. Science 267:1972–1975

    Google Scholar 

  • Suzuki I, Anderson OL (1983) Elasticity and thermal expansion of a natural garnet up to 1000 K. J phys Earth 31:125–138

    Google Scholar 

  • 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 191–231

    Google Scholar 

  • Tsuneyuki S, Tsukada M, Aoki H, Matsui Y (1988) First-principles interatomic potential of silica applied to molecular dynamics. Phys Rev Lett 61: 869–872

    Google Scholar 

  • Vaughan MT, Weidner DJ (1978) The relationship of elasticity and crystal structure in andalusite and sillimanite. Phys Chem Minerals 3:133–144

    Google Scholar 

  • Wainwright JE, Starkey J (1971) A refinement of the structure of anorthite. Z Kristallogr 133:75–84

    Google Scholar 

  • Weidner DJ, Ito E (1985) Elasticity of MgSiO3 in the ilmenite phase. Phys Earth Planet Inter 40:65–70

    Google Scholar 

  • Weidner DJ, Wang H, Ito J (1978) Elasticity of orthoenstatite. Phys Earth Planet Inter 17:P7-P13

    Google Scholar 

  • Weidner DJ, Bass JD, Ringwood AE, Sinclair W (1982) The single-crystal elastic moduli of stishovite. J Geophys Res 87:4740–4746

    Google Scholar 

  • Weidner DJ, Sawamoto H, Sasaki S, Kumazawa M (1984) Single-crystal elastic properties of the spinel phase of Mg2SiO4. J Geophys Res 89:7852–7860

    Google Scholar 

  • Wentzcovitch RM, Martins JL, Price GD (1993) Ab initio molecular dynamics with variable cell shape: application to MgSiO3. Phys Rev Lett 70:3947–3950

    Google Scholar 

  • Winkler B, Dove MT (1992) Thermodynamic properties of MgSiO3 perovskite derived from large scale molecular dynamics simulations. Phys Chem Minerals 18:407–415

    Google Scholar 

  • Winkler B, Dove MT, Leslie M (1991) Static lattice energy minimization and lattice dynamics calculations on aluminosilicate minerals. Am Mineral 76:313–331

    Google Scholar 

  • Winter JK, Ghose S (1979) Thermal expansion and high-temperature crystal chemistry of the Al2SiO3 polymorphs. Am Mineral 64:573–586

    Google Scholar 

  • Yagi T, Uchiyama Y, Akaogi M, Ito E (1992) Isothermal compression curve of MgSiO3 tetragonal garnet. Phys Earth Planet Inter 74:1–7

    Google Scholar 

  • Yeganeh-Haeri A, Weidner DJ, Parise JB (1992) Elasticity of α-cristobalite: a silicon dioxide with a negative Poison's ratio. Science 257:650–652

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Earth and Planetary Sciences, Faculty of Science, Kyushu University, Hakozaki, 812-81, Fukuoka, Japan

    Masanori Matsui

Authors
  1. Masanori Matsui
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Matsui, M. Molecular dynamics study of the structures and bulk moduli of crystals in the system CaO-MgO-Al2O3-SiO2 . Phys Chem Minerals 23, 345–353 (1996). https://doi.org/10.1007/BF00199500

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00199500

Keywords

Search

Navigation