Skip to main content

Molecular Dynamics and Diffusion in Silicate Melts

  • Chapter

Part of the book series: Advances in Physical Geochemistry ((PHYSICAL GEOCHE,volume 8))

Abstract

The molecular dynamics (MD) computer simulation technique is a simple, flexible, and powerful method for studying the statistical mechanics of complex many-body systems. Computer “experiments” using MD give a detailed picture of atomic movements with time. Molecular dynamics techniques expand the application of the theory of statistical mechanics beyond the use of analytic solutions for simple systems. The computational power in today’s computers enables scientists utilizing MD techniques to both capitalize on this theory with MD and further catalyze theoretical developments. The data obtained in an MD simulation allow the investigator to probe the subtle relationships between the atomic motion and the observable thermodynamic, structural, and kinetic properties. The ability to predict particle trajectories through time is what sets MD apart from all other approaches to the study of transport phenomena.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Alder, B.J., and Wainwright, T.E. (1957) Phase transition for a hard-sphere system. J. Chem. Phys. 27, 1208–1209.

    Article  Google Scholar 

  • Alder, B.J., Gass, D.M., and Wainwright, T.E. (1970) Studies in molecular dynamics. VIII. The transport coefficients for a hard-sphere fluid. J. Chem. Phys 53, 3813–3826.

    Article  Google Scholar 

  • Andersen, H.C. (1980) Molecular dynamics simulations at constant pressure and/or temperature. J. Chem. Phys. 72, 2384–2393.

    Article  Google Scholar 

  • Angell, C.A., Cheeseman, P.A and Tammaddon, S. (1982) Pressure enhancement of ion mobilities in liquid silicates from computer simulation studies to 800 kbars. Science 218, 885–887.

    Article  Google Scholar 

  • Angell, C.A., Cheeseman, P., and Tammaddon, S. (1983) Water-like transport property anomalies in liquid silicates investigated at high T and P by computer simulation techniques. Bull. Mineral. 106, 87–97.

    Google Scholar 

  • Angell, C.A., Scamehorn, C.A, Phifer, C.C., Kadiyala, R.R., and Cheeseman, P.A. (1988) Ion dynamics studies of liquid and glassy silicates, and gas-in-liquid solutions. Phys. Chem. Miner. 15, 221–227.

    Article  Google Scholar 

  • Ashcroft N.W., and Mermin, N.D. (1976) Solid State Physics. Holt, Rinehart, and Winston, Philadelphia, PA.

    Google Scholar 

  • Barker, J.A., and Henderson, D. (1976) What is “liquid?” Understanding the states of matter. Rev. Mod. Phys. 48, 587–671.

    Article  Google Scholar 

  • Berne, B.J., and Foster, D. (1971) Topics in time-dependent statistical mechanics. Annu. Rev. Phys. Chem. 563–596.

    Google Scholar 

  • Birch, F. (1978) Finite strain isotherm and velocities for single-crystal and polycrystalline NaCl at high pressures and 300 K. J. Geophys. Res. 83, 1257–1268.

    Article  Google Scholar 

  • Brawer, S.A. (1981) Defects and fluorine diffusion in sodium fluoroberyllate glass: a molecular dynamics study. J. Chem. Phys. 25, 3516–3521.

    Article  Google Scholar 

  • Brawer, S.A. (1983) Ab-initio calculation of the vibrational spectra of BeF2 glass simulated by molecular dynamics. J. Chem. Phys. 79, 4539–4545.

    Article  Google Scholar 

  • Broughton, J.Q., and Gilmer, G.H. (1983) Molecular dynamics investigation of the crystal- fluid interface. I. Bulk properties. J. Chem. Phys. 79, 5095–5104.

    Article  Google Scholar 

  • Busing, W.R. (1981) WMIN. A computer program to model molecules and crystals in terms of potential energy functions. Oak Ridge National Laboratory, Oak Ridge.

    Google Scholar 

  • Ciccotti, G., and Hoover, W.G., editors (1986) Molecular Dynamics Simulations of Statistical-Mechanical Systems. North-Holland, Amsterdam.

    Google Scholar 

  • Ciccotti, G., Frenkel, D., and McDonald, I.R., editors (1987) Simulation of Liquids and Solids-Molecular Dynamics and Monte Carlo Methods in Statistical Mechanics. North- Holland, Amsterdam.

    Google Scholar 

  • Cleveland, C.L. (1988) New equations of motion for molecular dynamics systems that change shape. J. Chem. Phys. 89, 4987–4993.

    Article  Google Scholar 

  • Cohen, A. J., and Gordon, R.G. (1976) Modified electron-gas study of the stability, elastic properties and high-pressure behavior of MgO and CaO crystals. Phys. Rev. B 14, 4503–4605.

    Article  Google Scholar 

  • Cohen, R.E., Boyer, L.L., and Mehl, M.J. (1987) Lattice dynamics of the potential-induced breathing model: phonon dispersion in the alkaline-earth oxides. Phys. Rev. B 35, 5749–5760.

    Article  Google Scholar 

  • Cummings, P.T., and Varner, T.L., Jr. (1988) Nonequilibrium molecular dynamics calculation of the shear viscosity of liquid water. J. Chem. Phys., 89, 6391–6398.

    Article  Google Scholar 

  • Da Fano, A., and Jacucci, G. (1977) Vacancy double jumps and atomic diffusion in aluminum and sodium. Phys. Rev. Lett. 39, 950–952.

    Article  Google Scholar 

  • Damrauer, R., Burggraf, L.W., Davis, L.P., and Gordon, M.S. (1988) Gas-phase and computational studies of pentacoordinate silicon. J. Amer. Chem. Soc. 110, 6601–6606.

    Article  Google Scholar 

  • Evans, M.W., Lie, G.C., and Clementi, E. (1988) Molecular dynamics simulation of water from 10 to 1273 K. J. Chem. Phys. 88, 5157–5165.

    Article  Google Scholar 

  • Feuston, B.P., and Garofalini, S.H. (1988) Empirical three-body potential for vitreous silica. J. Chem. Phys. 89, 5818–5824.

    Article  Google Scholar 

  • Frenkel, D. (1986) Free-energy computation and first-order phase transitions, in Molecular-

    Google Scholar 

  • Dynamics Simulation of Statistical-Mechanical Systems, edited by G. Ciccotti and W.G. Hoover, pp. 151–188. Proceedings of the International School of Physics. North- Holland, Amsterdam.

    Google Scholar 

  • Frenkel, D., and Ladd, A.J.C. (1984) New Monte Carlo method to compute the free energy of arbitrary solids. Applicaton to the fee and hep phases of hard spheres. J. Chem. Phys. 81, 3188–3193.

    Article  Google Scholar 

  • Frisch, M. (1983) Gaussian 86 User’s Guide. Carnegie-Mellon University, Pittsburgh, PA.

    Google Scholar 

  • Garofalini, S.H. (1982) Molecular dynamics simulation of the frequency spectrum of amorphous silica. J. Chem. Phys. 76, 3189–3192.

    Article  Google Scholar 

  • Garofalini, S.H. (1983) A molecular dynamics simulation of the vitreous silica surface. J. Chem. Phys. 78, 2069–2072.

    Article  Google Scholar 

  • Gibbs, G.V. (1982) Molecules as models for bonding in silicates. Amer. Mineral. 67, 421–450.

    Google Scholar 

  • Gibbs, G.V., Finger, L.W., and Boisen, M.B. (1987) Molecular mimicry of the bond length-bond strength variations in oxide crystals. Phys. Chem. Miner. 14, 327–331.

    Article  Google Scholar 

  • Gordon, R.G., and Kim, Y.S. (1972) Theory for the forces between closed-shell atoms and molecules. J. Chem. Phys. 56, 3122–3133.

    Article  Google Scholar 

  • Green, H.S. (1961) Theories of transport in fluids. J. Math. Phys. 2, 344.

    Article  Google Scholar 

  • Haile, J.M., and Gupta, S. (1983) Extensions of the molecular dynamics simulation method. II. Isothermal systems. J. Chem. Phys. 79, 3067–3076.

    Article  Google Scholar 

  • Heinzinger, K., and Vogel, P.C. (1976) A molecular dynamics study of aqueous solutions. III. A comparison of selected alkali halides. Z. Naturforsch. 31a, 463–475.

    Google Scholar 

  • Hemley, R.J., Cohen, R.E., Yeganeh-Haeri, A., Mao, H.-K., Weidner, D.J., and Ito, E. (1988) Raman spectroscopy and lattice dynamics of MgSi03-perovskite at high pressure, in Perovskites: A Structure of Great Interest to Geophysics and Materials Science, edited by A. Navrotsky and D.J. Weidner, pp. 35–44. American Geophysical Union, Washington, DC.

    Google Scholar 

  • Heyes, D.M. (1983) Molecular dynamics simulations of ionic crystal films. J. Chem. Phys. 79, 4010–4027.

    Article  Google Scholar 

  • Hill, T.L. (1962) An Introduction to Statistical Thermodynamics. Addison-Wesley, New York.

    Google Scholar 

  • Hofmann, A.W. (1980) Diffusion in natural silicate melts: A critical review, in Physics of Magmatic Processes, edited by R.B. Hargraves, pp. 385–410. Princeton University Press, Princeton, NJ.

    Google Scholar 

  • Hoover, W.G. (1985) Canonical dynamics: Equilibrium phase-space distributions. Phys. Rev. A 31, 1695–1697.

    Article  Google Scholar 

  • Hoover, W.G., Ladd, A.J.C., and Moran, B. (1982) High-strain-rate plastic flow studied via non-equilibrium molecular dynamics. Phys. Rev. Lett. 48, 1818–1820.

    Article  Google Scholar 

  • Iler, R.K. (1979) The Chemistry of Silica. Wiley, New York.

    Google Scholar 

  • Impey, R.W., Madden, P.A., and McDonald, I.R. (1983) Hydration and mobility of ions in solution. J. Phys. Chem. 87, 5071–5083.

    Article  Google Scholar 

  • Inoue, H., and Yasui, I. (1986) A molecular dynamics simulation of the structure of silicate glasses. Phys. Chem. Glasses 28, 63–69.

    Google Scholar 

  • Jackson, M.D. (1986) Theoretical Investigations of Chemical Bonding in Minerals. Ph.D. Thesis, Harvard University.

    Google Scholar 

  • Jacucci, G., and McDonald, I.R. (1975) Structure and diffusion in mixtures of rare-gas liquids. Physica 80A, 607–625.

    Article  Google Scholar 

  • Karim, O.A., and Haymet, A.D.J. (1988) The ice/water interface: A molecular dynamics simulation study. J. Chem. Phys. 89, 6889–6896.

    Article  Google Scholar 

  • Kincaid, J.M., and Erpenbeck, J.J. (1986) The mutual diffusion constant of binary, isotopic hard-sphere mixtures: Molecular dynamics calculations using the Green-Kubo and steady-state methods. J. Chem. Phys. 84, 3418–3431.

    Article  Google Scholar 

  • Kubicki, J.D., and Lasaga, A.C. (1987) Computer animation of reactions in silicate melts and glasses. EOS Trans. Amer. Geophys. Union 68, 1539.

    Google Scholar 

  • Kubicki, J.D., and Lasaga, A.C. (1988) Molecular dynamics simulations of Si02 melt and glass: Ionic and covalent models. Amer. Mineral. 73, 945–955.

    Google Scholar 

  • Kubicki, J.D., Lasaga, A.C., and Hemley, R.J. (1989) Ab-initio molecular dynamics simulations of forsterite and MgSi03-perovskite. EOS Trans. Amer. Geophys. Union 70, 349 (abstract).

    Google Scholar 

  • Kubicki, J.D., and Lasaga, A.C. (1990) Molecular dynamics simulation of pressure and temperature effects on MgSi03 and Mg2Si04 melts and glasses. Phys. Chem. Miner. (in press).

    Google Scholar 

  • Kushiro, I. (1980) Viscosity, density, and structure of silicate melts at high pressures, and their penological applications, in Physics of Magmatic Processes, edited by R.B. Hargraves, pp. 93–120. Princeton University Press, Princeton, NJ.

    Google Scholar 

  • Kushiro, I. (1983) Effect of pressure on the diffusivity of network-forming cations in melts of jadeitic compositions. Geochim. Cosmochim. Acta 47, 1415–1422.

    Article  Google Scholar 

  • Landman, U., Luedtke, W.D., Barnett, R.N., Cleveland, C.L., Ribarsky, M.W., Arnold, E., Ramesh, S., Baumgart, H., Martinez, A., and Khan, B. (1986) Faceting at the silicon (100) crystal-melt interface: Theory and experiment. Phys. Rev. Lett. 56, 155–158.

    Article  Google Scholar 

  • Lasaga, A.C., and Gibbs, G.V. (1987) Applications of quantum mechanical potential surfaces to mineral physics calculations. Phys. Chem. Miner. 14, 107–117.

    Article  Google Scholar 

  • Lasaga, A.C., and Gibbs, G.V. (1988) Quantum mechanical potential surfaces and calculations on minerals and molecular clusters. Phys. Chem. Miner. 16, 29–41.

    Article  Google Scholar 

  • Lasaga, A.C., and Gibbs, G.V. (1990) Ab-initio quantum mechanical calculations of water-rock interactions. Adsorption and hydrolysis reactions. Amer. J. Sci. 290, 263–295.

    Article  Google Scholar 

  • Leinenweber, K., and Navrotsky, A. (1988) A transferable interatomic potential for crystalline phases in the system Mg0-Si02. Phys. Chem. Miner. 15, 588–596.

    Article  Google Scholar 

  • Lutsko, J.F., Wolf, D., and Yip, S. (1988a) Molecular dynamics calculation of free energy. J. Chem. Phys. 88, 6525–6528.

    Article  Google Scholar 

  • Lutsko, J.F., Wolf, D., Yip, S., Phillpot, S.R., and Nguyen, T. (1988b) Molecular-dynamics method for the simulation of bulk-solid interfaces at high temperatures. Phys. Rev. B 38, 11572–11581.

    Article  Google Scholar 

  • Madden, P.A. (1986) Simulation of properties of spectroscopic interest, in Molecular-Dynamics Simulation of Statistical-Mechanical Systems, edited by G. Ciccotti and W.G. Hoover, pp. 371–400. Proceedings of the International School of Physics. North- Holland, Amsterdam.

    Google Scholar 

  • Maple, J.R., Dinur, U., and Hagler, A.T. (1988) Derivation of force fields for molecular mechanics and dynamics from ab-initio energy surfaces. Proc. Nat. Acad. Sci. U.S.A. 85, 5350–5354.

    Article  Google Scholar 

  • March, N.H., and Deb, B.M. (1987) The Single Particle Density in Physics and Chemistry. Academic Press, New York.

    Google Scholar 

  • Matsui, M., (1988) Molecular dynamics study of MgSi03 perovskite. Phys. Chem. Miner. 16, 234–238.

    Article  Google Scholar 

  • Matsui, Y., Kawamura, K., and Syono, Y. (1981) Molecular dynamics calculations applied to silicate systems: Molten and vitreous MgSi03 and Mg2Si04, in High Pressure Research in Geophysics, Advances in Earth and Planetary Science, Vol. 12, S. Akimoto and M.H. Manghnani, pp. 511–524. Reidel, Boston.

    Google Scholar 

  • Mehl, M.J., Hemley, R.J., and Boyer, L.L. (1986) Potential-induced breathing model for the elastic moduli and high-pressure behavior of the cubic alkaline-earth oxides. Phys. Rev. B 33, 8685–8696.

    Article  Google Scholar 

  • Mitra, S.K. (1982) Molecular dynamics simulation on silicon dioxide glass. Phil. Mag. B 45, 529–548.

    Article  Google Scholar 

  • Mitra, S.K., and Hockney, R.W. (1983) Molecular dynamics simulation of the structure of soda silica. Philos. Mag. B 48, 151–167.

    Article  Google Scholar 

  • Mitra, S.K., Amini, M., Fincham, D., and Hockney, R.W. (1981) Molecular dynamics simulation of silicon dioxide glass. Philos. Mag. B 43, 365–372.

    Article  Google Scholar 

  • Mozzi, R.L., and Warren, B.E. (1969) The structure of vitreous silica. J. Appl. Crystall. 2, 164–172.

    Article  Google Scholar 

  • Muhlhausen, C., and Gordon, R.G. (1981) Electron-gas thepry of ionic crystals, including many-body effects. Phys. Rev. B 23, 900–923.

    Article  Google Scholar 

  • Nosé, S. (1984) A unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys. 81, 511–519.

    Article  Google Scholar 

  • Nose, S., and Yonezawa, F. (1986) Isothermal-isobaric computer simulations of melting and crystallization of a Lennard-Jones system. J. Chem. Phys. 84, 1803–1814.

    Article  Google Scholar 

  • Oishi, Y., Nanba, M., and Pask, J.A. (1981) Analysis of liquid-state interdiffusion in the system Ca0-Al203-Si02 using multiatomic models. J. Amer. Ceram. Soc. 65, 247–253.

    Article  Google Scholar 

  • Palinkas, G., Riede, W.O., and Heinzinger, K. (1977) A molecular dynamics study of aqueous solutions. VII. Improved simulation and comparison with X-ray investigations of a NaCl solution. Z. Naturforsch. 32a, 1137–1145.

    Google Scholar 

  • Parinello, M., and Rahman, A. (1981) Polymorphic transitions in single crystals: A new molecular dynamics method. J. Appl. Phys. 52, 7182–7190.

    Article  Google Scholar 

  • Parker, S.C., and Price, G.D. (1990) Computer modelling of the structure and thermodynamic properties of silicate minerals, in Computer Modelling of Fluids, Polymers and Solids, edited by C.R.A. Catlow, S.C. Parker, and M.P. Allen, Series C: Mathematical and Physical Sciences, Vol. 293, pp. 405–429. Kluwer Academic Publishers, Dordrecht, The Netherlands.

    Google Scholar 

  • Parr, R.G., and Yang, W. (1989) Density Functional Theory of Atoms and Molecules. Oxford University Press, Oxford.

    Google Scholar 

  • Rahman, A. (1964) Correlation in the motion of atoms in liquid argon. Phys. Rev. 136, A405–A411.

    Article  Google Scholar 

  • Rahman, A. (1976) Particle motions in superionic conductors. J. Chem. Phys. 65, 4845–4848.

    Article  Google Scholar 

  • Rahman, A., and Stillinger, F.H. (1971) Molecular dynamics study of liquid water. J. Chem. Phys. 55, 3336–3359.

    Article  Google Scholar 

  • Scarfe, C.M., Mysen, B.O., and Virgo, D. (1987) Pressure dependence of the viscosity of silicate melts, in Magmatic Processes: Physiochemical Principles, edited by B.O. Mysen, pp. 59–67. Special Publication No. 1. The Geochemical Society, University Park, PA.

    Google Scholar 

  • Schofleld, P. (1973) Computer simulation studies of the liquid state. Comput. Phys. Commun. 5, 17–23.

    Article  Google Scholar 

  • Soules, T.F. (1979) A molecular dynamics calculation of the structure of sodium silicate glasses. J. Chem. Phys. 71, 4570–4578.

    Article  Google Scholar 

  • Sprik, M., and Klein, M.L. (1988) A polarizable model for water using distributed charge sites. J. Chem. Phys. 89, 7556–7560.

    Article  Google Scholar 

  • Stixrude, L., and Bukowinski, M.S.T. (1988) Simple covalent potential models of tetra- hedral Si02: applications to a-quartz and coesite at pressure. Phys. Chem. Miner. 16, 199–206.

    Article  Google Scholar 

  • Szasz, G.I., and Heinzinger, K. (1983) A molecular dynamics study of the translational and rotational motions in an aqueous Lil solution. J. Chem. Phys. 79, 3467–3473.

    Article  Google Scholar 

  • Tanaka, H., Nakanishi, K., and Watanabe, N. (1983) Constant temperature molecular dynamics calculation on Lennard-Jones fluid and its application to water. J. Chem. Phys. 78, 2626–2634.

    Article  Google Scholar 

  • Tsai, D.H., Bullough, R., and Perrin, R.C. (1970) Molecular dynamical studies of the motion of point defects in a crystalline lattice. J. Phys. C 3, 2022–2036.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Verlet, L. (1967) Computer experiments on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Phys. Rev. 159, 98–103.

    Article  Google Scholar 

  • Wall, A., and Price, G.D. (1988) Defects and diffusion in MgSi03 perovskite: a computer simulation, in Perovskite: A Structure of Great Interest to Geophysics and Materials Science, edited by A. Navrotsky and D.J. Weidner, pp. 45–53. American Geophysical Union, Washington, DC.

    Google Scholar 

  • Watson, R.E. (1958) Analytic Hartree-Fock solutions for 02-. Phys. Rev. 1ll, 1108–1110.

    Google Scholar 

  • Welch D.O., Dienes, G.J. and Paskin, A. (1978) A molecular dynamical study of the equation of state of solids at high temperature and pressure. J. Phys. Chem. Solids 39, 589–603.

    Article  Google Scholar 

  • Wilson, M.A., Pohorille, and Pratt, L.R. (1985) Molecular dynamics test of the Brownian description of Na+ motion in water. J. Chem. Phys. 83, 5832–5836.

    Article  Google Scholar 

  • Woodcock, L.V. (1975) Molecular dynamics calculations on molten ionic salts, in Advances in Molten Salt Chemistry, Vol. 3, edited by J. Braunstein, G. Mamantov, and G.P. Smith, pp. 1–74. Plenum Press, New York and London.

    Chapter  Google Scholar 

  • Woodcock, L.V., Angell, C.A., and Cheeseman, P. (1976) Molecular dynamics studies of the vitreous state: Ionic systems and silica. J. Chem. Phys. 65, 1565–1567.

    Article  Google Scholar 

  • Xue, X., Stebbins, J.F., Kanzaki, M., and Tromes, R.G. (1989) Silicon coordination and speciation changes in a silicate liquid at high pressure, Science, 245, 962–964.

    Article  Google Scholar 

  • Yin, C.D., Okuno, M., Morikawa, H., and Marumo, F. (1983) Structure analysis of MgSi03 glass. J. Non-Cryst. Solids 55, 131–141.

    Article  Google Scholar 

  • Yoder, H.S. (1976) Generation of Basatic Magma, National Academy of Sciences, Washington, DC.

    Google Scholar 

  • Zwanzig, R. (1965) Time-correlation functions and transport coefficients in statistical mechanics. Ann. Rev. Phys. Chem. 16, 67–102.

    Article  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag New York Inc.

About this chapter

Cite this chapter

Kubicki, J.D., Lasaga, A.C. (1991). Molecular Dynamics and Diffusion in Silicate Melts. In: Ganguly, J. (eds) Diffusion, Atomic Ordering, and Mass Transport. Advances in Physical Geochemistry, vol 8. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9019-0_1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-9019-0_1

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-9021-3

  • Online ISBN: 978-1-4613-9019-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics