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
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
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.
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.
Andersen, H.C. (1980) Molecular dynamics simulations at constant pressure and/or temperature. J. Chem. Phys. 72, 2384–2393.
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.
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.
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.
Ashcroft N.W., and Mermin, N.D. (1976) Solid State Physics. Holt, Rinehart, and Winston, Philadelphia, PA.
Barker, J.A., and Henderson, D. (1976) What is “liquid?” Understanding the states of matter. Rev. Mod. Phys. 48, 587–671.
Berne, B.J., and Foster, D. (1971) Topics in time-dependent statistical mechanics. Annu. Rev. Phys. Chem. 563–596.
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.
Brawer, S.A. (1981) Defects and fluorine diffusion in sodium fluoroberyllate glass: a molecular dynamics study. J. Chem. Phys. 25, 3516–3521.
Brawer, S.A. (1983) Ab-initio calculation of the vibrational spectra of BeF2 glass simulated by molecular dynamics. J. Chem. Phys. 79, 4539–4545.
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.
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.
Ciccotti, G., and Hoover, W.G., editors (1986) Molecular Dynamics Simulations of Statistical-Mechanical Systems. North-Holland, Amsterdam.
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.
Cleveland, C.L. (1988) New equations of motion for molecular dynamics systems that change shape. J. Chem. Phys. 89, 4987–4993.
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.
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.
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.
Da Fano, A., and Jacucci, G. (1977) Vacancy double jumps and atomic diffusion in aluminum and sodium. Phys. Rev. Lett. 39, 950–952.
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.
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.
Feuston, B.P., and Garofalini, S.H. (1988) Empirical three-body potential for vitreous silica. J. Chem. Phys. 89, 5818–5824.
Frenkel, D. (1986) Free-energy computation and first-order phase transitions, in Molecular-
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.
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.
Frisch, M. (1983) Gaussian 86 User’s Guide. Carnegie-Mellon University, Pittsburgh, PA.
Garofalini, S.H. (1982) Molecular dynamics simulation of the frequency spectrum of amorphous silica. J. Chem. Phys. 76, 3189–3192.
Garofalini, S.H. (1983) A molecular dynamics simulation of the vitreous silica surface. J. Chem. Phys. 78, 2069–2072.
Gibbs, G.V. (1982) Molecules as models for bonding in silicates. Amer. Mineral. 67, 421–450.
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.
Gordon, R.G., and Kim, Y.S. (1972) Theory for the forces between closed-shell atoms and molecules. J. Chem. Phys. 56, 3122–3133.
Green, H.S. (1961) Theories of transport in fluids. J. Math. Phys. 2, 344.
Haile, J.M., and Gupta, S. (1983) Extensions of the molecular dynamics simulation method. II. Isothermal systems. J. Chem. Phys. 79, 3067–3076.
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.
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.
Heyes, D.M. (1983) Molecular dynamics simulations of ionic crystal films. J. Chem. Phys. 79, 4010–4027.
Hill, T.L. (1962) An Introduction to Statistical Thermodynamics. Addison-Wesley, New York.
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.
Hoover, W.G. (1985) Canonical dynamics: Equilibrium phase-space distributions. Phys. Rev. A 31, 1695–1697.
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.
Iler, R.K. (1979) The Chemistry of Silica. Wiley, New York.
Impey, R.W., Madden, P.A., and McDonald, I.R. (1983) Hydration and mobility of ions in solution. J. Phys. Chem. 87, 5071–5083.
Inoue, H., and Yasui, I. (1986) A molecular dynamics simulation of the structure of silicate glasses. Phys. Chem. Glasses 28, 63–69.
Jackson, M.D. (1986) Theoretical Investigations of Chemical Bonding in Minerals. Ph.D. Thesis, Harvard University.
Jacucci, G., and McDonald, I.R. (1975) Structure and diffusion in mixtures of rare-gas liquids. Physica 80A, 607–625.
Karim, O.A., and Haymet, A.D.J. (1988) The ice/water interface: A molecular dynamics simulation study. J. Chem. Phys. 89, 6889–6896.
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.
Kubicki, J.D., and Lasaga, A.C. (1987) Computer animation of reactions in silicate melts and glasses. EOS Trans. Amer. Geophys. Union 68, 1539.
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.
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).
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).
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.
Kushiro, I. (1983) Effect of pressure on the diffusivity of network-forming cations in melts of jadeitic compositions. Geochim. Cosmochim. Acta 47, 1415–1422.
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.
Lasaga, A.C., and Gibbs, G.V. (1987) Applications of quantum mechanical potential surfaces to mineral physics calculations. Phys. Chem. Miner. 14, 107–117.
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.
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.
Leinenweber, K., and Navrotsky, A. (1988) A transferable interatomic potential for crystalline phases in the system Mg0-Si02. Phys. Chem. Miner. 15, 588–596.
Lutsko, J.F., Wolf, D., and Yip, S. (1988a) Molecular dynamics calculation of free energy. J. Chem. Phys. 88, 6525–6528.
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.
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.
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.
March, N.H., and Deb, B.M. (1987) The Single Particle Density in Physics and Chemistry. Academic Press, New York.
Matsui, M., (1988) Molecular dynamics study of MgSi03 perovskite. Phys. Chem. Miner. 16, 234–238.
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.
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.
Mitra, S.K. (1982) Molecular dynamics simulation on silicon dioxide glass. Phil. Mag. B 45, 529–548.
Mitra, S.K., and Hockney, R.W. (1983) Molecular dynamics simulation of the structure of soda silica. Philos. Mag. B 48, 151–167.
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.
Mozzi, R.L., and Warren, B.E. (1969) The structure of vitreous silica. J. Appl. Crystall. 2, 164–172.
Muhlhausen, C., and Gordon, R.G. (1981) Electron-gas thepry of ionic crystals, including many-body effects. Phys. Rev. B 23, 900–923.
Nosé, S. (1984) A unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys. 81, 511–519.
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.
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.
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.
Parinello, M., and Rahman, A. (1981) Polymorphic transitions in single crystals: A new molecular dynamics method. J. Appl. Phys. 52, 7182–7190.
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.
Parr, R.G., and Yang, W. (1989) Density Functional Theory of Atoms and Molecules. Oxford University Press, Oxford.
Rahman, A. (1964) Correlation in the motion of atoms in liquid argon. Phys. Rev. 136, A405–A411.
Rahman, A. (1976) Particle motions in superionic conductors. J. Chem. Phys. 65, 4845–4848.
Rahman, A., and Stillinger, F.H. (1971) Molecular dynamics study of liquid water. J. Chem. Phys. 55, 3336–3359.
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.
Schofleld, P. (1973) Computer simulation studies of the liquid state. Comput. Phys. Commun. 5, 17–23.
Soules, T.F. (1979) A molecular dynamics calculation of the structure of sodium silicate glasses. J. Chem. Phys. 71, 4570–4578.
Sprik, M., and Klein, M.L. (1988) A polarizable model for water using distributed charge sites. J. Chem. Phys. 89, 7556–7560.
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.
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.
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.
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.
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.
Verlet, L. (1967) Computer experiments on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Phys. Rev. 159, 98–103.
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.
Watson, R.E. (1958) Analytic Hartree-Fock solutions for 02-. Phys. Rev. 1ll, 1108–1110.
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.
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.
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.
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.
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.
Yin, C.D., Okuno, M., Morikawa, H., and Marumo, F. (1983) Structure analysis of MgSi03 glass. J. Non-Cryst. Solids 55, 131–141.
Yoder, H.S. (1976) Generation of Basatic Magma, National Academy of Sciences, Washington, DC.
Zwanzig, R. (1965) Time-correlation functions and transport coefficients in statistical mechanics. Ann. Rev. Phys. Chem. 16, 67–102.
Editor information
Editors and Affiliations
Rights 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