Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-22T21:09:33.020Z Has data issue: false hasContentIssue false
  • English
  • Français

Ab initio total energy studies of minerals using density functional theory and the local density approximation

Published online by Cambridge University Press:  05 July 2018

Björn Winkler ,
Victor Milman  and
Michael C. Payne
Björn Winkler
Affiliation:
Mineralogisch-Petrographisches Institut der Christian-Albrechts Universität, Olshausenstr. 40, D 24098 Kiel 1, Germany
Victor Milman
Affiliation:
Molecular Simulations, 240/250 The Quomm, Barnwell Road, Cambridge CB5 8RE, UK
Michael C. Payne
Affiliation:
Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

Ab initio total energy calculations based on the local density approximation (LDA) and using a conjugate-gradient solver for the Kohn-Sham equations have been performed for cordierite, brucite, (Mg(OH)2) and diaspore (AlOOH). The calculated fractional coordinates of all structures are in good agreement with experimental diffraction data. The angle of the non-linear hydrogen bond in diaspore is reproduced well. The Raman active OH stretching frequency in brucite has been calculated using the frozen phonon approach and the calculated stretching frequency is in very good agreement with the observed value. The energetically most favourable calculated orientation of the proton-proton vector of an H2O molecule incorporated in the structural channels of cordierite agrees with findings deduced from spectroscopic data, and the calculated energy of hydration is in reasonable agreement with calorimetric data. It is therefore concluded that ab initio total energy calculations can confidently be used to predict properties of hydrogen bonded structures, which is difficult with conventional parameterized static lattice energy minimization calculations. An extension to the model is necessary to improve the agreement of the predicted to the observed lattice parameters for small structures.

Keywords

total energy calculationslocal density approximationbrucitediasporecordieritehydrogen bondCASTEP
Type
Research Article
Information
Mineralogical Magazine , Volume 59 , Issue 397 , December 1995 , pp. 589 - 596
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abbott, R.N. Jr (1991) A short-range O-H potential for amphiboles based on OH stretching frequencies. Canad. Mineral, 29, 131–42.Google Scholar
Abbott, R.N. Jr, Post, J.E. and Burnham, C.W. (1989) Treatment of the hydroxyl in structure-energy calculations. Amer. Mineral, 74, 141–50.Google Scholar
Bachelet, G.B., Hamann, D.R., and Schliiter, M. (1982) Pseudopotentials that work: from H to Pu. Phys. Rev., B26, 4199-228.CrossRefGoogle Scholar
Bass, J.M., Matthai, C.C. and Payne, M.C. (1993) Electronic structure of the Si6/Ge6 (111) superlattice strained to a Ge substrate. Semiconductor Sci. Tech., 8, 2121–4.CrossRefGoogle Scholar
Blaha, P., Schwarz, K. and Herzig, P. (1985) 1st principle calculation of the electric field gradient of Li3N. Phys. Rev. Letters, 32, 575–80.Google Scholar
Busing, W.R. and Levy, H.A. (1958) A single crystal neutron diffraction study of diaspore, AIO(OH). Ada Crystallogr., 11, 798–803.CrossRefGoogle Scholar
Car, R. and Parrinello, M. (1985) Unified approach for molecular dynamics and density functional theory. Phys. Rev. Letters, 55, 2471–4.CrossRefGoogle ScholarPubMed
Carey, J.W. and Navrotsky, A. (1992) The molar enthalpy of dehydration of cordierite. Amer. Mineral, 67, 284–91.Google Scholar
Cohen, R.E. (1992) Origin of ferroelectricity in perovskite oxides. Nature, 358, 136–8.CrossRefGoogle Scholar
Collins, D.R. (1990) Computer simulation and neutron scattering of layer silicate minerals. Ph.D. thesis, University of Keele.Google Scholar
De Vita, A., Manassidis, L, Lin, J.S. and Gillan, M.J. (1992a) The energetics of Frenkel defects in Li2O from first principles. Europhys. Letters, 19, 605–10.CrossRefGoogle Scholar
De Vita, A., Gillan, M.J., Lin, J.S., Payne, M.C, Stich, I. and Clarke, L.J. (19926) Defect energies in oxide materials from first principles. Phys. Rev. Letters, 68, 3319–22.CrossRefGoogle Scholar
Devreese, J.T. and van Camp, P. (eds.) (1985) Electronic Structure, dynamics, and quantum structural properties of condensed matter. NATO ASI, Series B, 121. Plenum Press, New York.CrossRefGoogle Scholar
Dove, M.T., Cool, T., Palmer, D.C., Putnis, A., Salje, E.K.H. and Winkler, B. (1993) On the role of Al-Si ordering in the cubic-tetragonal phase transition of leucite. Amer. Mineral, 78, 486–92.Google Scholar
Farrel, E.F. and Newnham, R.E. (1967) Electronic and vibrational absorption spectra in cordierite. Amer. Mineral, 51, 1068–87.Google Scholar
Francis, G.P. and Payne, M.C. (1990) Finite basis set corrections to total energy pseudopotential calculations. J. Phys.: Condensed Matter, 2, 4395–404.Google Scholar
Gillan, M.J. (1991) Calculating the properties of materials from scratch. In Computer simulation in materials science. (Meyer, M. and Pontikis, V., eds.). NATO ASI, Series E, 205. Kluwer Academic Publishers, Dordrecht.Google Scholar
Gonze, X., Kackell, P. and Scheffler, M. (1990) Ghost states for separable norm-conserving ab initio pseudopotentials. Phys. Rev., B41, 12264–7.CrossRefGoogle Scholar
Gonze, X., Charlier, J.C., Allan, D.C. and Teter, M.P. (1994) Interatomic force constants from first principles — the case of alpha quartz. Phys. Rev., B50, 13035–8.CrossRefGoogle Scholar
Gunderson, K., Hammer, B., Jacobsen, K.B., Norskov, J.K., Lin, J.S. and Milman, V. (1993) Chemisorption and vibration of a hydrogen on Cu(lll). Surface Set, 285, 27–30.CrossRefGoogle Scholar
Hammer, B., Jacobsen, K.W., Milman, V. and Payne, M.C. (1992) Stacking fault energies in Aluminium. J. Phys.: Condensed Matter, 4, 10453–60.Google Scholar
Hammer, B., Jacobsen, K.W. and Norskov, J.K. (1993a) Polarization and charge-transfer during the dissociation of H2 on Al(110). Surface Sci., 297, 68–72.CrossRefGoogle Scholar
Hammer, B., Jacobsen, K.W. and Norskov, J.K. (19936) Role of nonlocal exchange-correlation in activated adsorption. Phys. Rev. Letters, 70, 3971–4.CrossRefGoogle Scholar
Hill, R.J. (1979) Crystal structure refinement and electron density distribution in diaspore. Phys. Chem. Minerals, 5, 1979–200.CrossRefGoogle Scholar
Kerker, G.P. (1980) Non-singular atomic pseudopotentials for solid state applications. J. Phys.: Condensed Matter, 13, L189–L194.Google Scholar
Kleinman, L. and Bylander, D.M. (1982) Efficacious form for model pseudopotentials. Phys. Rev. Letters, 48, 1425–8.CrossRefGoogle Scholar
Kunc, K. (1985) Recent results in semiconductor dynamics by ab initio ‘direct’ approach. In Electronic Structure, dynamics, and quantum structural properties of condensed matter. (Devreese, J.T. and van Camp, P., eds.). NATO ASI, Series B, 121. Plenum Press, New York.Google Scholar
Langer, K. and Schreyer, W. (1976) Apparent effects of molecular water on the lattice geometry of cordierite: A discussion. Amer. Mineral, 61, 1036–40.Google Scholar
Lee, C, Vanderbilt, D., Laasonen, K., Car, R. and Parrinello, M. (1992) Ab initio studies on high pressure phases of ice. Phys. Rev. Letters, 69, 462–5.CrossRefGoogle ScholarPubMed
Lin, J.S., Qteish, A., Payne, M.C. and Heine, V. (1992) Optimized and transferable non-local pseudo-potentials. Phys. Rev. B (in press).Google Scholar
Line, C.M.B., Winkler, B. and Dove, M.T. (1994) Quasielastic incoherent neutron scattering study of the rotational dynamics of the water molecules in analcime. Phys. Chem. Minerals, 21, 451–9.CrossRefGoogle Scholar
Meyer, M. and Pontikis, V. (eds.) (1991) Computer simulation in materials science. NATO ASI, Series E, 205. Kluwer Academic Publishers, Dordrecht.CrossRefGoogle Scholar
Milman, V., Jesson, D.E., Pennycook, S.J., Payne, M.C, Lee, M.H. and Stich, I. (1994) Large scale ab initio study of the binding and diffusion of a Ge adatom on the Si(100) surface. Phys. Rev. B: Condensed Matter, B50, 2663–6.CrossRefGoogle Scholar
Milman, V., Payne, M.C, Heine, V., Needs, R.J., Lin, J.S. and Lee, M.H. (1993) Free-energy and entropy of diffusion by ab initio molecular dynamics — alkali ions in silicon. Phys. Rev. Letters, 70, 2928–31.CrossRefGoogle ScholarPubMed
Monkhorst, H.J. and Pack, J.D. (1976) Special points for Brillouin-zone integration. Phys. Rev., B13, 5188–92.CrossRefGoogle Scholar
Payne, M.C, Teter, M.P., Allan, D.C., Arias, T.A. and Johannopoulos, J.D. (1992) Iterative minimization techniques for ab initio total energy calculations — molecular dynamics and conjugate gradients. Rev. Modern Phys., 64, 1045–97.CrossRefGoogle Scholar
Perdew, J. and Zunger, A. (1981) Self-interaction correction to density-functional approximations for many electron systems. Phys. Rev., B23, 5048–79.CrossRefGoogle Scholar
Price, G.D. and Parker, S.C. (1988) The computer simulation of the lattice dynamics of silicates. In Physical Properties and thermodynamic behaviour of minerals. (Salje, E.K.H., ed.). NATO ASI Series C, Vol 225.Google Scholar
Ryskin, Y.I. (1974) The vibrations of protons in minerals: hydroxyl, water and ammonium. In: Farmer, V.C. (ed.) The infrared spectra of minerals. Mineralogical Society Monograph 4.Google Scholar
Schwarz, K., Ambroschdraxl, C. and Blaha, P. (1990) Charge distribution and electric field gradients in YBa2Cu3O7 . Phys. Rev., B42, 2051–61.CrossRefGoogle Scholar
Singh, D.J., Schwarz, K. and Blaha, P. (1992) Electric field gradients in YBa2Cu3O7 — discrepancy between experimental and local density approximation charge distributions. Phys. Rev., B46, 5849–52.CrossRefGoogle Scholar
Stout, J.H. (1975) Apparent effects of molecular water on the lattice geometry of cordierite. Amer. Mineral., 60, 229–34.Google Scholar
Stout, J.H. (1976) Apparent effects of molecular water on the lattice geometry of cordierite: A reply. Amer. Mineral, 61, 1041–4.Google Scholar
Teter, M.P., Payne, M.C. and Allan, D.C. (1989) Solution of Schrodinger equations for large systems. Phys. Rev., B40, 12255–63.CrossRefGoogle Scholar
Wei, S. and Chou, M.Y. (1992) Ab initio calculation of force constants and full phonon dispersions. Phys. Rev. Letters, 69, 2799–802.CrossRefGoogle ScholarPubMed
Winkler, B. and Biihrer, W. (1990) Lattice dynamics of andalusite: prediction and experiment. Phys. Chem. Minerals, 17, 453-61.CrossRefGoogle Scholar
Winkler, B. and Dove, M.T. (1992) Thermodynamic properties of MgSiO3 Perovskite derived from large scale Molecular dynamics simulations. Phys. Chem. Minerals, 18, 407–15.CrossRefGoogle Scholar
Winkler, B. and Hennion, B. (1994) Low temperature dynamics of molecular H2O in bassanite, gypsum and cordierite investigated by high resolution incoherent inelastic neutron scattering. Phys. Chem. Minerals, 21, 539–45.CrossRefGoogle Scholar
Winkler, B., Dove, M.T. and Leslie, M. (1991) Static lattice energy minimization and lattice dynamics calculations on aluminosilicate minerals. Amer. Mineral, 76, 313–31.Google Scholar
Winkler, B., Milman, V. and Payne, M.C. (1994a) Orientation, location and total energy of hydration of channel H2O in cordierite investigated by ab initio total energy calculations. Amer. Mineral, 79, 200–5.Google Scholar
Winkler, B., Coddens, G. and Hennion, B. (19946) Movement of channel H2O in cordierite observed with quasieleastic neutron scattering. Amer. Mineral, 79, 801–8.Google Scholar
Zigan, F. and Rothbauer, R. (1967) Neutronenbeugungs-messungen am Brucit. Neues Jahrb. Mineral M., 137-43.Google Scholar