Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-16T17:23:50.776Z Has data issue: false hasContentIssue false

Quantum mechanical study of Al/Si disorder in leucite and bicchulite

Published online by Cambridge University Press:  05 July 2018

B. Winkler*
Affiliation:
Institut für Mineralogie, Abteilung für Kristallographie, Universität Frankfurt, Senckenberganlage 30, D-60054 Frankfurt a. M., Germany
V. Milman
Affiliation:
Accelrys, 334 Cambridge Science Park, Cambridge CB4 0WN, UK
C. J. Pickard
Affiliation:
TCM Group, Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE, UK
*

Abstract

We have studied the structures of Al/Si disordered leucite and bicchulite with a quantum mechanical version of the virtual crystal approximation, VCA. In leucite, the average tetrahedron has a composition of (AlSi2)O4, while bicchulite represents an extreme case with (Al2Si)O4 tetrahedra. Both structures are well described with the VCA. In conjunction with an earlier study, where we have shown that the (AlSi)O4 tetrahedra in gehlenite and Al,Si-disordered octahedra are also well reproduced, we have now established that the VCA gives a reliable description of the averaged structure of disordered aluminosilicates over the whole compositional range. The current calculations confirm that Al/Si ordering is not driving the cubic to tetragonal phase transformation in leucite. In bicchulite, the model calculations are consistent with hydrogen on Wyckoff position 8c, in agreement with the result of a single crystal X-ray diffraction study, but in variance with results based on a neutron powder diffraction study.

Type
Research Article
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 2004

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

Bachelet, G.B., Hamann, D.R. and Schlüter, M. (1982) Pseudopotentials that work: from H to Pu. Physical Review, B26, 41994228.CrossRefGoogle Scholar
Bellaiche, L. and Vanderbilt, D. (2000) Virtual crystal approximation revisited: Application to dielectric and piezoelectric properties of perovskites. Physical Review B, 61, 78777882.CrossRefGoogle Scholar
Dann, S.E., Mead, P.J. and Weller, M.T. (1996) Löwenstein's rule extended to an aluminium rich framework. The structure of bicchulite, Ca8(Al2SiO6)4(OH)8, by MASNMR and neutron diffraction. Inorganic Chemistry, 35, 14271428.Google Scholar
de Gironcoli, S., Giannozzi, P. and Baroni, S. (1991) Structure and thermodynamics of Si x Ge1–x alloys from ab initio Monte Carlo simulations. Physical Review Letters, 66, 21162119.CrossRefGoogle Scholar
Depmeier, W. (1984) Tetragonal tetrahedra distortions in cubic sodalite frameworks. Acta Crystallographica, B40, 185191.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 in leucite. American Mineralogist, 78, 486492.Google Scholar
George, A.M., Iniguez, J. and Bellaiche, L. (2001) Anomalous properties in ferroelectrics induced by atomic ordering. Nature, 413, 5457.CrossRefGoogle ScholarPubMed
Goniakowski, J., Holender, J.M., Kantorovich, L.N., Gillan, M.J. and White, J.A. (1996) Influence of gradient corrections on the bulk and surface properties of TiO2 and SnO2 . Physical Review B, 53, 957960.CrossRefGoogle ScholarPubMed
Hamann, D.R. (1996) Generalized gradient theory for silica phase transitions. Physical Review Letters, 76, 660663.CrossRefGoogle ScholarPubMed
Hammer, B., Jacobsen, K.W. and Norskov, J.K. (1993) Role of non local exchange-correlation in activated adsorption. Physical Review Letters, 70, 39713974.CrossRefGoogle Scholar
Hohenberg, P. and Kohn, W. (1964) Inhomogeneous electron gas. Physical Review, 136, B864B871.CrossRefGoogle Scholar
Iniguez, J. and Bellaiche, L. (2001) Ab Initio design of perovskite alloys with predetermined properties: The case of Pb(Sc0.5Nb0.5)O3 . Physical Review Letters, 87, 095503-1-095503-4.CrossRefGoogle Scholar
Jones, R.O. and Gunnarsson, O. (1989) The density functional formalism, its applications and prospects. Reviews of Modern Physics, 61, 689746.CrossRefGoogle Scholar
Kleinman, L. and Bylander, D.M. (1982) Efficacious form for model pseudopotentials. Physical Review Letters, 48, 14251428.CrossRefGoogle Scholar
Kohn, W. and Sham, L.J. (1965) Self-consistent equations including exchange and correlation effects. Physical Review, 140, A1133A1138.CrossRefGoogle Scholar
Kresse, G. and Hafner, J. (1994) Norm-conserving and ultrasoft pseudopotentials for first-row and transition elements. Journal of Physics: Condensed Matter, 6, 82458257.Google Scholar
Kryachko, E.S. and Ludena, E.V. (1990) Energy Density Functional Theory of many-electron Systems. Understanding Chemical Reactivity, vol. 4. Kluwer Academic Publishers, Dordrecht, The Netherlands.Google Scholar
Leung, T.C., Chan, C.T. and Harmon, B.N. (1991) Ground-state properties of Fe, Co, Ni and their monoxides: results of the generalized gradient approximation. Physical Review B, 44, 29232927.CrossRefGoogle ScholarPubMed
Marzari, N., de Gironcoli, S. and Baroni, S. (1994) Structure and phase stability of Ga x In1–x P solid solutions from computational alchemy. Physical Review Letters, 72, 40014004.CrossRefGoogle Scholar
Milman, V., Winkler, B., White, J.A., Pickard, C.J., Payne, M.C., Akhmatskaya, E.V. and Nobes, R.H. (2000) Electronic structure, properties, and phase stabilities of inorganic crystals: a pseudopotential plane-wave study. International Journal of Quantum Chemistry, 77, 895910.3.0.CO;2-C>CrossRefGoogle Scholar
Monkhorst, H.J. and Pack, J.D. (1976) Special points for Brillouin-zone integration. Physical Review B, 13, 51885192.CrossRefGoogle Scholar
Myers, E.R., Heine, V. and Dove, M.T. (1998) Thermodynamics of Al/Al avoidance in the ordering of Al/Si tetrahedral framework structures. Physics and Chemistry of Minerals, 25, 457464.CrossRefGoogle Scholar
Palmer, D.C., Salje, E.K.H. and Schmahl, W.W. (1989) Phase transitions in leucite: X-ray diffraction studies. Physics and Chemistry of Minerals, 16, 714719.CrossRefGoogle Scholar
Parr, R.G. and Yang, W. (1989) Density-functional Theory of Atoms and Molecules. Oxford University Press, Oxford, UK.Google Scholar
Pauling, L. (1930) The structure of sodalite and helvite. Zeitschrift für Kristallographie, 74, 213225.Google Scholar
Perdew, J.P., Burke, K. and Ernzerhof, M. (1996) Generalized Gradient approximation made simple. Physical Review Letters, 77, 38653868.CrossRefGoogle ScholarPubMed
Ramer, N.J. and Rappe, A.M. (2000) Virtual crystal approximation that works: locating a compositional phase boundary in Pb(Zr1-x Ti x )O3 . Physical Review B, 62, R743R746.CrossRefGoogle Scholar
Sahl, K. (1980) Refinement of the crystal structure of bicchulite, Ca2(Al2SiO6)(OH)2 . Zeitschrift für Kristallographie, 152, 1321.CrossRefGoogle Scholar
Segall, M.D., Lindan, P.J.D., Probert, M.J., Pickard, C.J., Hasnip, P.J., Clark, S.J. and Payne, M.C. (2002) First-principles simulation: ideas, illustrations and the CASTEP code. Journal of Physics: Condensed Matter, 14, 27172744.Google Scholar
Soven, P. (1967) Coherent-potential model of substitutional disordered alloys. Physical Review, 156, 809813.CrossRefGoogle Scholar
Taylor, D. and Henderson, C.M.B. (1978) A computer model for the cubic sodalite structure. Physics and Chemistry of Minerals, 2, 325336.CrossRefGoogle Scholar
Thayaparam, S., Dove, M.T. and Heine, V. (1994) A computer simulation study of Al/Si ordering in gehlenite and the paradox of the low transition temperature. Physics and Chemistry of Minerals, 21, 110116.CrossRefGoogle Scholar
Vanderbilt, D. (1990) Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Physical Review, B41, 78927895.CrossRefGoogle Scholar
Winkler, B., Dove, M.T. and Leslie, M. (1991) Static lattice energy minimization and lattice dynamics calculations on aluminosilicate minerals. American Mineralogist, 76, 313331.Google Scholar
Winkler, B., Pickard, C. and Milman, V. (2002) Applicability of a quantum mechanical ‘virtual crystal approximation’ to study Al/Si-disorder. Chemical Physics Letters, 362, 266270.CrossRefGoogle Scholar