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Computational methods for the study of energies of cation distributions: applications to cation-ordering phase transitions and solid solutions

Published online by Cambridge University Press:  05 July 2018

A. Bosenick ,
M. T. Dove ,
E. R. Myers ,
E. J. Palin ,
C. I. Sainz-Diaz ,
B. S. Guiton ,
M. C. Warren ,
M. S. Craig  and
S. A. T. Redfern
A. Bosenick
Affiliation:
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, UK Present address: Martenshofweg 9, 24109 Kiel, Germany
M. T. Dove*
Affiliation:
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, UK
E. R. Myers
Affiliation:
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, UK Present address: Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, UK
E. J. Palin
Affiliation:
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, UK
C. I. Sainz-Diaz
Affiliation:
Estacion Experimental del Zaidin, CSIC, C/Profesor Albareda, 1, 18008-Granada, Spain
B. S. Guiton
Affiliation:
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, UK
M. C. Warren
Affiliation:
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, UK Present address: Department of Earth Sciences, The University of Manchester, Manchester M13 9PL, UK
M. S. Craig
Affiliation:
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, UK
S. A. T. Redfern
Affiliation:
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, UK
*
*E-mail: [email protected]
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Abstract

The structural and thermodynamic properties of minerals are strongly affected by cation site-ordering processes. We describe methods to determine the main interatomic interactions that drive the ordering process, which are based on parameterizing model Hamiltonians using empirical interatomic potentials and/or ab initio quantum mechanics methods. The methods are illustrated by a number of case study examples, including Al/Si ordering in aluminosilicates, Mg/Ca ordering in garnets, simultaneous Al/Si and Mg/Al ordering in pyroxenes, micas and amphiboles, and Mg/Al non-convergent ordering in spinel using only quantum mechanical methods.

Keywords

Monte Carlo simulationcation orderinginteratomic potentialsphase transitionsaluminosilicates
Type
Research Article
Information
Mineralogical Magazine , Volume 65 , Issue 2 , April 2001 , pp. 193 - 219
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 2001

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Footnotes

†

Corresponding author

References

Artacho, E., Sánchez-Portal, D., Ordejón, P., García, A. and Soler, J.M. (1999) Linear-scaling ab-initio calculations for large and complex systems. Physica Status Solidi (b), 215, 809–17.3.0.CO;2-0>CrossRefGoogle Scholar
Allan, N.L., Barrera, G.D., Fracchia, R.M., Pongsai, B.K. and Purton, J.A. (2000) Configurational lattice dynamics and hybrid Monte Carlo approaches to thermodynamic properties of solid solutions. J. Molecular Structure – Thermochem., 506, 45-53.CrossRefGoogle Scholar
Bertram, U.C., Heine, V., Jones, I.L. and Price, G.D. (1990) Computer modeling of Al/Si ordering in sillimanite. Phys. Chem. Miner., 17, 326–33.CrossRefGoogle Scholar
Balabin, A.I. and Sack, R.O. (2000) Thermodynamics of (Zn,Fe)S sphalerite: A CVM approach with large basis clusters. Mineral. Mag., 64, 923–44.CrossRefGoogle Scholar
Bosenick, A., Dove, M.T., Warren, M.C. and Fisher, A. (1999) Local cation distribution of Diopside–Ca-Tschermak solid solutions: A computational and 29Si MAS NMR spectroscopic study. Eur. J. Mineral., 9, 39.Google Scholar
Bosenick, A., Dove, M.T. and Geiger, C.A. (2000) Simulation studies of pyrope–grossular solid solutions. Phys. Chem. Miner., 27, 398-418.CrossRefGoogle Scholar
Bosenick, A., Dove, M.T., Heine, V. and Geiger, C.A. (2001) Scaling of thermodynamic mixing properties in garnet solid solutions. Phys. Chem. Miner. (in press).CrossRefGoogle Scholar
Carpenter, M.A., Powell, R., Salje, E.K.H. (1994) thermodynamics of nonconvergent cation ordering in minerals. 1. An alternative approach. Amer. Mineral., 79, 1053–67.Google Scholar
Carpenter, M.A. and Salje, E.K.H. (1994) Thermodynamics of nonconvergent cation ordering in minerals. 2. Spinels and the ortho-pyroxene solidsolution. Amer. Mineral., 79, 1068–83.Google Scholar
Clarke, L.J., Stich, I. and Payne, M.C. (1992) Largescale ab initio total energy calculations on parallel computers. Computer Phys. Comm., 72, 14-28.CrossRefGoogle Scholar
Craig, M.S., Warren, M.C., Dove, M.T., Gale, J.D., Sanchez-Portal, D., Ordejon, P., Soler, J.M. and Artacho, E. (2001) Simulations of minerals using linear-scaling density functional theory based on atomic orbitals. Phys. Chem. Miner. (submitted).Google Scholar
Dove, M.T. (1999) Order/disorder phenomena in minerals: ordering phase transitions and solid solutions. Pp. 451–75 in: Microscopic Processes in Minerals (Catlow, C.R.A. and Wright, K., editors). Kluwer, The Netherlands.CrossRefGoogle Scholar
Dove, M.T. and Redfern, S.A.T. (1997) Lattice simulation studies of the ferroelastic phase transitions in (Na,K)AlSi3O8 and (Sr,Ca)Al2Si2O8 feldspar solid solutions. Amer. Mineral., 82, 8-15.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. Amer. Mineral., 78, 486–92.Google Scholar
Dove, M.T., Thayaparam, S., Heine, V. and Hammonds, K.D. (1996) The phenomenon of low Al/Si ordering temperatures in aluminosilicate framework structures. Amer. Mineral., 81, 349–62.CrossRefGoogle Scholar
Dove, M.T., Bosenick, A., Myers, E.R., Warren, M.C. and Redfern, S.A.T. (2000) Modelling in relation to cation ordering. Phase Trans., 71, 205–26.CrossRefGoogle Scholar
Gale, J.D. (1997) GULP: A computer program for the symmetry-adapted simulation of solids. J. Chem. Soc.: Faraday Trans., 93, 629–37.Google Scholar
Gasparik, T. (1984) Experimentally determined stability of clinopyroxene + garnet + corundum in the system CaO-MgO-Al2O3-SiO2 . Amer. Mineral., 69, 1025–35.Google Scholar
Hawthorne, F.C. (1997) Short range order in amphiboles: A bond valence approach. Canad. Mineral., 35, 210–16.Google Scholar
Lee, M.H., Cheng, C.F., Heine, V. and Klinowski, J. (1997) Distribution of tetrahedral and octahedral Al sites in gamma alumina. Chem. Phys. Lett., 265, 673–6.CrossRefGoogle Scholar
McConnell, J.D.C., DeVita, A., Kenny, S.D. and Heine, V. (1997) Determination of the origin and magnitude of Al/Si ordering enthalpy in framework aluminosilicates from ab initio calculations. Phys. Chem. Miner., 25, 15-23.CrossRefGoogle Scholar
Myers, E.R. (1999) Al/Si ordering in silicate minerals. PhD thesis, Univ. Cambridge, UK.Google 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. Phys. Chem. Miner., 25, 457–64.CrossRefGoogle Scholar
Oberti, R., Ungaretti, L., Cannillo, E., Hawthorne, F.C. and Memmi, I. (1995) Temperature-dependent Al order–disorder in the tetrahedral double chain o. C2/m amphiboles. Eur. J. Mineral., 7, 1049–63.CrossRefGoogle Scholar
Okamura, F.P., Ghose, S. and Ohashi, H. (1974) Structure and crystal chemistry of Calcium Tschermak's pyroxe ne, CaAlAlSiO6 . Amer. Mineral., 59, 549–57.Google Scholar
Ordejón, P., Artacho, E. and Soler, J.M. (1996) Selfconsistent order-N density-functional calculations for very large systems. Phys. Rev. B, 15, 10441–4.CrossRefGoogle Scholar
Palin, E.J., Dove, M.T., Redfern, S.A.T., Bosenick, A., Sainz-Diaz, C.I. and Warren, M.C. (2001) Computational study of tetrahedral Al-Si ordering in muscovite. Phys. Chem. Miner. (in press).CrossRefGoogle Scholar
Patel, A., Price, G.D. and Mendelssohn, M.J. (1991) A computer-simulation approach to modeling the structure, thermodynamics and oxygen isotope equilibria of silicates. Phys. Chem. Miner., 17, 690–9.CrossRefGoogle Scholar
Payne, M.C., Teter, M.P., Allan, D.C., Arias, T.A. and Joannopoulos, J.D. (1992) Iterative minimization techniques for abinitio total-energy calculations - molecular-dynamics and conjugate gradients. Rev. Modern Phys., 64, 1045–97.CrossRefGoogle Scholar
Post, J.E. and Burnham, C.W. (1986) Ionic modeling of mineral structures and energies in the electron gas approximation: TiO2 polymorphs, quartz, forsterite, diopside. Amer. Mineral., 71, 142–50.Google Scholar
Putnis, A. (1992) Introduction to Mineral Sciences. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Redfern, S.A.T., Harrison, R.J., O'Neill, H.St.C. and Wood, D.R.R. (1999) Thermodynamics and kinetics of ordering in MgAl2O4 spinel from 1600°C from in situ neutron diffraction Amer. Mineral., 84, 299-310.CrossRefGoogle Scholar
Sainz-Diaz, C.I., Hernandez-Laguna, A. and Dove, M.T. (2001) Modelling of dioctahedral 2:1 phyllosilicates by means of transferable empirical potentials. Phys. Chem. Miner. (in press).CrossRefGoogle Scholar
Sanders, M.J., Leslie, M. and Catlow, C.R.A. (1984) Interatomic potentials for SiO2. J. Chem. Soc.: Chem. Comm., 1271–3.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. Phys. Chem. Miner., 21, 110–6.CrossRefGoogle Scholar
Thayaparam, S., Heine, V., Dove, M.T. and Hammonds, K.D. (1996) A computational study of Al/Si ordering in cordierite. Phys. Chem. Miner., 23, 127–39.CrossRefGoogle Scholar
Vinograd, V.L. and Putnis, A. (1999) The description of Al, Si ordering in aluminosilicates using the cluster variation method. Amer. Mineral., 84, 311–24.CrossRefGoogle Scholar
Vinograd, V.L., Putnis, A. and Kroll, H. (2001) Structural discontinuities in plagioclase and constraints on mixing properties of the low series: A computational study. Mineral. Mag., 65, 1–32.CrossRefGoogle Scholar
Warren, M.C., Dove, M.T. and Redfern, S.A.T. (2000 a) Ab initio simulations of cation ordering in oxides: application to spinel. J. Phys.: Cond. Matter, 12, L43–8.Google Scholar
Warren, M.C., Dove, M.T. and Redfern, S.A.T. (2000 b) Disordering of MgAl2O4 spinel from first principles. Mineral. Mag., 64, 311–7.CrossRefGoogle Scholar
Warren, M.C., Dove, M.T., Myers, E.R., Bosenick, A., Palin, E.J., Sainz-Diaz, C.I., Guiton, B. and Redfern, S.A.T. (2001) Monte Carlo methods for the study of cation ordering in minerals. Mineral. Mag., 65, 221–47.CrossRefGoogle Scholar
Winkler, B., Dove, M.T. and Leslie, M. (1991) Static lattice energy minimization and lattice dynamics calculations on minerals using three-body potentials. Amer. Mineral., 76, 313–31.Google Scholar
Wood, B.J., Kirkpatrick, R.J. and Montez, B. (1986) Order-disorder phenomena in MgAl2O4 spine. Amer. Mineral., 71, 999-1006.Google Scholar