Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-24T08:13:54.133Z Has data issue: false hasContentIssue false
  • English
  • Français

Monte Carlo methods for the study of cation ordering in minerals

Published online by Cambridge University Press:  05 July 2018

M. C. Warren ,
M. T. Dove ,
E. R. Myers ,
A. Bosenick ,
E. J. Palin ,
C. I. Sainz-Diaz ,
B. S. Guiton  and
S. A. T. Redfern
M. C. Warren
Affiliation:
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, UK
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
A. Bosenick
Affiliation:
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, 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
S. A. T. Redfern
Affiliation:
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, UK
*
*E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper reviews recent applications of Monte Carlo methods for the study of cation ordering in minerals. We describe the program Ossia99, designed for the simulation of complex ordering processes and for use on parallel computers. A number of applications for the study of long-range and short-range order are described, including the use of the Monte Carlo methods to compute quantities measured in an NMR experiment. The method of thermodynamic integration for the determination of the free energy is described in some detail, and several applications of the method to determine the thermodynamics of disordered systems are outlined.

Keywords

Monte Carlo simulationcation orderingNMRphase transitionsaluminosilicates
Type
Research Article
Information
Mineralogical Magazine , Volume 65 , Issue 2 , April 2001 , pp. 221 - 248
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 2001

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.)

Footnotes

2

Present address: Department of Earth Sciences, The University of Manchester, Manchester M13 9PL, UK

3

Present address: Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, UK

4

Present address: Martenshofweg 9, 24109 Kiel, Germany

References

Bosenick, A., Geiger, C.A., Schaller, T. and Sebald, A. (1995) An 29Si MAS NMR and IR spectroscopic investigation of synthetic pyrope-grossular garnet solid solutions. Amer. Mineral., 80, 691-704.CrossRefGoogle Scholar
Bosenick, A., Dove, M.T., Warren, M.C. and Fisher, A. (1999 a) 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., Geiger, C.A. and Phillips, B.L. (1999 b) Local Ca-Mg distribution of Mg- rich pyropegrossular garnets synthesized at different temperatures revealed by 29Si MAS NMR spectroscopy. Amer. Mineral., 84, 1423–33.CrossRefGoogle 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., Myers, E.R., Palin, E.J., Sainz-Diaz, C.I., Guiton, B., Warren, M.C., Craig, M.S. and Redfern, S.A.T. (2001 a) Computational methods for the study of energies of cation distributions: applications to cation-ordering phase transitions and solid solutions. Mineral. Mag., 65, 193-219.CrossRefGoogle Scholar
Bosenick, A., Dove, M.T., Heine, V. and Geiger, C.A. (2001 b) Scaling of thermodynamic mixing properties in garnet solid solutions. Phys. Chem. Miner. (in press).CrossRefGoogle 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, 1068–8.Google Scholar
Carpenter, M.A., Powell, R. and Salje, E.K.H. (1994) Thermodynamics of nonconvergent cation ordering in minerals. 1. An alternative approach. Amer. Mineral., 79, 1053–67.Google Scholar
Circone, S., Navrotsky, A., Kitkpatrick, R.J. and Graham, C.M. (1991) Substitution of [6,4]Al in phlogopite: Mica characterization, unit-cell variation, 27Al and 29Si MAS-NMR spectroscopy, and Al- Si distribution in the tetrahedral sheet. Amer. Mineral., 76, 1485–501.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., 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
Gasparik, T. (1984) Experimentally determined stability of clinopyroxene + garnet + corundum in the system CaO-MgO-Al2O3-SiO2 . Amer. Mineral., 69, 1025–35.Google Scholar
Herrero, C.P. and Sanz, J. (1991) Short-range order of the Si,Al distribution in layer silicates. J. Phys. Chem. Solids, 52, 1129–35.CrossRefGoogle Scholar
Herrero, C.P., Sanz, J. and Serratosa, J.M. (1985) Tetrahedral cation ordering in layer silicates by 29Si NMR spectroscopy. Solid State Comm., 53, 151–4.CrossRefGoogle Scholar
Herrero, C.P., Sanz, J. and Serratosa, J.M. (1986) The electrostatic enery of micas as a function of Si, Al tetrahedral ordering. J. Physics: Cond. Matter, 19, 4169–81.Google Scholar
Herrero, C.P., Gregorkiewitz, M., Sanz, J. and Serratosa, J.M. (1987) Si-29 MAS-NMR spectroscopy of micatype silicates - observed and predicted distribution of tetrahedral Al-Si. Phys. Chem. Miner., 15, 84-90.CrossRefGoogle Scholar
Herrero, C.P., Sanz, J. and Serratosa, J.M. (1989) Dispersion of charge deficits in the tetrahedral sheet of phyllosilicates. Analysis from 29Si NMR spectra. J. Phys. Chem., 93, 4311–5.CrossRefGoogle Scholar
Millard, R.L. and Luth, R.W. (1998) Tetrahedral Si/Al distribution in Di-CaTs clinopyroxenes using 29Si MAS NMR. EOS Trans. Amer. Geophys. Union, 79, S162.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
Navrotsky, A. and Kleppa, O.J. (1967) The thermodynamics of cation distributions in simple spinels. J. Inorg. Nucl. Chem., 29, 2701–14.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
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
Putnis, A. and Vinograd, V. (1999) Principles of solid state NMR spectrosco py and applicati ons to determining local order in minerals. Pp. 389-425 in: Microscopic Processes in Minerals (Catlow, C.R.A. and Wright, K., editors). Kluwer, The Netherlands.CrossRefGoogle Scholar
Putnis, A., Fyfe, C.A. and Gobbi, G.C. (1985) Al,Si ordering in cordierite using magic angle spinning NMR. 1. Si-29 spectra of synthetic cordierites. Phys. Chem. Miner., 12, 211–6.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
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. (1998) Calculation of the configurational entropy of Al, Si in layer silicates using the cluster variation method. Phys. Chem. Miner., 26, 135–48.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
Wood, B.J., Kirkpatrick, R.J. and Montez, B. (1986) Order-disorder phenomena in MgAl2O4 spine. Amer. Mineral., 71, 999-1006.Google Scholar
Yeomans, J.M. (1992) Statistical Mechanics of Phase Transitions. Oxford University Press, New York.Google Scholar