The description of Al, Si ordering in aluminosilicates using the cluster variation method

American Mineralogist

Volumn 84, Issue 3, 1999, Pages 311-324

  Vinograd, Victor L ^a   Putnis, Andrew ^a  

^a UNIVERSITY OF MÜNSTER   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALUMINOSILICATES; APPROXIMATION ALGORITHMS; FELDSPAR; ISING MODEL; THERMODYNAMICS; TOPOLOGY; ZEOLITES;

ALUMINOSILICATE MINERALS; CLUSTER VARIATION METHODS; COMPLEX TOPOLOGY; FUTURE PROSPECTS; HIGH-ORDER; ISING LATTICES; LONG RANGE ORDERS;

MONTE CARLO METHODS;

ALUMINOSILICATE; ALUMINUM; SILICON; THERMODYNAMICS;

EID: 0032987269     PISSN: 0003004X     EISSN: None     Source Type: Journal    
DOI: 10.2138/am-1999-0314     Document Type: Article

References (39)

1. Alexandrowicz, Z. (1971) Stochastic models for the statistical description of lattice systems. Journal of Chemical Physics, 55, 2765-2779.
2. Barker, J.A. (1952) Methods of approximation in the theory of regular mixtures. Proceedings of the Royal Society, London, A216, 45-56.
3. Carpenter, M.A. (1991) Mechanisms and kinetics of Al-Si ordering in anorthite: I. Incommensurate structure and domain coarsening. American Mineralogist, 76, 1110-1119.
4. _(1992) Equilibrium thermodynamics of Al/Si ordering in anorthite. Physics and Chemistry of Minerals, 19, 1-24.
5. Carpenter, M.A. and McConnell, J.D.C. (1984) Experimental delineation of the C1̄ ↔ I1̄ transformation in intermediate plagioclase. American Mineralogist, 69, 112-121.
6. de Fontaine, D. (1979) Configurational thermodynamics of solid solutions. Solid State Physics, 34, 73-274.
7. _(1994) Cluster approach to order disorder transformations in alloys. Solid State Physics, 47, 33-176.
8. 29Si MAS NMR data. American Mineralogist, 81, 39-44.
9. Dove, M.T., Thayaparam, S., Heine, V., and Hammonds, K. (1996) The phenomenon of low Al-Si ordering temperatures in aluminosilicate framework structures. American Mineralogist, 81, 349-362.
10. Herrero, C. P. (1991) Short-range order of the Si, Al distribution on the faujasite framework. Journal of Physical Chemistry, 95, 3282-3288.
11. _(1993) Monte Carlo simulations of the Si, Al distribution in A-type zeolites. Journal of Physical Chemistry, 97, 3238-3343.
12. Herrero, C.P., and Sanz, J. (1991) Short-range order of the Si, Al distribution in layer silicates. Journal of Physics and Chemistry of Solids, 52, 1129-1135.
13. Hijmans, J. and De Boer, J. (1955) An approximate method for order-disorder problems I. Physica, 21, 471-484.
14. Holland, T.J.B. and Powell, R. (1992) Plagioclase feldspars: activity-composition relations based upon Darken's quadratic formalism and Landau theory. American Mineralogist, 77, 53-61.
15. Inden, G. and Pitsch, W. (1991) Atomic ordering. In R.W. Cahn, P. Haasen, and E.J. Kramer, Eds., Materials Science and Technology. Phase Transformations in Materials, 5, 497-549. VCH, Weiheim, New York, Basel, Cambridge.
16. Ising, E. (1925) Beitrag zur Theorie des Ferromagnetismus. Zeitschrift für Physik, 31, 253-258.
17. Kikuchi, R. A. (1951) Theory of cooperative phenomena. Physical Review, 81. 988-1003.
18. _(1974) Superposition approximation and the natural iteration calculation in cluster-variation method. Journal of Chemical Physics, 60, 1071-1080.
19. Kikuchi, R. A. and Brush, S.G. (1967) Improvement of the cluster-variation method. Journal of Chemical Physics, 47, 195-203.
20. Kroll, H. and Müller, W.F. (1980) X-ray and electron-optical investigation of synthetic high-temperature plagioclases. Physics and Chemistry of Minerals, 5, 255-277.
21. Meirovitch, H. (1977) Calculation of entropy with computer simulation methods. Chemical Physics Letters, 45, 389-392.
22. Myers, E., Heine, V., and Dove, M.T. (1998) Some consequences of Al/ Al avoidance in the ordering of Al/Si tetrahedral framework structures. Physics and Chemistry of Minerals, 25, 457-464.
23. Onsager, L. (1944) Crystal statistics. I. A two-dimensional model with an order-disorder transition. Physical Review, 65, 117-149.
24. Palmer, D. (1994) CrystalMaker: Interactive crystallography for Macintosh and Power Macintosh. Lynxvale, Cambridge, U.K.
25. 20Si NMR spectroscopy of leucite, its Cs-and Rb-exchanged derivatives, and analcime. American Mineralogist. 79, 1025-1031.
26. 20Si MAS NMR spectroscopy. American Mineralogist, 77, 484-494.
27. Putnis, A. (1992) Introduction to Mineral Sciences, 457 p. Cambridge University Press.
28. Putnis, A. and Vinograd, V.L. (1999) Principles of solid state NMR spectroscopy and applications to determining local order in minerals. In K. Wright and C.R.A. Catlow, Eds., Microscopic Properties and Processes in Minerals Series. NATO ASI Reidel, (in press).
29. 20Si spectra of synthetic cordierites. Physics and Chemistry of Minerals, 12, 211-216.
30. Putnis, A., Salje, E., Redfern, S., Fyfe, C.A., and Strobl, H. (1987) Structural states of Mg-cordierite I: order parameters from synchrotron X-ray and NMR data. Physics and Chemistry of Minerals, 14, 446-454.
31. Ross, C.R., II (1991) Ising model and geological applications. In J. Ganguly, Ed., Advances in Physical Geochemistry, vol 8, Diffusion atomic ordering, and mass transport, p. 51-90. Springer-Verlag, New York.
32. Salje, E., Kuscholke, B., Wruck, B., and Kroll, H. (1985) Thermodynamics of sodium feldspar II: experimental results and numerical calculations. Physics and Chemistry of Minerals, 12, 99-107.
33. Sanchez, J.M. and de Fontaine, D. (1978) The fee Ising model in the cluster variation approximation. Physical Review B, 17, 2926-2936.
34. Sanchez, J.M., de Fontaine, D., and Teiter, W. (1982) Comparison of approximate methods for the study of antiferromagnetism in the fee lattice. Physical Review B, 26, 1465-1468.
35. Sanchez, J.M., Ducastelle, F., and Gratias, D. (1984) Generalized cluster description of multicomponent systems. Physica, 128A, 334-350.
36. Thayaparam, S., Dove, M.T., and Heine, V. (1994) A computer simulation study of Al/Si ordering in gehlenite and the paradox of low transition temperature. Physics and Chemistry of Minerals, 21, 110-116.
37. Thayaparam, S., Heine, V., Dove, M.T., and Hammonds, K. (1996) A computational study of Al/Si ordering in cordierite. Physics and Chemistry of Minerals, 23, 127-139.
38. Vinograd, V.L. and Putnis, A. (1998) Calculation of the configurational entropy of Al, Si in layer silicates using the cluster variation method. Physics and Chemistry of Minerals, (in press).
39. Vinograd, V.L., Saxena, S.K., and Putnis, A. (1997) Calculation of the probability distribution of basic clusters involved in cluster variation approximations to the Ising model. Physical Review B, 56, 11493-11502.