Al and Si cations often occupy tetrahedral sites in the crystal structures of silicates, and then it is frequently found that the specific sites can be disordered at high temperatures. The Al/Si site-ordering phase transitions have been studied in many silicates using a variety of techniques.
Our interest arose from the fact that in some cases the ordering temperatures are so low that ordering never happens, whereas in other cases the ordering temperatures appear to be well above melting temperatures. This strikes me as odd, since in most other respects the behaaviour of the Al and Si cations is not substantially dependent on the specific structure.
Our approach has been to use empirical pair potentials to model the ordering interactions in the actual crystal structures of silicates. Our first finding is that the interactions do depend on the actual crystal structure, since different structures can accomodate the size mismatch in different ways. But this fact alone does not account for the low ordering temperatures. To see what is happening we have performed detailed Monte Carlo simulations. In short, we find that different structures have different ways to accomodate short-range order, involving avoidance of Al-O-Al linkages, without needing to develop long-range order. This is very dependent on the Al:Si ratio. We also found that some ordering schemes involve stronger ordering along specific directions, leading to effective one-dimensional order at high temperatures. From statistical physics theories of phase transitions we know that one-dimensional ordering cannot drive long-range order.
As part of this work we have developed a method and associated computer program to analyse the Al/Si ordering in an aluminosilicate from NMR data. This uses a Monte Carlo approach (which usually is operated in the mode of a simulated annealing) to adjust the distribution of Al and Si cations in a given crystal to give the best possible agreement with the experimental data. This method avoids any possible calculation of an unphysical negative value for the number of Al-O-Al linkages. The program, called NMRFIT is freely available for anyone who wants to try running it, and any questions can be answered by email.
Credit has to go to S Thayaparam, the PhD student who did much of the hard work, which is now being picked up by Eva Myers. Volker Heine has been a great collaborator. Kenton Hammonds has helped with the computational work.
Our papers on this subject include (in reverse chronological order):
V Heine, M T Dove, A De Vita, J Ortega and E Myers, "Computational studies of Si/Al ordering in aluminosilicate framework structures". Phase Transitions (in press)
A summary of various bits of this programme.M T Dove, S Thayaparam, V Heine and K D Hammonds, "The phenomenon of low Al/Si ordering temperatures in aluminosilicate framework structures". American Mineralogist 81, 349-362, 1996.
Here we address the general question of why ordering temperatures can be substantially lower than you might expect from mean-field theory. And "no!", it is nothing to do with the usual critical fluctuations that lower the transition temperature by 30% or so - the issue here is much more dramatic!
M T Dove and V Heine, "The use of Monte Carlo methods to determine the distribution of Al and Si cations in framework aluminosilicates from 29Si MAS-NMR data". American Mineralogist 81, 39-44, 1996.
In principle we can get information about Al/Si ordering from NMR, but it isn't simple. Here we propose a Monte Carlo solution as described briefly above.
S Thayaparam, V Heine, M T Dove and K D Hammonds, "A computational study of Al/Si ordering in cordierite". Physics and Chemistry of Minerals 23, 127-139, 1996.
This is a detailed study of ordering in cordierite, supposedly to test our potentials and methods, but we opened a can of worms!
S Thayaparam, M T Dove and V Heine, "A computer simulation study of Al/Si ordering in gehlenite and the paradox of the low transition temperature", Physics and Chemistry of Minerals 21, 110-116, 1994.
This was our first venture into this programme, and gives our basic methodology.
M T Dove, T Cool, D C Palmer, A Putnis, E K H Salje and B Winkler, "On the role of Al/Si ordering in the cubic-tetragonal phase transition in leucite". American Mineralogist 78, 486-492, 1993.
Here my interest in the issue begins, and this paper contains some of the initial ideas.
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