ORIGINAL PAPER E. J. Palin á M. T. Dove á S. A. T. Redfern A. Bosenick á C. I. Sainz-Diaz á M. C. Warren Computational study of tetrahedral Al±Si ordering in muscovite Received: 28 August 2000 /Accepted: 12 March 2001 Abstract The nature of Al±Si ordering across the tet- rahedral sites in muscovite, K 2 Al 4 Si 6 Al 2 O 20 )OH) 4 , was investigated using various computational tech- niques. Values of the atomic exchange interaction pa- rameters J l were obtained. From these parameters, a two-dimensional Al±Si ordering scheme was deduced. The transition temperature T c for this two-dimensional ordering is 1900 K. There are several possible ordering schemes in three dimensions, based on dierent stack- ing sequences of ordered sheets of tetrahedral sites. Monte Carlo simulations of both two-dimensional and three-dimensional ordering were performed, but in the three-dimensional simulation only the two-dimensional ordering is seen, implying that three-dimensional ordering is too slow to be attained during the timescale of the simulation. The eect of the three-dimensional interactions is to raise the two-dimensional ordering temperature to 2140 K. From the three-dimensional Monte Carlo simulation, the frequency of occurrence of 4Si0Al, 3Si1Al, 2Si2Al and 1Si3Al clusters was determined, which match those inferred by 29 Si MAS±NMR measurements reasonably well. In fact, the match suggests that the cation ordering seen in exper- iments corresponds to a con®guration with consider- able short-range order but no long-range order, similar to a state that is at a temperature just above an ordering phase transition. Key words Muscovite á Al±Si ordering á Layer silicates á Phase transitions á Monte Carlo simulations Introduction The phenomenon of Al±Si ordering in aluminosilicate minerals has long been recognised as one of the impor- tant aspects of mineral behaviour, particularly since it can have a signi®cant eect on thermodynamic proper- ties. Recently, we have used computer simulations to complement experimental data, particularly using a combination of lattice energy methods to calculate or- dering energies and Monte Carlo simulations to calcu- late the dependence of ordering on temperature Thayaparam et al. 1994, 1996; Dove et al. 1996, 2000; Dove 1999). Among the main ®ndings of these studies were that the exact Al:Si ratio can have a considerable eect on the ordering temperatures Dove et al. 1996; Myers et al. 1998), particularly as this ratio decreases from 1:1, and that the detailed topology of the structure can provide ways to allow short-range order to develop without necessarily forcing long-range order to be es- tablished Dove et al. 1996), thereby leading to a con- siderable reduction in the ordering temperature that would be predicted by methods that consider only co- ordination numbers such as Bragg±Williams and other lower-order cluster variation methods). Both factors come into play in a signi®cant way in the ordering process in cordierite Thayaparam et al. 1996). At the simplest level, Al±Si ordering can be said to be driven by the phenomenon of aluminium avoidance LoÈwenstein's rule), that is, that in equilibrium there is a driving energy that acts to avoid the formation of Al±O±Al linkages. The eect of a low Al:Si ratio allows the possibility of avoiding formation of any Al±O±Al linkages without the need for long-range ordering. In this case, the driving force for long-range order comes from interactions be- tween tetrahedral sites that are not nearest neighbours Dove et al. 1996). Phys Chem Minerals 2001) 28: 534±544 Ó Springer-Verlag 2001 E. J. Palin á M. T. Dove &) á S. A. T. Redfern A. Bosenick á M. C. Warren Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, UK e-mail: martin@esc.cam.ac.uk C. I. Sainz-Diaz Estacion Experimental del Zaidin, CSIC, C/Profesor Albareda, 1, 18008-Granada, Spain Present addresses: A. Bosenick Martenshofweg 9, 24109 Kiel, Germany M. C. Warren Department of Earth Sciences, The University of Manchester, Manchester, M13 9PL