Computational study of tetrahedral Al-Si ordering in muscovite

The nature of Al-Si ordering across the tetrahedral sites in muscovite, computational techniques. Values of the atomic exchange interaction parameters J₁ 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. These are several possible ordering schemes in three dimensions, based on different stacking 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 effect 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 4SiOAl, 3Si1Al, 2Si2Al and 1Si3Al clusters was determined, which match those inferred by ²⁹Si MAS-NMR measurements reasonably well. In fact, the match suggests that the cation ordering seen in experiments corresponds to a configuration with considerable short-range order but no long-range order, similar to a state that is at a temperature just above an ordering phase transition.