Microsommite: crystal chemistry, phase transitions, Ising model and Monte Carlo simulations

摘要

Microsommite, ideal formula [Na_4K_2(SO_4)] [Ca_2Cl_2][Si_6Al_6O_(24)], is a rare feldspathoid that occurs in volcanic products of Vesuvius. It belongs to the cancrinite-davyne group of minerals, presenting an ABAB… stacking sequence of layers that contain six-membered rings of tetrahedra, with Si and Al cations regularly alternating in the tetrahedral sites. The structure was refined in space group P6_3 to R = 0.053 by means of single-crystal X-ray diffraction data. The cell parameters are a = 22.161 A = √3a_(dav), c = 5.358 A = c_(dav); Z = 3. The superstructure arises due to the long-range ordering of extra-framework ions within the channels of the structure. This ordering progressively decreases with rising temperature until it is completely lost and microsommite transforms into davyne. The order-disorder transformation has been monitored in several crystals by means of X-ray superstructure reflections and the critical parameters T_c ≈ 750 ℃ and β ≈ 0.12 were obtained. The kinetics of the ordering process were followed at different temperatures and the activation energy was determined to be about 125 kJ mol~(-1). The continuous order-disorder phase transition in microsommite has been discussed on the basis of a two-dimensional Ising model in a triangular lattice with nn (nearest neighbours) and nnn (next-nearest neighbours) interactions. Such a model was simulated using a Monte Carlo technique. The theoretical model well matches the experimental data; two phase transitions were indicated by the simulated runs: at low temperature only one of the three sublattices begins to disorder, whereas the second transition involves all three sublattices.