The Al/Si and Al/Mg order-disorder behaviour of minerals in the tremolite-tschermakite solid solution (namely, end-member tschermakite and the 50:50 composition, magnesiohornblende) has been investigated by Monte Carlo simulation, using a model Hamiltonian in which atomic interaction parameters Ji
were derived from empirical lattice energy calculations, and chemical potential terms μj
(to express the preferences of cations for particular crystallographic sites) were derived from ab initio methods. The simulations performed were increasingly complex. Firstly, ordering in one tetrahedral double chain with Al:Si = 1:3 (tschermakite) was simulated. Although the low-temperature cation distribution in this system was ordered, there was no phase transition (due to the quasi-one-dimensional nature of the system). Next, interactions between tetrahedral Al:Si = 1:3 double chains were included, and a phase transition was observed, with the cation distribution in one double chain lining up with respect to that in the next. Finally, interactions between tetrahedral and octahedral sites were incorporated, to model the whole unit cell, and compositions corresponding to tschermakite and magnesiohornblende were investigated. The whole-cell simulation results compare favourably with experimental conclusions for magnesiohornblende, in that Al at T1 is preferred over Al at T2, and Al at M2 is favoured over that at M1 and M3, but the significant amount of Al at M1 is at odds with experimental observation.