A microscopic model for a very stable incommensurate modulated mineral: mullite

Abstract

A microscopic model is used to discuss the long-range ordering behaviour of the oxygen vacancies in mullite. This aluminosilicate of composition Al₂(Al_2+2xSi_2-2x)O_10-x (vacancy)_x presents an extremely stable incommensurate modulated structure with a wave vector Q_Ic(x) which depends on the composition index x. Earlier computer simulations showed that the oxygen vacancies strongly order the Al/Si tetrahedral sites in their local environment. When two vacancies approach too closely, their dressings overlap which results in a repulsive interaction. The system is mapped onto an ANNNI model with frustration and an additional constraint on composition x. The solutions of the authors model at thermal equilibrium are discussed in q-space as well as in real space in order to calculate Q_Ic(x). Reasonable agreement is found with observations for x0.5.