A MICROSCOPIC MODEL FOR A VERY STABLE INCOMMENSURATE MODULATED MINERAL - MULLITE

A microscopic model is used to discuss the long-range ordering behaviour of the oxygen vacancies in mullite. This aluminosilicate of composition Al2(Al2+2xSi2-2x)O10-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 our 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 x < 0.5. At high concentrations of vacancies it is necessary to renormalize the coupling terms, which then accounts for the doubly modulated structure that occurs in mullite at x > 0.5.