Abstract

A new complete scheme of symmetry analysis for incommensurate modulated structures is applied for the first time to the important ceramic material mullite ${\mathrm{Al}}_{2}$(${\mathrm{Al}}_{2+2\mathrm{x}}$${\mathrm{Si}}_{2\mathrm{\ensuremath{-}}2\mathrm{x}}$)O $_{10\mathrm{\ensuremath{-}}x}\ensuremath{\square}_{x}$. Together with what is known of the average structure, the symmetry suffices to determine the complete Al-Si and oxygen-vacancy ordering patterns. The reason why the incommensurate structure is so stable becomes immediately apparent.

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