Ordered vacancy distribution in 2/1 mullite: a superspace model.

A mullite single crystal with composition Al4.84 Si1.16 O9.58 (2) exhibiting sharp satellite reflections was investigated by means of X-ray diffraction. For the refinement of a superspace model in the superspace group Pbam(α0½)0ss different scale factors for main and satellite reflections were used in order to describe an ordered mullite structure embedded in a disordered polymorph. The ordered fraction of the mullite sample exhibits a completely ordered vacancy distribution and can be described as a block structure of vacancy blocks (VBs) that alternate with vacancy-free blocks (VFBs) along a and c. The incommensurate nature of mullite originates from a modulation of the block size, which depends on the composition. The displacive modulation is analyzed with respect to the vacancy distribution and a possible Al/Si ordering scheme is derived, although the measurement itself is not sensitive to the Al/Si distribution. An idealized, commensurate approximation for 2/1 mullite is also presented. Comparison of the ordered superspace model with different preceding models reconciles many key investigations of the last decades with partly contradicting conclusions, where mullite was usually treated as either ordered or disordered instead of considering simultaneously different states of order.