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

Abstract

A mullite single crystal with composition AlSiO 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.

Exploiting superspace to clarify vacancy and Al/Si ordering in mullite

“…Reflection conditions are in agreement with the superspace group Pbam(a0 1 2 )0ss, as in former studies (Birkenstock et al, 2015;Klar et al, 2017); equivalent settings are discussed by Klar et al (2017). This superspace group is used for all subsequent structure model refinements.…”

“…The compositions of samples SA2, SA3 and QG were refined to x = 0.416 (4), 0.434 (6) and 0.426 (3), respectively. Elemental analyses of other studies of mullite report a higher uncertainty than the standard uncertainty estimated by the fitting algorithm, and therefore the uncertainties given here might be underestimated (Birkenstock et al, 2015;Klar et al, 2017). Nevertheless, the present samples all have a comparable composition close to the vacancy concentration of 2/1mullite, including sample QG, for which the synthesis aimed for a vacancy concentration of 0.5.…”

“…Samples SA1, SA2 and SA3 originate from a batch of commercial aluminium silicate (Sigma-Aldrich), SA1 being the same crystal that was used for the work by Klar et al (2017). From the previous study it was known that the composition of these samples corresponds to a vacancy concentration of about 0.4.…”

“…A superspace model was developed that describes mullite as a mostly disordered structure with a weak occupational modulation, implying a low degree of vacancy ordering (Birkenstock et al, 2015). In contrast, crystal structure models with an ordered distribution of vacancies were suggested earlier (Saalfeld, 1979;Ylä -Jä ä ski & Nissen, 1983;Kahn-Harari et al, 1991;Klar et al, 2017), but only the most recent of these models was refined against diffraction data, which did not show any signs of diffuse scattering but sharp first-order satellite reflections. The refinement used different scale factors for the main and satellite reflections, assuming that the crystal consists of a component with complete vacancy ordering within a disordered polymorph, and the ordered superspace model only accounts for the ordered component.…”

DFT of incommensurate, disordered structures:ordering phenomena in mullite

“…Diffuse scattering and satellite reflections with a modulation wave vector q that depends on the vacancy concentration x require a comprehensive model. Recently, the superspace approach was used to reveal the underlying pattern of the vacancy distribution, presenting either a highly disordered vacancy distribution [1] or a fully ordered vacancy distribution [2]. However, a clear Al/Si ordering pattern could not be established experimentally.…”