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

Abstract

New superspace models with different modulation amplitudes indicate that any degree of ordering, from disordered to ordered, can be observed in mullite.

Characterizing modulated structures with first-principles calculations: a unified superspace scheme of ordering in mullite

“…M40 #1 and M50 #1 contain Si in triclusters indicating that this is a stable and favourable environment for Si. The identification of Si in triclusters and the presence of Si-Si diclusters between vacancies are consistent with the Al/Si ordering pattern suggested by Klar et al (2018). As M40 #2 and M50 #2 contain Si on the T* site, the presence of this tricluster configuration is energetically not forbidden (Table S4).…”

“…In the second step ( Fig. 4), triclusters and diclusters are distributed according to the vacancy distribution with atom coordinates derived from the average atom positions taken from Klar et al (2018). In the last step, the appropriate amount of Si atoms must be distributed over the tetrahedral sites, whereas all remaining cations are Al.…”

“…In the last step, the appropriate amount of Si atoms must be distributed over the tetrahedral sites, whereas all remaining cations are Al. Apart from the analysis of the modulated volumes of tetrahedra, there are only qualitative indications of which sites are favoured by Al and which sites are favoured by Si (Klar et al, 2018). Therefore, we decided to systematically investigate all symmetry-compliant Al/Si ordering patterns for M0, M25, M33, M40 and M50 with FF methods.…”

“…The precise positions and intensities of satellite reflections with a modulation wavevector q = ( 0 1 2 ) depend on the chemical composition as the structural modulation changes with the Al/Si ratio (Agrell & Smith, 1960;Cameron, 1977b;Ylä -Jä ä ski & Nissen, 1983). Different degrees of ordering exist, but the tendency to long-range vacancy ordering is rather low in mullite (Klar et al, 2018). For most samples only weak, low-order satellite reflections are visible in reciprocal space and diffuse scattering is present in all reciprocal-space sections due to correlated disorder (Tokonami et al, 1980;Welberry & Butler, 1996;.…”

“…Despite several nuclear magnetic resonance measurements and neutron diffraction studies, a clear Al/Si ordering pattern cannot yet be identified (Angel et al, 1991;Schmü cker et al, 2005;Birkenstock et al, 2015;Schneider et al, 2015). From the modulation of the volumes of tetrahedra it was suggested that Si-Si diclusters tend to be sandwiched between vacancies (Klar et al, 2018).…”