The modulated average structure of mullite

Abstract

Homogeneous and inclusion-free single crystals of 2:1 mullite (Al(4.8)Si(1.2)O(9.6)) grown by the Czochralski technique were examined by X-ray and neutron diffraction methods. The observed diffuse scattering together with the pattern of satellite reflections confirm previously published data and are thus inherent features of the mullite structure. The ideal composition was closely met as confirmed by microprobe analysis (Al(4.82 (3))Si(1.18 (1))O(9.59 (5))) and by average structure refinements. 8 (5) to 20 (13)% of the available Si was found in the T* position of the tetrahedra triclusters. The strong tendencey for disorder in mullite may be understood from considerations of hypothetical superstructures which would have to be n-fivefold with respect to the three-dimensional average unit cell of 2:1 mullite and n-fourfold in case of 3:2 mullite. In any of these the possible arrangements of the vacancies and of the tetrahedral units would inevitably be unfavorable. Three directions of incommensurate modulations were determined: q1 = [0.3137 (2) 0 ½], q2 = [0 0.4021 (5) 0.1834 (2)] and q3 = [0 0.4009 (5) -0.1834 (2)]. The one-dimensional incommensurately modulated crystal structure associated with q1 was refined for the first time using the superspace approach. The modulation is dominated by harmonic occupational modulations of the atoms in the di- and the triclusters of the tetrahedral units in mullite. The modulation amplitudes are small and the harmonic character implies that the modulated structure still represents an average structure in the overall disordered arrangement of the vacancies and of the tetrahedral structural units. In other words, when projecting the local assemblies at the scale of a few tens of average mullite cells into cells determined by either one of the modulation vectors q1, q2 or q3 a weak average modulation results with slightly varying average occupation factors for the tetrahedral units. As a result, the real structure of mullite is locally ordered (as previously known), but on the long-range its average is not completely disordered, the modulated structure of mullite may be denoted the true 'average structure of mullite'.

Mullite: Crystal Structure and Related Properties

“…However, such an arrangement of O vacancies inevitably leads to an unfavorable lining up of vacancies in chains or layers in the structure, which has the consequence that the O vacancies in mullite cannot be ordered. On the other hand the structure cannot be completely disordered as well, but shows a modulation as indicated by satellite reflections in the diffraction pattern, which can be described by three q ‐vectors in reciprocal space . Birkenstock et al concluded that the real structure of mullite due to the arrangement of tetrahedral di‐ and triclusters and of O vacancies is locally ordered, but on the long range is strongly but not completely disordered.…”

“…We interpret superstructure reflections and diffuse scattering as to be due to partial ordering of oxygen vacancies and/or of the tetrahedral Al and Si atoms, which altogether produces the incommensurably modulated structure of mullite. 37,[48][49][50][51] The distribution scheme of Al, Si atoms and/ or of O vacancies in mullite is very stable: According to Paulmann 52 it persists up to the melting point near to 1900°C ( Fig. 1).…”

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

“…Structural models were not refined, but Klar et al (2018) have shown that different degrees of order exist and that with the same constraint scheme the occupational modulation functions of partially and highly ordered mullite can be described. To date, only refinements of disordered structures based on first-order satellite reflections using modulation functions with first-order harmonics have been published (Birkenstock et al, 2015;Klar et al, 2017bKlar et al, , 2018. A superspace model refined against synchrotron single-crystal X-ray diffraction measurements (SA1 in Klar et al, 2018) was chosen as experimental reference for comparison with the superspace model of M40 AS1 (PBEsol-D) determined with the method presented in Section 3.2.…”

“…The complexity of mullite in reciprocal space must originate from vacancy and Al/Si ordering because sillimanite (Al 2 SiO 5 ), which has a very similar average struc-ture, is fully ordered and not modulated (Smith & McConnell, 1966). 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).…”

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.…”