title: 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'.
authors.affiliation: FB5 - Geowissenschaften/Kristallographie, Universität Bremen, Klagenfurter Str., 28359 Bremen, Germany.
authors.forename: Johannes
authors.initials: J
authors.lastname: Birkenstock
authors.affiliation: Department of Structure Analysis, Institute of Physics, Academy of Sciences of the Czech Republic v.v.i., Na Slovance 2, 18221 Praha 8, Czech Republic.
authors.forename: Václav
authors.initials: V
authors.lastname: Petříček
authors.affiliation: Heinz Maier-Leibnitz Zentrum (MLZ) Garching, Technische Universität Muenchen, Lichtenbergstr. 1, Garching, 85748 Bayern, Germany.
authors.forename: Bjoern
authors.initials: B
authors.lastname: Pedersen
authors.affiliation: FB5 - Geowissenschaften/Kristallographie, Universität Bremen, Klagenfurter Str., 28359 Bremen, Germany.
authors.forename: Hartmut
authors.initials: H
authors.lastname: Schneider
authors.affiliation: FB5 - Geowissenschaften/Kristallographie, Universität Bremen, Klagenfurter Str., 28359 Bremen, Germany.
authors.forename: Reinhard X
authors.initials: RX
authors.lastname: Fischer
keywords: 2:1 mullite; ceramics; diffuse scattering; disordered modulated structure; neutron diffraction