"Disorder": Structured Diffuse Scattering and Local Crystal Chemistry [chapter]

Ray L. Withers
2008 Advances in Imaging and Electron Physics  
A review of the application of electron microscopy, in particular electron diffraction, to the detection and local structural characterization of 'disordered' materials exhibiting highly structured diffuse intensity distributions is given. A modulation wave approach to structural disorder is taken whereby the observed diffuse distribution is described in terms of what are presumed to be essentially independent, uncorrelated modulation waves, one for each point on the observed diffuse
more » ... n. An equation governing the scattering from such a 'disordered' modulated structure is thereby derived and used to to understand and interpret important qualitative as well as quantitative features of structured diffuse intensity distributions including the notion of transverse and longitudinal polarization, the existence of 'extinction conditions' in diffuse distributions etc. The review concludes with some case studies of materials types which typically exhibit highly structured diffuse intensity distributions. A very large number of compositionally 'disordered' solid solution phases e.g. (i) the wide range non-stoichiometric (1-x)M 2+ S.xLn2x/3 3+ S, M = Ca, Mg, Mn, Ln = rare earth or Y, solid solution phases (Flahaut, 1979 , Withers et al, 1994a , 2007 , (ii) the widely sub-stoichiometric, transition metal carbide (TC1-x) and nitride (TN1-x) solid solution phases (see e.g. Billingham et al, 1972 , Brunel et al, 1972 , Sauvage and Parthé, 1972 , Anderson, 1984 or (iii) the large family of disordered alloy, and disordered semiconductor alloy, solid solution phases (Sato et al, 1962 , Ohsima and Watananbe, 1973, Gomyo et al, 1988 , Matsumura et al, 1991 etc. 2. Inherently flexible framework structures e.g. (i) the ReO3 or ideal perovskite structure types (Glazer, 1972 , Brink et al, 2002 , (ii) the quartz, cristobalite and tridymite forms of silica, SiO2, and AlPO4 (van Tendeloo et al, 1976 , Withers et al, 1989 , 1994b or (iii) the large family of zeotypic, microporous molecular sieve materials (Hartmann and Kevan, 1999 , Liu et al, 2003 etc. Materials susceptible to electronic or Fermi surface driven structural instabilities e.g. (i) low dimensional materials susceptible to Charge Density Wave (CDW) type instabilities such as the layered transition metal dichalcogenides, the organic charge transfer salts or the non-magnetic Kondo effect materials ThAsSe and UAsSe (Wilson et al, 1975 , Khanna et al, 1977 , (ii) certain 'defect' transition metal oxide phases (e.g. Castles et al, 1971) or (iii) various alloy phases (e.g. Norman et al, 1985) etc. Dynamically disordered, solid electrolyte and related phases e.g. (i) BaTiO3, in all but its lowest temperature rhombohedral polymorphic form, and BaTiO3-doped relaxor ferroelectric phases (Comes et al, 1968, Harada and Honjo, 1967 , Liu et al, 2007 , (ii) ionic conductors such as e.g. -AgI or -RbAg4I5 (see e.g. Andersson et al, 1985, Funke and Banhatti, 2006) and the cubic stabilized zirconias or (iii) Ag or Cu-containing mineral sulfosalts such as e.g. the mineral pearceite (Bindi et al, 2006) etc. Materials susceptible to ferroelastic strain distortions e.g. (i) the tetragonal  form of PbO and Sn1-xO (Withers et al, 1993 , Withers and Schmid, 1994 , Moreno et al, 1997 , (ii) partially ordered potassium feldspars such as the orthoclase, adularia and intermediate microcline feldspars (McClaren and Fitz Gerald, 1987, Putnis and Salje, 1994) or (iii) the Ni rich, Ni1-xAlx, alloy phase (van Tendeloo and Amelinckx, 1998) and the InxGa1-xAsyP1-y semiconductor alloy phase (Treacy et al, 1985) etc. Significant insight into the local order (and hence the underlying crystal chemistry) of 'disordered' materials of the above types can very often be obtained simply from the 'shapes' of the various structured diffuse intensity distributions characteristic of them (see e.g. de Ridder et al, 1976a ,b, 1977a ,b, Withers et al, 2007 ; see also Section IV.A below). Reciprocal space mapping of this type, however, requires a diffraction probe that is sufficiently sensitive to weak features of reciprocal space. Electron diffraction is an ideal such probe as a result of the strength of the interaction between fast electrons and matter. The current paper is thus a review on the application of electron microscopy, in particular electron diffraction, to the detection and characterization of 'disordered'/locally ordered phases. It builds on much earlier pioneering work in the area (see, in particular, Honjo et al, 1964, Harada and Honjo, 1967) as well as on many later subsequent reviews (e.g. van Tendeloo, 1998 , Withers, 2005 . A. Crystal chemical and other types of flexibility A review on 'disordered'/locally ordered phases is simultaneously and inevitably also a review of crystal chemical flexibility and of the numerous ways in which this can be manifested on local, mesoscopic and/or macroscopic length scales (see, for example, Fig.2) . A major theme will be that nature, when thoroughly and carefully investigated, often throws up surprises that don't fit into pre-existing categories of how atoms/objects should be arranged and hence, unfortunately, are often neglected or worse ignored! A good example is State Chem. 155, 359-365. Brunel, M., de Bergevin, F. and Gondrand, M. (1972). Determination theorique et domaines d'existence des differentes surstructures dans les composes A 3+ B 1+ X2 2de type NaCl. . Diffuse absences due to the atomic size effect. Acta Cryst. A 48, 737-746. Castles, J.R., Cowley, J.M. and Spargo, A.E.C (1971). Short-range ordering of vacancies and Fermi surface of TiO. Acta Cryst. A 27, 376-383. Comes, R., Lambert, M. and Guinier, A. (1968). The chain structure of BaTiO3 and KNbO3. Solid State Commun. 6, 715-719 Dove, M.T., Heine, V. Hammonds, K.D., Gambhir, M. and Pryde, A.K.A. (1998). Short range disorder and long range order: implications of the Rigid Unit Mode model: In: Local Structure from Diffraction (Eds. S.J.L.Billinge and M.F.Thorpe), Plenum Press, New York, 253-271. Dove, M.T., Tucker, M.G. and Keen, D.A. (2002) Neutron total scattering method: simultaneous determination of long-range and short range order in disordered materials. Eur. J. Mineral. 14, 331-348. Esmaeilzadeh, S., Lundgren, S., Halenius, U. and Grins, J (2001). Bi1-xCrxO1.5+1.5x, 0.05<x<0.15: A new high temperature solid solution with a three-dimensional incommensurate modulation. Journal of Solid State Chem. 156, 168-180.
doi:10.1016/s1076-5670(08)00606-x fatcat:adyfpi3rendx5p4kwldlxeo3k4