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14.6.2 Nonstoichiometric Fluorites as Examples of Nanostructured Materials
It was suggested that the micro-heterogeneity appears in the disordered fluorite-like solid
solution structure by means of ordering superclusters [43]. The superclusters accumulate R 3 þ
dopant cations and form small areas. These ordered areas with structures similar to those of
ordered phases are distributed in the matrix of non-distorted cubic fluorite. In Figure 14.24][43]
two models of this micro-ordering in the disordered M 2 x R x F 2 þ x phase (a,b) as well as an
extended superstructure in ordered phases (c,d) are presented. In this figure the two-dimensional
section of the cationic sublattice is shown. The single {M 8 [R 6 F 69 ]} supercluster is presented in
the left top corner of Figure 14.24a. Four R 3 þ cations can be seen in this section of the sublattice.
Other cations of the supercluster, 8M 2 þ and 2R 3 þ , are located in neighbouring layers.
Figure 14.24 Models of M 1x R x F 2þx structure: a), c) - micro-ordering areas in nonstoichio-
metric crystals with x ¼0,15 and 0,40; b), d) ordered phases at x¼0.1538 (hypothetic phase)
and at x¼0.4286 (real Ba 4 Yb 3 F 17 phase [54]). Light circles denote R , black ones, M .
(Reprinted with permission from [43] Copyright (2003) Pleiades Publishing Inc.)
Microordering areas are about 10-100 nm long. It is impossible to detect these randomly
oriented nanometric areas by means of classical XRD because both the fluorite matrix and
ordered inclusions have an almost identical cationic sublattice. Slight cation displacements
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