L. Kienle, V. Duppel, and A. Simon The crystalline state is usually characterized by
a unit cell which is reproduced in three dimen-sions by translation. For many important mate-rials (e.g., YSZ and other ionic conductors) the 3D periodicity is broken, due to the existence of prominent disorder in the crystals. Experi-mentally the disorder results in diffuse scatter-ing which can be observed by diffraction exper-iments. A second useful tool for the direct ob-servation of disorder is high resolution electron microscopy (HREM).
We examined complex chalcogenides which are characterized by diffuse ring-shaped intensities in defined layers of the reciprocal space. These diffuse reflections show no significant extension in001 corresponding to 1D ordering of the crystallites in [001] of direct space. A common
feature of all compounds is the hexagonal lat-tice and the possibility to divide the structures into two parts, an ordered honeycomb host lat-tice and rods which are inserted in the latter ones, respectively, see Fig. 104(a).
The translational symmetry of the host lat-tice allows two different positions (referring to [001]) of the otherwise identical rods (called rod A and rod B). The configurations of neigh-bored rods (AA, BB or AB) are essential for the understanding of the diffuse scattering.
In the case of K2In12Se19 a dynamical disorder of the configurations is observed at T400ÆC which is transformed into a statical one at lower temperatures. The associated formation of antiphase domains (configurations AA or
BB) limits the disorder to the domain bound-aries which are characterized by the configura-tion AB. A structural analysis of the possible configurations of neighbored rods shows sig-nificant differences in the local structure. The configurations AA and BB result in a remark-ably short interatomic distance for some indium atoms of neighbored rods (dInIn= 3.528 ˚A), see Fig. 104(b). The alternative configuration AB exhibits an enlarged distance between the in-dium atoms (dInIn= 4.049 ˚A), see Fig. 104(c).
Hence the formation of crystals with a high den-sity of the antiphase boundaries (APB) can be expected.
Figure 104: (a) Description of the structure of K2In12Se19 (right) by the concept of rods (middle) which are inserted in a host structure (left). Pro-jections on (001). (b) and (c) Neighbored rods in the structure ofK2In12Se19. The coordination of the atoms Se1 (by In) and K1 and K2 (by Se) are dis-played in polyhedral representation. (b) Neighbored rods in position A generate an unusually short dis-tancedInIn (indicated by the line), (c) one rod in position A and one rod in position B, the short dis-tance does not occur.
Figure 105: (a) HREM of ordered domains sep-arated by APB for K2In12Se19 (zone axis [¯111],
∆f = 10 nm). The arrows indicate the shift of the structure at the boundary. (b) Cutting of a torus by a layer results in two intensity maxima. Schematically representation left, selected area diffraction (SAED) of zone axis [100] right.
For K2In12Se19the formation of the partially or-dered crystals can be observed experimentally.
At the boundary of two domains a characteris-tic shift of the structure occurs, see the HREM micrograph in Fig. 105(a), which can be inter-preted using a model of a real structure that in-cludes the above mentioned antiphase bound-aries. The relative shift of the domains rep-resents the difference of the positions A and B of the rods. The sizes of the single or-dered domains and the orientations of the do-main boundaries exhibit an essential influence on the shape of the diffuse intensities. The dif-fuse scattering manifests itself only in higher order Laue zones of [001] as diffuse rings. In all other orientations we observed two sharp and very close intensity maxima which result from cutting the diffuse rings through their centers (e.g., for [100], see Fig. 105(b) ).
Figure 106: (a) HREM micrographs after image processing. The different orientations of the domain boundaries (referring to the host lattice) is evident, see broken lines. (b) Enlarged sections of SAED patterns recorded on one crystallite.
Our observations indicate random orientations of the domain boundaries in (001) to be re-sponsible for the circular shape of the diffuse scattering (see the processed micrographs in
Fig. 106(a) for zone axis [¯111]). Only in small areas of the crystallites the averaging is not per-fect and the circular shape of the diffuse scat-tering is modified as indicated by selected area diffraction (SAED). A second important point concerns the sizes of the domains, which deter-mine the diameter of the diffuse rings. Experi-mentally we found for instance variations of the distance between the diffuse intensity maxima in dependence of the domain size. The SAED patterns in Fig. 106(b) were taken from differ-ent regions of one crystal. As indicated by the smaller distance of the intensity maxima the left pattern was recorded by focusing on an area with larger domains.
Figure 107: (a) HREM of ordered domains sepa-rated by APB for K2In12Se15Te4 (zone axis [¯111],
∆f = 10 nm). The arrows indicate the shift of the structure at the boundary, (b) SAED performed on this crystal exhibits no diffuse scattering (see en-larged section in (c)), (d) enen-larged section of the Fourier transform of picture (a) displaying clearly diffuse scattering.
Chemistry also has a large influence on the real structure and therefore on diffuse scattering. In the cases of K2In12Se14Te5and In4SSe2Te3no diffuse reflections can be observed by
diffrac-tion methods (X-ray and electrons), but the HREM micrographs display clearly the pres-ence of APB (see Fig. 107 for zone axis [¯111]) and the existence of very large ordered sin-gle domains related to the pure selenium com-pound. The Fourier transforms of selected
re-gions of the images emphasize the diffuse char-acter of the reflections (see enlarged sections in Fig. 107) and underline that it is possible to get information about the real structure by HREM that could not be derived by any diffraction method.