Non-commensurate structures

There are crystals that pose unusual difficulties in working with them. Among the problems encountered are disorder, twinning and non-commensurate structures. While all can be handled using modern instruments and software, they are beyond the norm for the typical chemist. This is the realm of the professional crystallographer. 

Figure 17. A non-commensurate, layer misfit structure (o), composed of alternating layers of two types, and the recombination structures (i-iii) derived from (o) by means of (i) composition-conservative and of (ii-iii) two kinds of composition non-conservative antiphase boundaries (or glide planes), (iv) A layered non-commensurate structure with corrugated layers that are composed of alternating strips of two kinds that exhibit layer misfit on interfaces.

Makovicky E, Hyde BG (1981) Non-Commensurate (Misfit) layer Structures. 46 101-170... 

Makovicky, E Hyde, B. G. Non-Commensurate (Misfit) Layer Structures, pp. 101-170. 

Because h is small for the V-amyloses, a wide-diameter helix is characteristic of these structures. Complexing agents, such as DMSO, iodine, or water, are found inside the helix channel. For example, in VQygo-amylose, six DMSO molecules are accommodated inside the channel within one crystallggraphic repeat, which consists of three helix turns (c=24.39 A). This fiber repeat is not the result of the intrachannel DMSO but is caused solely by the packing of the interstitial. DMSO. A non-commensurable fiber repeat for the amylose helix and the intrahelical iodine is observed in V -iodine approximately three iodines occupy the helix channel within one fiber repeat, but the iodines form an almost linear polyiodide chain of an undetermined length. In this respect, the structures of the V -iodine complex and the a-cyclodextrin-iodine complex (30) are similar. 

A discussion of types of inter-layer bonding, layer types and layer matching is followed by a consideration of disorder in such structures, as well as symmetry aspects and some growth mechanisms. Structures transitional between this type of structure and commensurate structures, i.e. structures which are really non-commensurate layers joined at anti-phase boundaries which restore commensurability, are then considered and classified with a detailed consideration of known examples from inorganic chemistry and mineralogy. Finally, some broad, general conclusions are enumerated. 

Fig. S. Types of octahedral layers observed in non-commensurate layer structures A, a brucite-like layer with undifferentiated octahedra B, the brudte-Uke layer in tochilinites, with the octahedra preferred by Fe indicated by stippling C, the SnS2-like layer in cylindrite, with the octahedra preferentially occupied by Sb and/or Fe indicated by stippling D, the FeCls layers (occupied octahedra stippled) and, E, the M0CI5 layers (empty octahedra stippled) in the metal chloride-graphite intercalates F, the two orientations (to be superimposed) of the octahedral layers in Phase 1 of Organova et al. ...

Fig. 7a-d. Idealised lepresentations of various layer types observed in non-commensurate layer structures (a) octahedral layer, MX2, (111) B1 type (b) galena-like half octahedral (square pyramidal) layer, MX, (100) B1 type (c) the valleriite-like tetrahedral layer, MX, (111) anti-C 1 type (d) the mackinawite-like tetrahedral layer, MX, (100) anti-Cl type... 

Table 2. Non-commensurate layer structures with H/H interface (Lattice vectors in A, angles in degrees.)... 

Table 4. Non-commensurate complex sulphides/sulphosalt structures. ...

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