Non-commensurability

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. 

Table 1. Selected non-commensurate graphite intercalates" (Lattice vectors in A, angles in degrees.)... 

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... 

Non-commensurability can be observed in the published diffraction patterns of tochilinite I from Cyprus It is of the SI type instead of the SC type which occurs in the original tochilinite I from the Mamonovo (U.S.S.R.) deposit. Small chemical differences, resulting in altered layer charges and periodicities, appear to be responsible for the changes in the interlayer fit - here (Table 3), and in the valleriites (Table 2). 

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

The pseudo-tetragonal layer is a slightly deformed, (100) galena-like layer, LaS, two atomic planes thick, with half-octahedral (square pyr2unidal) coordination of La (Fig. 7 b). The La atoms on either side of this layer form bonds to the peripheral sulphurs of the adjacent (non-commensurate) octahedral, SnS2- [i.e. (lll)-galena-] like layers of... 

T and H components are the same as in the yttrium oxyfluorides etc., but now they occur as strips intergrown in each layer the entire structure is divided by anti-phase boundaries perpendicular to the layers, with a slip vector R equal to half the unit-cell vector in the layer-stacking direction. These structures (often slightly monoclinic ) are CC types, with finite incommensiurate portions. They will be considered more fully in Chap. 6 below. Meanwhile, we will simply point out that anti-phase-boundary structures of this sort are strictly limited to ternaries with two cations and one anion. The related ternaries considered earlier in this section - those containing one cation and two anions - do not have these boundaries they are truly non-commensurate. This difference we take to be significant. 

Table 6. Combinations of layer types in non-commensurate layer structures. (Roman numerals conform to Sect. 5.2.)... 

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