Misfit layer structures

In the book by Hyde and Andersson (1989), the Nowotny phases are presented as a special case of a group of ID, columnar misfit structures which also include compounds such as Bam(Fe2S4) and other complex sulphides. Layer misfit structures, such as those of some oxide-fluorides, arseno-sulphides, etc., are also presented and classified with reference to a concept of structure commensurability based on the recognition that (along one or more axes) the ratios between the different repeat units of various interpenetrating substructures can (or cannot) be represented as ratios between integer numbers. 

But our concern here is with the two-dimensional cases layered misfit structures, in which the lack of commensurability is between the intralayer periodicities of layers of two types, which alternate regularly through the structure. The layers may be simple or complex (i.e. composite groups of several, physically distinct layers). In most cases the two layer types compensate each other s valency and consequently alternate with strict regularity, forming double-layer or two-component layered structures. Both intralayer identity vectors of one layer set A) may differ fi-om those of the other layer set (B), so that each layer set has its own periodicities, and the vectors defining the net common to both (if it exists) are more or less complicated resultants (e.g. lowest common multiples) of these basic, intralayer vectors. In some cases the basic vectors are identical in one... 

Known examples of layered misfit structures are listed in Tables 1 to 5. It is interesting that they have been recognised, and independently described as such, in at least four instances Cowley and Ibers Allmann, Lohse and Hellner Makovicky " and Hyde et al.. (The general absence of rigid, two-dimensional layers in organic structures suggests that layered misfit structures will be improbable for organic compounds. We know of no examples.)... 

In the layered misfit structures each layer set A and B can be described in terms of three basic translations, i.e. by its own component lattice. [The existence of the third vector is contingent upon a strict sequence in the layer stacking. If this is absent, the two three-dimensional subcells/lattices will, in the following discussion, be replaced by two two-dimensional subcells, i.e. by submeshes (nets) built only on the intralayer vectors.] In normal layered structures the unit cells of A and B are commensurate, i.e. their unit vectors are commensurable and the periodicity of the entire structure may be described in terms of a single unit cell. In contrast, we deal with those less-frequent cases in which this is not so at least one of the basic periodicities of A and of B are incommensurate. Then the component unit cell of set A has at least one intralayer unit cell parameter which is not commensurable with the corresponding parameter of set B. Such structures have two incommensurate, interpenetrating, component lattices and can be defined as composite) layered structures with two incommensurate component unit cells. Intermediate cases, in which the nodes of the two component lattices coincide at relatively large... 

The terms incommensurate and semi-commensurate are analogous to incoherent and semi-coherent for interfaces - in grain boundaries, heterophase interfaces and epitaxial layers (cf. also Nabarro - with which layered misfit structures have much in common. In extreme cases noncommensurability may arise by mutual rotation (to varying degrees) of component layers with identical component lattices... 

A considerable number of layer-misfit structures have brucite-like hydroxide layers M(0H)2 (see Fig. 7 a and A in Fig. 5) as one component, the cation sites being occupied by Mg and Fe and/or AP. The presence of the trivalent cations ensures a positively-charged layer, i.e. unsaturated valences. 

Among the complex natural and synthetic sulphides of lead, tin, antimony, bismuth and arsenic, often with minor amounts of iron, copper and/or silver, there is another group of layer-misfit structures. And recently a synthetic lanthanum-chromium sulphide has been described which is closely related to them structurally. 

In layered misfit structures of the type we are discussing, bonds at the layer surfaces (within and between the layers) will be strained periodically along a non-commensurate lattice direction parallel to the layers after a certain number of subcells there is a near match of the layers. Clapp has pointed out that, for a simple case, layer mismatch will cause tension in one layer type and compression in the other. The resulting strain energy may be relieved by the introduction of periodic antiphase boundary (apb) planes so that alternate contraction and extension occurs in all layers (Fig. 22) and hence cancels out (at the price of a small deformation of coordination polyhedra). 

It would seem that such a strain-relieving mechanism could be an alternative to, or additional to, non-commensurability in layer misfit structures (with only one non-com-mensurate lattice vector). It is observed as an addition, converting non-commensurable to commensurable layer misfit structmes. ... 

Table 7. Selected compounds transitional between the layer-misfit structures and the CC structures. (Intralayer vectors are underlined.)... 

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.

G. A. Wiegers, Misfit Layer Compounds Structures and Physical Properties, Prog. Solid State Chem., 24, 1-139 (1996). 

The analysis in the last paragraph has shown that the incommensurate Xe layer on Pt(lll) at misfits of about 6% is a striped phase with fully relaxed domain walls, i.e. a uniaxially compressed layer. For only partially relaxed domain walls and depending on the extent of the wall relaxation and on the nature of the walls (light, heavy or superheavy) additional statellites in the (n, n) diffraction patterns should appear. Indeed, closer to the beginning of the C-I transition, i.e. in the case of a weakly incommensurate layer (misfits below 4%) we observe an additional on-axis peak at Qcimm + e/2 in the (2,2) diffraction pattern. In order to determine the nature of the domain walls we have calculated the structure factor for the different domain wall types as a function of the domain wall relaxation following the analysis of Stephens et al. The observed additional on-axis satellite is consistent with the occurrence of superheavy striped domain wails the observed peak intensities indicate a domain wall width of A=i3-5Xe inter-row distances. With... 

Makovicky Hyde (1981) have reviewed incommensurate misfit structures in graphite intercalation compounds, brucite-type compounds, sulphides and related layered systems. A simple two-dimensional incommensurate system is provided by graphite with adsorbed rare gas monolayers. At low densities and high temperatures. 

After an introductory discussion of such misfit structures, various terms that have previously been applied are reviewed, and degrees of incommensurability are used as the basis for a systematic nomenclature. The known structures of specific examples are then discussed graphite intercalates minerals with brudte-like layers as one component (koenenite, valleriite, tochilinites) silicates heavy metal sulphides (cylindrite, incaite, franckeite, cannizzarite, lengenbachite, lanthanum-chromium sulphide) anion-excess, fluorite-related yttrium oxy-fluorides and related compounds. 

Layer misfit was first recognised in the structures of two metal chloride-graphite intercalation compounds. Intercalates of graphite with many other metal halides, including fluorides and bromides, have since been reported, but they seem to be of the CC type and are not discussed here. 

On the other hand, if such flexibility is absent the layer misfit may be compensated by rolling up the double layers, producing a cylindrical (CC) structure on an atomic scale, as in chrysotile An alternative possibility is the undulatory double layers of, for example, antigorite where the misfit-compensating curvature changes its sense at regular intervals as a result of layer-switching [anti-phase boundaries, cf. (Zr,Nb)Oj, Sects. 4.4 and 6]. 

The interplay of variously capped (and oriented) trigonal coordination prisms with coordination octahedra is essential also for the complex lanthanide sulfides and the layer misfit compounds. Through the entire range of structures and compositions the relative plasticity (ability for minor adjustments) of large coordination polyhedra created around large or lone-electron-pair cations is of primary importance in the interlayer and interblock adjustments. 

Layered cobaltite ( 3300409) presents a misfit structure builtup with alternating single Cdl2-type [Co02]oo layers and triple [CaO-CoO-CaO] rock salt t3qie layers. The proposed structural model for involving a supercell with b 8hi 13 2 is shown in Scheme 5.4. This layered structure enables electrons behave in an anisotropic... 

Figure 4.17 The misfit structure of Ca3Co409 . The plane of edge-shared octahedral corresponds to a Cdli-type C0O2 layer. The second sublattice (in the centre) is made of three layers, 2 CaO layers surrounding a central layer made of...

The study of ultra-thin Fe thin films on Cu(OOl) substrate has attracted a lot of interest in the past. This is due to the abundance of interesting phenomena associated with this system. Due to the small epitaxial misfit a good layer by layer growth is expected stabilizing the film in a structure related to the fee phase of bulk Fe which is otherwise unstable at low temperatures It also become a test system for magnetic measurements. 

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

Of special interest to intercalation studies are complex non-stoichiometric systems, such as the so-called misfit layer chalcogenides that were first synthesized in the 1960s [45]. Typically, the misfit compounds present an asymmetry along the c-axis, evidencing an inclination of the unit cell in this direction, due to lattice mismatch in, say, the -axis therefore these solids prefer to fold and/or adopt a hollow-fiber structure, crystallizing in either platelet form or as hollow whiskers. One of the first studied examples of such a misfit compound has been the kaolinite mineral. 

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