Non-commensurate (misfit) layer structures.

We consider incommensurate structures of the type which have two more or less independent, though modulated, sub-lattices derived from misfitting layers of two types, alternating regularly in the layer-stacking direction. These are the two-dimensional analogues of the so-called “chimney-ladder” structures (which are one-dimensional). 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 brucite-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. 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. [ABSTRACT FROM AUTHOR]