The (twin) composition plane as an extended defect and structure-building entity in crystals

The burden of this paper is the recognition of the composition plane as an extended (planar) “defect” in twinned crystals, together with the notion that new structure types may be generated from simple prototype structures by regular and frequent repetition of a twinning operation, usually on a very fine scale. Less regular application of the operation leads to disorder and variation in stoichiometry, without point defects being necessary.

The range of compounds whose structures may be described in these terms is very wide, from metal alloys through metal carbides and borides etc. and inorganic materials, such as metal oxides and sulphides, to minerals, including silicates and the “sulphosalts” of the heavy metals (Pb, Bi etc.). Isostructural compounds frequently span this whole gamut of substances.

The main reasons for the twinning appear to be () the generation of new types of interstices (not present in the prototype) of appropriate size for some of the constituent atoms, and/or (b) a variation in the concentration of appropriate interstices, i.e. in the stoichiometric ratio anion/cation.

After a general introduction to the relevant aspects of twinning, attention is successively concentrated on reflection-twinned h.c.p., then c.c.p. and finally mixed c.p. arrays: first with “interstitial” atoms only in the composition planes; and then with other interstices also occupied. In each case lamellar twinning is first considered, and then cyclic twinning. Glide-reflection-twinning of similar arrays is then considered.

Attention is also drawn to small topological distortions that, for example, convert the octahedra in a c.c.p. array (twinned or even un-twinned) to arrays of capped trigonal prisms (or to cubes). In this way the apparently complex structures of a number of compounds are derived from those of much simpler twinned c.c.p. arrays.

Finally, the not-very-large amount of available, relevant, experimental evidence is reviewed. As far as it goes, this confirms that the notion of the composition plane as an extended defect is well founded. But more experimental data are needed.

[In most cases specific literature references are provided for each structure. For a few, rather common, structures they are not. In such cases reference may be made to standard texts, e.g. for alloys, to Schubert⁹⁹ or Pearson¹³³ and, for more ionic structures, to Wyckoff¹³⁴ or Povarennykh¹³⁵. Diagrams are to scale: 1 cm = 4.0 Å.]