Institute of Metals Division - Atomic Relationships in the Cubic Twinned State - Discussion

D. Whitwham, M. Mouflard, and P. Lacombe (British Council Research Fellow, Labratoire du Professor Chaudron, Vitry-sur-Seine; Inqenieur de Recherches, Labratoire de Vitry; and Maitre de Recherches, Labratoire de Vitry, Professeur Adjoint de Metallurgie, Ecole des Mines, Paris)—The authors' work is of great interest in bringing out the geometrical relations existing between twinned lattices, and for the notion of a coincidence super lattice developed from this. We should like to point out that a similar idea was put forward by Friedel8 in his book on the subject of lattice merohedrism "merihedrie réticulaire:"—When two crystals A and B are twinned with respect to a mirror plane, there exists a common superlattice, "réseau periode," which is independent of the contact surface between the two crystals. The volume V of this superlattice is a simple multiple of the volume v of the lattice of crystals A, or B, (Fig. 5). This "multiple cell" is defined by the twin plane (p q r) and a row of atoms [h k l] normal to this plane, the base being taken as the smallest unit (two-dimensional) of this plane. Two cases must be considered. First when the multiple cell, as defined, has no atom site at its center nor at the center of its faces other than (p q r), v the twinning index is defined by —. In the second v case, when one of the two above conditions does not v apply, then the twinning index is V 2v A more intuitive definition of the twinning index would be the proportion of atoms of C, which would coincide with those of C1 when the C, lattice is imagined to extend on the other side of the contact surface. In the case of cubic crystals, the twinning index