Determination of all misorientations of tetragonal lattices with low multiplicity; connection with Mallard's rule of twinning.
Two congruent lattices are considered, which are misoriented in such a way that they have a fraction 1/Sigma of symmetry translations in common. Whereas for cubic lattices body or face centring does not affect the 'multiplicity' or 'twin index' Sigma, this is not generally true for tetragonal lattices. Consider a fixed misorientation and let Sigma(P) and Sigma(I) be the multiplicities for tP and tI lattices with the same axial ratio c/a. Grimmer [Mater. Sci. Forum (1993), 126-128, 269-272] has given an explicit formula for Sigma(P) (depending on the misorientation and the axial ratio) and showed that Sigma(I) = Sigma(P)/2, Sigma(P) or 2Sigma(P). Here stronger results on the occurrence of the three possibilities are presented. Lists of all axial ratios c/a of tP and tI lattices admitting misorientations with Sigma < or = 5 are given. For each of these misorientations, the twin mirror planes and their normals are listed, so that a synopsis of all possible twin laws of tetragonal crystals by reticular merohedry with Sigma < or = 5 is obtained. It is shown that the two twin laws observed in beta-Sn can be described by reticular pseudomerohedry with Sigma(I) = 2 and obliquity delta = 2.6134 degrees.
Grimmer
Hans
H
Laboratory for Neutron Scattering, ETHZ and PSI, CH-5232 Villigen PSI, Switzerland. hans.grimmer@psi.ch