Selection rules for the double space group O1h

Abstract

The octahedral symmorphic space group O1h is the symmetry group of the simple cubic. the caesium chloride, the perovskites and the rhenium trioxide structures. The direct products of irreducible representations of the double space group O1h are reduced for the four points of highest symmetry of the Brillouin zone

Clebsch-Gordan coefficients for M x M in beta tungsten

“…tk }, { P-I tk }, { pk» tk-, } are calculated and are shown in table III. The first wave vectors satisfying the selection rule 5 km + 9 km = km are as shown in We transform by these space operations the small representations [26,27] Thus in the summation in eq. (4) the ordered group elements in the first factor, transformed from dkl, are dkM (1, 3, 4, 2, 25, 27, 28, 26), in the second factor, transformed from dk'l', are dkM (1, 4, 2, 3, 25, 28, 26, 27), and in the third factor, transformed from dk"l", are dkM (1,2,3,4,25,26,27,28).…”

“…For a computation of CG coefficients or scattering tensors an elaboration of the selection rules is a first necessary step. The selection rules for the double space group 0'(Pm3n) of the A-15 structure have been determined [26,27] and checked with an output of the computer program written for determining the reduction of the Kronecker products of the irreducible representations of crystallographic space groups [28,29].…”

Allowed symmetries of soft-modes in cubic crystals

“…T ) point according to Aleksandrov et al [5]. The comparisons of the labels of the IR's for 0'(Pm3m), 0'(Pm3n) and 0'(Pn3m) have been published in papers [40,[43][44][45].…”