The role of the inversion centre in texture analysis

Polycrystalline samples of non-centrosymmetrical enantiomorphic materials may be considered as two-phase materials consisting of a right-handed and a left-handed phase, each of which has its own texture. Centrosymmetrical crystals may be considered as right- or left-handed at the same time. If the right- and left-handed nature of the crystals is fully to be taken into account then the statistical sample symmetry is correctly to be described by black-white point groups rather than by the ordinary ones. If the sample symmetry does not belong to one of the `grey' groups then the series expansion of the texture functions contains terms of odd order which are blotted out in polycrystal diffraction experiments by virtue of the inversion centre in the crystal symmetry or by Friedel's law. In certain cases it seems possible, however, to obtain an approximation to the odd part by making use of the non-negativity condition in the zero ranges of the texture function. Many important physical properties are centrosymmetric (even if the crystals themselves are not). In these cases the odd part of the texture function does not enter into the expression relating the polycrystal property to the corresponding one of the single crystals.