The role of the inversion centre in texture analysis

Abstract

Polycrystalline samples of non-centrosymmetrical enantiomorphic materials may be considered as twophase materials consisting of a right-handed and a lefthanded phase, each of which has its own texture. Centrosymmetrical crystals may be considered as rightor left-handed at the same time. If the right-and lefthanded 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.

Twin relationships of 5M modulated martensite in Ni–Mn–Ga alloy

“…4e and f, respectively. The resultant orientations, specified with a set of three Euler angles (in Bunge's notation [26]) with respect to the sample coordinate system, are given at the bottom right of each indexed pattern. Note that the two patterns indexed with the modulated monoclinic superstructure represent two different orientations ( Fig.…”

Determination of the orientation relationship between austenite and incommensurate 7M modulated martensite in Ni–Mn–Ga alloys

“…By convention, individual orientations acquired by EBSD measurement are represented by a set of rotations (expressed in Euler angles [31]) transforming the macroscopic sample coordinate system to the orthonormal crystal coordinate system. In this study, the orthonormal crystal coordinate system is linked to the monoclinic …”

Crystallographic textures

“…Hence the ODF is generally written as the sum of an even part, which can be determined from experimental data, and an odd part which has no effect on PF but, if neglected, may induce artefacts and spurious peaks (named "ghost peaks") in the ODF. Several methods have been developed to deal with this issue which is especially critical in non-centrosymmetric crystal symmetries [12][13][14][15][16].…”