Observations of the Gibeon meteorite and the inverse Greninger–Troiano orientation relationship

All the possible parallelism conditions associated with low-index crystallographic planes and directions in face- and body-centred cubic crystals are enumerated in terms of their minimum angle–axis misorientations. These include the Kurdjumov–Sachs (K-S), Nishiyama–Wassermann (N-W) and Pitsch orientation relationships, which are expressed in terms of close-packed (and near-close-packed) planes, close-packed directions, or both in the two crystal systems. By classifying these into either coplanar or codirectional relationships, it is possible to specify intermediate relations with either high-index directions or planes. In such a way, the Greninger–Troiano (G-T) relationship is approximated as a coplanar relation lying between the K-S and N-W relations. Based on geometric symmetry, a further correspondence relationship, which falls into the codirectional category and is located between the K-S and Pitsch relations, is represented both in pole-figure form and in Rodrigues–Frank space. It is referred to here as the inverse G-T, or G-T′. Experimental evidence from the plessite regions of the Gibeon meteorite is presented to support the validity of this relationship. It is shown that, in plessite, all the well known models, as well as their intermediates, are applicable to the γ-to-α transformation. By contrast, in the Widmanstätten portions, the misorientations are largely limited to the K-S, G-T and N-W relations.