Tables are given of all coincidence orientations with multiplicity Z 9 3 6 for rhombahedral lattices with axial ratios in the range of corundum type structures (2.696 < c/a < 2.765). Measurements of the relative orientation of 133 pairs of neighbouring grains in sintered a-alumina showed that near-coincidence boundaries (14 cases) and one-dimensional coincidence boundaries (17 cases) occurred more frequently than would be the case for randomly distributed orientations and that many of these special boundaries contained periodic arrays of grain boundary dislocations. Their Burgers vectors have been determined for a rhombohedral twin boundary in order to decide which one among three possible coincidence descriptions best represents the boundary structure.
$1. INTRODUCTIONThe relative orientation of 133 pairs of neighbouring grains in sintered a-alumina has been determined using transmission electron microscopy (TEM). It has been found that relative orientations with symmetry translation vectors of both grains in near coincidence appear more frequently than would be the case for randomly distributed orientations. Near-coincidence grain boundaries often contain periodic arrays of dislocations, suggesting that small deviations from a low-energy boundary are compensated by grain-boundary dislocations. The experimental results are interpreted by means of systematic mathematical results on the exact or approximatecoincidence of symmetry translations of the rhombohedral lattices of neighbouring grains.The symmetry translations of two neighbouring grains of u-alumina form two rhombohedral lattices 1 and 2 respectively. If lattice 2 is obtained from lattice 1 by a 180" rotation around a lattice vector perpendicular to the threefold axis of lattice 1, then the two lattices will have vectors in common which form a three-dimensional lattice. Its traditional name coincidence site lattice is somewhat misleading because common translations do not imply the coincidence of sites. A more appropriate name is coincidence lattice (CL). The volume ratio of unit cells for the CL and the original lattice 014l%alO/90 3300 Q 1990 Taylor 8 Francis Ltd.
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.