Theoretical and experimental descriptions of grain boundaries in rhombohedral α-Al₂O₃

Abstract

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.

Disconnection arrays in a rhombohedral twin in α-alumina

“…In previous work, the characteristics of interfacial dislocations were analyzed on the basis of near coincidence descriptions for the rhombohedral symmetry [8,9]. In the present paper we report an exact characterization of line defects linked to rhombohedral twins using the topological theory of interfacial defects based on geometrical considerations [10].…”

Structure and chemistry of grain boundaries in yttria doped aluminas

“…Indeed, silicon contamination can arise from evaporation of the glassy phase probably present at the GB's of the commercial polycrystalline alumina fumace tube. [8,16]. The orientation of the GB plane is also determined.…”

“…At this stage, it seems useful to discuss the concept of speciality: in previous studies, so-called special GB's were close to a coincidence orientation relationship, the allowed angular deviation from the exact coincidence orientation being less than a limit that depends on 03A3 [6]; the orientation of the GB plane is not considered. It is recognized that there is no simple correlation between the existence of a 3D coincidence and a special property of a GB, i.e., there is no absolute criterion of speciality; however this geometrical criterion permits to make a first selection of GB's that are likely to present special properties, and has been found to account for particular GB mechanical properties [7,8]. This criterion will be retained in the present work as a starting point to precise the distribution of GB's in alumina polycrystals, but it does not assume necessarily a special GB segregation.…”

Atomistic modeling of dopant segregation in α-alumina ceramics: Coverage dependent energy of segregation and nominal dopant solubility

“…This sample contains however a significant proportion of highly special low Σ boundaries, which in real ␣-alumina microstructures constitute only a very small fraction of the grain boundary population. [38][39][40][41] An average taken only over high-Σ, high-energy boundaries, which should have more general character, is therefore likely to result in a better description of experiment. The average value of 5.29 La/nm 2 over the Σ93 (1 1 · 0), Σ13 (1 1 · 3) and Σ43 (2 2 · 3) boundaries shows that indeed these more general boundaries can accommodate a higher dopant content, as suggested by their more open structure (see Supporting Information Table S2 for coordinative environment).…”

“…[38][39][40][41] Therefore for the calculation of nominal solubilities representative of real microstructures, only the three high-energy, high-Σ grain boundaries Σ93 (1 1 · 0), Σ13 (1 1 · 3) and Σ43 (2 2 · 3) were considered. To limit the number of possible dopant configurations per unit cell, segregation was assumed to be limited to the 12 lowest energy sites for Y and Mg, and the 18 lowest energy sites for oxygen vacancies.…”