On the anion and cation positions within and nearby R(101¯2)$R(10\overline{1}2)$, Σ(202¯4)$\mathrm{\Sigma}(20\overline{2}4)$, and Π(101¯4)$\mathrm{\Pi}(10\overline{1}4)$ planes of α‐Al₂O₃ corundum structure

Abstract

The positions of aluminum cations and oxygen anions within and nearby the 𝑅(10 12), 𝑅 ′ (30 36), Σ(20 24), and Π(10 14) planes of 𝛼-Al 2 O 3 corundum structure are determined and compared with the corresponding ion positions within and nearby their conjugate-adjacent planes 𝑟(1 102), 𝑟 ′ (3 306), 𝜎(2 204), and 𝜋(1 104) planes. The plane 𝑅(10 12) contains neither aluminum nor oxygen ions, while the planes 𝜋(1 104), Σ(20 24), and 𝜎(20 24) contain only oxygen anions, whose planar densities are 𝜌 𝜋 = 6∕nm 2 and 𝜌 Σ = 𝜌 𝜎 = 8.2∕nm 2 . The planes 𝑅 ′ (30 36), 𝑟 ′ (3 306), and 𝑟(1 102) contain only aluminum cations with planar densities 𝜌 𝑅 ′ = 8.2∕nm 2 and 𝜌 r = 𝜌 r ′ = 5.47∕nm 2 . The Π(10 14) plane contains both aluminum and oxygen ions, whose planar densities are 𝜌 Al Π = 4∕nm 2 and 𝜌 O Π = 6∕nm 2 . The nearest ions to the 𝑅(10 12), 𝑟(1 102), 𝑅 ′ (30 36), and 𝑟 ′ (3 306) planes are at a normal distance of 0.58 Å from these planes, which is one-half of the normal distance between the adjacent 𝑅 and 𝑅 ′ , or 𝑟 and 𝑟 ′ planes. The ions nearest to the Σ(20 24) and 𝜎(2 204) planes are also at a normal distance of 0.58 Å from these planes. The nearest ions to the Π(10 14) and 𝜋(1 104) planes are 0.85 Å from these planes, which is one-half the interplanar spacing between the adjacent Π or 𝜋 planes.The obtained results are of interest for the evaluation of ionic bonding and surface energies, epitaxial film growth over differently oriented sapphire substrates, and for the analysis of plastic deformation and cleavage fracture of sapphire crystals under different loading and temperature conditions.