Besides the so-called β-Al2O3 (R2O·11Al2O3; R=Na or K), there have been found two kindred compounds with approximate formulas, R2O·7Al2O3 (β′-Al2O3) and R2O·5Al2O3(β″-Al2O3). The structure determination of the latter two compounds was undertaken; the results are compared with the structure of β-Al2O3 in the present paper. These three structures are composed of spinel layers of the same configuration. The structures of β and β′ are very similar to each other, both equally bearing a layer-stacking according to a two-fold screw symmetry, while β″ differs from these two in exhibiting another way of layer-stacking, according to a three-fold screw symmetry.

Highly crystallized θ-alumina was obtained by a two-step treatment, by hydrothermal and thermal treatment, of η-alumina. Its X-ray-powder diffraction pattern was interpreted based on the structure of θ-gallia, and least-squares refinements were carried out. The electron diffraction pattern of θ-alumina from boehmite was also interpreted, and the directional relations between the phases were established.

A compound between aluminum oxide and aluminum nitride can be produced in a reductive atmosphere above 1650°C. A new spinel formula AlN–Al2O3 should be adopted instead of the previous one Al2O–5Al2O3 or Al3O4. The physical constants of AlN-Al2O3 are as follows: crystal structure Fd3m, Z=8, a=7.940 Å; density 3.78g./cc.; dielectric constant 23.8; refractive index 1.80; magnetic susceptibility −0.34×10−6/g

The dehydration of tohdite 5Al2O3·H2O is well followed by means of the single-crystal electron-diffraction patterns, the X-ray powder patterns, differential thermal analysis, and the measurement of the density. Thermogravimetric measurements were also performed, both under a normal atmosphere and in a high vacuum. Just after the dehydration, an unstable intermediate phase was obtained; it was denoted as κ′-Al2O3(from tohdite). The mechanism of the transformation series: tohdite→κ′-Al2O3→κ-Al2O3→α-Al2O3 was discussed, and some basic data to serve as clues to elucidate the crystal structure of κ′- and κ-Al2O3 were obtained.

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