The crystal structure of β-Ga2O3 has been determined from single-crystal three-dimensional x-ray diffraction data. The monoclinic crystal has cell dimensions a=12.23±0.02, b=3.04±0.01, c=5.80±0.01 A and β=103.7±0.3° as originally reported by Kohn, Katz, and Broder [Am. Mineral. 42, 398 (1957)]. There are 4 Ga2O3 in the unit cell. The most probable space group to which the crystal belongs is C2h3—C2/m; the atoms are in five sets of special positions 4i: (000, ½½0)±(x0z). There are two kinds of coordination for Ga3+ ions in this structure, namely tetrahedral and octahedral. Average interionic distances are: tetrahedral Ga–O, 1.83 A; octahedral Ga–O, 2.00 A; tetrahedron edge O–O, 3.02 A; and octahedron edge O–O, 2.84 A. Because of the reduced coordination of half of the metal ions, the density of β-Ga2O3 is lower than that of α-Ga2O3 which has the α-corundum structure. Also the closest approach of two Ga3+ ions in β-Ga2O3 is 3.04 A which is considerably larger than the closest approach of metal ions in the sesquioxides with the α-corundum-type structure and, in agreement with the results of thermodynamic measurements, the β phase appears to be the structurally more stable one. The average Ga–O distances in the structure seem to account for the fact that although the Ga3+ ion is substantially larger than the Al3+ ion its quantitative preference for tetrahedrally coordinated sites when substituted for Fe3+ ion in the iron garnets is very nearly the same as that of the Al3+ ion. The structure accounts for a recent result obtained by Peter and Schawlow from paramagnetic-resonance measurements on Cr3+-ion-doped β-Ga2O3, namely that the Cr3+ ion substitutes for the Ga3+ ions in a single set of equivalent octahedral sites. The magnetic aspects of the β-Ga2O3 structure are discussed and it is shown that a possible Fe2O3 isomorph could be expected to be at least antiferromagnetic with a Néel temperature of about 700°K Furthermore, a knowledge of the β-Ga2O3 structure and of the nature of site preferences of the Ga3+ and Fe3+ ions in the garnets lead to a prediction regarding the structure of the ferrimagnetic crystals of formula Ga2—xFexO3 recently discovered by Remeika.
The aluminates of the trivalent ions of Gd, Eu, and Sm are isostructural with GdFeO 3. They belong to space group YD~-Pbnm with four distorted perovskite units in the true crystallographic cell. The aluminates of the trivalent ions of Nd, Pr and La are rhombohedral belonging to space group D~d--R3m with two formula units in the unit cell. These crystals bear a very close structural relationship to the orthorhombie ones.LaA103 undergoes a transition at 435±25 ° C. to the simple cubic cell containing one formula unit. Evidently, the transition is one of higher than first order. There is no crystallographic transition of PrAI03 below 950 ° C. but a gradual change toward the cubic phase similar to that in LaAl03 is indicated. 1020 CRYSTALLOGRAPHIC STUDIES OF PEROVSKITE-LIKE COMPOUNDS. II
The crystal structure of gadolinium orthoferrite, GdFeO3, has been determined from single-crystal x-ray data. There are four GdFeO3 distorted perovskite units in the orthorhombic cell with lattice constants a=5.346, b=5.616, c=7.668, all ±0.004 A. The structure is solved on the basis that the most probable space group is D2h(16)— Pbnm. However, although the atomic coordinates lead to very good agreement between calculated and observed reflection amplitudes, there are at least very slight deviations from the centrosymmetric space group because the iron sublattices are imperfectly antiferromagnetic.
The high temperature modification of AgSbS%, AgSbTe 2, AgBiS~, and AgBiSe2 has a face-centered cubic statistically NaCl-type structure with Ag and Bi (or Sb) atoms distributed indistinguishably and on the average in one set of positions (0, 0, 0; 0, ½, ½; O) and the Group VI atoms distributed on the average in the other set of positions (½, ½, ½; 0, 0, ½; ~). Because it is extremely unlikely that the Ag, Bi and Sb atoms all have the same effective sizes in these compounds, at least one group of atoms (4(a) or 4(b)) must not be centered exactlyat the space group sites.For AgSbSe 2 and AgSbTe 2, the cubic structure persists at room temperature. However, in the cases of AgBiS~. and AgBiSe 2 an ordering of the Ag and Bi atoms takes place at temperatures well above room temperature. In the case of AgBiS% (on which most of the detailed work has been done), above 287 °C., the disordered NaCl-type exists; between 287 °C. and about 120 °C., a rhombohedral phase exists which belongs to space group D3d (5)-R3m with Ag in 1 (a) : (0, 0, 0), Bi in 1 (b) : ~-, ½) and Se in 2(c) : ± (x, x, x) with x ~ 0-26. The lattice constants of this phase at 240 °C. are a = 7.022 A, a ----34 ° 40". Between 120 °C. and 25 °C. (and probably lower), there is another phase. The most probable space group of this modification is Dad(3)-P3ml with three formula units per Lmit cell of dimensions a = 4.18:t:0.02, c ----19.67±0.05 A. This cell is the original triply primitive hexagonal cell on which the rhombohedral modification may be indexed but with slight additional displacements of the atoms. In particular, pairs of Ag and of Bi atoms are no longer in the most highly specialized positions, and the three pairs of Se atoms are no longer equivalent.The structure of the room temperature modification has been solved with the use of single crystal and powder X-ray diffraction data. Displacements of the atoms from the ideal positions are not large. Good agreement of calculated with observed intensities is obtained when parameters are adjusted such that the average Ag-Se and Bi-Se distances in AgBiS% are 2-83 and 3.01 A, respectively.The room temperature form of AgBiS~ is isostructural (a = 4.07+0.02, c = 19.06±0-05 A) with that of AgBiS% and presumably has an intermediate form analogous to that of AgBiSe2.
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