Ferroelectric Ba0.27Sr0.75Nb2O5.78, with Tc = 348° ± 15°K, is a tungsten bronze-type structure crystallizing in the tetragonal system, with lattice constants a = 12.43024 ± 0.00002 and c = 3.91341 ± 0.00001 Å at 298°K, space group P4bm, and five formulas in the unit cell. The integrated intensities of 6781 structure factors were measured with PEXRAD, 875 symmetry-independent structure factors being significantly above background. The metal-atom positions were determined from the three-dimensional Patterson function and the oxygen atoms from subsequent Fourier series. The final agreement factor between measured and calculated structure factors is 0.0508. The structure consists of close-packed slightly puckered layers of oxygen atoms separated by nearly c / 2. The Nb atoms are slightly displaced from one layer, the Ba and Sr atoms from the other and in the same sense. The oxygen atoms in the Ba and Sr layer are disordered. Neither of the two independent sites occupied by the Ba and Sr atoms is fully filled. The 2a site is preferred by Sr, which is in distorted cubo-octahedral coordination; the Sr–O distances range from 2.547 ± 0.008 Å to 2.919 ± 0.008 Å. The 4c site, occupied by Ba and Sr, has distorted tricapped trigonal prismatic symmetry; the Ba/Sr–O distances range from 2.604 ± 0.009 Å to 3.035 ± 0.010 Å. The two independent Nb atoms fully occupy the 2b and 8d sites and are each in relatively regular octahedral coordination. The 2b site has Nb–O distances ranging from 1.92 ± 0.03 Å to 2.03 ± 0.03 Å; the 8d-site Nb–O distances range from 1.88 ± 0.03 Å to 2.11 ± 0.03 Å. A ferroelectric mechanism is proposed in which the metal atoms in the 2a, 2b, and 4c sites move, at the Curie temperature, into the oxygen layers. These metal atoms then acquire 4̄,222, or 2 point symmetry, respectively, as the space group transforms to P4̄b2. The remaining Nb atoms, in the 8d position, also rearrange so as to have half above and half below the oxygen layer. The absolute displacements of the metal atoms from their nearest mean planes of oxygen atoms, in space group P4̄bm, are directly related to the ferroelectric polarization sense.

The X-ray scattering pattern of hexagonal ZnO at 298°K, within a reciprocal lattice hemisphere of radius (sin 0)/2= 1.02 A,-~ containing the polar c* axis as diameter, was measured with PEXRAD. The integrated intensities of 374 reflections, resulting in 141 independent Fracas, were determined. The structure was refined by the method of least squares: the final agreement index R was 0"0378. The sole position parameter is u = 0.3825 + 0.0014. The predicted value is 0.3799, obtained from the measured c/a ratio of 1.602107 and assuming equal Zn-O distances in the ZnO4 tetrahedra. The characteristic Debye temperature O, in isotropically vibrating ZnO, is 370°K. The absolute configuration of the ZnOa tetrahedra is such as to present a triangular oxygen face normal, directed from the face, toward the positive sense of the piezoelectric polarization as induced by a compressive stress applied along the polar axis. The piezoelectric coefficients are predicted to have a small temperature dependence.

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The x-ray scattering by two different rutile crystals, within a hemisphere of reciprocal space having radius (sin θ) /λ=1.02 Å−1, was measured at 298°K with PEXRAD. The integrated intensities of 780 reflections from each crystal were determined, resulting in 136 symmetry independent Fmeas from Crystal 1 and 122 Fmeas from Crystal 2. The crystal structure was refined by the method of least squares: The agreement factor R for all Fmeas is 0.0286, and the single position parameter x(0)=0.30479±0.00010. Normal probability plot analysis shows the least squares derived standard deviations are underestimated by 33%, and the two sets of Fmeas contain an appreciable parallel bias. The lattice constants, measured at or corrected to 298°K on two different crystals, are a=4.593659±0.000019 and c=2.958682±0.000008 Å. The Ti–O distances are 1.9800±0.0009 and 1.9485±0.0005 Å. Pairs of shorter bonds define O–Ti–O angles of 81.21° and 98.79°, forming a plane normal to the two longer bonds. The resulting octahedral Ti–O bond arrangement is apically extended, as is found in all AIVB2 compounds with rutile structure: The remaining nine well-determined non-Group IV AB2 family members contain, without exception, apically compressed AB6 octahedra. Bauer and Khan's, and also Niizeki's, x-ray results on rutile are compared with the present measurements.

CuGaS2 and CuInS2 are typical AIBIIIC2VI members of the chalcopyrite structure family. The lattice constants of tetragonal CuGaS2 are a = 5.34741 ± 0.00007 and c = 10.47429 ± 0.00006 Å at 298 °K, and of CuInS2 are a = 5.52279 ± 0.00007 and c = 11.13295 ± 0.00022 Å at 298 °K. Both materials have four formulas in a unit cell with space group I 42d. A total of 984 reflections for CuGaS2 and 1413 for CuInS2 were measured with PEXRAD, and the resulting 134 symmetry-independent CuGaS2 and 310 CuInS2 structure factors, in least-squares refinement, led to final agreement factors of 0.029 and 0.038, respectively. Both materials are slightly nonstoichiometric. Final x coordinates are 0.2593 ± 0.0004 for CuGaS2 and 0.2295 ± 0.0004 for CuInS2. As was also found with AgGaS, these values are significantly different from those expected for a geometrically regular B atom tetrahedron. The resulting sublattice distortion is predictable from a linear sum of atomic electronegativities, which is also used to predict the x coordinate and interatomic bond lengths in 17 other AIBIIIC2VI chalcopyrites. The sublattice distortion in AIIBIVC2V chalcopyrites is generally small, but also significant. The experimental Cu–S distance is 2.312 ± 0.001 Å in CuGaS2 and 2.335 ± 0.001 Å in CuInS2, the Ga–S distance is 2.288 ± 0.001, and In–S is 2.464 ± 0.002 Å. The amplitudes of thermal vibration for the A and B atoms in AgGaS2, CuGaS2, and CuInS2 are essentially isotropic, with considerable anisotropy in the C atom motion.