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The ac (alternating current) conductivity of Pb5Al3F19 between 293 and 743 K has been analyzed within a combined complex impedance, modulus, and permittivity formalism. The antiferroelectric phase IV to ferroelastic phase III, and the phase III to paraelastic phase II, transitions have been characterized; the latter is shown to be accompanied by higher F− ion mobility above T=368±5 K. A new dielectric anomaly observed isochronously in e′(f,T) at 670 K corresponds to an expected, but hitherto unobserved, transition from phase II to the paraelectric prototype phase I of Pb5Al3F19. A 19F NMR investigation between 125 and 430 K of F− ion diffusion properties in Pb5Al3F19 shows that half the anions have become mobile at the ferroelectric phase V to phase IV transition temperature and that almost all the anions are mobile at the phase IV to phase III transition temperature. These motions are shown to be short range, and no correlation is found between phase formation and F− ion diffusion properties in Pb5Al3F19...

Lithium sulfate monohydrate has been studied at 293, 80, and 20 K by neutron diffraction using the same ground spherical crystal. Li2SO4⋅H2O is monoclinic, space group P21, with lattice dimensions at 293 K of a=5.450(3), b=4.872(3), c=8.164(4) A, β=107.31(3)°; at 80 K: a=5.449(2), b=4.832(2), c=8.141(2) A, β=107.21(1)°; and at 20 K: a=5.449(2), b=4.832(2), c=8.137(2) A, β=107.19(1)°. There are two formula units in the unit cell. Least‐squares refinement based on 1749 (293 K), 1712 (80 K), and 880 (20 K) reflections gave final R(F) values of 0.022, 0.016, and 0.014, respectively. All structure factors were corrected for thermal diffuse scattering. A Gram–Charlier expansion of the probability density function was used to describe the thermal vibrations of the water molecule which at 293 K are consistent with a previously postulated flipping motion. The O(W)⋅⋅⋅O(W) hydrogen bond distance is 0.091(3) A shorter and the O(W)⋅⋅⋅O(W)⋅⋅⋅O(W) angle is 3.9(1)° larger at 20 K than at 293 K: the O(W)⋅⋅⋅O(1) distance t...

Potassium cobaltous cyanoaurate(I), KCo[Au(CN)2]3, a new piezoelectric material that is also a component in the electrodeposition process for cobalt‐hardened gold, crystallizes in the trigonal system with space group P312 and one formula in the unit cell. The lattice constants at 298 K are a =6.82802±0.00005, c=7.80807±0.00009 A (λCuKα1=1.540598 A). The integrated intensities of most reflections within an extant of reciprocal space having radius (sin ϑ)/λ?1.15 A−1 were measured diffractometrically, resulting in 1130 independent nonzero structure factors. The crystal structure was solved by use of Patterson and Fourier series and refined by the method of least squares, with final agreement factor R=0.0578. The Au(CN)2− ion is close to linear, with Au–C distance of 1.994±0.011 A, C–N=1.147±0.014 A, and C–Au–C angle of 178.2±1.7°. The Co2+ ion occupies an octahedral environment, with six equal Co–N distances of 2.124±0.010 A. The K+ ion is 12‐coordinated with six N atoms at 2.950±0.022 A and six C atoms at 3...

Values of crystalline‐solid Debye temperatures depend both on the method and temperature of measurement. Simple relationships between Debye temperatures and such cohesive properties as compressibility and melting point were derived over 60 years ago by Madelung, by Einstein, and by Lindemann. Debye temperatures ΘXR of a number of piezoelectric semiconductors with chalcopyrite structure have been determined at room temperature by x‐ray diffraction. A new series of heat capacity measurements over the temperature range 1.2–40 °K, for four chalcopyrites, give ΘD values at 0 °K. A common proportionality is found between each of these ΘXR and ΘD values and microhardness, and also melting point: Acceptable reproducibility is given for the AIBIIICVI2 chalcopyrites and, separately, the AIIBIVCV2 compounds. Values of Θ are predicted for 15 additional chalcopyrites. Excellent proportionality between Θelastic and compressibility is found for the europium chalcogenides, based on the data of Shapira and Reed.

A new phase transition at 538 K has been found in Sr(NO2)2 with an entropy gain, on passing from phase II to phase I, of 18.9(9) J mol−1 K−1. On quenching, phase I is metastable to 296 K but reverts on heating to phase II at about 467 K. Phase II is orthorhombic, with lattice constants at 296 K of a=7.5320(8), b=8.1496(9), c=6.4820(8) A, and four Sr(NO2)2 per unit cell. Thermal expansion coefficients, as given by aT=a296[1+αΔT+β(ΔT)2], are: α(a)=33(4), α(b)=39(3), and α(c)=62(1)×10−6 K−1, β(a)=−119(17), and β(b)=61(13)×10−9 K−2, i.e., the thermal expansion of the a and b axes is nonlinear, that of the c axis is linear. The volume expansion, as given by VT=V296[1+βΔT], is linear with β(V)=123(2)×10−6 K−1. Phase I is cubic with a=7.5752(8) A at 538 K, α(a)=29(2)×10−6 K−1; crystals of phase I melt at 637 K. The increase in volume at the phase transition is 6.0%. The postulate of threefold positional disorder by the nitrite ions about the cubic body diagonals results in an expected entropy increase of R ln 9=...

Alpha‐cupric iodate, α‐Cu(IO3)2, is pyroelectric and piezoelectric at room temperature and crystallizes in the monoclinic space group P21 with two formulas in the unit cell. The lattice constants at 298 °K are a =5.56902 ± 0.00010, b=5.11098 ± 0.00009, c=9.26976 ± 0.00036 A and β=95.82 ± 0.02 ° (λCuKα1 − 1.540562 A). The integrated intensities of most reflections within a hemisphere of reciprocal space with radius (sinϑ)/λ?1.02 A−1 were measured on two different crystals using two different diffractometers, resulting in 1814 Fmeas for one set and 4272 Fmeas for the second set of independent structure factors. The crystal structure was solved using Patterson and Fourier series and refined by the method of least squares, the final agreement factor R becoming 0.063 for the first set, and 0.035 for the second set of Fmeas. The iodate ions form a nearly‐regular hexagonal closest‐packed array, with Cu2+ in the resulting octahedral interstices. The two independent iodate groups, each with three short I–O distanc...

CuGaSe2 and CdGeAs2 crystallize in the chalcopyrite‐type structure. The lattice constants of tetragonal CuGaSe2 are a = 5.5963 ± 0.0001 and c = 11.0036 ± 0.0002 A at 298 °K, those of CdGeAs2 are a = 5.9432 ± 0.0001 and c = 11.2163 ± 0.0003 A at 298°K. The space group is I42d with four formulas in a unit cell. 1747 reflections were measured with PEXRAD for CuGaSe2 and 1892 for CdGeAs2 using MoKα x radiation. Least squares refinement of the structural parameters using 149 symmetry‐independent CuGaSe2 and 300 CdGeAs2 structure factors led to final agreement factors of 0.035 and 0.038, respectively. CuGaSe2 is slightly Cu deficient: the value of the x coordinate in the final model is 0.2431 ± 0.0002, with considerable vibrational anisotropy. CdGeAs2 is stoichiometric: the final model has x = 0.2785 ± 0.0002, also with significant vibrational anisotropy, but less than that in CuGaSe2. The two compounds confirm the pattern of sublattice distortion in AIBIIIC2VI and AIIBIVC2V chalcopyrites previously found. The...

Cobalt cyanoaurate (I) Co[Au(CN)2]2 is a new material derived from cobalt‐hardened gold electroplating bath solutions that crystallizes in the hexagonal system with space group P6422 and six formula weights in a unit cell with a = 8.434±0.004 and c = 20.695±0.006 A at 298 K. The integrated intensities of a full sphere of reciprocal space, within a radius of (sin ϑ)/λ = 0.85 A−1, were measured using graphite monochromated MoKα with a CAD‐4 diffractometer. The resulting total of 12 037 structure factors gave 1969 terms after averaging, of which 717 were accepted as reliably observed. Patterson and Fourier series were used to solve the crystal structure, which was refined by the method of least squares: the final agreement factor R = 0.0358. The atomic thermal vibrations are highly anisotropic. The Au(CN)−2 ion departs slightly but significantly from linearity with a C–Au–C angle of 173.1±1.5° and mean Au–C–N angle of 170.6±1.7°. The cyano groups also form tetrahedral Co(NC)2−4 ions: conversion to the octahe...

Lithium sulfate monohydrate has been studied at 80 and 298 K by x‐ray diffraction. The monoclinic crystal with space group P21 has lattice dimensions at 298 K of a=5.4553(1), b=4.8690(1), c=8.1761(2) A, and β=107.337(2)°; lattice dimensions at 80 K were reported in our neutron study [J. Chem. Phys. 80, 423 (1984)]. Least‐squares refinement based on 3486 (80 K) and 3390 (298 K) independent reflections, assuming a spherical atom model, results in final R( F 2) values of 0.024 (80 K) and 0.026 (298 K). Static deformation and charge density model refinement, based on Hirshfeld‐type multipole functions, greatly reduces the residual electron density and gives R( F 2) values of 0.017 (80 K) and 0.016 (298 K). Refinement of the resulting multipole parameters within the Gaussian radial dependence model allows a qualitative estimation of the differences in electron densities between 80 and 298 K. A change of about 0.2 e A−3 in the deformation density of the O–H bonds in the water molecule over this temperature rang...

The laser and phosphor host material with nominal composition LaMgAl11O19 is shown to be nonstoichiometric. Czochralski grown crystals are hexagonal, with space group P63/mmc, and a=5.589 82(5), c=21.9738(12) A at 295 K. The thermal expansivity has been determined over the range 295 to 860 K: at 295 K, α1=4.97(2)×10−6 K−1 and α3=8.14(3)×10−6 K−1and at 775 K, α1=7.01(1)×10−6 K−1 and α3=10.1(2)×10−6 K−1. The integrated intensities of 20 487 reflections within a reciprocal lattice sphere of radius (sin θ)/λ=1.0 A−1 were measured on a CAD‐4 diffractometer with MoKα radiation, resulting in 18 232 reflections above background. Correction and averaging gave 864 independent structure factors with an internal agreement factor of 0.0145. The crystal structure was solved from the Patterson function and Fourier series and refined by the method of least squares. The final agreement factor R=0.013 98. The composition corresponds to La1−xMgAl11+xO19, with x=0.0502(8): the La deficiency is exactly compensated by excess A...

MnB4O7 is paramagnetic at room temperature, with effective paramagnetic moment of 5.84 μB, and orders antiferromagnetically at about 3°K. The lattice constants of orthorhombic MnB4O7 are a =8.62354±0.00003, b =14.0071±0.0001, c =8.07237±0.00002 A at 298°K, with space group Pbca and eight formulas in the unit cell. A total of 11 317 reflections were measured with PEXRAD resulting in 1060 symmetry‐independent structure factors. The structure was solved by a combination of Patterson and Fourier series and refined by the method of least squares. The final R factor for a model with all atoms undergoing anisotropic motion is 0.046. The structure is shown by half‐normal probability plot analysis to be accurately isomorphic to that of CdB4O7. The B4O7 group consists of two BO4 tetrahedra with one oxygen atom in common, each sharing two other oxygen atoms with two triangular BO3 groups. Each triangular group contains an oxygen atom from both tetrahedra. The dihedral angle between planes containing the two tetrahed...

Laevorotatory Bi12 SiO20 crystallizes in the cubic system with space group 123 and a=10.10433±0.00005 A at 298 K. The integrated intensities of 5488 reflections within a hemisphere of reciprocal space with (sinϑ/γ?1.15 A−L were measured with monochromatic MoKα radiation. A total of 977 independent and significantly nonzero Fmeas were used to determine the crystal structure by the method of least squares. The final agreement factor R=0.0316. The Si–O distance within the geometrically regular SiO4 tetrahedron is 1.647±0.005 A. The Bi–O bond distances, ranging from 2.064±0.009 to 2.647±0.003 A, with two additional contacts of 3.06 and 3.161 A formed by the Bi inert 6s2 electron pair are all within 0.025 A of the corresponding distances Bi12 GeO2. The absolute sense of the piezoelectric d14 coefficient is such that tensile stress along [111] generates positive polarity on (111), the face toward which the oxygen apex of the SiO4 tetrahedra points,i.e.,d1450. The magnitude of d14 was determined in a static expe...

Ba(NO2)2⋅H2O undergoes a sluggish reversible phase transition on heating to 350 K, followed by water loss to form the hemihydrate at about 425–435 K. The final half‐molecule of water is lost by 455 K. Differential thermal analysis, thermogravimetry, differential scanning calorimetry, infrared spectroscopy, x‐ray diffraction, and optical microscopic techniques were used. The entropy change of 36 J K−1 mol−1 measured at the phase transition is consistent with five new orientations becoming available to each water molecule above 350 K, accompanied by related reorientations of the two independent NO2− ions as new hydrogen bonds are formed. Both the high temperature monohydrate and the hemihydrate phases are unstable.

Lead tungsten oxyfluoride, Pb5W3O9F10, is a new ferroelectric material that crystallizes in the tetragonal system with space group I4 and four formulas in the unit cell. The lattice constants at 295 K are a=14.583(3) and c=7.365(1) A for λ(MoKα1,2)=0.709 30, 0.713 59 A. The integrated intensities of all 10 757 reflections within a reciprocal hemisphere of radius (sin θ)/λ ≤0.91 A−1 were measured on a CAD‐4 diffractometer with MoKα radiation and resulted in 7080 F2m ≥2σF2m. Correction for linear anisotropic radiation damage, followed by averaging the symmetry equivalent reflections, gave 2933 independent 〈 F2m〉≥2σ〈 F2m〉 with internal agreement factor Rint〈Fm〉 =0.0289.The crystal structure was solved from the Patterson function and difference Fourier series and refined on w〈 F2m〉 by the method of least squares. The final agreement factors between measurement and model were R=0.0382 and wR=0.0329 on 〈 Fm〉. The as‐grown crystal contained equal volumes of ±Z domains. The three independent tungsten atoms form WO6, WO3F3, and WO2F4 octahedra, and the three independent lead atoms form two different PbO4F5 and a PbO4F4 polyhedron. The major local dipole contribution to the spontaneous polarization is associated with a tungsten atom that is displaced 0.172(43) A from the center of its octahedron. The corresponding predicted Curie temperature is 590(260) K, in agreement with the experimental value of 785(15) K. All six metal atoms undergo anharmonic thermal vibrations, which are fitted either to fifth or sixth order in a Gram–Charlier expansion of the probability density function. The average interatomic distances are W–F=1.798(8) A, W–O=1.944(18) A, Pb–F=2.68(19) A, and Pb–O=2.72(21) A: standard deviations are from Bessel’s relationship. The atomic rearrangement required in forming Pb5W3O9F10 from PbF2 and WO3 is discussed, and similarities and contrasts between the related families for which Pb5W3O9F10, SrAlF5, and Sr3(FeF6)2 provide the archetype structures are considered. All three families exhibit ferroelectric behavior.

Nickel bromine boracite Ni3B7O13Br is a fully coupled ferroelectric–ferroelastic crystal with a Curie temperature of 398 K that crystallizes in the orthorhombic system with space group Pca21 and four formula units per unit cell. The lattice constants at 298 K are a = 8.5218±0.0002, b = 8.5127±0.0002, and c = 12.0408±0.0002 A. The integrated intensities of 11 682 reflections were measured with an Enraf‐Nonius CAD‐4 diffractometer using monochromatic Mo Kα radiation and a small single‐domain crystal. The crystal structure was refined by the method of least squares, using the coordinates of isomorphous Mg3B7O13Cl as the initial model, with 1531 symmetry‐independent Fmeas. The final agreement factor is 0.0492, based on anisotropic thermal vibrations for all atoms. Six independent boron atoms form tetrahedra with nearest‐neighbor oxygen atoms at an average B–O distance of 1.478 A. The remaining B(3) is 0.140 A from a plane formed by three oxygen atoms, wth average B–O = 1.378 A, and is 2.198 A from a fourth oxygen. Each Ni has four O neighbors at 2.024 A, one Br at 2.667 A, and a more distant Br at 3.370 A, on average. Two ferroelectric–ferroelastic tranformation mechanisms are applicable, each fully coupled. In the first, the sense of the spontaneous polarization is reversed as the spontaneous strain is reoriented: it has a magnitude calculated to be about 0.9×10−2 C m−2, based on a point charge model. The largest atomic displacement in this transformation is 0.72 A for a Ni2+ ion: All other displacements are less than 0.5 A. In the second mechanism, the spontaneous polarization is rotated through 90° as the spontaneous strain is also reoriented: it has a calculated magnitude of 2.6×10−2 C m−2. The largest corresponding atomic displacement is 0.60 A for a Ni2+ ion. As‐grown crystals could be only partially detwinned in an electric or a stress field. Ni3B7O13Br is closely isomorphous with Mg3B7O13Cl, the largest difference between coordinates of corresponding atoms being only 0.175 A, with an average difference of 0.055 A.

Strontium nitrite monohydrate [Sr(NO2)2⋅H2O] has been studied at 294, 100, and 20 K by neutron diffraction. Integrated intensities of 2958 (294 K), 4239 (100 K), and 2154 (20 K) reflections were measured at the Brookhaven National Laboratory high flux beam reactor, resulting in 2068 (294 K), 2030 (100 K), and 1934 (20 K) independent structure factors. Structural refinement in monoclinic space group P21 led to R(F)=0.029 (294 K), 0.019 (100 K), and 0.034 (20 K). Lattice constants at 295 K are a=12.5831(4), b=8.94941(15), c=4.4860(2) A, β=99.111(4)°; at 100 K, a=12.539(2), b=8.909(1), c=4.475(1) A, β=99.086(20)°; and at 20 K, a=12.542(2), b=8.901(1), c=4.472(1) A, β=99.030(20)°.The expansivity of all four lattice parameters is nonlinear, with α1=32.8×10−6 K−1, β1=76×10−9 K−2; α2=31.6×10−6 K−1, β2=44×10−9 K−2; α3=15.6×10−6 K−1, β3=15×10−9 K−2; α4=−2.8×10−6 K−1, β4=−21×10−9 K−2 for αTi =α295i [1+αiΔT+βi(ΔT)2], ΔT=T−295 K. The mean‐square amplitude of Sr varies linearly with temperature between 20 and 294 K, a...

K2Cd2(SO4)3 is orthorhombic below 432°K, with space group P212121, and cubic above with space group P213. A structural study has been completed at 298, 351, 390.5, 417.5, and 443.5°K based, respectively, on 3383, 1377, 1803, 1724, and 1022 symmetry‐independent structure factors. Measurement of integrated intensities was made using a CAD‐4 diffractometer with Nb‐filtered MoKα radiation. An air‐flow microfurnace with temperature controller provided a thermal stability better than ±1°. The a, b, c lattice constants in the orthorhombic phase are 10.2084(8), 10.2813(8), 10.1684(8) A at 298°K; 10.2239(8), 10.2897(8), 10.1821(8) A at 351°K; 10.2386(8), 10.2951(8), 10.1981(8) A at 390.5°K; and 10.2501(10), 10.2972(8),10.2132(9) A at 417.5°K. In the cubic phase, a=10.2704(10) A at 443.5°K. The model previously obtained at room temperature [J. Chem. Phys. 67, 2146(1977)] was refined by the method of least squares using the new sets of measurements. The final agreement factors are R=0.028 (298°K), 0.032(351°K), 0.02...

Neutron diffraction studies of barium nitrite monohydrate [Ba(NO2)2⋅H2O] have been made at 20, 102, and 298 K on the same crystal. Intensities of 954 (20 K), 2179 (102 K), and 2393 (298 K) reflections were measured at the Brookhaven National Laboratory high flux beam reactor. The structures were refined on the basis of the hexagonal space group P65 to yield agreement factors R(F2) = 0.028 (20 K), 0.034 (102 K), and 0.061 (298 K). The thermal expansion is nonlinear along both a and c axes, with α1 = 3.8×10−6 K−1, β1 = 2.8×10−8 K−2, α3 = 21.3×10−6 K−1, β3 = 10.9×10−8 K−2. The cell dimensions are a = 7.0524(24) A, c = 17.6372(80) A at 20 K, a = 7.0559(23) A, c = 17.6810(77) A at 102 K, and a = 7.074 90(3) A, c = 17.890 87(12) A at 298 K. The mean‐square amplitude of thermal motion of Ba is proportional to temperature in the range 298 to 20 K, with small departures from linearity for the O and N amplitudes and larger departures for the H nuclear amplitudes. The Ba2+ ion is coordinated by nine oxygen atoms and one nitrogen atom at an average distance of 2.881 A at 20 K, 2.884 A at 102 K, and 2.902 A at 298 K. The increase in length corresponds completely to the lattice expansion. A maximum difference within a nitrite ion of 0.015 A in N–O bond lengths, observed at 298 K, is reduced to 0.008 A at 20 K for a mean N–O distance of 1.254 A. One O–H bond of 0.958 A, which forms a bifurcated hydrogen bond with two oxygen atoms, is identical in length to that in the free water molecule; the other is slightly elongated by formation of a nearly linear hydrogen bond to a nitrogen atom. The largest nuclear displacement between 298 and 20 K in this pyroelectric crystal is only 0.038 A along the polar axis.

X‐ray diffraction and specific heat measurements have identified two independent strain‐coupled processes in a broad phase transition at about 400 K and a normal lambda‐type phase transition at 434 K in K2TeBr6 between 20 K and decomposition at 590 K. Phase I is cubic Fm3m with four K2TeBr6 per unit cell, a435=10.7456(14) A, and expansion coefficients to third‐order of α=0.134(3)×10−3 A K−1, β=0.198(17)×10−6 A K−2, and γ=0.162(27)×10−9 A K−3: it transforms on cooling to phase II at 434 K with an entropy change of 1.3 J mol−1 K−1. Phase II is tetragonal, P4/mnc, with two K2TeBr6 per unit cell, a410=7.5755(10) and c410=10.7702(22) A, with expansion coefficients to third‐order for the tetragonal a axis identical to those of the cubic a axis, and linear coefficient αc=−0.103(12) ×10−3 A K−1: it transforms on cooling to phase III at about 400 K with an entropy change of 2.9 J mol−1 K−1. Phase III is monoclinic, P21/n, with two K2TeBr6 per unit cell, a295=7.4908(10), b 295=7.5492(7), c295=10.6984(11) A, β 295=9...

Na(H3O)[I(OH)3O3] is pyroelectric at room temperature and crystallizes in the space group R3 with lattice constants at 298 °K of a=6.04272(6) and c=13.23165(2) A for CuKα1 =1.54062 A. There are three formulas in the unit cell. The integrated intensities of 2081 structure factors, within two‐thirds of a sphere of reflection with (sinϑ) λ?1.2 A−1, were measured on a CAD‐4 diffractometer with Nb‐filtered MoKα radiation. The crystal structure was solved by Patterson and Fourier series methods and refined by the method of least squares with 1102 symmetry‐independent Fmeas. The final agreement index R =0.015 for a model in which all atoms undergo anisotropic thermal vibration except for the hydrogens, which were refined with isotropic temperature factors. The I(OH)3O3−2 ion is octahedral, with I–O distance of 1.844(2) A and I–OH distance of 1.920(2) A. Strong hydrogen bonds of 2.544(1) A connect oxonium and I(OH)3O3−2 ions in sheets normal to the polar axis. Weaker intersheet hydrogen bonds of 2.697(2) A connec...

Tb2(MoO4)3 is orthorhombic below Tc=436 K with space group Pba2 and tetragonal above with space group P421m. The crystal structure, previously studied at 298 K, has been determined at four higher temperatures. The integrated intensities of 2909, 1325, 1340, and 1310 symmetry‐independent structure factors were measured, respectively, at 373, 438, 463, and 523 K with a CAD‐4 diffractometer using graphite monochromatized MoKα radiation. The lattice constants at 373 K are a=10.3625(13), b=10.3936(18), c=10.6446(29) A. A face‐centered tetragonal cell with space group C4m21, for orientation identical to that of the orthorhombic cell, has lattice constants a=10.4107(4), c=10.6273(1) A at 438 K; a=10.4126(4), c=10.6267(1) A at 463 K; and a=10.4167(4), c=10.6257(1) A at 523 K. The final agreement factors following structural refinement by the method of least squares are R=0.0274(373 K), 0.0145(438 K), 0.0176(463 K) and 0.0322(523 K). Atomic displacements from the positions occupied at 438 K are greater, by as much as 0.1 A, at 298 K than those at 373 K: above Tc, the largest comparable displacement is 0.02 A. The atomic displacements required for polarization reversal or strain reorientation at 373 K are less than those at 298 K by a maximum of slightly over 0.1 A. Differences in the atomic paths followed under the application of an electric or stress field from those in a thermal field are highly significant, ranging in length to more than 0.2 A for two oxygen atoms. Two of the three independent MoO42− tetrahedra vibrate highly, the third somewhat less, anisotropically both above and below Tc. The three independent tetrahedra rotate gradually from the positions occupied at Tc, through angles less than 8°, as the crystal is cooled to 298 K.

Cesium dithionate, Cs2S2O6, is moderately strongly piezoelectric at room temperature and crystallizes in the hexagonal system with space group P63mc and two formula units in the unit cell. The lattice constants at 298 K are a=6.356 58±0.000 04 and c=11.539 07±0.000 04 A (λCuKα1=1.5405 98 A). The integrated intensities of most reflections with (sin ϑ)/λ?1.08 or 1.15 A−1 were measured using two crystals and diffractometers. The first crystal gave a total of 1116 independent Fmeas, the second gave two separate sets of structure factors: 415 Fmeas with the crystal having received more radiation exposure than the first crystal and a further 431 Fmeas with still greater radiation exposure. The crystal structure was solved from the Patterson function and Fourier series and refined by the method of least squares. The final agreement factor R=0.033 for the first set, 0.049 and 0.060 for the second two sets of Fmeas. The crystal undergoes x‐irradiation damage, with some reflections decreasing in integrated intensit...

K3Ta3B2O12 is a new piezoelectric material that crystallizes in the hexagonal system with space group P62m and one formula unit in the unit cell. The lattice constants are a = 8.781 58±0.000 04 and c = 3.899 02±0.000 02 A at 298 K (λCuKα = 1.540 598 A). The integrated intensities of a full sphere of reciprocal space, with radius (sin ϑ)/λ?1.15 A−1, were measured with a CAD‐4 diffractometer and resulted in 1050 independent reliable structure factors. The crystal structure was solved by means of Patterson and Fourier series and was refined by the method of least squares, with final agreement factor R = 0.0133. Corner‐sharing triads of TaO6 octahedra are stacked along the c axis and are connected by planar BO3 groups. The resulting large trigonally girdled pentagonal prismatic interstices are occupied by the K+ ions. The average Ta–O distance is 1.973 A in a strongly distorted octahedron. The B–O distance is 1.364±0.004 A and the average K–O distance is 2.992 A. The absolute sense of each polar axis has bee...

Paramagnetic α‐Nd2(MoO4)3, prepared below the transition temperature of 960°C, crystallizes in a subtle variant of the scheelite structure. The lattice constants of the basic tetragonal unit cell are a = 5.298 ± 0.007 and c = 11.705 ± 0.023 A, with space group I41/a and 43 of a Nd2(MoO4)3 formula per unit cell. The ordered distribution of two Nd atoms over every three available sites results in additional weak scattering corresponding to a monoclinic unit cell with a = 27.02, b = 11.705, and c = 11.85 A, with β = 105.3°, space group C2. The integrated intensities of 2490 scheelitelike reflections within a reciprocal hemisphere of radius (sinθ) / λ = 1.02 A−1 were measured with PEXRAD, of which 198 were independent and above background. Refinement of the atomic positions, assuming a statistical distribution of 23 Nd on each scheelite 4b site, resulted in an agreement factor between measured and calculated structure factors of 0.0375. Each Nd atom is dodecahedrally coordinated to eight oxygen atoms, with four Nd–O distances of 2.492 ± 0.010 A and four others of 2.509 ± 0.011 A. Each Mo atom occupies a tetrahedron of oxygen atoms, with four identical Mo−O distances of 1.800 ± 0.011 A. An arrangement of Nd atoms and vacancies in the monoclinic cell giving a predicted scattering pattern in satisfactory agreement with observation is presented.

Barium cobalt fluoride, BaCoF4, ferroelectric and paramagnetic at room temperature, crystallizes in the orthorhombic system with lattice constants a = 5.8519 ± 0.0003, b = 14.628 ± 0.002, and c = 4.2102 ± 0.0003 A at 298°K and space group A21am. The integrated intensities of 1526 reflections within a hemisphere of reciprocal space of radius (sinθ) / λ = 1.02 A−1 were measured with one crystal, and 2986 reflections with a second crystal of BaCoF4, using PEXRAD. The crystal structure was refined by the method of least squares, using 386 symmetry‐independent Fmeas from the first crystal and 875 from the second. The combined set of 1261 Fmeas, together with anisotropic thermal coefficients for all atoms, resulted in a final agreement factor R = 0.0679. The structure is isomorphous with BaMnF4 and contains CoF6 octahedra sharing corners to form puckered sheets parallel to (010). These sheets are linked by Ba2+ ions only. The octahedra are distorted, with Co–F distances ranging from 1.972 to 2.109 A, with an av...

Paramagnetic DyMn2O5 crystallizes in the orthorhombic system with lattice constants a=7.2940±0.0008, b=8.5551±0.0008, and c=5.6875±0.0008 A, in the space group Pbam(D2h9). There are four DyMn2O5 per unit cell. The crystal structure was solved by a combination of three‐dimensional Patterson and Fourier series and refined by the method of least squares. The integrated intensities of 5094 reflections were measured by PEXRAD, with 976 symmetry‐independent structure factors significantly above background. The final agreement factor between measured and calculated structure factors is 0.0401. There are two independent Mn atoms. One is pentacoordinated, with a slightly distorted tetragonal pyramidal configuration: two basal Mn–O distances are 1.926±0.006 A, the other two are 1.911±0.005 A, and the apical Mn–O bond, nearly normal to the basal plane, is 2.020±0.005 A. The other Mn occupies a slightly compressed octahedron, with four planar Mn–O bonds of 1.940±0.004 A and two, normal to this plane, of 1.873±0.004 A...

Ammonium iodate, NH4IO3, is pyroelectric at room temperature and crystallizes in the orthorhombic system with space group Pc21n and four formulas in the unit cell. The lattice constants at 297°K are a = 6.4115 ± 0.0005, b = 9.1706 ± 0.0005, and c = 6.3740 ± 0.0005 A. The integrated intensities of 4591 reflections within a hemisphere of reciprocal space of radius (sinθ) / λ = 1.02 A−1 were measured using PEXRAD. The crystal structure was solved by Patterson and Fourier series and refined by the method of least‐squares using 1458 symmetry independent Fmeas. The final agreement factor R is 0.054, based on a model with anisotropic iodine and oxygen and isotropic nitrogen thermal vibrations, and with a spherical distribution of hydrogen around the nitrogen atom. The structure consists of discrete IO3− pyramidal ions arranged to give a highly distorted octahedral environment about the iodine. The IO3− ions and NH4− ions form chains parallel to the polar axis. Three I–O distances are in the range 1.765–1.836 A a...

Sc2(WO4)3, diamagnetic above 30°K, crystallizes in the orthorhombic system, Space Group Pnca, with lattice constants a=9.596±0.004, b=13.330±0.003, and c=9.512±0.004 A at 298°K. The complete x‐ray scattering pattern within a reciprocal lattice hemisphere of radius (sinθ)/λ=1.02 A−1 was measured with PEXRAD. The crystal structure was solved by use of three‐dimen sional Patterson and Fourier series and refined by the method of least squares, using 1731 independent structure factors. The final agreement factor R is 0.0622. Scandium atoms occupy slightly distorted octahedra, with average Sc–O=2.063 A and Sc–O distances ranging from 2.026±0.015 to 2.124±0.010 A. Two crystallographically independent W atoms are surrounded by somewhat distorted tetrahedra: the W–O distances vary from 1.695±0.009 to 1.829±0.016 A, the average being 1.761 A. The thermal vibrations are significantly anisotropic. Sc2(WO4)3 forms the structure type for 23 trivalent metal tungstates and molybdates, including the nine smaller rare‐earth tungstates. The larger rare‐earth tungstates, crystallizing in the Eu2(WO4)3 structure type, have 8 coordination about the rare‐earth ion; the smaller have 6 coordination. A simple correlation is found between the variation in radius ratio due to the lanthanide contraction and the change in coordination.

Beta‐gadolinium molybdate, β‐Gd2(MoO4)3, is ferroelectric and ferroelastic with a Curie temperature of about 160°C and is paramagnetic with a moment of 7.98 μB. β‐Gd2(MoO4)3 crystallizes in the orthorhombic system with space group Pba2 and four formulas in the unit cell. The lattice constants at 298°K are a = 10.38582 ± 0.00014, b = 10.41861 ± 0.00010, and c = 10.70039 ± 0.00004 A. The integrated intensities of 14 490 reflections were measured with PEXRAD, within a hemisphere of reciprocal space of radius (sinθ) / λ = 1.02 A−1. The crystal structure was solved by interpretation of Patterson and Fourier series and refined by the method of least squares, using a total of 2545 symmetry independent Fmeas. The final agreement factor R is 0.089, based on isotropic thermal vibrations for all atoms. X‐radiation exposure introduces appreciable nonrandom error in the Fmeas. The structure consists of three crystallographically independent discrete sets of (MoO4)2− tetrahedra; one set is oriented with apex oxygen ato...

Silver thiogallate, AgGaS2, is a representative member of the AIBIIIC 2VI family with chalcopyrite structure. AgGaS2 is strongly piezoelectric and is phase matchable for second harmonic generation. The lattice constants of this tetragonal crystal are a = 5.75722 ± 0.00003 and c = 10.3036 ± 0.0002 A at 298 °K. The space group is I 42d, with four formulas per unit cell. The integrated intensities of 1978 reflections were measured within a hemisphere of reciprocal space having radius (sin θ)/λ = 1.02 A−1 using PEXRAD, resulting in 268 symmetry‐independent structure factors. The x coordinate of sulfur (0.2908 ± 0.0004) is 0.088 A less than the value calculated on the assumption of a geometrically regular tetrahedral bond distribution about the B atom. By contrast, four AIIBIVC2V compounds previously reported have x coordinates for the Cv atom either slightly greater than (for ZnSiP2, CdSiP2, and ZnSiAs2), or not significantly different from (for ZnGeP2) that calculated. The experimental Ag–S distance is 2.556...

A neutron diffraction study of CuF2·2H2O below the Neel point has determined the crystal and magnetic structure. As compared with this crystal at 298°K, the long Cu–F axial bonds of the distorted octahedron around the Cu2+ ion are reduced in length from 2.465±6 to 2.391±4 A: the short Cu–F bond of 1.899±6 A and the Cu–O bond of 1.945±4 A are unchanged. The H–O–H angle is reduced from 115.5° at 298°K to 110.1±0.4° at 4.2°K, and the O–H distance from 0.980±7 to 0.959±5 A. The amplitudes of vibrational displacement of the Cu, O, and F atoms at 4.2°K are about one‐half that at 298°K: The hydrogen atoms have about the same motion, due to zero‐point energy. The magnetic unit cell is identical with the nuclear cell, but the spin on the body‐centered copper atom is antiparallel to that at the origin. The spin direction is very nearly along the c axis, although an alternative model with the spin along the long octahedral direction fits the magnetic scattering almost as well. The difference between the Neel temperature of 10.9° and that of 26°K at which the magnetic susceptibility is a maximum is consistent with the observed magnetic structure. The revised nuclear scattering length for fluorine of 0.529×10—12 cm found in the analysis of CuF2·2H2O at 298°K is in excellent agreement with the experimental value of 0.534±12 obtained in the present study.

A neutron‐diffraction study of Fe3(PO4)2·4H2O below the Curie temperature has determined both the crystal and the magnetic structure. At 4.2°K, the crystal remains monoclinic, with lattice constants a=10.541±0.010, b=4.638±0.008, c=9.285±0.010 A, β=100°43.7′±4.0′ and two formula weights in the unit cell. The nuclear and Shubnikov space groups are both P21/a. The iron—oxygen octahedral distances range from 2.019±0.010 through 2.317±0.010 A, with average distance 2.154 A. The phosphate group is very nearly a regular tetrahedron, with the phosphorus—oxygen distance ranging from 1.521±0.008 through 1.553±0.007 A. The average O–H distance is 1.00 A, and the shortest O–H···O bond is 2.546±0.005 A. The magnetic unit cell coincides with the nuclear cell. The spins on each linear triad of iron atoms, separated by 3.267±0.004 A, are ferromagnetically coupled and are essentially parallel. Triad spin components in the ac plane, related by the screw‐axis or glide‐plane operators, are antiferromagnetically coupled. Spi...

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 A 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....

Paramagnetic alpha‐MnMoO4, the stable phase at STP, is monoclinic with lattice constants a=10.469±0.005, b=9.516±0.005, c=7.143±0.005 A, and β=106°17′±6′, and space group C2/m. The crystal structure has been solved and refined by a combination of three‐dimensional Patterson and Fourier series and by the method of least squares. 1873 independent integrated intensities were measured by PEXRAD; the final agreement factor between measured and calculated structure factors is 0.0574. Two crystallographically independent Mn atoms are surrounded by highly distorted oxygen octahedra; the Mn–O distance varies between 2.091±0.006 and 2.252±0.003 A, with average length 2.164 A. Two crystallographically independent Mo atoms are surrounded by slightly distorted oxygen tetrahedra, with Mo–O distances ranging from 1.724±0.005 to 1.851±0.004 A, the average being 1.761 A. The thermal vibrations are significantly anisotropic. An analysis is given of various current methods for estimating the standard deviation in the measur...

A neutron determination of the crystal structure of cupric fluoride dihydrate at 298°K has been made. The structure consists of puckered sheets of nearly square CuF2O2 groups, linked together by hydrogen bonds of 2.715±6 A, with the sheets connected by longer Cu–F bonds to form distorted octahedra around the Cu2+ ions. Dimensions within the octahedra are, two Cu–O distances of 1.941±5, two Cu–F of 1.898±8 and two Cu–F of 2.465±6 A. The long F–Cu–F axis is inclined at 7½° from the normal to the plane containing the remaining CuF2O2 group of the octahedron. The Cu–O bonds bisect the H–O–H angle of 115.5±0.4°. The O–H bond is 0.980±7 A and the O–H···F angle is 164.9±0.7°. The amplitudes of thermal displacement of the atoms along various directions are given. The nuclear scattering length of fluorine is revised to 0.529±13 (10—12 cm).

The x‐ray scattering by two different rutile crystals, within a hemisphere of reciprocal space having radius (sin θ) /λ=1.02 A−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 A. The Ti–O distances are 1.9800±0.0009 and 1.9485±0.0005 A. 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 bo...

ZnSiP2 crystallizes with the chalcopyrite structure: there is no detectable difference in x‐ray scattering between luminescent and nonluminescent crystals. The level of impurity, either in the form of chemical dopant, physical defect, or a departure of less than about 1% from complete order at the Zn and Si sites hence determines if the crystal luminesces or not on excitation by an electron beam. The lattice constants of this tetragonal crystal at 298°K are a = 5.399 ± 0.001 and c = 10.435 ± 0.002 A. The space group is I42d, and there are four formulas in the unit cell. A total of 2023 reflections were measured with the luminescent crystal, and 1600 with the nonluminescent crystal, using pexrad. The final agreement factor, based on a combination of 197 symmetry‐independent reflections from the first crystal and 176 from the second, is 0.049. Each Zn is tetrahedrally surrounded by 4 P atoms at 2.375 ± 0.001 A distance, and each Si by 4 P atoms at 2.254 ± 0.001 A. All phosphorus tetrahedra have four P–P ed...

Paramagnetic Fe3(PO4)2·4H2O is monoclinic, with lattice constants a=10.541±0.005, b=4.646±0.004, c=9.324±0.005 A and β=100°25.8′±1.0′ at 298°K, with two formula weights in the unit cell. The space group is P21/a. The positions of the iron, phosphorus, and oxygen atoms, determined by Ito and Mori in 1951, together with those of the hydrogen atoms, have been refined by the method of least squares. The integrated intensities of 6212 reflections in a reciprocal lattice hemisphere of radius (sinθ)/λ=1.02 A−1 were measured with PEXRAD; 1919 symmetry‐independent F(hkl) were significantly above background. The final agreement factor between measured and calculated structure factors was 0.0336. There are two crystallographically unrelated iron atoms per unit cell, each occupying a distorted oxygen octahedron; the iron—oxygen distances range from 2.016±0.002 through 2.362±0.002 A. The average distance is 2.156 A. The phosphate group is very nearly a regular tetrahedron, the range in P–O distance being from 1.536±0....

The crystal structure of Ga2—xFexO3, with 0.7≤x≤1.4, has been determined at 298°K by x‐ray diffraction. Ga2—xFexO3 crystallizes in the orthorhombic system, space group Pc21n, with lattice constants a = 8.7512±0.0008, b = 9.3993±0.0003, c = 5.0806±0.0002 A and eight formula weights in the unit cell. The complete scattering pattern was measured with PEXRAD to (sinθ)/λ≤1.02 A−1. One gallium atom in the asymmetric unit is in a tetrahedral site, the other gallium and the two iron atoms are in octahedral sites. For x>1, the excess iron partly occupies the octahedral gallium site: the iron sites are to a smaller extent occupied by gallium. The gallium tetrahedron is very nearly regular, with Gatetr−0 = 1.846±0.005 A. The gallium octahedron is irregular, with average Gaoct−0 = 2.026±0.004 A; the iron octahedra are somewhat more irregular, with average Feoct−0 = 2.036±0.004 and 2.049±0.004 A in the two crystallographically independent octahedra. The oxygen atoms pack in pseudohexagonal layers with a double‐hexagon...

BaMnF4, pyroelectric at room temperature and paramagnetic above 30°K, crystallizes in the orthorhombic system with space group A21am and lattice constants a = 5.9845 ± 0.0003, b = 15.098 ± 0.002, and c = 4.2216 ± 0.0003 A at 298°K. The integrated intensities of 5085 reflections within a reciprocal lattice hemisphere of radius (sinθ) / λ = 1.02 A−1 were measured using pexrad. The crystal structure has been solved and refined by a combination of Patterson and Fourier series and the method of least squares, using 455 independent and significantly nonzero F(meas). The final agreement factor R, for atoms with anisotropic temperature coefficients, is 0.0466. The structure consists of MnF6 octahedra sharing corners to form puckered sheets parallel to (010). These sheets are linked by Ba2+ ions only, giving rise to excellent (010) cleavage. Within the sheets there are nearly linear –Mn–F–Mn–F– chains parallel to c. Parallel to a there is a second set of planar zigzag –Mn–F–Mn–F– chains, formed by adjacent shared ...

Piezoelectric Bi12GeO20 crystallizes in the cubic system with space group I23 and lattice constant a = 10.1455±0.0008 A at 298°K. The complete x‐ray scattering pattern within a reciprocal lattice hemisphere of radius (sinθ)/λ = 1.02 A−1 was determined with PEXRAD. A total of 4812 reflections were measured, resulting in 631 independent and significantly nonzero Fmeas. The crystal structure was solved using three‐dimensional Patterson and Fourier series, and refined by the method of least squares. The final agreement factor R is 0.062. The germanium atoms occupy geometrically regular tetrahedra, with Ge–O=1.717±0.028 A. The bismuth atoms are heptacoordinated: five oxygen atoms form an incomplete octahedral arrangement, with Bi–O distances ranging from 2.076±0.027 to 2.640±0.028 A. The remaining two oxygen atoms are electrostatically coordinated, on either side of the 6s2 inert electron pair in Bi3+, at distances of 3.082 and 3.170 A from bismuth. The Bi atom vibrates anisotropically. The absolute configuration of the atomic arrangement has been determined. The positive piezoelectric polarization induced by compressive stress applied along 〈111〉 is given by the normal to a triangular GeO4 tetrahedral face in the direction from the Ge atom to the face.

Nickel iodate dihydrate, paramagnetic at room temperature and weakly ferromagnetic below 3 °K, crystallizes in the orthorhombic system with space group Pbca and four formulas in the unit cell. The lattice constants at 298 °K are a = 9.14986 ± 0.00008, b = 12.20896 ± 0.00022, and c = 6.58353 ± 0.00013 A. The crystal structure has been investigated independently in two laboratories. In one, the integrated intensities of 8883 reflections were measured with PEXRAD, within a hemisphere of reciprocal space of radius (sinθ)/λ = 1.02 A−1. In the other, all independent reflections with (sinθ)/λ ≤ 0.70 A−1 were measured on a Nonius automatic three‐circle diffractometer. The crystal structure was solved by interpretation of Patterson and Fourier series, and refined by the method of least squares, using respectively 824 or 864 symmetry‐independent structure factors. The final agreement factor is 0.047 for one set and 0.048 for the other, based on anisotropic temperature coefficients for all atoms except hydrogen, for which isotropic values were used. The structure consists of a network of corner‐sharing IO6 octahedra with the Ni ions occupying octahedral interstices at the inversion centers. The water oxygen forms part of the octahedra around Ni, and is not directly bonded to I. The IO6 octahedra are highly distorted, with three I–O distances in the range 1.801–1.820 A and three more in the range 2.804–2.935 A. The NiO6 octahedra are almost regular, with Ni–O distances in the range 2.042–2.062 A and O–Ni–O angles in the range 88.3–89.9°. The hydrogen atoms of the water molecule were detectable, and refinement gave acceptable molecular dimensions. Normal probability plot analysis was used to compare the results of the two independent structural investigations.

A neutron‐diffraction study of LiCuCl3·2H2O in the temperature range 1.4°—5.1°K, together with a magnetic susceptibility study in the range 1.4°—300°K, has determined its magnetic and crystal structure. The crystal contains linear Li–Cu–Cu–Li, planar Li2Cu2Cl6 groups. Each cation is at the center of a distorted octahedron, of composition LiCl3O3 and CuCl5O: the four octahedra share Cl–Cl edges. The most important distances in this complex are Cu–Cl at 2.25, 2.34, and 2.96 A; Cu–O at 2.56 A; Li–O at 2.04 and 2.18 A; Li–Cl at 2.44 and 2.97 A; Li–Cu at 3.34 A; and Cu–Cu at 3.47 A. The ``nonbridging'' Cl atoms in the Li2Cu2Cl6 group form OH···Cl bonds of 3.17 and 3.26 A to other complexes in the crystal. The spins (S = ½) on the Cu2+ within each complex are antiparallel and lie on the 3.47‐A Cu–Cu internuclear line. The spin‐density maximum is displaced 0.15 A from the nearest neighbor Cu2+ of opposite spin. The neutron‐scattering data indicates dx2—y2 to be the ground‐state orbital. Above a critical field Hc...

Ferroelectric K(6−x−y)Li(4+x)Nb(10+y)O30, with x ≃ 0.07, y ≃ 0.23, and a Curie temperature of 613°K, crystallizes with a tungsten bronze‐type structure in the tetragonal system. The lattice constants are a = 12.5764 ± 0.0002 and c = 4.0149 ± 0.0001 A at 298°K. The space group is P4bm. There is one formula per unit cell. The integrated intensities of 6578 structure factors, inside a reciprocal hemisphere of radius (sinθ) / λ = 1.02 A−1, were measured with PEXRAD. There are 998 symmetry‐independent Fmeas significantly above background. Isomorphism with BaxSr(5−x)Nb10O30 allowed the metal atom positions to be deduced. Oxygen atom positions were obtained by Fourier series methods. Refinement of structural parameters by the method of least squares resulted in a final agreement factor R = 0.0401. The structure is generally like that of other tungsten bronzes of formula (A1)2(A2)4C4(B1)2(B2)8O30, with the A1 site occupied by 87% K and 13% Li, the A2 site by 99% K and 1% Li, and the C site by 94% Li and 6% Nb. Th...

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 A at 298 °K, and of CuInS2 are a = 5.52279 ± 0.00007 and c = 11.13295 ± 0.00022 A 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 A in CuGaS2 and 2.335 ± 0.001 A in CuInS2, the Ga–S distance is 2.288 ± 0.001, and In–S is 2.464 ± 0.002 A. 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.

Ferroelectric Ba(4+x)Na(2 − 2x)Nb10O30, with a Curie temperature of 833°K, has a tungsten bronze‐type structure and crystallizes in the orthorhombic system, with subcell lattice constants a = 17.59182 ± 0.00001, b = 17.62560 ± 0.00005, and c = 3.994915 ± 0.000004 A at 298°K. The space group is Cmm2, and there are two formulas in the subcell. The c axis of the true cell is double that of the subcell. The integrated intensities of 6911 reflections within a reciprocal hemisphere of radius (sinθ)/λ = 1.02 A−1 were measured with PEXRAD, 1873 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 metal‐phased Fourier series. The final agreement index between measured and calculated structure factors is 0.0579. The structure differs only in detail from previously determined tetragonal tungsten bronze structures. In the general formula (A1)2(A2)4C4(B1)2(B2)8O30, the B1 and B2 sites are fully occupied by Nb, the A2 sites by Ba and the A1 site by 87.0% Na and 6.5% Ba. Evidence from chemical analysis, x‐ray density calculations and the present determination suggests that the best approximation to the formula of the crystal studied is Ba4.13Na1.74Nb10O30. The Ba and O atoms at z ≃ 12 are disordered in a manner similar to the O atoms in the Ba layer in barium strontium niobate. The four crystallographically independent Nb atoms, each in octahedral coordination, are linked to O atoms by distances ranging from 1.765 ± 0.021 to 2.270 ± 0.021 A, with a mean value of 1.989 A. Ba is 10 coordinated, with Ba–O distances ranging upward from 2.671 ± 0.013 A. Na is 12 coordinated, with Na–O distances ranging from 2.660 ± 0.014 to 2.990 ± 0.015 A, with a mean of 2.788 A. The Nb‐atom displacements from the mean oxygen planes lie in the range 0.171–0.205 A; the parabolic relation with Curie temperature predicts a displacement of 0.204 A. The measured value of Ps at room temperature is 40 μC cm−2: the linear relation between displacement and polarization predicts a saturation value of 44–53 μC cm−2. All metal atoms are displaced from the oxygen planes in the sense given by the macroscopic positive polarity.

CdSiP2 is a typical member of the AIIBIVC2V family with chalcopyrite structure. The x‐ray scattering for luminescent and nonluminescent material is essentially identical: The atomic order at the Cd and Si sites is at least 99.8% complete. The lattice constants of this tetragonal crystal are a = 5.680 ± 0.001 and c = 10.431 ± 0.003 A at 298°K. The space group is I42d, and there are four formulas per unit cell. A total of 2370 reflections from a nonluminescent crystal, and 2156 from a luminescent CdSiP2 crystal, were measured with PEXRAD. Least squares refinement, based on 320 symmetry‐independent reflections from both crystals, led to a final agreement factor of 0.047. Normal probability plot analysis shows the least squares derived standard deviations to be underestimated by a factor of 3.0, and the two sets of measured structure factors to possess a small parallel bias. The bond angles about the Si atom do not differ significantly from the regular tetrahedral angle of 109.47°. Regular tetrahedral bond a...