J. L. Bernstein

Ferroelectric Tungsten Bronze‐Type Crystal Structures. I. Barium Strontium Niobate Ba0.27Sr0.75Nb2O5.78

Ferroelectric Ba0.27Sr0.75Nb2O5.78, with Tcu2009=u2009348°u2009±u200915°K, is a tungsten bronze‐type structure crystallizing in the tetragonal system, with lattice constants au2009=u200912.43024u2009±u20090.00002 and cu2009=u20093.91341u2009±u20090.00001 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 cu2009/u20092. 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....

Ferroelectric Tungsten Bronze‐Type Crystal Structures. II. Barium Sodium Niobate Ba(4 + x)Na(2 − 2x)Nb10O30

Ferroelectric Ba(4+x)Na(2u2009−u20092x)Nb10O30, with a Curie temperature of 833°K, has a tungsten bronze‐type structure and crystallizes in the orthorhombic system, with subcell lattice constants au2009=u200917.59182u2009±u20090.00001, bu2009=u200917.62560u2009±u20090.00005, and cu2009=u20093.994915u2009±u20090.000004 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)/λu2009=u20091.02 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 site...

Rutile: Normal Probability Plot Analysis and Accurate Measurement of Crystal Structure

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...

Piezoelectric nonlinear optic CuGaS2 and CuInS2 crystal structure: Sublattice distortion in AIBIIIC2VI and AIIBIVC2V type chalcopyrites

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 coo...

Crystal Structure of Piezoelectric Bismuth Germanium Oxide Bi12GeO20

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 configurat...

Crystal Structure of Pyroelectric Paramagnetic Barium Manganese Fluoride, BaMnF4

BaMnF4, pyroelectric at room temperature and paramagnetic above 30°K, crystallizes in the orthorhombic system with space group A21am and lattice constants au2009=u20095.9845u2009±u20090.0003, bu2009=u200915.098u2009±u20090.002, and cu2009=u20094.2216u2009±u20090.0003 A at 298°K. The integrated intensities of 5085 reflections within a reciprocal lattice hemisphere of radius (sinθ)u2009/u2009λu2009=u20091.02 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 ...

Ferroelectric Tungsten Bronze‐Type Crystal Structures. III. Potassium Lithium Niobate K(6−x−y)Li(4+x)Nb(10+y)O30

Ferroelectric K(6−x−y)Li(4+x)Nb(10+y)O30, with xu2009≃u20090.07, yu2009≃u20090.23, and a Curie temperature of 613°K, crystallizes with a tungsten bronze‐type structure in the tetragonal system. The lattice constants are au2009=u200912.5764u2009±u20090.0002 and cu2009=u20094.0149u2009±u20090.0001 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)u2009/u2009λu2009=u20091.02 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 Ru2009=u20090.0401. 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...

Crystal Structure of the Transition‐Metal Molybdates and Tungstates. II. Diamagnetic Sc2(WO4)3

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‐eart...

Ferroelectric Ferroelastic Paramagnetic Beta‐Gd2(MoO4)3 Crystal Structure of the Transition‐Metal Molybdates and Tungstates. VI

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 au2009=u200910.38582u2009±u20090.00014, bu2009=u200910.41861u2009±u20090.00010, and cu2009=u200910.70039u2009±u20090.00004 A. The integrated intensities of 14 490 reflections were measured with PEXRAD, within a hemisphere of reciprocal space of radius (sinθ)u2009/u2009λu2009=u20091.02 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...

Luminescent Piezoelectric CdSiP2: Normal Probability Plot Analysis, Crystal Structure, and Generalized Structure of the AIIBIVC2V Family

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 au2009=u20095.680u2009±u20090.001 and cu2009=u200910.431u2009±u20090.003 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...