R. Liminga

Neutron diffraction structural study of pyroelectric Li2SO4⋅H2O at 293, 80, and 20 K

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...

Structural temperature dependence in α‐lithium iodate: Neutron and x‐ray study between 20 and 500 K

The crystal structure of hexagonal α‐LiIO3 has been determined by neutron and x‐ray diffraction at ten temperatures from 20 to 500 K. Four sets (1248 to 1622 reflections per set) of neutron data at λ=1.0467 A were measured at the Brookhaven High Flux Beam Reactor at 20, 100, 200, and 295 K. The integrated intensities of a further 13 data sets (1706 to 2963 reflections per set) were measured using MoKα radiation on a CAD‐4 x‐ray diffractometer. The structure at each temperature was refined by least squares in space group P63. The final agreement factors fell between 0.023 and 0.050. The unit cell dimensions at 295 K are a=5.481 27(6), c=5.171 65(4) A, with nonlinear thermal expansions. The principal change in structure with temperature is in the atomic positions of Li and O relative to I: The positions are given by O(z)T=−0.8435(3) A+62(4)×10−9 T2 A K−2 and Li(z)T=0.3808(10) A+167 (18)×10−9 T2 A K−2. The iodate ion has a constant I–O bond length of 1.8081(4) A, but the O–I–O angle increases from 99.97(2)° ...

Pyroelectric Ba(NO2)2⋅H2O: Room temperature crystal structure

Barium nitrite monohydrate, Ba(NO2)2⋅H2O, is strongly pyroelectric at room temperature and crystallizes in the hexagonal system with space group P65, or the enantiomorphous P61, and with six formulas in the unit cell. The lattice constants at 298 K are a=7.074 90±0.000 03 and c=17.890 87±0.000 12 A (λCuKα1=1.540598 A). The integrated intensities of most reflections within a quadrant of reciprocal space having radius (sinϑ)/λ?1.15 or 1.08 A−1 were measured on two different crystals, each with different diffractometer, resulting in 3218 Fmeas for one set and 3671 Fmeas for the second set of independent structure factors. The crystal structure was solved from Patterson and Fourier series, and refined by the method of least squares. The final agreement factor R=0.026 for the first set, 0.018 for the second set of Fmeas. The two sets of Fmeas and the derived structural parameters are compared using normal probability plot analysis. The two NO−2 ions have a mean N–O distance of 1.246±0.002 A and O–N–O angle of ...

Neutron diffraction structural study of pyroelectricBa(NO2)2⋅H2O at 298, 102, and 20 K

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.

Gamma‐lithium iodate structure at 515 K and the α‐LiIO3 to γ‐LiIO3, γ‐LiIO3 to β‐LiIO3 phase transitions

The crystal structure of γ‐LiIO3 at 515 K has been determined by profile refinement of x‐ray diffraction powder data measured with a Hagg–Guinier focusing camera. The space group is Pna21, with lattice constants at 515 K of a = 9.422(2), b = 5.861(2), and c = 5.301(2) A. A model was derived from the Patterson function and by similarities with the α‐LiIO3 structure and refined by the method of least squares. For all 59 reflections resolved by the profile refinement method, RF = 0.109. The structural rearrangement at the α‐LiIO3 to γ‐LiIO3 phase transition involves ionic displacements of about 0.5 A, with consequent rotations of the iodate ion by about 20° and elongation of the oxygen octahedron about the Li+ ion. The symmetry change from point group 6 to mm2 is accompanied by unit cell doubling and an increased separation between layers of iodate ions normal to [100]. A further unit cell doubling occurs at the γ‐LiIO3 to β‐LiIO3 phase transition, with reorientation of iodate ions to form inversion centers ...

Phase transition at 350 K and dehydration of barium nitrite monohydrate

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.

Charge density in pyroelectric lithium sulfate monohydrate at 80 and 298 K

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...

Phase transitions at 462 and 495 K in barium nitrite

New phase transitions at 462 and 495 K have been found in Ba(NO2)2. The increase in entropy at each transition is about 13 J mol−1 K−1. A gain of two orientations per independent NO−2 ion at each transition corresponds to an entropy increase of 11.5 J mol−1 K−1. The crystal melts at 516 K. The high‐temperature phase I is metastably retained at 298 K on rapid solidification, reverting to phase III on reheating above 350 K. Phase III is orthorhombic with lattice constants at 298 K of a = 7.657, b = 8.355, and c = 6.742 A and four Ba(NO2)2 in the unit cell. The linear thermal expansion coefficients are 30.7, 14.0, and −5.9×10−6 A K−1 for the a, b, and c axes, respectively. The powder pattern for phase II has not been indexed. Phase I may be fitted by a monoclinic unit cell with a = 6.692, b = 7.052, and c = 9.638 A and β = 104.61° at 507 K with four Ba(NO2)2 in the unit cell. A dielectric anomaly is observed at 468 K in the frequency range 0.1–1 MHz: dielectric losses obscure the anomaly at lower frequencies.

Piezoelectric Cs2S2O6: Room temperature crystal structure

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...

Diffraction-derived spontaneous polarization in lithium sulfate monohydrate at 80 and 298 K

The principal axes of the sulfate ion minimum‐equipotential contact surface with respect to its charge center, and the charge and electric dipole moment distribution in the sulfate ion and in the water molecule, are derived for Li2SO4⋅H2O on the basis of previously determined net atomic charges [J. Chem. Phys. 85, 5221 (1986)]. The sulfate ion has a nonzero dipole moment of about 2.3×10−30 C m at 80 K that rotates 9° in the crystallographic a,c plane between 298 and 80 K. The dipole moment of the water molecule increases from about 6.7×10−30 C m at 298 K to 7.8×10−30 C m at 80 K, as it rotates 3.6° in the b,c plane. The total spontaneous polarization at 298 K is calculated to be 3.19(62)×10−2 C m−2, and at 80 K it is 4.37(51)×10−2 C m−2, along the positive direction of the polar axis. The sense and magnitude of the resulting calculated 1.18×10−2 C m−2 polarization change compare well with the experimental value of 1.04×10−2 C m−2 measured on heating through the same temperature interval. Determination of ...