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. The fast reorientational disorder of the anions was determined for the ambient temperature modification [
; Jeffrey (1974). Can. J. Phys. 52, 2370-2378]. Single crystals are available now as protonated or deuterated specimens. With neutron single-crystal diffraction at room temperature, a considerable anharmonicity of the atom potential of the H or D atoms was observed. Even the thermal motions of K and S atoms show small deviations from an isotropic probability density function, which can be modelled using anharmonic temperature factors. The temperature factors of the atoms were expanded into a Gram-Charlier series [Kuhs (1992). Acta Cryst. A48, 80-98] in order to evaluate the anharmonicity quantitatively. Parameters up to a fourth-order approximation are relevant for the D atoms. Results from neutron single-crystal diffraction are compared with split-atom models extracted from neutron powder diffraction patterns of fully deuterated samples.Supporting information
 | Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768100011952/sn0007sup1.cif |
 | Structure factor file (CIF format) https://doi.org/10.1107/S0108768100011952/sn0007sup2.hkl |
Single crystals of the potassium and the rubidium compound can be synthesized by recrystallization of the samples from liquid ammonia at ambient temperature and 7 bar pressure of the solvent. Carefully handled glass containers were used to grow the crystals by slow evaporation of the solvent. The temperature was controlled by a thermostat during the process. For details see Haarmann, (2000). Protonated and deuterated crystals can be obtained by the choice of the solvent NH3 or ND3 respectively. Single-crystals of NaHS/DS are not available by this method. A reaction of the salt with the solvent gives NaNH2 and NH4HS as the main products.
The crystal structure, including the positions of deuterium was known (Jacobs et al., 1991). The data were analyzed and refined with the computer program package JANA98 (Petricek, V. & Dusek, M., 1998). A numerical correction for absorption was applied. For extinction correction an isotropic Zachariasen model with Gaussian mosaic spread was applied. The refinement of the g-value of extinction resulted in a value close to zero not significantly larger then its standard deviation. Therefore this correction has been dropped. Thermal diffuse scattering (TDS) corrections were not taken into account.
| DKS | Dx = 1.692 Mg m−3 |
| Mr = 73.16 | Neutron radiation, λ = 0.912 Å |
| Trigonal, R3m | Cell parameters from 110 reflections |
| Hall symbol: -R 3 2" | θ = 6–52° |
| a = 4.988 (3) Å | µ = 0.001887 mm−1 |
| c = 9.997 (7) Å | T = 298 K |
| V = 215.4 (3) Å3 | Rhombohedral, colourless |
| Z = 3 | 3.2 × 2.6 × 1.5 mm |
| F(000) = 39.684 |
| Four-circle diffractometer | Rint = 0.067 |
| ω–2θ scans | θmax = 52.0°, θmin = 6.6° |
| Absorption correction: gaussian Petricek, and Dusek (1998) | h = −8→7 |
| Tmin = 0.946, Tmax = 0.968 | k = −7→8 |
| 659 measured reflections | l = −17→9 |
| 161 independent reflections | 1 standard reflections every 20 reflections |
| 100 reflections with > 3σ(I) | intensity decay: none |
| Refinement on F | 12 parameters |
| R[F2 > 2σ(F2)] = 0.058 | Weighting scheme based on measured s.u.'s w = 1/σ2(F) |
| wR(F2) = 0.031 | (Δ/σ)max = 0.0001 |
| S = 2.24 | Δρmax = 0.76 e Å−3 |
| 659 reflections | Δρmin = −0.91 e Å−3 |
| DKS | Z = 3 |
| Mr = 73.16 | Neutron radiation, λ = 0.912 Å |
| Trigonal, R3m | µ = 0.001887 mm−1 |
| a = 4.988 (3) Å | T = 298 K |
| c = 9.997 (7) Å | 3.2 × 2.6 × 1.5 mm |
| V = 215.4 (3) Å3 |
| Four-circle diffractometer | 100 reflections with > 3σ(I) |
| Absorption correction: gaussian Petricek, and Dusek (1998) | Rint = 0.067 |
| Tmin = 0.946, Tmax = 0.968 | 1 standard reflections every 20 reflections |
| 659 measured reflections | intensity decay: none |
| 161 independent reflections |
| R[F2 > 2σ(F2)] = 0.058 | 12 parameters |
| wR(F2) = 0.031 | Δρmax = 0.76 e Å−3 |
| S = 2.24 | Δρmin = −0.91 e Å−3 |
| 659 reflections |
| x | y | z | Uiso*/Ueq | Occ. (<1) | |
| K | 0 | 0 | 0 | 0.0406 (2) | |
| S | 0 | 0 | 0.5 | 0.0324 (2) | |
| D | 0 | 0 | 0.3735 (2) | 0.1032 (7) | 0.5 |
| U11 | U22 | U33 | U12 | U13 | U23 | |
| D | 0.1207 (7) | 0.1207 (7) | 0.068 (2) | 0.0604 (4) | 0 | 0 |
| K—D | 2.9077 (3) | D—Kv | 2.9077 (3) |
| K—D | 2.9077 (3) | D—Kvi | 2.9077 (3) |
| K—D | 2.9077 (3) | D—Kvii | 2.9077 (3) |
| K—Di | 2.9077 (3) | D—S | 1.264 (2) |
| K—Dii | 2.9077 (3) | D—Div | 2.529 (3) |
| K—Diii | 2.9077 (3) | D—D | 2.9899 (7) |
| S—D | 1.264 (2) | D—D | 2.9899 (7) |
| S—Div | 1.264 (2) | D—D | 2.9899 (7) |
| D—K—D | 118.12 (1) | Kv—D—Div | 97.95 (4) |
| D—K—D | 118.12 (1) | Kv—D—D | 59.06 (1) |
| D—K—Di | 61.88 (1) | Kv—D—D | 59.06 (1) |
| D—K—Dii | 61.88 (1) | Kv—D—D | 156.46 (8) |
| D—K—Diii | 180 | Kvi—D—Kv | 118.12 (2) |
| D—K—D | 118.12 (1) | Kvi—D—Kvii | 118.12 (2) |
| D—K—D | 118.12 (1) | Kvi—D—S | 97.95 (4) |
| D—K—Di | 61.88 (1) | Kvi—D—Div | 97.95 (4) |
| D—K—Dii | 180 | Kvi—D—D | 59.06 (1) |
| D—K—Diii | 61.88 (1) | Kvi—D—D | 156.46 (8) |
| D—K—D | 118.12 (1) | Kvi—D—D | 59.06 (1) |
| D—K—D | 118.12 (1) | Kvii—D—Kv | 118.12 (2) |
| D—K—Di | 180 | Kvii—D—Kvi | 118.12 (2) |
| D—K—Dii | 61.88 (1) | Kvii—D—S | 97.95 (4) |
| D—K—Diii | 61.88 (1) | Kvii—D—Div | 97.95 (4) |
| Di—K—D | 61.88 (1) | Kvii—D—D | 156.46 (8) |
| Di—K—D | 61.88 (1) | Kvii—D—D | 59.06 (1) |
| Di—K—D | 180 | Kvii—D—D | 59.06 (1) |
| Di—K—Dii | 118.12 (1) | S—D—Div | 0 |
| Di—K—Diii | 118.12 (1) | S—D—D | 105.60 (5) |
| Dii—K—D | 61.88 (1) | S—D—D | 105.60 (5) |
| Dii—K—D | 180 | S—D—D | 105.60 (5) |
| Dii—K—D | 61.88 (1) | Div—D—D | 105.60 (5) |
| Dii—K—Di | 118.12 (1) | Div—D—D | 105.60 (5) |
| Dii—K—Diii | 118.12 (1) | Div—D—D | 105.60 (5) |
| Diii—K—D | 180 | D—D—Div | 105.60 (5) |
| Diii—K—D | 61.88 (1) | D—D—D | 113.05 (4) |
| Diii—K—D | 61.88 (1) | D—D—D | 113.05 (4) |
| Diii—K—Di | 118.12 (1) | D—D—Div | 105.60 (5) |
| Diii—K—Dii | 118.12 (1) | D—D—D | 113.05 (4) |
| D—S—Div | 180 | D—D—D | 113.05 (4) |
| Div—S—D | 180 | D—D—Div | 105.60 (5) |
| Kv—D—Kvi | 118.12 (2) | D—D—D | 113.05 (4) |
| Kv—D—Kvii | 118.12 (2) | D—D—D | 113.05 (4) |
| Kv—D—S | 97.95 (4) |
| Symmetry codes: (i) x−2/3, y−1/3, z+2/3; (ii) x−2/3, y+2/3, z+2/3; (iii) x+1/3, y+2/3, z+2/3; (iv) −x, −y, −z+1; (v) −x−1/3, −y−2/3, −z+1/3; (vi) −x−1/3, −y+1/3, −z+1/3; (vii) −x+2/3, −y+1/3, −z+1/3. |
Experimental details
| Crystal data | |
| Chemical formula | DKS |
| Mr | 73.16 |
| Crystal system, space group | Trigonal, R3m |
| Temperature (K) | 298 |
| a, c (Å) | 4.988 (3), 9.997 (7) |
| V (Å3) | 215.4 (3) |
| Z | 3 |
| Radiation type | Neutron, λ = 0.912 Å |
| µ (mm−1) | 0.001887 |
| Crystal size (mm) | 3.2 × 2.6 × 1.5 |
| Data collection | |
| Diffractometer | Four-circle diffractometer |
| Absorption correction | Gaussian Petricek, and Dusek (1998) |
| Tmin, Tmax | 0.946, 0.968 |
| No. of measured, independent and observed [ > 3σ(I)] reflections | 659, 161, 100 |
| Rint | 0.067 |
| (sin θ/λ)max (Å−1) | 0.864 |
| Refinement | |
| R[F2 > 2σ(F2)], wR(F2), S | 0.058, 0.031, 2.24 |
| No. of reflections | 659 |
| No. of parameters | 12 |
| No. of restraints | ? |
| Δρmax, Δρmin (e Å−3) | 0.76, −0.91 |
Single-crystal neutron diffraction has clearly shown, that the pdf of deuterium atoms in the hydrogensulfide of potassium is strongly anharmonic. This is due to the repulsive forces between cations and deuterium atoms, which influence the librational motion of the anions. A deviation from an isotropic pdf of sulfur and potassium atoms is visible in Fourier sections but cannot be quantified by the measurement.
Qualitative information about the anharmonicity of deuterium atoms in KDS was already obtained by powder diffraction data (Haarmann et al., 2000). Reflection profile decomposition using the Rietveld method is required to extract more quantitative information from powder data, but current computer programs do not include the Gram-Chalier series expansion.
Rather than powder diffraction, which is impaired by peak overlap, single-crystal diffraction yields unambiguous quantitative information about the density distribution.