The structure of Rb2Cd2(SO4)3 at room temperature has been refined using X-ray diffraction data. The structure is similar to that of other cubic langbeinites. However, the title compound differs from other type I langbeinites in that the bond-valence sums of the metal cations (in particular the Rb atoms) are practically equal to their nominal chemical valences.
Supporting information
Single crystals of Rb2Cd2(SO4)3 were grown from saturated aqueous stoichiometric solutions by a steady-state method at 363 K. The stock reagents used for synthesis were chemically pure Rb2CO3, CdCO3 and H2SO4. The product of the synthesis was purified by recrystallization from distilled water; the pH of the solution was adjusted to be approximately 1.5. The crystals obtained measured 4x4x4mm, and were colorless and of good optical quality. Their morphology was similar to that of Rb2Cd2(SO4)3 and Tl2Cd2(SO4)3 crystals obtained by Brezina and Havránková (1974). A sphere of radius 0.18 (1) mm, ground using an Enraf–Nonius grinder, was mounted on a glass fiber for data collection.
Data collection: STOE IPDS Software (STOE, 1998); cell refinement: STOE IPDS Software (STOE, 1998); data reduction: STOE IPDS Software (STOE, 1998); program(s) used to refine structure: JANA2000 (Petricek & Dusek, 2000); molecular graphics: ORTEP (Davenport et al., 1999); software used to prepare material for publication: JANA2000.
Crystal data top
Rb2Cd2(SO4)3 | Dx = 4.048 Mg m−3 |
Mr = 683.9 | Mo Kα radiation, λ = 0.71073 Å |
Cubic, P213 | Cell parameters from 1357 reflections |
Hall symbol: P 2ac 2ab 3 | θ = 2.8–26.1° |
a = 10.391 (2) Å | µ = 13.03 mm−1 |
V = 1121.8 (4) Å3 | T = 293 K |
Z = 4 | Sphere, colorless |
F(000) = 1256 | 0.18 (1) mm (radius) |
Data collection top
STOE IPSD diffractometer | 745 independent reflections |
Radiation source: fine-focus sealed tube | 712 reflections with I > 3σ(I) |
Graphite monochromator | Rint = 0.072 |
Detector resolution: 6.7 pixels mm-1 | θmax = 26.1°, θmin = 2.8° |
image plate with oscillating crystal geometry scans | h = −12→12 |
Absorption correction: for a sphere (IPDS Software; Stoe & Cie, 1998) | k = −12→12 |
Tmin = ?, Tmax = ? | l = −12→12 |
15800 measured reflections | |
Refinement top
Refinement on F2 | (Δ/σ)max = 0.0004 |
R[F2 > 2σ(F2)] = 0.025 | Δρmax = 0.95 e Å−3 |
wR(F2) = 0.054 | Δρmin = −1.02 e Å−3 |
S = 2.79 | Extinction correction: B-C type 1 Lorentzian isotropic (Becker & Coppens, 1974) |
745 reflections | Extinction coefficient: 0.0274 (16) |
60 parameters | Absolute structure: Flack (1983) |
Weighting scheme based on measured s.u.'s w = 1/(σ2(I) + 0.000144I2) | Absolute structure parameter: −0.01 (2) |
Crystal data top
Rb2Cd2(SO4)3 | Z = 4 |
Mr = 683.9 | Mo Kα radiation |
Cubic, P213 | µ = 13.03 mm−1 |
a = 10.391 (2) Å | T = 293 K |
V = 1121.8 (4) Å3 | 0.18 (1) mm (radius) |
Data collection top
STOE IPSD diffractometer | 745 independent reflections |
Absorption correction: for a sphere (IPDS Software; Stoe & Cie, 1998) | 712 reflections with I > 3σ(I) |
Tmin = ?, Tmax = ? | Rint = 0.072 |
15800 measured reflections | |
Refinement top
R[F2 > 2σ(F2)] = 0.025 | Δρmax = 0.95 e Å−3 |
wR(F2) = 0.054 | Δρmin = −1.02 e Å−3 |
S = 2.79 | Absolute structure: Flack (1983) |
745 reflections | Absolute structure parameter: −0.01 (2) |
60 parameters | |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | |
Rb1 | 0.06482 (7) | 0.06482 (7) | 0.06482 (7) | 0.02863 (18) | |
Rb2 | 0.30139 (8) | 0.30139 (8) | 0.30139 (8) | 0.03068 (19) | |
Cd1 | 0.41797 (4) | 0.08203 (4) | −0.08203 (4) | 0.01977 (13) | |
Cd2 | 0.16180 (5) | 0.33820 (5) | −0.33820 (5) | 0.01932 (13) | |
S1 | 0.12567 (15) | 0.02603 (16) | −0.26329 (16) | 0.0170 (4) | |
O1 | 0.0272 (5) | −0.0613 (5) | −0.2161 (6) | 0.0378 (19) | |
O2 | 0.0799 (5) | 0.1579 (5) | −0.2475 (6) | 0.0363 (18) | |
O3 | 0.2419 (6) | 0.0044 (7) | −0.1867 (6) | 0.043 (2) | |
O4 | 0.1581 (7) | 0.0009 (7) | −0.3966 (5) | 0.043 (2) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Rb1 | 0.0286 (3) | 0.0286 (3) | 0.0286 (3) | −0.0010 (3) | −0.0010 (3) | −0.0010 (3) |
Rb2 | 0.0307 (3) | 0.0307 (3) | 0.0307 (3) | 0.0017 (3) | 0.0017 (3) | 0.0017 (3) |
Cd1 | 0.0198 (2) | 0.0198 (2) | 0.0198 (2) | 0.0008 (2) | −0.0008 (2) | 0.0008 (2) |
Cd2 | 0.0193 (2) | 0.0193 (2) | 0.0193 (2) | 0.00078 (19) | −0.00078 (19) | 0.00078 (19) |
S1 | 0.0166 (7) | 0.0169 (8) | 0.0175 (8) | −0.0022 (6) | −0.0003 (6) | 0.0004 (6) |
O1 | 0.026 (3) | 0.031 (3) | 0.057 (4) | −0.016 (2) | 0.016 (3) | 0.005 (3) |
O2 | 0.037 (3) | 0.015 (2) | 0.057 (4) | 0.009 (2) | 0.018 (3) | 0.005 (3) |
O3 | 0.032 (3) | 0.052 (4) | 0.045 (4) | −0.010 (3) | −0.026 (3) | 0.010 (3) |
O4 | 0.054 (4) | 0.058 (4) | 0.019 (3) | −0.007 (3) | 0.004 (3) | −0.019 (3) |
Geometric parameters (Å, º) top
Rb1—O1 | 3.223 (6) | Cd1—O4i | 2.254 (6) |
Rb1—O3 | 3.258 (7) | Cd2—O1iii | 2.294 (6) |
Rb1—O4i | 2.986 (7) | Cd2—O2 | 2.263 (6) |
Rb2—O1i | 3.071 (6) | S1—O1 | 1.454 (6) |
Rb2—O2ii | 2.978 (6) | S1—O2 | 1.459 (6) |
Rb2—O3i | 3.212 (7) | S1—O3 | 1.464 (7) |
Cd1—O3 | 2.276 (6) | S1—O4 | 1.449 (6) |
| | | |
O1—S1—O2 | 108.6 (3) | O2—S1—O3 | 110.6 (4) |
O1—S1—O3 | 107.6 (4) | O2—S1—O4 | 110.6 (4) |
O1—S1—O4 | 112.0 (4) | O3—S1—O4 | 107.5 (4) |
Symmetry codes: (i) −x+1/2, −y, z+1/2; (ii) x+1/2, −y+1/2, −z; (iii) −x, y+1/2, −z−1/2. |
Experimental details
Crystal data |
Chemical formula | Rb2Cd2(SO4)3 |
Mr | 683.9 |
Crystal system, space group | Cubic, P213 |
Temperature (K) | 293 |
a (Å) | 10.391 (2) |
V (Å3) | 1121.8 (4) |
Z | 4 |
Radiation type | Mo Kα |
µ (mm−1) | 13.03 |
Crystal size (mm) | 0.18 (1) (radius) |
|
Data collection |
Diffractometer | STOE IPSD diffractometer |
Absorption correction | For a sphere (IPDS Software; Stoe & Cie, 1998) |
No. of measured, independent and observed [I > 3σ(I)] reflections | 15800, 745, 712 |
Rint | 0.072 |
(sin θ/λ)max (Å−1) | 0.618 |
|
Refinement |
R[F2 > 2σ(F2)], wR(F2), S | 0.025, 0.054, 2.79 |
No. of reflections | 745 |
No. of parameters | 60 |
No. of restraints | ? |
Δρmax, Δρmin (e Å−3) | 0.95, −1.02 |
Absolute structure | Flack (1983) |
Absolute structure parameter | −0.01 (2) |
Selected geometric parameters (Å, º) topRb1—O1 | 3.223 (6) | Cd1—O4i | 2.254 (6) |
Rb1—O3 | 3.258 (7) | Cd2—O1iii | 2.294 (6) |
Rb1—O4i | 2.986 (7) | Cd2—O2 | 2.263 (6) |
Rb2—O1i | 3.071 (6) | S1—O1 | 1.454 (6) |
Rb2—O2ii | 2.978 (6) | S1—O2 | 1.459 (6) |
Rb2—O3i | 3.212 (7) | S1—O3 | 1.464 (7) |
Cd1—O3 | 2.276 (6) | S1—O4 | 1.449 (6) |
| | | |
O1—S1—O2 | 108.6 (3) | O2—S1—O3 | 110.6 (4) |
O1—S1—O3 | 107.6 (4) | O2—S1—O4 | 110.6 (4) |
O1—S1—O4 | 112.0 (4) | O3—S1—O4 | 107.5 (4) |
Symmetry codes: (i) −x+1/2, −y, z+1/2; (ii) x+1/2, −y+1/2, −z; (iii) −x, y+1/2, −z−1/2. |
Bond-valence sums (v.u) of the atoms of Rb2Cd2(SO4)3 and Tl2Cd2(SO4)3 (Guelylah, Madariaga & Brezcewski, 1996) top | Rb2Cd2(SO4)3 | Tl2Cd2(SO4)3 |
Rb1 | 0.846 (6) | 0.61 (3) (Tl1) |
Rb2 | 0.995 (5) | 0.83 (4) (Tl2) |
Cd1 | 2.264 (15) | 2.13 (10) |
Cd2 | 2.181 (14) | 2.03 (9) |
S | 6.29 (5) | 6.7 (3) |
O1 | 2.12 (3) | 1.96 (9) |
O2 | 2.08 (3) | 2.18 (9) |
O3 | 2.05 (3) | 2.17 (11) |
O4 | 2.13 (3) | 2.25 (9) |
Dirubidium dicadmium sulfate, Rb2Cd2(SO4)3 (RCdS), belongs to the langbeinite family, whose general formula is A2B2(XY4)3, where A is K, Tl, Cs, Rb and NH4, B is Mg, Zn, Fe, Ni, Cd, Co, Ca and Mn, and XY4 is a divalent tetrahedral group, such as SO4, BeF4 or SeO4. Langbeinites, have a common high-temperature cubic phase (space group P213) and take their names from the natural mineral K2Mg2(SO4)3 (langbeinite), the structure of which was solved at room temperature by Zeemann & Zeemann (1957). RCdS undergoes three successive phase transitions at 129 K, 103 K and 68 K, which have been studied by several experimental techniques, viz. dielectric measurements (Hikita et al., 1976; Hikita et al., 1980; Maeda, 1980), X-ray diffraction (Yamada & Kawano, 1977), thermal expansion (Kahrizi & Steinitz, 1988), elastic measurements (Hikita et al., 1976; Maeda, 1980), electric polarization (Yamada, 1979), light scattering (Latush et al., 1983) and electron paramagnetic resonance (Franco et al., 1996). On the basis of the theoretical work of Dvorák (1972, 1974), the space groups of the three low-temperature phases were determined to be P21, P1 and P212121, respectively (Hikita et al., 1976; Yamada & Kawano, 1977 and Maeda, 1980). Nevertheless, none of the four phases of RCdS have been determined. The present work reports the structure of RCdS at room temperature.
The cubic structure of RCdS (see Fig. 1) is similar to that of the sulfates belonging to the langbeinite family (Speer & Salje, 1986; Abrahams et al., 1978, Yamada et al., 1981; Zeemann & Zeemann, 1957; Guelylah, Madariaga & Breczewski, 1996a) and comprises SO4 tetrahedra and distorted coordination polyhedra around the Rb and Cd cations. The metal cations occupy special positions along the threefold axes. Each Rb atom is surrounded by nine O atoms (up to the third coordination shell, i.e. contacts below 3.3 Å) that form complicated polyhedra of similar volume (Fig. 2). Cd1 and Cd2 are each coordinated by six O atoms, forming distorted octahedra that are generated by the application of the threefold axes on the symmetry independent O3, O4, O1 and O2 atoms. Cd1 and Cd2 are not at the midpoint of the octahedra, but are shifted by 0.033 (2) Å toward the O4 triplet for Cd1 and 0.139 (2) Å toward the O2 triplet for Cd2. These displacements within the octahedra are practically identical to those observed in the cubic structure of TCdS (Guelylah, Madariaga & Brezcewski, 1996a). Unlike the SO4 deformation observed in the cubic structure of TCdS, the SO4 group in RCdS is regular, with S—O distances in the range 1.449 (6)–1.464 (7) Å [mean value 1.455 (6)] and O—S—O bond angles in the range 107.5 (4)– 112.0 (4)° [mean value 109.5 (4)°]. The atomic displacement parameters of the Rb, Cd and S atoms are virtually isotropic. As for other langbeinite compounds, strong anisotropy appears for the O atoms, which show small displacements along and large displacements perpendicular to the S—O direction. The displacement ellipsoids are, therefore, very large and disk-shaped. This anisotropy is a common characteristic of the sulfate groups in cubic langbeinite structures and has also been observed in different potassium langbeinites (Abrahams et al., 1978; Yamada et al., 1981; Speer & Salje, 1986), TCdS and K2Mn2(BeF4)3 (Guelylah, Breczewski & Madariaga, 1996b).
In order to compare the cation binding, the bond-valence sums (Brown & Altermatt, 1985; Brese & O'Keeffe, 1991) were calculated (Table 3). Unlike the TCdS structure, in which some atoms were loosely bonded (Tl1) and others tightly bonded (S), bond-valence sums in RCdS are closer to the respective chemical valences, indicating that the atoms are normally bonded. Even the strong asymmetry in bond strength observed in TCdS for the Tl1 and Tl2 cations is reduced in RCdS, although it is still higher than 0.14 v.u. (valence units). Nevertheless, for type II langbeinites, such as K2Cd2(SO4)3 (KCdS), which differ only in the monovalent cations from RCdS and TCdS, the bond valence-sums for the two K atoms are almost equal (0.83 and 0.88 for K1 and K2, respectively; Guelylah, Breczewski & Madariaga, 1996a). This asymmetry in the bond strength of monovalent cations could be responsible for the different sequence of phase transitions observed in both types of langbeinites.