Single crystals of Ir2S3 (diiridium trisulfide) and Rh2S3 (dirhodium trisulfide) were grown in evacuated silica-glass tubes using a chemical transport method and their crystal structures were determined by single-crystal X-ray diffraction analysis. These compounds have a unique sesquisulfide structure in which pairs of face-sharing octahedra are linked into a three-dimensional structure by further edge- and vertex-sharing. Ir2S3 and Rh2S3 had similar unit-cell parameters and bond distances. The atomic displacement parameter (MSD: mean-square displacement) of each atom in Ir2S3 was considerably smaller than that in Rh2S3. The Debye temperatures (ΘD) estimated from the observed MSDs for the Ir, S1 and S2 sites in Ir2S3 were 259, 576 and 546 K, respectively, and those for Rh, S1 and S2 in Rh2S3 were 337, 533 and 530 K, respectively. The bulk Debye temperature for Ir2S3 kashinite (576 K) was found to rank among the higher values reported for many known sulfides. The bulk Debye temperature for Rh2S3 bowieite (533 K) was lower than that for Ir2S3 kashinite, which crystallizes in the early sequences of mineral crystallization differentiation from the primitive magma in the Earth's mantle.
Supporting information
CCDC references: 2210363; 2210362
For both structures, data collection: CrysAlis PRO (Rigaku OD, 2019); cell refinement: CrysAlis PRO (Rigaku OD, 2019); data reduction: CrysAlis PRO (Rigaku OD, 2019); program(s) used to solve structure: SHELXS (Sheldrick, 2008); program(s) used to refine structure: SHELXL2018 (Sheldrick, 2015); molecular graphics: OLEX2 (Dolomanov et al., 2009) and VESTA (Momma & Izumi, 2011).; software used to prepare material for publication: WinGX (Farrugia, 2012).
Diiridium trisulfide (I)
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Crystal data top
Ir2S3 | F(000) = 808 |
Mr = 480.58 | Dx = 10.177 Mg m−3 |
Orthorhombic, Pbcn | Mo Kα radiation, λ = 0.71073 Å |
Hall symbol: -P 2n 2ab | Cell parameters from 5651 reflections |
a = 8.4728 (3) Å | θ = 4.8–44.7° |
b = 6.01563 (18) Å | µ = 86.43 mm−1 |
c = 6.1537 (2) Å | T = 293 K |
V = 313.65 (2) Å3 | Block, silver |
Z = 4 | 0.003 mm (radius) |
Data collection top
XtaLAB Synergy, single source at offset/far, HyPix6000 diffractometer | 1092 independent reflections |
Mirror monochromator | 790 reflections with I > 2σ(I) |
Detector resolution: 10.0000 pixels mm-1 | Rint = 0.060 |
ω scans | θmax = 42.0°, θmin = 4.2° |
Absorption correction: for a sphere (CrysAlis PRO; Rigaku OD, 2019) | h = −15→15 |
Tmin = 0.291, Tmax = 0.329 | k = −11→11 |
16599 measured reflections | l = −11→11 |
Refinement top
Refinement on F2 | 0 restraints |
Least-squares matrix: full | w = 1/[σ2(Fo2) + 0.820P] where P = (Fo2 + 2Fc2)/3 |
R[F2 > 2σ(F2)] = 0.017 | (Δ/σ)max = 0.001 |
wR(F2) = 0.032 | Δρmax = 2.90 e Å−3 |
S = 1.05 | Δρmin = −1.83 e Å−3 |
1092 reflections | Extinction correction: SHELXL2018 (Sheldrick, 2015), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4 |
25 parameters | Extinction coefficient: 0.00069 (6) |
Special details top
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes)
are estimated using the full covariance matrix. The cell esds are taken
into account individually in the estimation of esds in distances, angles
and torsion angles; correlations between esds in cell parameters are only
used when they are defined by crystal symmetry. An approximate (isotropic)
treatment of cell esds is used for estimating esds involving l.s. planes. |
Refinement. Reflections were merged by SHELXL according to the crystal
class for the calculation of statistics and refinement. _reflns_Friedel_fraction is defined as the number of unique
Friedel pairs measured divided by the number that would be
possible theoretically, ignoring centric projections and
systematic absences. The intensities of reflections were measured using Mo Kα
radiation (0.71073 Å) focused by a mirror. The details of the data correction
method are described in the CIF file. Independent reflections were used to
refine the crystal structure using the full-matrix least-square method, which
was performed using the SHELXL program (Sheldrick, 2015). The R1
indices (R1 = Σ||Fo|-|Fc||/Σ|Fo|) for Ir2S3 and Rh2S3 converged to
0.0174 and 0.0176, respectively, using anisotropic temperature factors. The structure refinement data, atomic coordinates,
displacement parameters, estimated ΘD values and selected interatomic
distances are listed in Tables 1–4. The crystal structures were illustrated
using VESTA (Momma & Izumi 2011). |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | |
Ir1 | 0.39220 (2) | 0.24934 (3) | 0.03060 (2) | 0.00331 (3) | |
S2 | 0.34979 (9) | 0.10920 (14) | 0.39080 (13) | 0.00401 (11) | |
S3 | 0.000000 | 0.04444 (19) | 0.250000 | 0.00446 (17) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Ir1 | 0.00320 (5) | 0.00322 (4) | 0.00352 (5) | −0.00007 (5) | 0.00005 (3) | −0.00002 (6) |
S2 | 0.0039 (3) | 0.0041 (3) | 0.0041 (3) | 0.0003 (2) | 0.0005 (2) | −0.0002 (2) |
S3 | 0.0043 (4) | 0.0044 (4) | 0.0047 (4) | 0.000 | −0.0007 (3) | 0.000 |
Geometric parameters (Å, º) top
Ir1—S2i | 2.3497 (8) | Ir1—S2iii | 2.3923 (8) |
Ir1—S2ii | 2.3808 (8) | Ir1—S3iv | 2.4101 (9) |
Ir1—S2 | 2.3985 (8) | Ir1—S3ii | 2.3140 (6) |
| | | |
S2i—Ir1—S2ii | 93.67 (2) | S3ii—Ir1—S3iv | 82.736 (9) |
S2ii—Ir1—S2 | 109.30 (2) | Ir1iii—S2—Ir1 | 85.76 (3) |
S2i—Ir1—S2iii | 83.70 (3) | Ir1v—S2—Ir1iii | 96.30 (3) |
S2iii—Ir1—S2 | 79.99 (3) | Ir1vi—S2—Ir1iii | 126.01 (3) |
S2i—Ir1—S2 | 89.588 (18) | Ir1v—S2—Ir1vi | 109.12 (3) |
S2ii—Ir1—S2iii | 170.381 (13) | Ir1vi—S2—Ir1 | 109.71 (3) |
S2—Ir1—S3iv | 78.34 (2) | Ir1v—S2—Ir1 | 129.65 (4) |
S2iii—Ir1—S3iv | 78.46 (2) | Ir1vi—S3—Ir1vii | 115.16 (5) |
S2ii—Ir1—S3iv | 105.40 (3) | Ir1viii—S3—Ir1ix | 85.12 (4) |
S2i—Ir1—S3iv | 159.91 (3) | Ir1vi—S3—Ir1viii | 131.553 (14) |
S3ii—Ir1—S2 | 159.58 (2) | Ir1vii—S3—Ir1ix | 131.553 (14) |
S3ii—Ir1—S2iii | 88.80 (2) | Ir1vii—S3—Ir1viii | 97.264 (9) |
S3ii—Ir1—S2i | 106.22 (3) | Ir1vi—S3—Ir1ix | 97.264 (9) |
S3ii—Ir1—S2ii | 83.03 (2) | | |
Symmetry codes: (i) x, −y, z−1/2; (ii) −x+1/2, −y+1/2, z−1/2; (iii) −x+1, y, −z+1/2; (iv) x+1/2, y+1/2, −z+1/2; (v) x, −y, z+1/2; (vi) −x+1/2, −y+1/2, z+1/2; (vii) x−1/2, −y+1/2, −z; (viii) −x+1/2, y−1/2, z; (ix) x−1/2, y−1/2, −z+1/2. |
Dirhodium trisulfide (II)
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Crystal data top
Rh2S3 | F(000) = 552 |
Mr = 302.00 | Dx = 6.447 Mg m−3 |
Orthorhombic, Pbcn | Mo Kα radiation, λ = 0.71073 Å |
Hall symbol: -P 2n 2ab | Cell parameters from 6842 reflections |
a = 8.4672 (3) Å | θ = 4.8–45.0° |
b = 5.98537 (18) Å | µ = 12.34 mm−1 |
c = 6.13921 (19) Å | T = 293 K |
V = 311.13 (2) Å3 | Block, silver |
Z = 4 | 0.03 × 0.02 × 0.02 mm |
Data collection top
XtaLAB Synergy, single source at offset/far, HyPix6000 diffractometer | 1025 independent reflections |
Mirror monochromator | 893 reflections with I > 2σ(I) |
Detector resolution: 10.0000 pixels mm-1 | Rint = 0.046 |
ω scans | θmax = 41.0°, θmin = 4.2° |
Absorption correction: gaussian (CrysAlis PRO; Rigaku OD, 2019) | h = −15→15 |
Tmin = 0.777, Tmax = 0.822 | k = −11→11 |
14229 measured reflections | l = −11→11 |
Refinement top
Refinement on F2 | 0 restraints |
Least-squares matrix: full | w = 1/[σ2(Fo2) + (0.0278P)2] where P = (Fo2 + 2Fc2)/3 |
R[F2 > 2σ(F2)] = 0.018 | (Δ/σ)max = 0.001 |
wR(F2) = 0.045 | Δρmax = 1.11 e Å−3 |
S = 1.14 | Δρmin = −2.75 e Å−3 |
1025 reflections | Extinction correction: SHELXL2018 (Sheldrick, 2015), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4 |
25 parameters | Extinction coefficient: 0.0400 (10) |
Special details top
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes)
are estimated using the full covariance matrix. The cell esds are taken
into account individually in the estimation of esds in distances, angles
and torsion angles; correlations between esds in cell parameters are only
used when they are defined by crystal symmetry. An approximate (isotropic)
treatment of cell esds is used for estimating esds involving l.s. planes. |
Refinement. The intensities of reflections were measured using Mo Kα
radiation (0.71073 Å) focused by a mirror. The details of the data correction
method are described in the CIF file. Independent reflections were used to
refine the crystal structure using the full-matrix least-square method, which
was performed using the SHELXL program (Sheldrick, 2015). The R1
indices (R1 = Σ||Fo|-|Fc||/Σ|Fo|) for Ir2S3 and Rh2S3 converged to
0.0174 and 0.0176, respectively, using anisotropic temperature factors. The structure refinement data, atomic coordinates,
displacement parameters, estimated ΘD values and selected interatomic
distances are listed in Tables 1–4. The crystal structures were illustrated
using VESTA (Momma & Izumi 2011). |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | |
Rh1 | 0.10640 (2) | 0.25130 (2) | 0.03346 (2) | 0.00365 (5) | |
S1 | 0.15166 (5) | 0.39098 (6) | 0.39307 (6) | 0.00468 (7) | |
S2 | 0.000000 | 0.95214 (9) | 0.250000 | 0.00473 (9) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Rh1 | 0.00369 (7) | 0.00356 (7) | 0.00372 (7) | −0.00002 (3) | −0.00013 (3) | 0.00005 (3) |
S1 | 0.00448 (14) | 0.00453 (14) | 0.00502 (14) | 0.00015 (11) | −0.00027 (11) | −0.00032 (11) |
S2 | 0.00530 (19) | 0.00429 (19) | 0.00460 (19) | 0.000 | −0.00040 (15) | 0.000 |
Geometric parameters (Å, º) top
Rh1—S1i | 2.3396 (4) | Rh1—S1iii | 2.3826 (4) |
Rh1—S1ii | 2.3801 (4) | Rh1—S2iv | 2.4052 (4) |
Rh1—S1 | 2.3916 (4) | Rh1—S2v | 2.3071 (3) |
| | | |
S1i—Rh1—S1ii | 93.041 (12) | S2v—Rh1—S2iv | 82.977 (6) |
S1ii—Rh1—S1 | 108.750 (11) | Rh1iii—S1—Rh1 | 84.556 (13) |
S1i—Rh1—S1iii | 84.194 (14) | Rh1vi—S1—Rh1iii | 95.806 (14) |
S1iii—Rh1—S1 | 81.345 (16) | Rh1vii—S1—Rh1iii | 126.529 (17) |
S1i—Rh1—S1 | 89.651 (9) | Rh1vi—S1—Rh1vii | 109.574 (16) |
S1ii—Rh1—S1iii | 169.564 (8) | Rh1vii—S1—Rh1 | 110.312 (15) |
S1—Rh1—S2iv | 79.051 (12) | Rh1vi—S1—Rh1 | 129.325 (18) |
S1iii—Rh1—S2iv | 79.228 (12) | Rh1v—S2—Rh1vi | 116.29 (2) |
S1ii—Rh1—S2iv | 104.843 (13) | Rh1viii—S2—Rh1ix | 83.775 (18) |
S1i—Rh1—S2iv | 161.128 (14) | Rh1v—S2—Rh1viii | 131.573 (9) |
S2v—Rh1—S1 | 160.625 (13) | Rh1vi—S2—Rh1ix | 131.573 (9) |
S2v—Rh1—S1iii | 88.276 (12) | Rh1vi—S2—Rh1viii | 97.023 (5) |
S2v—Rh1—S1i | 105.609 (15) | Rh1v—S2—Rh1ix | 97.023 (6) |
S2v—Rh1—S1ii | 82.767 (11) | | |
Symmetry codes: (i) x, −y+1, z−1/2; (ii) −x+1/2, −y+1/2, z−1/2; (iii) −x, y, −z+1/2; (iv) x, y−1, z; (v) −x, −y+1, −z; (vi) x, −y+1, z+1/2; (vii) −x+1/2, −y+1/2, z+1/2; (viii) −x, y+1, −z+1/2; (ix) x, y+1, z. |
Atomic coordinates, equivalent atomic displacement parameters and Debye temperature ΘD for Ir2S3 and Rh2S3 top | x | y | z | Ueq (Å2) | ΘD (K) |
Ir2S3 | | | | | |
Ir | 0.39220 (2) | 0.24934 (3) | 0.03060 (2) | 0.00331 (3) | 259 |
S1 | 0.34979 (9) | 0.10920 (14) | 0.39080 (13) | 0.00401 (11) | 576 |
S2 | 0.0 | 0.04444 (19) | 0.25 | 0.00446 (17) | 546 |
| | | | | |
Rh2S3 | | | | | |
Rh | 0.10640 (2) | 0.25130 (2) | 0.03346 (2) | 0.00365 (5) | 337 |
S1 | 0.15166 (5) | 0.39098 (6) | 0.39307 (6) | 0.00468 (7) | 533 |
S2 | 0.0 | 0.95214 (9) | 0.25 | 0.00473 (9) | 530 |
Anisotropic atomic displacement parameters for Ir2S3 and Rh2S3 top | U11 | U22 | U33 | U23 | U13 | U12 |
Ir2S3 | | | | | | |
Ir | 0.00320 (5) | 0.00322 (4) | 0.00352 (5) | -0.00002 (6) | 0.00005 (3) | -0.00007 (5) |
S1 | 0.0039 (3) | 0.0041 (3) | 0.0041 (3) | -0.0002 (2) | 0.0005 (2) | 0.0003 (2) |
S2 | 0.0044 (4) | 0.0044 (4) | 0.0047 (4) | 0.0 | -0.0007 (3) | 0.0 |
| | | | | | |
Rh2S3 | | | | | | |
Rh | 0.00369 (7) | 0.00356 (7) | 0.00372 (7) | 0.00005 (3) | -0.00013 (3) | -0.00002 (3) |
S1 | 0.00448 (14) | 0.00453 (14) | 0.00502 (14) | -0.00032 (11) | -0.00027 (11) | 0.00015 (11) |
S2 | 0.00530 (19) | 0.00429 (19) | 0.00460 (19) | 0.0 | -0.00040 (15) | 0.0 |
Selected bond distances (Å) in Ir2S3, Rh2S3 and Rh2O3 top | Ir2S3 | Rh2S3 | Rh2O3* |
M—S1 | 2.3497 (8) | 2.3396 (4) | 2.018 (6) |
| 2.3808 (8) | 2.3801 (4) | 2.056 (6) |
| 2.3923 (8) | 2.3826 (4) | 2.068 (6) |
| 2.3985 (8) | 2.3916 (4) | 2.077 (6) |
M—S2 | 2.3140 (6) | 2.3071 (3) | 1.986 (5) |
| 2.4101 (9) | 2.4052 (4) | 2.095 (7) |
Average | 2.3742 | 2.3677 | 2.050 |
Note: (*) data from Shannon & Prewitt (1970). |