Single-crystal structure refinements and Debye temperatures of Ir₂S₃ kashinite and Rh₂S₃ bowieite

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 (Θ_D) 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.

Computing details

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)

Crystal data

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) Å^3	Block, silver
Z = 4	0.003 mm (radius)

Data collection

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

Refinement on F^2	0 restraints
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + 0.820P] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.017	(Δ/σ)max = 0.001
wR(F^2) = 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+0.001xFc^2λ^3/sin(2θ)]^-1/4
25 parameters	Extinction coefficient: 0.00069 (6)

Special details

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 Θ_D 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 (Ų)

	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 (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
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)

Ir1—S2^i	2.3497 (8)	Ir1—S2^iii	2.3923 (8)
Ir1—S2^ii	2.3808 (8)	Ir1—S3^iv	2.4101 (9)
Ir1—S2	2.3985 (8)	Ir1—S3^ii	2.3140 (6)
S2^i—Ir1—S2^ii	93.67 (2)	S3^ii—Ir1—S3^iv	82.736 (9)
S2^ii—Ir1—S2	109.30 (2)	Ir1^iii—S2—Ir1	85.76 (3)
S2^i—Ir1—S2^iii	83.70 (3)	Ir1^v—S2—Ir1^iii	96.30 (3)
S2^iii—Ir1—S2	79.99 (3)	Ir1^vi—S2—Ir1^iii	126.01 (3)
S2^i—Ir1—S2	89.588 (18)	Ir1^v—S2—Ir1^vi	109.12 (3)
S2^ii—Ir1—S2^iii	170.381 (13)	Ir1^vi—S2—Ir1	109.71 (3)
S2—Ir1—S3^iv	78.34 (2)	Ir1^v—S2—Ir1	129.65 (4)
S2^iii—Ir1—S3^iv	78.46 (2)	Ir1^vi—S3—Ir1^vii	115.16 (5)
S2^ii—Ir1—S3^iv	105.40 (3)	Ir1^viii—S3—Ir1^ix	85.12 (4)
S2^i—Ir1—S3^iv	159.91 (3)	Ir1^vi—S3—Ir1^viii	131.553 (14)
S3^ii—Ir1—S2	159.58 (2)	Ir1^vii—S3—Ir1^ix	131.553 (14)
S3^ii—Ir1—S2^iii	88.80 (2)	Ir1^vii—S3—Ir1^viii	97.264 (9)
S3^ii—Ir1—S2^i	106.22 (3)	Ir1^vi—S3—Ir1^ix	97.264 (9)
S3^ii—Ir1—S2^ii	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)

Crystal data

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) Å^3	Block, silver
Z = 4	0.03 × 0.02 × 0.02 mm

Data collection

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

Refinement on F^2	0 restraints
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.0278P)^2] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.018	(Δ/σ)max = 0.001
wR(F^2) = 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+0.001xFc^2λ^3/sin(2θ)]^-1/4
25 parameters	Extinction coefficient: 0.0400 (10)

Special details

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 Θ_D 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 (Ų)

	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 (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
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)

Rh1—S1^i	2.3396 (4)	Rh1—S1^iii	2.3826 (4)
Rh1—S1^ii	2.3801 (4)	Rh1—S2^iv	2.4052 (4)
Rh1—S1	2.3916 (4)	Rh1—S2^v	2.3071 (3)
S1^i—Rh1—S1^ii	93.041 (12)	S2^v—Rh1—S2^iv	82.977 (6)
S1^ii—Rh1—S1	108.750 (11)	Rh1^iii—S1—Rh1	84.556 (13)
S1^i—Rh1—S1^iii	84.194 (14)	Rh1^vi—S1—Rh1^iii	95.806 (14)
S1^iii—Rh1—S1	81.345 (16)	Rh1^vii—S1—Rh1^iii	126.529 (17)
S1^i—Rh1—S1	89.651 (9)	Rh1^vi—S1—Rh1^vii	109.574 (16)
S1^ii—Rh1—S1^iii	169.564 (8)	Rh1^vii—S1—Rh1	110.312 (15)
S1—Rh1—S2^iv	79.051 (12)	Rh1^vi—S1—Rh1	129.325 (18)
S1^iii—Rh1—S2^iv	79.228 (12)	Rh1^v—S2—Rh1^vi	116.29 (2)
S1^ii—Rh1—S2^iv	104.843 (13)	Rh1^viii—S2—Rh1^ix	83.775 (18)
S1^i—Rh1—S2^iv	161.128 (14)	Rh1^v—S2—Rh1^viii	131.573 (9)
S2^v—Rh1—S1	160.625 (13)	Rh1^vi—S2—Rh1^ix	131.573 (9)
S2^v—Rh1—S1^iii	88.276 (12)	Rh1^vi—S2—Rh1^viii	97.023 (5)
S2^v—Rh1—S1^i	105.609 (15)	Rh1^v—S2—Rh1^ix	97.023 (6)
S2^v—Rh1—S1^ii	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.