X-ray structure determination of the monoclinic (121 K) and orthorhombic (85 K) phases of ­langbeinite-type dithallium dicadmium sulfate

Guelylah, A.; Madariaga, G.; Morgenroth, W.; Aroyo, M.I.; Breczewski, T.; Bocanegra, E.H.

doi:10.1107/S0108768100009514

X-ray structure determination of the monoclinic (121 K) and orthorhombic (85 K) phases of langbeinite-type dithallium dicadmium sulfate

A. Guelylah, G. Madariaga, W. Morgenroth, M. I. Aroyo, T. Breczewski and E. H. Bocanegra

The structures of the monoclinic and the orthorhombic phases of type I langbeinite Tl₂Cd₂(SO₄)₃ have been determined at 121 and 85 K, respectively, by X-ray diffraction. A precise analysis of these structures shows the existence of some differences compared to langbeinites of type II. The monoclinic structure differs very little from the high-temperature cubic structure and the distortion relating the monoclinic structure to the cubic one is very small. SO₄ tetrahedra seem to rotate under orthorhombic symmetry in the monoclinic phase. A symmetry distortion analysis of the ferroelectric monoclinic distortion discloses the importance of the secondary modes with orthorhombic symmetry, especially for the O atoms of the SO₄ groups.

Keywords: Langbeinite; Low temperature; Twinning.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768100009514/na0103sup1.cif Contains datablocks global, 121K, 85K
	Structure factor file (CIF format) https://doi.org/10.1107/S0108768100009514/na0103121Ksup2.hkl Contains datablock default
	Structure factor file (CIF format) https://doi.org/10.1107/S0108768100009514/na010385Ksup3.hkl Contains datablock default

Computing details top

Data collection: DIF4 for 121K; CAD4VPC for (85K). Cell refinement: DIF4 for 121K; CAD4VPC for (85K). Data reduction: AVSORT, REDUCE, xtal_ABSORB for 121K; JANA98 for (85K). For both compounds, program(s) used to solve structure: JANA98; program(s) used to refine structure: JANA98; molecular graphics: ORTEP; software used to prepare material for publication: JANA98.

(121K) top

Crystal data top

Tl₂Cd₂(SO₄)₃	F(000) = 1608
M_r = 921.7	D_x = 5.515 Mg m⁻³
Monoclinic, P112₁	Synchrotron radiation, λ = 0.5502 Å
Hall symbol: P 21	Cell parameters from 27 reflections
a = 10.356 (4) Å	θ = 7.4–29.2°
b = 10.350 (2) Å	µ = 17.53 mm⁻¹
c = 10.353 (6) Å	T = 121 K
β = 90°	Parallelepiped, colourless
V = 1109.7 (8) Å³	0.59 × 0.35 × 0.35 mm
Z = 4

Data collection top

Huber CAD-4 κ geometry diffractometer	8392 reflections with I > 3σ(I)
θ/2θ scans	θ_max = 20.0°, θ_min = 1.5°
Absorption correction: analytical (Alcock, 1974)	h = −12→12
T_min = 0.009, T_max = 0.046	k = −12→12
9312 measured reflections	l = −12→12
8392 independent reflections	2 standard reflections every 20 min

Refinement top

Refinement on F	Weighting scheme based on measured s.u.'s w = 1/σ²(F)
R[F² > 2σ(F²)] = 0.044	(Δ/σ)_max = 0.001
wR(F²) = 0.064	Δρ_max = 2.43 e Å⁻³
S = 13.78	Δρ_min = −1.86 e Å⁻³
8392 reflections	Extinction correction: B-C type 1 Gaussian isotropic
132 parameters	Extinction coefficient: 0.182 (4)

Crystal data top

Tl₂Cd₂(SO₄)₃	V = 1109.7 (8) Å³
M_r = 921.7	Z = 4
Monoclinic, P112₁	Synchrotron radiation, λ = 0.5502 Å
a = 10.356 (4) Å	µ = 17.53 mm⁻¹
b = 10.350 (2) Å	T = 121 K
c = 10.353 (6) Å	0.59 × 0.35 × 0.35 mm
β = 90°

Data collection top

Huber CAD-4 κ geometry diffractometer	8392 independent reflections
Absorption correction: analytical (Alcock, 1974)	8392 reflections with I > 3σ(I)
T_min = 0.009, T_max = 0.046	2 standard reflections every 20 min
9312 measured reflections

Refinement top

R[F² > 2σ(F²)] = 0.044	132 parameters
wR(F²) = 0.064	Δρ_max = 2.43 e Å⁻³
S = 13.78	Δρ_min = −1.86 e Å⁻³
8392 reflections

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Tl21	0.80235 (4)	0.05287 (4)	0.043756	0.0136 (1)
Tl11	0.56739 (4)	0.81699 (5)	0.81002 (6)	0.0144 (1)
Tl12	0.06866 (4)	0.68261 (4)	0.17413 (6)	0.0149 (1)
Tl22	0.30273 (4)	0.44800 (4)	0.93967 (7)	0.0145 (1)
Cd11	0.08851 (6)	0.33194 (9)	0.32064 (9)	0.00722 (8)
Cd12	0.58546 (7)	0.16893 (9)	0.66497 (8)	0.00957 (8)
Cd21	0.33856 (7)	0.59002 (7)	0.57932 (9)	0.00526 (7)
Cd22	0.83717 (7)	0.91000 (7)	0.40177 (9)	0.00797 (8)
S1a	0.0298 (2)	0.6217 (2)	0.5043 (2)	0.0046 (1)
O1a	−0.0582 (3)	0.7173 (3)	0.4514 (4)	0.0130 (4)
O2a	0.1604 (2)	0.6676 (4)	0.4767 (4)	0.0054 (4)
O3a	0.0059 (4)	0.4974 (3)	0.4361 (4)	0.0118 (5)
O4a	0.0049 (4)	0.5999 (4)	0.6455 (3)	0.0154 (5)
S1b	0.5331 (2)	0.8839 (2)	0.4799 (2)	0.0046 (1)
O1b	0.4452 (3)	0.7855 (3)	0.5279 (4)	0.0130 (4)
O2b	0.6637 (2)	0.8377 (4)	0.5066 (4)	0.0054 (4)
O3b	0.5080 (4)	1.0049 (3)	0.5533 (4)	0.0118 (5)
O4b	0.5091 (4)	0.9117 (4)	0.3397 (3)	0.0154 (5)
S1c	0.2647 (2)	0.2710 (2)	0.6201 (2)	0.0046 (1)
O1c	0.2257 (4)	0.1843 (4)	0.7233 (3)	0.0130 (4)
O2c	0.2252 (4)	0.4008 (3)	0.6593 (4)	0.0054 (4)
O3c	0.1942 (4)	0.2321 (4)	0.5011 (3)	0.0118 (5)
O4c	0.4065 (2)	0.2596 (4)	0.5928 (4)	0.0154 (5)
S1d	0.7626 (2)	0.2300 (2)	0.3648 (2)	0.0046 (1)
O1d	0.7322 (4)	0.3210 (4)	0.2625 (3)	0.0130 (4)
O2d	0.7187 (4)	0.1033 (3)	0.3205 (4)	0.0054 (4)
O3d	0.6891 (4)	0.2692 (4)	0.4818 (3)	0.0118 (5)
O4d	0.9036 (2)	0.2339 (4)	0.3982 (4)	0.0154 (5)
S1e	0.3767 (2)	0.5145 (2)	0.2718 (2)	0.0046 (1)
O1e	0.4782 (3)	0.4691 (4)	0.1864 (4)	0.0130 (4)
O2e	0.4319 (4)	0.5181 (4)	0.4018 (3)	0.0054 (4)
O3e	0.2692 (3)	0.4192 (4)	0.2669 (4)	0.0118 (5)
O4e	0.3244 (4)	0.6423 (2)	0.2277 (4)	0.0154 (5)
S1f	0.8772 (2)	0.9859 (2)	0.7125 (2)	0.0046 (1)
O1f	0.9815 (3)	1.0335 (4)	0.7933 (4)	0.0130 (4)
O2f	0.9290 (4)	0.9755 (4)	0.5816 (3)	0.0054 (4)
O3f	0.7713 (3)	1.0830 (4)	0.7157 (4)	0.0118 (5)
O4f	0.8239 (4)	0.8610 (2)	0.7636 (4)	0.0154 (5)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Tl21	0.0150 (2)	0.0118 (2)	0.0139 (2)	−0.0065 (2)	0.0011 (2)	−0.0005 (2)
Tl11	0.0134 (2)	0.0177 (2)	0.0121 (2)	−0.0051 (2)	0.0017 (2)	−0.0004 (2)
Tl12	0.0148 (2)	0.0160 (2)	0.0140 (2)	−0.0061 (2)	0.0009 (2)	−0.0020 (2)
Tl22	0.0160 (2)	0.0126 (2)	0.0147 (2)	−0.0057 (2)	−0.0005 (1)	0.0003 (2)
S1a	0.0035 (2)	0.0056 (2)	0.0046 (1)	−0.0001 (1)	0.0002 (1)	−0.0017 (1)
O1a	0.0094 (6)	0.0119 (6)	0.0178 (7)	0.0010 (5)	−0.0071 (5)	−0.0009 (5)
O2a	0.0024 (5)	0.0013 (6)	0.012 (1)	0.0003 (4)	0.0027 (7)	−0.0003 (7)
O3a	0.014 (1)	0.0086 (7)	0.0124 (8)	−0.0013 (6)	0.0040 (7)	0.0012 (6)
O4a	0.026 (1)	0.0070 (7)	0.0132 (7)	0.0019 (7)	0.0053 (6)	0.0029 (5)
S1b	0.0035 (2)	0.0057 (2)	0.0045 (1)	0.0001 (1)	−0.0002 (1)	−0.0016 (1)
O1b	0.0093 (6)	0.0120 (6)	0.0178 (7)	−0.0013 (5)	0.0070 (5)	−0.0012 (5)
O2b	0.0024 (5)	0.0013 (6)	0.012 (1)	−0.0001 (4)	−0.0028 (7)	−0.0008 (7)
O3b	0.014 (1)	0.0086 (7)	0.0125 (8)	0.0015 (6)	−0.0039 (7)	0.0010 (6)
O4b	0.026 (1)	0.0067 (7)	0.0134 (7)	−0.0016 (7)	−0.0053 (6)	0.0025 (5)
S1c	0.0044 (1)	0.0035 (2)	0.0057 (2)	0.0002 (1)	−0.0016 (1)	−0.0002 (1)
O1c	0.0191 (7)	0.0081 (6)	0.0119 (6)	−0.0061 (5)	−0.0010 (5)	0.0014 (5)
O2c	0.012 (1)	0.0031 (5)	0.0013 (6)	0.0037 (7)	−0.0010 (7)	0.0000 (4)
O3c	0.0117 (8)	0.015 (1)	0.0087 (7)	0.0037 (7)	0.0009 (6)	−0.0018 (6)
O4c	0.0124 (7)	0.027 (1)	0.0066 (7)	0.0041 (6)	0.0021 (5)	0.0007 (7)
S1d	0.0043 (1)	0.0036 (2)	0.0059 (2)	−0.0002 (1)	0.0015 (1)	−0.0003 (1)
O1d	0.0195 (7)	0.0075 (6)	0.0120 (6)	0.0055 (5)	0.0015 (5)	0.0015 (5)
O2d	0.011 (1)	0.0034 (5)	0.0014 (6)	−0.0041 (6)	0.0013 (7)	−0.0002 (5)
O3d	0.0115 (8)	0.015 (1)	0.0086 (7)	−0.0034 (7)	−0.0010 (6)	−0.0017 (6)
O4d	0.0122 (7)	0.028 (1)	0.0065 (7)	−0.0033 (6)	−0.0019 (5)	0.0012 (7)
S1e	0.0062 (2)	0.0040 (2)	0.0035 (2)	−0.0013 (1)	0.0000 (1)	0.0001 (1)
O1e	0.0128 (6)	0.0148 (7)	0.0115 (6)	−0.0019 (5)	0.0027 (5)	−0.0076 (5)
O2e	0.0019 (6)	0.012 (1)	0.0018 (5)	−0.0025 (6)	0.0001 (5)	0.0011 (6)
O3e	0.0082 (7)	0.0139 (9)	0.013 (1)	0.0001 (6)	−0.0020 (6)	0.0037 (7)
O4e	0.0062 (7)	0.0162 (7)	0.024 (1)	0.0017 (5)	0.0012 (7)	0.0072 (6)
S1f	0.0062 (2)	0.0040 (2)	0.0035 (2)	0.0013 (1)	−0.0001 (1)	0.0000 (1)
O1f	0.0127 (6)	0.0140 (7)	0.0124 (6)	0.0016 (5)	−0.0029 (5)	−0.0077 (5)
O2f	0.0019 (6)	0.012 (1)	0.0017 (6)	0.0027 (6)	−0.0002 (5)	0.0006 (6)
O3f	0.0083 (7)	0.0143 (9)	0.013 (1)	0.0002 (6)	0.0022 (6)	0.0036 (7)
O4f	0.0061 (7)	0.0169 (7)	0.023 (1)	−0.0014 (5)	−0.0005 (7)	0.0076 (6)

Geometric parameters (Å, º) top

Tl21—O2aⁱ	3.000 (4)	Cd12—O4b^vi	2.220 (4)
Tl21—O1bⁱ	3.066 (4)	Cd12—O4c	2.208 (3)
Tl21—O3bⁱ	3.270 (4)	Cd12—O3d	2.413 (4)
Tl21—O1cⁱⁱ	3.092 (4)	Cd12—O4e^vi	2.260 (3)
Tl21—O3cⁱⁱ	2.983 (4)	Cd12—O3f^xii	2.185 (4)
Tl21—O2d	3.039 (4)	Cd21—O2a	2.276 (3)
Tl21—O1fⁱⁱⁱ	3.195 (4)	Cd21—O1b	2.365 (4)
Tl21—O2f^iv	2.825 (4)	Cd21—O2c	2.429 (3)
Tl11—O1b	3.200 (4)	Cd21—O1d^vi	2.232 (4)
Tl11—O3b^v	3.218 (4)	Cd21—O1e^vi	2.281 (4)
Tl11—O4b^v	2.934 (4)	Cd21—O2e	2.207 (3)
Tl11—O3c^vi	3.205 (4)	Cd22—O1a^xiii	2.328 (4)
Tl11—O4c^vi	3.045 (5)	Cd22—O2b	2.228 (3)
Tl11—O2d^vi	3.078 (4)	Cd22—O1cⁱ	2.188 (4)
Tl11—O1e^vi	3.259 (4)	Cd22—O2d^xiv	2.494 (3)
Tl11—O3e^vi	3.008 (4)	Cd22—O1f^xv	2.265 (4)
Tl11—O4f	2.737 (4)	Cd22—O2f	2.197 (3)
Tl12—O1a	3.177 (4)	S1a—O1a	1.452 (4)
Tl12—O2a	3.277 (4)	S1a—O2a	1.462 (3)
Tl12—O3a^vii	3.184 (4)	S1a—O3a	1.488 (4)
Tl12—O4a^vii	3.035 (4)	S1a—O4a	1.501 (4)
Tl12—O2c^vii	3.166 (4)	S1b—O1b	1.452 (4)
Tl12—O3dⁱ	3.241 (4)	S1b—O2b	1.462 (3)
Tl12—O4dⁱ	2.998 (5)	S1b—O3b	1.488 (4)
Tl12—O4e	2.738 (4)	S1b—O4b	1.501 (4)
Tl12—O1f^viii	3.229 (4)	S1c—O1c	1.452 (4)
Tl12—O3f^viii	2.969 (4)	S1c—O2c	1.462 (4)
Tl22—O1a^ix	3.058 (4)	S1c—O3c	1.488 (4)
Tl22—O3a^ix	3.247 (4)	S1c—O4c	1.501 (3)
Tl22—O2b^vi	3.057 (4)	S1d—O1d	1.452 (4)
Tl22—O2c	3.051 (4)	S1d—O2d	1.462 (4)
Tl22—O1d^vi	3.036 (4)	S1d—O3d	1.488 (4)
Tl22—O3d^vi	2.960 (4)	S1d—O4d	1.501 (3)
Tl22—O1e^x	3.142 (4)	S1e—O1e	1.452 (4)
Tl22—O2e^vi	2.798 (4)	S1e—O2e	1.462 (4)
Cd11—O3a	2.258 (4)	S1e—O3e	1.488 (4)
Cd11—O4a^vii	2.173 (4)	S1e—O4e	1.501 (4)
Cd11—O3c	2.399 (4)	S1f—O1f	1.452 (4)
Cd11—O4d^xi	2.311 (3)	S1f—O2f	1.462 (4)
Cd11—O3e	2.150 (4)	S1f—O3f	1.488 (4)
Cd11—O4fⁱ	2.272 (3)	S1f—O4f	1.501 (4)
Cd12—O3b^xii	2.205 (4)

O2aⁱ—Tl21—O1bⁱ	64.44 (8)	O3a^ix—Tl22—O2c	76.0 (1)
O2aⁱ—Tl21—O3bⁱ	107.99 (8)	O3a^ix—Tl22—O1d^vi	74.8 (1)
O2aⁱ—Tl21—O1cⁱⁱ	156.4 (1)	O3a^ix—Tl22—O3d^vi	81.8 (1)
O2aⁱ—Tl21—O3cⁱⁱ	156.6 (1)	O3a^ix—Tl22—O1e^x	124.5 (1)
O2aⁱ—Tl21—O2d	95.1 (1)	O3a^ix—Tl22—O2e^vi	160.7 (1)
O2aⁱ—Tl21—O1fⁱⁱⁱ	78.4 (1)	O2b^vi—Tl22—O2c	95.2 (1)
O2aⁱ—Tl21—O2f^iv	90.4 (1)	O2b^vi—Tl22—O1d^vi	155.9 (1)
O1bⁱ—Tl21—O3bⁱ	43.89 (9)	O2b^vi—Tl22—O3d^vi	156.9 (1)
O1bⁱ—Tl21—O1cⁱⁱ	112.8 (1)	O2b^vi—Tl22—O1e^x	79.4 (1)
O1bⁱ—Tl21—O3cⁱⁱ	122.8 (1)	O2b^vi—Tl22—O2e^vi	92.3 (1)
O1bⁱ—Tl21—O2d	73.6 (1)	O2c—Tl22—O1d^vi	61.29 (9)
O1bⁱ—Tl21—O1fⁱⁱⁱ	118.4 (1)	O2c—Tl22—O3d^vi	107.82 (8)
O1bⁱ—Tl21—O2f^iv	152.6 (1)	O2c—Tl22—O1e^x	159.5 (1)
O3bⁱ—Tl21—O1cⁱⁱ	75.2 (1)	O2c—Tl22—O2e^vi	98.3 (1)
O3bⁱ—Tl21—O3cⁱⁱ	80.6 (1)	O1d^vi—Tl22—O3d^vi	46.67 (9)
O3bⁱ—Tl21—O2d	73.9 (1)	O1d^vi—Tl22—O1e^x	120.4 (1)
O3bⁱ—Tl21—O1fⁱⁱⁱ	125.7 (1)	O1d^vi—Tl22—O2e^vi	86.2 (1)
O3bⁱ—Tl21—O2f^iv	160.8 (1)	O3d^vi—Tl22—O1e^x	78.2 (1)
O1cⁱⁱ—Tl21—O3cⁱⁱ	46.00 (9)	O3d^vi—Tl22—O2e^vi	82.5 (1)
O1cⁱⁱ—Tl21—O2d	62.80 (9)	O1e^x—Tl22—O2e^vi	62.44 (9)
O1cⁱⁱ—Tl21—O1fⁱⁱⁱ	119.5 (1)	O3a—Cd11—O4a^vii	91.5 (2)
O1cⁱⁱ—Tl21—O2f^iv	85.8 (1)	O3a—Cd11—O3c	95.0 (1)
O3cⁱⁱ—Tl21—O2d	108.25 (8)	O3a—Cd11—O4d^xi	80.5 (2)
O3cⁱⁱ—Tl21—O1fⁱⁱⁱ	79.1 (1)	O3a—Cd11—O3e	98.5 (2)
O3cⁱⁱ—Tl21—O2f^iv	84.6 (1)	O3a—Cd11—O4fⁱ	163.0 (2)
O2d—Tl21—O1fⁱⁱⁱ	160.4 (1)	O4a^vii—Cd11—O3c	173.1 (2)
O2d—Tl21—O2f^iv	99.7 (1)	O4a^vii—Cd11—O4d^xi	93.7 (2)
O1fⁱⁱⁱ—Tl21—O2f^iv	62.23 (9)	O4a^vii—Cd11—O3e	92.0 (2)
O1b—Tl11—O3b^v	132.6 (1)	O4a^vii—Cd11—O4fⁱ	104.3 (2)
O1b—Tl11—O4b^v	94.93 (9)	O3c—Cd11—O4d^xi	85.3 (2)
O1b—Tl11—O3c^vi	148.4 (1)	O3c—Cd11—O3e	89.2 (2)
O1b—Tl11—O4c^vi	152.4 (1)	O3c—Cd11—O4fⁱ	69.0 (2)
O1b—Tl11—O2d^vi	71.3 (1)	O4d^xi—Cd11—O3e	174.3 (2)
O1b—Tl11—O1e^vi	59.48 (9)	O4d^xi—Cd11—O4fⁱ	92.0 (2)
O1b—Tl11—O3e^vi	90.3 (1)	O3e—Cd11—O4fⁱ	87.4 (2)
O1b—Tl11—O4f	103.9 (1)	O3b^xii—Cd12—O4b^vi	88.7 (2)
O3b^v—Tl11—O4b^v	45.89 (9)	O3b^xii—Cd12—O4c	81.1 (2)
O3b^v—Tl11—O3c^vi	78.2 (1)	O3b^xii—Cd12—O3d	94.6 (2)
O3b^v—Tl11—O4c^vi	54.4 (1)	O3b^xii—Cd12—O4e^vi	165.1 (2)
O3b^v—Tl11—O2d^vi	65.5 (1)	O3b^xii—Cd12—O3f^xii	97.6 (2)
O3b^v—Tl11—O1e^vi	142.44 (9)	O4b^vi—Cd12—O4c	93.7 (2)
O3b^v—Tl11—O3e^vi	136.0 (1)	O4b^vi—Cd12—O3d	176.5 (2)
O3b^v—Tl11—O4f	106.1 (1)	O4b^vi—Cd12—O4e^vi	105.8 (2)
O4b^v—Tl11—O3c^vi	107.2 (1)	O4b^vi—Cd12—O3f^xii	92.3 (2)
O4b^v—Tl11—O4c^vi	99.9 (1)	O4c—Cd12—O3d	85.7 (2)
O4b^v—Tl11—O2d^vi	58.6 (1)	O4c—Cd12—O4e^vi	94.4 (2)
O4b^v—Tl11—O1e^vi	150.6 (1)	O4c—Cd12—O3f^xii	173.8 (2)
O4b^v—Tl11—O3e^vi	161.1 (1)	O3d—Cd12—O4e^vi	70.8 (2)
O4b^v—Tl11—O4f	97.0 (1)	O3d—Cd12—O3f^xii	88.4 (2)
O3c^vi—Tl11—O4c^vi	45.32 (8)	O4e^vi—Cd12—O3f^xii	85.4 (2)
O3c^vi—Tl11—O2d^vi	139.7 (1)	O2a—Cd21—O1b	88.3 (1)
O3c^vi—Tl11—O1e^vi	102.1 (1)	O2a—Cd21—O2c	93.0 (1)
O3c^vi—Tl11—O3e^vi	61.9 (1)	O2a—Cd21—O1d^vi	89.1 (2)
O3c^vi—Tl11—O4f	52.2 (1)	O2a—Cd21—O1e^vi	174.9 (2)
O4c^vi—Tl11—O2d^vi	97.0 (1)	O2a—Cd21—O2e	94.9 (2)
O4c^vi—Tl11—O1e^vi	98.8 (1)	O1b—Cd21—O2c	172.7 (2)
O4c^vi—Tl11—O3e^vi	83.2 (1)	O1b—Cd21—O1d^vi	89.5 (2)
O4c^vi—Tl11—O4f	97.2 (1)	O1b—Cd21—O1e^vi	87.2 (1)
O2d^vi—Tl11—O1e^vi	96.81 (9)	O1b—Cd21—O2e	84.1 (2)
O2d^vi—Tl11—O3e^vi	139.96 (9)	O2c—Cd21—O1d^vi	83.4 (1)
O2d^vi—Tl11—O4f	153.59 (8)	O2c—Cd21—O1e^vi	91.1 (2)
O1e^vi—Tl11—O3e^vi	44.33 (9)	O2c—Cd21—O2e	102.9 (1)
O1e^vi—Tl11—O4f	102.85 (9)	O1d^vi—Cd21—O1e^vi	88.4 (2)
O3e^vi—Tl11—O4f	64.07 (9)	O1d^vi—Cd21—O2e	172.3 (2)
O1a—Tl12—O2a	42.41 (9)	O1e^vi—Cd21—O2e	87.1 (1)
O1a—Tl12—O3a^vii	131.7 (1)	O1a^xiii—Cd22—O2b	88.9 (1)
O1a—Tl12—O4a^vii	95.38 (9)	O1a^xiii—Cd22—O1cⁱ	86.7 (2)
O1a—Tl12—O2c^vii	71.2 (1)	O1a^xiii—Cd22—O2d^xiv	172.5 (2)
O1a—Tl12—O3dⁱ	149.05 (9)	O1a^xiii—Cd22—O1f^xv	86.8 (1)
O1a—Tl12—O4dⁱ	150.2 (1)	O1a^xiii—Cd22—O2f	82.9 (2)
O1a—Tl12—O4e	103.5 (1)	O2b—Cd22—O1cⁱ	91.3 (2)
O1a—Tl12—O1f^viii	59.03 (9)	O2b—Cd22—O2d^xiv	92.1 (1)
O1a—Tl12—O3f^viii	90.4 (1)	O2b—Cd22—O1f^xv	175.3 (2)
O2a—Tl12—O3a^vii	141.5 (1)	O2b—Cd22—O2f	92.3 (2)
O2a—Tl12—O4a^vii	96.92 (9)	O1cⁱ—Cd22—O2d^xiv	85.8 (1)
O2a—Tl12—O2c^vii	108.19 (9)	O1cⁱ—Cd22—O1f^xv	86.7 (2)
O2a—Tl12—O3dⁱ	111.71 (8)	O1cⁱ—Cd22—O2f	168.9 (2)
O2a—Tl12—O4dⁱ	153.71 (8)	O2d^xiv—Cd22—O1f^xv	92.0 (1)
O2a—Tl12—O4e	61.2 (1)	O2d^xiv—Cd22—O2f	104.6 (1)
O2a—Tl12—O1f^viii	74.0 (1)	O1f^xv—Cd22—O2f	89.0 (1)
O2a—Tl12—O3f^viii	74.8 (1)	O1a—S1a—O2a	106.6 (3)
O3a^vii—Tl12—O4a^vii	45.57 (8)	O1a—S1a—O3a	107.8 (3)
O3a^vii—Tl12—O2c^vii	64.6 (1)	O1a—S1a—O4a	111.2 (3)
O3a^vii—Tl12—O3dⁱ	78.6 (1)	O2a—S1a—O3a	109.9 (3)
O3a^vii—Tl12—O4dⁱ	56.9 (1)	O2a—S1a—O4a	113.5 (3)
O3a^vii—Tl12—O4e	107.6 (1)	O3a—S1a—O4a	107.6 (3)
O3a^vii—Tl12—O1f^viii	142.10 (9)	O1b—S1b—O2b	106.6 (3)
O3a^vii—Tl12—O3f^viii	136.5 (1)	O1b—S1b—O3b	107.8 (3)
O4a^vii—Tl12—O2c^vii	59.5 (1)	O1b—S1b—O4b	111.2 (3)
O4a^vii—Tl12—O3dⁱ	106.4 (1)	O2b—S1b—O3b	109.9 (3)
O4a^vii—Tl12—O4dⁱ	102.0 (1)	O2b—S1b—O4b	113.5 (3)
O4a^vii—Tl12—O4e	96.6 (1)	O3b—S1b—O4b	107.6 (3)
O4a^vii—Tl12—O1f^viii	150.9 (1)	O1c—S1c—O2c	106.6 (3)
O4a^vii—Tl12—O3f^viii	160.2 (1)	O1c—S1c—O3c	107.8 (3)
O2c^vii—Tl12—O3dⁱ	139.1 (1)	O1c—S1c—O4c	111.2 (3)
O2c^vii—Tl12—O4dⁱ	97.14 (9)	O2c—S1c—O3c	109.9 (3)
O2c^vii—Tl12—O4e	153.87 (8)	O2c—S1c—O4c	113.5 (3)
O2c^vii—Tl12—O1f^viii	96.40 (9)	O3c—S1c—O4c	107.6 (3)
O2c^vii—Tl12—O3f^viii	139.96 (9)	O1d—S1d—O2d	106.6 (3)
O3dⁱ—Tl12—O4dⁱ	45.28 (8)	O1d—S1d—O3d	107.8 (3)
O3dⁱ—Tl12—O4e	53.1 (1)	O1d—S1d—O4d	111.2 (3)
O3dⁱ—Tl12—O1f^viii	102.7 (1)	O2d—S1d—O3d	109.9 (3)
O3dⁱ—Tl12—O3f^viii	62.1 (1)	O2d—S1d—O4d	113.5 (3)
O4dⁱ—Tl12—O4e	98.3 (1)	O3d—S1d—O4d	107.6 (3)
O4dⁱ—Tl12—O1f^viii	96.7 (1)	O1e—S1e—O2e	106.6 (2)
O4dⁱ—Tl12—O3f^viii	81.3 (1)	O1e—S1e—O3e	107.8 (3)
O4e—Tl12—O1f^viii	102.56 (9)	O1e—S1e—O4e	111.2 (3)
O4e—Tl12—O3f^viii	63.63 (9)	O2e—S1e—O3e	109.9 (3)
O1f^viii—Tl12—O3f^viii	44.84 (9)	O2e—S1e—O4e	113.5 (3)
O1a^ix—Tl22—O3a^ix	44.15 (9)	O3e—S1e—O4e	107.6 (3)
O1a^ix—Tl22—O2b^vi	62.90 (8)	O1f—S1f—O2f	106.6 (2)
O1a^ix—Tl22—O2c	74.4 (1)	O1f—S1f—O3f	107.8 (2)
O1a^ix—Tl22—O1d^vi	111.4 (1)	O1f—S1f—O4f	111.2 (3)
O1a^ix—Tl22—O3d^vi	124.8 (1)	O2f—S1f—O3f	109.9 (3)
O1a^ix—Tl22—O1e^x	119.0 (1)	O2f—S1f—O4f	113.5 (3)
O1a^ix—Tl22—O2e^vi	152.7 (1)	O3f—S1f—O4f	107.6 (2)
O3a^ix—Tl22—O2b^vi	106.46 (8)

Symmetry codes: (i) −x+1, −y+1, z−1/2; (ii) −x+1, −y, z−1/2; (iii) x, y−1, z−1; (iv) −x+2, −y+1, z−1/2; (v) −x+1, −y+2, z+1/2; (vi) −x+1, −y+1, z+1/2; (vii) −x, −y+1, z−1/2; (viii) −x+1, −y+2, z−1/2; (ix) −x, −y+1, z+1/2; (x) x, y, z+1; (xi) x−1, y, z; (xii) x, y−1, z; (xiii) x+1, y, z; (xiv) x, y+1, z; (xv) −x+2, −y+2, z−1/2.

(85K) top

Crystal data top

Tl₂Cd₂(SO₄)₃	F(000) = 1608
M_r = 921.7	D_x = 5.505 Mg m⁻³
Orthorhombic, P2₁2₁2₁	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2ac 2ab	Cell parameters from 25 reflections
a = 10.327 (3) Å	θ = 5.1–28.7°
b = 10.345 (4) Å	µ = 33.30 mm⁻¹
c = 10.406 (5) Å	T = 85 K
V = 1111.7 (8) Å³	Spherical, colourless
Z = 4	0.12 mm (radius)

Data collection top

Enraf-Nonius CAD-4 diffractometer	θ_max = 35.0°, θ_min = 2.8°
θ/2θ scans	h = 0→16
Absorption correction: for a sphere ?	k = 0→16
T_min = 0.002, T_max = 0.015	l = −16→16
5303 measured reflections	3 standard reflections every 120 min
4985 independent reflections	intensity decay: 4%
4028 reflections with I > 3σ(I)

Refinement top

Refinement on F	Weighting scheme based on measured s.u.'s w = 1/σ²(F)
R[F² > 2σ(F²)] = 0.057	(Δ/σ)_max = 0.0004
wR(F²) = 0.060	Δρ_max = 4.77 e Å⁻³
S = 1.94	Δρ_min = −4.73 e Å⁻³
4985 reflections	Extinction correction: B-C type 1 Gaussian isotropic
67 parameters	Extinction coefficient: 0.015 (3)

Crystal data top

Tl₂Cd₂(SO₄)₃	V = 1111.7 (8) Å³
M_r = 921.7	Z = 4
Orthorhombic, P2₁2₁2₁	Mo Kα radiation
a = 10.327 (3) Å	µ = 33.30 mm⁻¹
b = 10.345 (4) Å	T = 85 K
c = 10.406 (5) Å	0.12 mm (radius)

Data collection top

Enraf-Nonius CAD-4 diffractometer	4985 independent reflections
Absorption correction: for a sphere ?	4028 reflections with I > 3σ(I)
T_min = 0.002, T_max = 0.015	3 standard reflections every 120 min
5303 measured reflections	intensity decay: 4%

Refinement top

R[F² > 2σ(F²)] = 0.057	67 parameters
wR(F²) = 0.060	Δρ_max = 4.77 e Å⁻³
S = 1.94	Δρ_min = −4.73 e Å⁻³
4985 reflections

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Tl1	0.81231 (7)	0.82841 (7)	0.81649 (7)	0.0076 (1)
Tl2	0.05831 (7)	0.04009 (7)	0.05051 (7)	0.0093 (2)
Cd1	0.3325 (1)	0.3163 (1)	0.3408 (1)	0.0050 (3)
Cd2	0.5790 (1)	0.5998 (1)	0.5943 (1)	0.0052 (3)
S1ab	0.2602 (4)	0.6201 (4)	0.5082 (3)	0.0045
O1ab	0.175 (1)	0.700 (1)	0.434 (1)	0.0118
O2ab	0.3937 (8)	0.673 (1)	0.496 (1)	0.0095
O3ab	0.253 (1)	0.4866 (8)	0.454 (1)	0.0094
O4ab	0.221 (1)	0.616 (1)	0.6443 (8)	0.0071
S1cd	0.5234 (3)	0.2850 (3)	0.6269 (4)	0.0045
O1cd	0.511 (1)	0.195 (1)	0.731 (1)	0.0118
O2cd	0.491 (1)	0.4162 (8)	0.676 (1)	0.0095
O3cd	0.429 (1)	0.245 (1)	0.5252 (9)	0.0094
O4cd	0.6553 (8)	0.284 (1)	0.573 (1)	0.0071
S1ef	0.6325 (4)	0.5072 (3)	0.2860 (3)	0.0045
O1ef	0.736 (1)	0.440 (1)	0.222 (1)	0.0118
O2ef	0.682 (1)	0.554 (1)	0.4122 (8)	0.0095
O3ef	0.5245 (9)	0.413 (1)	0.305 (1)	0.0094
O4ef	0.585 (1)	0.6170 (8)	0.209 (1)	0.0071

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Tl1	0.0076 (3)	0.0082 (2)	0.0072 (3)	−0.0004 (2)	0.0009 (2)	−0.0003 (2)
Tl2	0.0078 (3)	0.0109 (3)	0.0090 (3)	−0.0005 (2)	−0.0005 (2)	−0.0001 (2)
Cd1	0.0053 (5)	0.0061 (5)	0.0037 (5)	0.0013 (4)	−0.0005 (3)	−0.0008 (4)
Cd2	0.0049 (5)	0.0069 (5)	0.0037 (5)	−0.0016 (4)	0.0007 (4)	−0.0001 (4)
S1ab	0.004938	0.00522	0.003451	−0.002064	0.000933	0.000926
O1ab	0.002104	0.020092	0.013215	−0.001758	−0.003367	0.002508
O2ab	0.006196	0.004226	0.018101	−0.002181	0.004078	−0.002335
O3ab	0.011804	0.006607	0.009694	−0.001359	−0.006412	−0.000746
O4ab	0.013867	0.005246	0.00233	−0.006195	0.004542	−0.003401
S1cd	0.004339	0.00483	0.00444	−0.000037	0.001905	−0.001787
O1cd	0.01683	0.001255	0.017326	0.000997	0.00408	0.001395
O2cd	0.012085	0.008336	0.008102	0.004672	−0.005264	−0.005353
O3cd	0.012734	0.007853	0.007518	−0.006216	−0.001687	0.000587
O4cd	0.000513	0.013273	0.007657	−0.002292	0.000937	−0.007716
S1ef	0.004607	0.004409	0.004593	0.000527	−0.002543	0.000365
O1ef	0.017813	0.012224	0.005374	0.004022	−0.001294	−0.006815
O2ef	0.007401	0.016002	0.00512	−0.00696	−0.001327	−0.000238
O3ef	0.007353	0.005407	0.015345	−0.001059	0.00104	−0.004518
O4ef	0.007545	0.002953	0.010945	−0.004024	−0.006654	0.005477

Geometric parameters (Å, º) top

Tl1—O1abⁱ	2.98 (1)	Cd1—O3cd	2.29 (1)
Tl1—O3abⁱⁱ	2.98 (1)	Cd1—O4cd^ix	2.287 (9)
Tl1—O4abⁱⁱ	3.03 (1)	Cd2—O1abⁱ	2.31 (1)
Tl1—O1efⁱⁱⁱ	2.99 (1)	Cd2—O2ab	2.296 (9)
Tl1—O3efⁱⁱⁱ	3.01 (1)	Cd2—O1efⁱⁱⁱ	2.36 (1)
Tl1—O4efⁱ	2.89 (1)	Cd2—O2ef	2.224 (9)
Tl1—O2cdⁱⁱ	3.27 (1)	Cd2—O1cdⁱⁱ	2.27 (1)
Tl1—O3cdⁱⁱ	3.11 (1)	Cd2—O2cd	2.269 (9)
Tl1—O4cdⁱⁱⁱ	2.92 (1)	S1ab—O1ab	1.44 (1)
Tl2—O1ab^iv	2.93 (1)	S1ab—O2ab	1.487 (9)
Tl2—O2ab^v	3.06 (1)	S1ab—O3ab	1.50 (1)
Tl2—O3ab^iv	3.27 (1)	S1ab—O4ab	1.475 (9)
Tl2—O2ef^vi	2.72 (1)	S1ef—O1ef	1.44 (1)
Tl2—O4ef^vii	3.16 (1)	S1ef—O2ef	1.49 (1)
Tl2—O1cd^viii	3.16 (1)	S1ef—O3ef	1.50 (1)
Tl2—O2cd^ix	2.96 (1)	S1ef—O4ef	1.47 (1)
Tl2—O3cd^viii	2.96 (1)	S1cd—O1cd	1.44 (1)
Cd1—O3ab	2.27 (1)	S1cd—O2cd	1.49 (1)
Cd1—O4ab^v	2.229 (9)	S1cd—O3cd	1.50 (1)
Cd1—O3ef	2.251 (9)	S1cd—O4cd	1.475 (9)
Cd1—O4ef^vi	2.289 (9)

O3ab—Cd1—O4ab^v	98.2 (4)	O1efⁱⁱⁱ—Cd2—O2ef	93.1 (4)
O3ab—Cd1—O3ef	93.5 (4)	O1efⁱⁱⁱ—Cd2—O1cdⁱⁱ	87.7 (4)
O3ab—Cd1—O4ef^vi	161.7 (4)	O1efⁱⁱⁱ—Cd2—O2cd	88.1 (4)
O3ab—Cd1—O3cd	88.5 (4)	O2ef—Cd2—O1cdⁱⁱ	166.6 (4)
O3ab—Cd1—O4cd^ix	81.8 (4)	O2ef—Cd2—O2cd	109.2 (4)
O4ab^v—Cd1—O3ef	85.7 (4)	O1cdⁱⁱ—Cd2—O2cd	84.2 (4)
O4ab^v—Cd1—O4ef^vi	99.6 (4)	O1ab—S1ab—O2ab	108.3 (6)
O4ab^v—Cd1—O3cd	168.2 (4)	O1ab—S1ab—O3ab	107.4 (6)
O4ab^v—Cd1—O4cd^ix	107.8 (4)	O1ab—S1ab—O4ab	111.2 (6)
O3ef—Cd1—O4ef^vi	92.0 (4)	O2ab—S1ab—O3ab	110.6 (6)
O3ef—Cd1—O3cd	84.2 (4)	O2ab—S1ab—O4ab	110.3 (6)
O3ef—Cd1—O4cd^ix	166.2 (4)	O3ab—S1ab—O4ab	109.1 (6)
O4ef^vi—Cd1—O3cd	74.7 (4)	O1cd—S1cd—O2cd	108.3 (6)
O4ef^vi—Cd1—O4cd^ix	88.8 (4)	O1cd—S1cd—O3cd	107.4 (6)
O3cd—Cd1—O4cd^ix	82.7 (4)	O1cd—S1cd—O4cd	111.2 (6)
O1abⁱ—Cd2—O2ab	90.3 (4)	O2cd—S1cd—O3cd	110.6 (6)
O1abⁱ—Cd2—O1efⁱⁱⁱ	83.2 (4)	O2cd—S1cd—O4cd	110.3 (6)
O1abⁱ—Cd2—O2ef	83.2 (4)	O3cd—S1cd—O4cd	109.1 (6)
O1abⁱ—Cd2—O1cdⁱⁱ	83.6 (4)	O1ef—S1ef—O2ef	108.3 (6)
O1abⁱ—Cd2—O2cd	165.3 (4)	O1ef—S1ef—O3ef	107.4 (6)
O2ab—Cd2—O1efⁱⁱⁱ	168.9 (4)	O1ef—S1ef—O4ef	111.2 (6)
O2ab—Cd2—O2ef	95.1 (4)	O2ef—S1ef—O3ef	110.6 (6)
O2ab—Cd2—O1cdⁱⁱ	82.5 (4)	O2ef—S1ef—O4ef	110.3 (6)
O2ab—Cd2—O2cd	96.2 (4)	O3ef—S1ef—O4ef	109.1 (6)

Symmetry codes: (i) x+1/2, −y+3/2, −z+1; (ii) −x+1, y+1/2, −z+3/2; (iii) −x+3/2, −y+1, z+1/2; (iv) −x, y−1/2, −z+1/2; (v) −x+1/2, −y+1, z−1/2; (vi) −x+1, y−1/2, −z+1/2; (vii) x−1/2, −y+1/2, −z; (viii) −x+1/2, −y, z−1/2; (ix) x−1/2, −y+1/2, −z+1.

Experimental details

	(121K)	(85K)
Crystal data
Chemical formula	Tl₂Cd₂(SO₄)₃	Tl₂Cd₂(SO₄)₃
M_r	921.7	921.7
Crystal system, space group	Monoclinic, P112₁	Orthorhombic, P2₁2₁2₁
Temperature (K)	121	85
a, b, c (Å)	10.356 (4), 10.350 (2), 10.353 (6)	10.327 (3), 10.345 (4), 10.406 (5)
α, β, γ (°)	90, 90, 90.04 (3)	90, 90, 90
V (Å³)	1109.7 (8)	1111.7 (8)
Z	4	4
Radiation type	Synchrotron, λ = 0.5502 Å	Mo Kα
µ (mm⁻¹)	17.53	33.30
Crystal size (mm)	0.59 × 0.35 × 0.35	0.12 (radius)

Data collection
Diffractometer	Huber CAD-4 κ geometry diffractometer	Enraf-Nonius CAD-4 diffractometer
Absorption correction	Analytical (Alcock, 1974)	For a sphere
T_min, T_max	0.009, 0.046	0.002, 0.015
No. of measured, independent and observed [I > 3σ(I)] reflections	9312, 8392, 8392	5303, 4985, 4028
R_int	?	?
(sin θ/λ)_max (Å⁻¹)	0.622	0.806

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.044, 0.064, 13.78	0.057, 0.060, 1.94
No. of reflections	8392	4985
No. of parameters	132	67
No. of restraints	?	?
Δρ_max, Δρ_min (e Å⁻³)	2.43, −1.86	4.77, −4.73

Computer programs: DIF4, CAD4VPC, AVSORT, REDUCE, xtal_ABSORB, JANA98, ORTEP.

Selected geometric parameters (Å, º) for (121K) top

Tl21—O2aⁱ	3.000 (4)	Cd12—O4b^vi	2.220 (4)
Tl21—O1bⁱ	3.066 (4)	Cd12—O4c	2.208 (3)
Tl21—O3bⁱ	3.270 (4)	Cd12—O3d	2.413 (4)
Tl21—O1cⁱⁱ	3.092 (4)	Cd12—O4e^vi	2.260 (3)
Tl21—O3cⁱⁱ	2.983 (4)	Cd12—O3f^xii	2.185 (4)
Tl21—O2d	3.039 (4)	Cd21—O2a	2.276 (3)
Tl21—O1fⁱⁱⁱ	3.195 (4)	Cd21—O1b	2.365 (4)
Tl21—O2f^iv	2.825 (4)	Cd21—O2c	2.429 (3)
Tl11—O1b	3.200 (4)	Cd21—O1d^vi	2.232 (4)
Tl11—O3b^v	3.218 (4)	Cd21—O1e^vi	2.281 (4)
Tl11—O4b^v	2.934 (4)	Cd21—O2e	2.207 (3)
Tl11—O3c^vi	3.205 (4)	Cd22—O1a^xiii	2.328 (4)
Tl11—O4c^vi	3.045 (5)	Cd22—O2b	2.228 (3)
Tl11—O2d^vi	3.078 (4)	Cd22—O1cⁱ	2.188 (4)
Tl11—O1e^vi	3.259 (4)	Cd22—O2d^xiv	2.494 (3)
Tl11—O3e^vi	3.008 (4)	Cd22—O1f^xv	2.265 (4)
Tl11—O4f	2.737 (4)	Cd22—O2f	2.197 (3)
Tl12—O1a	3.177 (4)	S1a—O1a	1.452 (4)
Tl12—O2a	3.277 (4)	S1a—O2a	1.462 (3)
Tl12—O3a^vii	3.184 (4)	S1a—O3a	1.488 (4)
Tl12—O4a^vii	3.035 (4)	S1a—O4a	1.501 (4)
Tl12—O2c^vii	3.166 (4)	S1b—O1b	1.452 (4)
Tl12—O3dⁱ	3.241 (4)	S1b—O2b	1.462 (3)
Tl12—O4dⁱ	2.998 (5)	S1b—O3b	1.488 (4)
Tl12—O4e	2.738 (4)	S1b—O4b	1.501 (4)
Tl12—O1f^viii	3.229 (4)	S1c—O1c	1.452 (4)
Tl12—O3f^viii	2.969 (4)	S1c—O2c	1.462 (4)
Tl22—O1a^ix	3.058 (4)	S1c—O3c	1.488 (4)
Tl22—O3a^ix	3.247 (4)	S1c—O4c	1.501 (3)
Tl22—O2b^vi	3.057 (4)	S1d—O1d	1.452 (4)
Tl22—O2c	3.051 (4)	S1d—O2d	1.462 (4)
Tl22—O1d^vi	3.036 (4)	S1d—O3d	1.488 (4)
Tl22—O3d^vi	2.960 (4)	S1d—O4d	1.501 (3)
Tl22—O1e^x	3.142 (4)	S1e—O1e	1.452 (4)
Tl22—O2e^vi	2.798 (4)	S1e—O2e	1.462 (4)
Cd11—O3a	2.258 (4)	S1e—O3e	1.488 (4)
Cd11—O4a^vii	2.173 (4)	S1e—O4e	1.501 (4)
Cd11—O3c	2.399 (4)	S1f—O1f	1.452 (4)
Cd11—O4d^xi	2.311 (3)	S1f—O2f	1.462 (4)
Cd11—O3e	2.150 (4)	S1f—O3f	1.488 (4)
Cd11—O4fⁱ	2.272 (3)	S1f—O4f	1.501 (4)
Cd12—O3b^xii	2.205 (4)

O1a—S1a—O2a	106.6 (3)	O1d—S1d—O2d	106.6 (3)
O1a—S1a—O3a	107.8 (3)	O1d—S1d—O3d	107.8 (3)
O1a—S1a—O4a	111.2 (3)	O1d—S1d—O4d	111.2 (3)
O2a—S1a—O3a	109.9 (3)	O2d—S1d—O3d	109.9 (3)
O2a—S1a—O4a	113.5 (3)	O2d—S1d—O4d	113.5 (3)
O3a—S1a—O4a	107.6 (3)	O3d—S1d—O4d	107.6 (3)
O1b—S1b—O2b	106.6 (3)	O1e—S1e—O2e	106.6 (2)
O1b—S1b—O3b	107.8 (3)	O1e—S1e—O3e	107.8 (3)
O1b—S1b—O4b	111.2 (3)	O1e—S1e—O4e	111.2 (3)
O2b—S1b—O3b	109.9 (3)	O2e—S1e—O3e	109.9 (3)
O2b—S1b—O4b	113.5 (3)	O2e—S1e—O4e	113.5 (3)
O3b—S1b—O4b	107.6 (3)	O3e—S1e—O4e	107.6 (3)
O1c—S1c—O2c	106.6 (3)	O1f—S1f—O2f	106.6 (2)
O1c—S1c—O3c	107.8 (3)	O1f—S1f—O3f	107.8 (2)
O1c—S1c—O4c	111.2 (3)	O1f—S1f—O4f	111.2 (3)
O2c—S1c—O3c	109.9 (3)	O2f—S1f—O3f	109.9 (3)
O2c—S1c—O4c	113.5 (3)	O2f—S1f—O4f	113.5 (3)
O3c—S1c—O4c	107.6 (3)	O3f—S1f—O4f	107.6 (2)

Domain fractions

f₁	34.2 (2)
f₂	2.4 (2)
f₃	30.6 (2)
f₄	0.0 (2)
f₅	28.8 (2)
f₆	4.0 (2)

Selected geometric parameters (Å, º) for (85K) top

Tl1—O1abⁱ	2.98 (1)	Cd1—O3cd	2.29 (1)
Tl1—O3abⁱⁱ	2.98 (1)	Cd1—O4cd^ix	2.287 (9)
Tl1—O4abⁱⁱ	3.03 (1)	Cd2—O1abⁱ	2.31 (1)
Tl1—O1efⁱⁱⁱ	2.99 (1)	Cd2—O2ab	2.296 (9)
Tl1—O3efⁱⁱⁱ	3.01 (1)	Cd2—O1efⁱⁱⁱ	2.36 (1)
Tl1—O4efⁱ	2.89 (1)	Cd2—O2ef	2.224 (9)
Tl1—O2cdⁱⁱ	3.27 (1)	Cd2—O1cdⁱⁱ	2.27 (1)
Tl1—O3cdⁱⁱ	3.11 (1)	Cd2—O2cd	2.269 (9)
Tl1—O4cdⁱⁱⁱ	2.92 (1)	S1ab—O1ab	1.44 (1)
Tl2—O1ab^iv	2.93 (1)	S1ab—O2ab	1.487 (9)
Tl2—O2ab^v	3.06 (1)	S1ab—O3ab	1.50 (1)
Tl2—O3ab^iv	3.27 (1)	S1ab—O4ab	1.475 (9)
Tl2—O2ef^vi	2.72 (1)	S1ef—O1ef	1.44 (1)
Tl2—O4ef^vii	3.16 (1)	S1ef—O2ef	1.49 (1)
Tl2—O1cd^viii	3.16 (1)	S1ef—O3ef	1.50 (1)
Tl2—O2cd^ix	2.96 (1)	S1ef—O4ef	1.47 (1)
Tl2—O3cd^viii	2.96 (1)	S1cd—O1cd	1.44 (1)
Cd1—O3ab	2.27 (1)	S1cd—O2cd	1.49 (1)
Cd1—O4ab^v	2.229 (9)	S1cd—O3cd	1.50 (1)
Cd1—O3ef	2.251 (9)	S1cd—O4cd	1.475 (9)
Cd1—O4ef^vi	2.289 (9)

O1ab—S1ab—O2ab	108.3 (6)	O2cd—S1cd—O3cd	110.6 (6)
O1ab—S1ab—O3ab	107.4 (6)	O2cd—S1cd—O4cd	110.3 (6)
O1ab—S1ab—O4ab	111.2 (6)	O3cd—S1cd—O4cd	109.1 (6)
O2ab—S1ab—O3ab	110.6 (6)	O1ef—S1ef—O2ef	108.3 (6)
O2ab—S1ab—O4ab	110.3 (6)	O1ef—S1ef—O3ef	107.4 (6)
O3ab—S1ab—O4ab	109.1 (6)	O1ef—S1ef—O4ef	111.2 (6)
O1cd—S1cd—O2cd	108.3 (6)	O2ef—S1ef—O3ef	110.6 (6)
O1cd—S1cd—O3cd	107.4 (6)	O2ef—S1ef—O4ef	110.3 (6)
O1cd—S1cd—O4cd	111.2 (6)	O3ef—S1ef—O4ef	109.1 (6)

Domain fractions

f₁	79.1 (2)
f₂	10.5 (2)
f₃	10.4 (2)

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X-ray structure determination of the monoclinic (121 K) and orthorhombic (85 K) phases of ­langbeinite-type dithallium dicadmium sulfate

Supporting information

X-ray structure determination of the monoclinic (121 K) and orthorhombic (85 K) phases of langbeinite-type dithallium dicadmium sulfate