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

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.

Computing details

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)

Crystal data

Tl2Cd2(SO4)3	F(000) = 1608
Mr = 921.7	Dx = 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) Å^3	0.59 × 0.35 × 0.35 mm
Z = 4

Data collection

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

Refinement

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

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
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 (Ų)

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

Tl21—O2a^i	3.000 (4)	Cd12—O4b^vi	2.220 (4)
Tl21—O1b^i	3.066 (4)	Cd12—O4c	2.208 (3)
Tl21—O3b^i	3.270 (4)	Cd12—O3d	2.413 (4)
Tl21—O1c^ii	3.092 (4)	Cd12—O4e^vi	2.260 (3)
Tl21—O3c^ii	2.983 (4)	Cd12—O3f^xii	2.185 (4)
Tl21—O2d	3.039 (4)	Cd21—O2a	2.276 (3)
Tl21—O1f^iii	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—O1c^i	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—O3d^i	3.241 (4)	S1b—O2b	1.462 (3)
Tl12—O4d^i	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—O4f^i	2.272 (3)	S1f—O4f	1.501 (4)
Cd12—O3b^xii	2.205 (4)
O2a^i—Tl21—O1b^i	64.44 (8)	O3a^ix—Tl22—O2c	76.0 (1)
O2a^i—Tl21—O3b^i	107.99 (8)	O3a^ix—Tl22—O1d^vi	74.8 (1)
O2a^i—Tl21—O1c^ii	156.4 (1)	O3a^ix—Tl22—O3d^vi	81.8 (1)
O2a^i—Tl21—O3c^ii	156.6 (1)	O3a^ix—Tl22—O1e^x	124.5 (1)
O2a^i—Tl21—O2d	95.1 (1)	O3a^ix—Tl22—O2e^vi	160.7 (1)
O2a^i—Tl21—O1f^iii	78.4 (1)	O2b^vi—Tl22—O2c	95.2 (1)
O2a^i—Tl21—O2f^iv	90.4 (1)	O2b^vi—Tl22—O1d^vi	155.9 (1)
O1b^i—Tl21—O3b^i	43.89 (9)	O2b^vi—Tl22—O3d^vi	156.9 (1)
O1b^i—Tl21—O1c^ii	112.8 (1)	O2b^vi—Tl22—O1e^x	79.4 (1)
O1b^i—Tl21—O3c^ii	122.8 (1)	O2b^vi—Tl22—O2e^vi	92.3 (1)
O1b^i—Tl21—O2d	73.6 (1)	O2c—Tl22—O1d^vi	61.29 (9)
O1b^i—Tl21—O1f^iii	118.4 (1)	O2c—Tl22—O3d^vi	107.82 (8)
O1b^i—Tl21—O2f^iv	152.6 (1)	O2c—Tl22—O1e^x	159.5 (1)
O3b^i—Tl21—O1c^ii	75.2 (1)	O2c—Tl22—O2e^vi	98.3 (1)
O3b^i—Tl21—O3c^ii	80.6 (1)	O1d^vi—Tl22—O3d^vi	46.67 (9)
O3b^i—Tl21—O2d	73.9 (1)	O1d^vi—Tl22—O1e^x	120.4 (1)
O3b^i—Tl21—O1f^iii	125.7 (1)	O1d^vi—Tl22—O2e^vi	86.2 (1)
O3b^i—Tl21—O2f^iv	160.8 (1)	O3d^vi—Tl22—O1e^x	78.2 (1)
O1c^ii—Tl21—O3c^ii	46.00 (9)	O3d^vi—Tl22—O2e^vi	82.5 (1)
O1c^ii—Tl21—O2d	62.80 (9)	O1e^x—Tl22—O2e^vi	62.44 (9)
O1c^ii—Tl21—O1f^iii	119.5 (1)	O3a—Cd11—O4a^vii	91.5 (2)
O1c^ii—Tl21—O2f^iv	85.8 (1)	O3a—Cd11—O3c	95.0 (1)
O3c^ii—Tl21—O2d	108.25 (8)	O3a—Cd11—O4d^xi	80.5 (2)
O3c^ii—Tl21—O1f^iii	79.1 (1)	O3a—Cd11—O3e	98.5 (2)
O3c^ii—Tl21—O2f^iv	84.6 (1)	O3a—Cd11—O4f^i	163.0 (2)
O2d—Tl21—O1f^iii	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)
O1f^iii—Tl21—O2f^iv	62.23 (9)	O4a^vii—Cd11—O3e	92.0 (2)
O1b—Tl11—O3b^v	132.6 (1)	O4a^vii—Cd11—O4f^i	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—O4f^i	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—O4f^i	92.0 (2)
O1b—Tl11—O3e^vi	90.3 (1)	O3e—Cd11—O4f^i	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—O1c^i	86.7 (2)
O1a—Tl12—O2c^vii	71.2 (1)	O1a^xiii—Cd22—O2d^xiv	172.5 (2)
O1a—Tl12—O3d^i	149.05 (9)	O1a^xiii—Cd22—O1f^xv	86.8 (1)
O1a—Tl12—O4d^i	150.2 (1)	O1a^xiii—Cd22—O2f	82.9 (2)
O1a—Tl12—O4e	103.5 (1)	O2b—Cd22—O1c^i	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)	O1c^i—Cd22—O2d^xiv	85.8 (1)
O2a—Tl12—O2c^vii	108.19 (9)	O1c^i—Cd22—O1f^xv	86.7 (2)
O2a—Tl12—O3d^i	111.71 (8)	O1c^i—Cd22—O2f	168.9 (2)
O2a—Tl12—O4d^i	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—O3d^i	78.6 (1)	O2a—S1a—O3a	109.9 (3)
O3a^vii—Tl12—O4d^i	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—O3d^i	106.4 (1)	O2b—S1b—O3b	109.9 (3)
O4a^vii—Tl12—O4d^i	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—O3d^i	139.1 (1)	O1c—S1c—O4c	111.2 (3)
O2c^vii—Tl12—O4d^i	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)
O3d^i—Tl12—O4d^i	45.28 (8)	O1d—S1d—O3d	107.8 (3)
O3d^i—Tl12—O4e	53.1 (1)	O1d—S1d—O4d	111.2 (3)
O3d^i—Tl12—O1f^viii	102.7 (1)	O2d—S1d—O3d	109.9 (3)
O3d^i—Tl12—O3f^viii	62.1 (1)	O2d—S1d—O4d	113.5 (3)
O4d^i—Tl12—O4e	98.3 (1)	O3d—S1d—O4d	107.6 (3)
O4d^i—Tl12—O1f^viii	96.7 (1)	O1e—S1e—O2e	106.6 (2)
O4d^i—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)

Crystal data

Tl2Cd2(SO4)3	F(000) = 1608
Mr = 921.7	Dx = 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) Å^3	Spherical, colourless
Z = 4	0.12 mm (radius)

Data collection

Enraf-Nonius CAD-4 diffractometer	θmax = 35.0°, θmin = 2.8°
θ/2θ scans	h = 0→16
Absorption correction: for a sphere ?	k = 0→16
Tmin = 0.002, Tmax = 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

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

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
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 (Ų)

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

Tl1—O1ab^i	2.98 (1)	Cd1—O3cd	2.29 (1)
Tl1—O3ab^ii	2.98 (1)	Cd1—O4cd^ix	2.287 (9)
Tl1—O4ab^ii	3.03 (1)	Cd2—O1ab^i	2.31 (1)
Tl1—O1ef^iii	2.99 (1)	Cd2—O2ab	2.296 (9)
Tl1—O3ef^iii	3.01 (1)	Cd2—O1ef^iii	2.36 (1)
Tl1—O4ef^i	2.89 (1)	Cd2—O2ef	2.224 (9)
Tl1—O2cd^ii	3.27 (1)	Cd2—O1cd^ii	2.27 (1)
Tl1—O3cd^ii	3.11 (1)	Cd2—O2cd	2.269 (9)
Tl1—O4cd^iii	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)	O1ef^iii—Cd2—O2ef	93.1 (4)
O3ab—Cd1—O3ef	93.5 (4)	O1ef^iii—Cd2—O1cd^ii	87.7 (4)
O3ab—Cd1—O4ef^vi	161.7 (4)	O1ef^iii—Cd2—O2cd	88.1 (4)
O3ab—Cd1—O3cd	88.5 (4)	O2ef—Cd2—O1cd^ii	166.6 (4)
O3ab—Cd1—O4cd^ix	81.8 (4)	O2ef—Cd2—O2cd	109.2 (4)
O4ab^v—Cd1—O3ef	85.7 (4)	O1cd^ii—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)
O1ab^i—Cd2—O2ab	90.3 (4)	O2cd—S1cd—O3cd	110.6 (6)
O1ab^i—Cd2—O1ef^iii	83.2 (4)	O2cd—S1cd—O4cd	110.3 (6)
O1ab^i—Cd2—O2ef	83.2 (4)	O3cd—S1cd—O4cd	109.1 (6)
O1ab^i—Cd2—O1cd^ii	83.6 (4)	O1ef—S1ef—O2ef	108.3 (6)
O1ab^i—Cd2—O2cd	165.3 (4)	O1ef—S1ef—O3ef	107.4 (6)
O2ab—Cd2—O1ef^iii	168.9 (4)	O1ef—S1ef—O4ef	111.2 (6)
O2ab—Cd2—O2ef	95.1 (4)	O2ef—S1ef—O3ef	110.6 (6)
O2ab—Cd2—O1cd^ii	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.

Domain fractions

f1	79.1 (2)
f2	10.5 (2)
f3	10.4 (2)