Two-dimensionally modulated structure of the rare-earth polysulfide GdS_2−x (x = 0.18 ≃ 13/72)

The crystal structure of GdS_2−x is determined by single-crystal X-ray diffraction as a 144-fold superstructure of the ZrSSi structure type. The superstructure is described as a two-dimensional, commensurately modulated structure with the superspace group P4/n(αβ½)(00)(ss) and with α = 1/4 and β = 1/3. Structure refinements within the classical approach, employing the 144-fold supercell, fail because most of the superlattice reflections have zero intensities within the experimental resolution. Within the superspace approach the absent superlattice reflections are systematically classified as higher-order satellite reflections. Accordingly, the superspace approach has been used to refine the structure model comprising the basic structure positions and the amplitudes of the modulation functions of the three crystallographically independent atoms. The quality of fit to the diffraction data and the values of the refined parameters are independent of the assumption on the true symmetry (incommensurate or a 12 × 12 × 2, I-centred superlattice with different symmetries). Arguments of structural plausibility then suggest that the true structure is a superstructure with space group I, corresponding to sections of superspace given by (t₁, t₂) equal to [(4n − 1)/48, (4m − 3)/48] or [(4n − 3)/48, (4m − 1)/48] (n and m are integers). Analysis of the structure, employing both superspace techniques (t plots) and the supercell structure model all show that the superstructure corresponds to an ordering of vacancies and an orientational ordering of S dimers within the square layers of the S2 atoms.

Computing details

Program(s) used to refine structure: (Jana2000; Petricek and Dusek, 2000); software used to prepare material for publication: (Jana2000; Petricek and Dusek, 2000).

(I)

Crystal data

GdS1.82	F(000) = 186
Mr = 215.5	Dx = 5.944 Mg m^−3 Dm = 5.88 Mg m^−3 Dm measured by Floatation in aqueous KI
Tetragonal, P4/n†	Mo Kα radiation, λ = 0.71069 Å
q1 = 0.25200a* + 0.33100b* + 0.50000c*; q2 = -0.33100a* + 0.25200b* + 0.50000c*	Cell parameters from 24 reflections
Hall symbol: -P 4a	θ = 60–90°
a = 3.8951 Å	µ = 28.69 mm^−1
c = 7.9343 Å	T = 293 K
V = 120.38 Å^3	Ellipsoid, yellowish-orange
Z = 2	0.21 × 0.20 × 0.18 mm

† Symmetry operations: (1) x₁, x₂, x₃, x₄, x₅; (2) 1/2−x₂, x₁, x₃, 1/2+x₃−x₅, 1/2+x₄; (3) 1/2−x₁, 1/2−x₂, x₃, x₃−x₄, x₃−x₅; (4) x₂, 1/2−x₁, x₃, 1/2+x₅, 1/2+x₃−x₄; (5) −x₁, −x₂, −x₃, −x₄, −x₅; (6) 1/2+x₂, −x₁, −x₃, 1/2−x₃+x₅, 1/2−x₄; (7) 1/2+x₁, 1/2+x₂, −x₃, −x₃+x₄, −x₃+x₅; (8) −x₂, 1/2+x₁, −x₃, 1/2−x₅, 1/2−x₃+x₄.

Data collection

IPDS STOE diffractometer	900 reflections with I > 3σ(I)
Detector resolution: 0.15 pixels mm^-1	Rint = 0.064
Phi oscillation scans	θmax = 27.9°, θmin = 2.5°
Absorption correction: integration W. Herrendorf 1992	h = −5→5
Tmin = 0.026, Tmax = 0.059	k = −5→5
25287 measured reflections	l = −12→12
3565 independent reflections

Refinement

Refinement on F	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0025F^2)
R[F^2 > 2σ(F^2)] = 0.040	(Δ/σ)max = 0.002
wR(F^2) = 0.094	Δρmax = 10.55 e Å^−3
S = 0.73	Δρmin = −11.52 e Å^−3
3565 reflections	Extinction correction: Becker, P. J. & Coppens
52 parameters	Extinction coefficient: 0.007445

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Gd1	0.25	0.25	0.27357 (5)	0.01299 (14)
S1	0.25	0.25	0.6340 (3)	0.0129 (4)
S2	0.75	0.25	0	0.0136 (5)	0.82 (1)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Gd1	0.0106 (2)	0.0106 (2)	0.0177 (3)	0	0	0
S1	0.0118 (5)	0.0118 (5)	0.0152 (9)	0	0	0
S2	0.0126 (9)	0.0126 (9)	0.0155 (10)	0	0	0

Bond lengths (Å)

	Average	Minimum	Maximum
Gd1—S1	2.861 (7)	2.770 (9)	2.949 (8)
Gd1—S1^i	2.854 (6)	2.760 (6)	2.942 (7)
Gd1—S1^ii	2.854 (6)	2.760 (7)	2.937 (7)
Gd1—S1^iii	2.854 (6)	2.760 (7)	2.937 (7)
Gd1—S1^iv	2.854 (6)	2.760 (6)	2.942 (7)
Gd1—S2^v	2.940 (11)	2.734 (10)	3.211 (11)
Gd1—S2	2.940 (11)	2.734 (10)	3.211 (11)
Gd1—S21^vi	2.940 (8)	2.745 (7)	3.201 (10)
Gd1—S21	2.940 (8)	2.745 (7)	3.200 (10)
S2—S21^vi	2.765 (17)	1.930 (18)	3.52 (2)
S2—S21	2.766 (17)	1.929 (18)	3.52 (2)
S2—S21^vii	2.765 (17)	1.929 (18)	3.52 (2)
S2—S21^viii	2.765 (17)	1.929 (18)	3.52 (2)

Symmetry codes: (i) −x₁−1/2, −x₂+1/2, x₃+1, x₃−x₄, x₃−x₅; (ii) −x₁−1/2, −x₂+3/2, x₃+1, x₃−x₄, x₃−x₅; (iii) −x₁+1/2, −x₂+1/2, x₃+1, x₃−x₄, x₃−x₅; (iv) −x₁+1/2, −x₂+3/2, x₃+1, x₃−x₄, x₃−x₅; (v) x₁−1, x₂, x₃, x₄, x₅; (vi) x₁, x₂−1, x₃, x₄, x₅; (vii) x₁+1, x₂−1, x₃, x₄, x₅; (viii) x₁+1, x₂, x₃, x₄, x₅.