Revision of pyrrhotite structures within a common superspace model

The structure of pyrrhotite (Fe_1 − xS with 0.05 ≤ x ≤ 0.125) has been reinvestigated in the framework of the superspace formalism. A common model with a centrosymmetric superspace group is proposed for the whole family. The atomic domains in the internal space representing the Fe atoms are parametrized as crenel functions that fulfil the closeness condition. The proposed model explains the x-dependent space groups observed and the basic features of the structures reported up to now. Our model yields for any x value a well defined ordered distribution of Fe vacancies in contrast to some of the structural models proposed in the literature. A new (3 + 1)-dimensional refinement of Fe_0.91S using the deposited dataset [Yamamoto & Nakazawa (1982). Acta Cryst. A38, 79–86] has been performed as a benchmark of the model. The consistency of the proposed superspace symmetry and its validity for other compositions has been further checked by means of ab initio calculations of both atomic forces and equilibrium atomic positions in non-relaxed and relaxed structures, respectively.

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

Fe0.91S	V = 473.15 (11) Å^3
Mr = 82.9	Z = 16
Orthorhombic, (000???†	F(000) = 1269
q = 0.18050c*	Dx = 4.652 Mg m^−3
a = 6.892 (1) Å	Mo Kα radiation, λ = 0.71069 Å
b = 11.952 (1) Å	µ = 12.54 mm^−1
c = 5.744 (1) Å	T = 293 K

† Symmetry operations: (1) x₁, x₂, x₃, x₄; (2) 1/4+x₁, −x₂, 1/2+x₃, 1/4+x₄; (3) x₁, 1/4−x₂, −x₃, 1/4−x₄; (4) 1/4+x₁, 1/4+x₂, 1/2−x₃, −x₄; (5) −x₁, −x₂, −x₃, −x₄; (6) 1/4−x₁, x₂, 1/2−x₃, 1/4−x₄; (7) −x₁, 1/4+x₂, x₃, 1/4+x₄; (8) 1/4−x₁, 1/4−x₂, 1/2+x₃, x₄; (9) 1/2+x₁, 1/2+x₂, x₃, x₄; (10) 3/4+x₁, 1/2−x₂, 1/2+x₃, 1/4+x₄; (11) 1/2+x₁, 3/4−x₂, −x₃, 1/4−x₄; (12) 3/4+x₁, 3/4+x₂, 1/2−x₃, −x₄; (13) 1/2−x₁, 1/2−x₂, −x₃, −x₄; (14) 3/4−x₁, 1/2+x₂, 1/2−x₃, 1/4−x₄; (15) 1/2−x₁, 3/4+x₂, x₃, 1/4+x₄; (16) 3/4−x₁, 3/4−x₂, 1/2+x₃, x₄; (17) x₁, 1/2+x₂, x₃, 1/2+x₄; (18) 1/4+x₁, 1/2−x₂, 1/2+x₃, 3/4+x₄; (19) x₁, 3/4−x₂, −x₃, 3/4−x₄; (20) 1/4+x₁, 3/4+x₂, 1/2−x₃, 1/2−x₄; (21) −x₁, 1/2−x₂, −x₃, 1/2−x₄; (22) 1/4−x₁, 1/2+x₂, 1/2−x₃, 3/4−x₄; (23) −x₁, 3/4+x₂, x₃, 3/4+x₄; (24) 1/4−x₁, 3/4−x₂, 1/2+x₃, 1/2+x₄; (25) 1/2+x₁, x₂, x₃, 1/2+x₄; (26) 3/4+x₁, −x₂, 1/2+x₃, 3/4+x₄; (27) 1/2+x₁, 1/4−x₂, −x₃, 3/4−x₄; (28) 3/4+x₁, 1/4+x₂, 1/2−x₃, 1/2−x₄; (29) 1/2−x₁, −x₂, −x₃, 1/2−x₄; (30) 3/4−x₁, x₂, 1/2−x₃, 3/4−x₄; (31) 1/2−x₁, 1/4+x₂, x₃, 3/4+x₄; (32) 3/4−x₁, 1/4−x₂, 1/2+x₃, 1/2+x₄.

Data collection

605 measured reflections	θmax = 26.0°, θmin = 2.6°
588 independent reflections	h = 0→5
391 reflections with I > 3σ(I)	k = 0→14
Rint = 0.786	l = −4→0

Refinement

Refinement on F	588 reflections
R[F^2 > 2σ(F^2)] = 0.115	46 parameters
wR(F^2) = 0.096	Unit
S = 4.81	(Δ/σ)max = 0.017

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

	x	y	z	Uiso*/Ueq
Fe1	0.1264 (4)	0.125	0	0.0120 (10)
S1	0.125	−0.0426 (2)	0.75	0.0073 (9)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Fe1	0.0102 (19)	0.0160 (11)	0.0098 (19)	0	0	0.0002 (10)