Daliranite, PbHgAs₂S₅: determination of the incommensurately modulated structure and revision of the chemical formula

The incommensurately modulated crystal structure of the mineral daliranite has been determined using 3D electron diffraction data obtained on nanocrystalline domains. Daliranite is orthorhombic with a = 21, b = 4.3, c = 9.5 Å and shows modulation satellites along c. The solution of the average structure in the Pnma space group together with energy-dispersive X-ray spectroscopy data obtained on the same domains indicate a chemical formula of PbHgAs₂S₅, which has one S fewer than previously reported. The crystal structure of daliranite is built from columns of face-sharing PbS₈ bicapped trigonal prisms laterally connected by ^[2+4]Hg polyhedra and (As³⁺₂S₅)⁴⁻ groups. The excellent quality of the electron diffraction data allows a structural model to be built for the modulated structure in superspace, which shows that the modulation is due to an alternated occupancy of a split As site.

Computing details

For both structures, data reduction: PETS 2.0 (Palatinus et al., 2011); program(s) used to solve structure: SIR2014 (Burla et al., 2015); program(s) used to refine structure: Jana2006 (Petricek et al., 2014); molecular graphics: Vesta (Momma & Izumi, 2011).

(average)

Crystal data

As2HgPbS5	Dx = 5.493 Mg m^−3
Mr = 717.9	Electron radiation, λ = 0.0335 Å
Orthorhombic, Pnma	Cell parameters from 2033 reflections
a = 21.246 (5) Å	θ = 0.1–1.2°
b = 4.2897 (9) Å	µ = 0 mm^−1
c = 9.5257 (12) Å	T = 298 K
V = 868.2 (3) Å^3	Needle, orange
Z = 4	0.0002 × 0.0001 × 0.0001 mm
F(000) = 1232

Data collection

TEM diffractometer	Rint = 0.335
Radiation source: LaB6	θmax = 1.2°, θmin = 0.1°
10451 measured reflections	h = −20→20
562 independent reflections	k = −4→3
401 reflections with I > 3σ(I)	l = −8→10

Refinement

Refinement on F	0 restraints
R[F^2 > 2σ(F^2)] = 0.244	0 constraints
wR(F^2) = 0.303	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
S = 13.93	(Δ/σ)max = 0.0002
562 reflections	Δρmax = 0.45 e Å^−3
34 parameters	Δρmin = −0.40 e Å^−3

Special details

Experimental. data have been collected by precession assisted 3D electron diffraction

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Pb1	0.2886 (7)	0.25	1.3368 (8)	0.083 (6)
Hg1	0.4150 (6)	0.25	0.9831 (7)	0.065 (5)
As1	0.1286 (13)	0.356 (3)	1.1428 (18)	0.030 (6)*	0.5
As2	0.0526 (12)	0.356 (3)	0.8089 (16)	0.019 (6)*	0.5
S1	0.2233 (15)	0.25	1.060 (2)	0.034 (7)*
S2	0.1437 (15)	0.25	0.690 (2)	0.036 (7)*
S3	0.3337 (16)	0.25	0.805 (2)	0.042 (7)*
S4	0.4132 (13)	0.25	1.4762 (19)	0.019 (6)*
S5	0.4954 (15)	0.25	1.160 (2)	0.040 (7)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Pb1	0.137 (16)	0.101 (8)	0.011 (5)	0	−0.002332	0
Hg1	0.118 (14)	0.069 (6)	0.009 (5)	0	0.001652	0

Geometric parameters (Å, º)

Pb1—S1	2.982 (17)
Pb1—S1—S2	177.9

(modulated)

Crystal data

As2HgPbS5	F(000) = 1232
Mr = 717.9	Dx = 5.493 Mg m^−3
Orthorhombic, Pnma(00γ)0s0†	Electron radiation, λ = 0.0335 Å
q = 0.262(2)c*	Cell parameters from 10451 reflections
a = 21.246 (5) Å	θ = 0.1–1.2°
b = 4.2897 (9) Å	µ = 0 mm^−1
c = 9.5257 (12) Å	T = 298 K
V = 868.2 (3) Å^3	Needle, orange
Z = 4	0.0002 × 0.0001 × 0.0001 mm

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

Data collection

TEM diffractometer	Rint = 0.335
Radiation source: LaB6	θmax = 1.2°, θmin = 0.1°
10451 measured reflections	h = −20→20
1503 independent reflections	k = −4→3
981 reflections with I > 3σ(I)	l = −8→10

Refinement

Refinement on F	0 restraints
R[F^2 > 2σ(F^2)] = 0.272	0 constraints
wR(F^2) = 0.310	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
S = 10.70	(Δ/σ)max = 0.001
1503 reflections	Δρmax = 0.45 e Å^−3
38 parameters	Δρmin = −0.40 e Å^−3

Special details

Experimental. data have been collected by precession assisted 3D electron diffraction

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Pb1	0.2885 (5)	0.25	1.3367 (5)	0.061 (4)
Hg1	0.4149 (5)	0.25	0.9835 (5)	0.063 (4)
As1	0.1285 (8)	0.371 (2)	1.1430 (11)	0.031 (3)*	0.5
As2	0.0517 (7)	0.365 (2)	0.8082 (10)	0.027 (3)*	0.5
S1	0.2236 (10)	0.25	1.0596 (15)	0.027 (4)*
S2	0.1430 (9)	0.25	0.6898 (14)	0.019 (4)*
S3	0.3344 (11)	0.25	0.8066 (15)	0.026 (4)*
S4	0.4134 (8)	0.25	1.4756 (12)	0.007 (4)*
S5	0.4962 (10)	0.25	1.1610 (15)	0.030 (5)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Pb1	0.132 (11)	0.033 (4)	0.018 (3)	0	−0.003 (4)	0
Hg1	0.122 (10)	0.060 (4)	0.006 (3)	0	0.002 (3)	0

Bond lengths (Å)

	Average	Minimum	Maximum
Pb1—S1	2.982 (17)	2.979 (17)	2.986 (17)
Pb1—S1^i	3.031 (11)	2.912 (11)	3.151 (11)
Pb1—S1^ii	3.029 (11)	2.912 (11)	3.151 (11)
Pb1—S2^i	2.948 (13)	2.808 (13)	3.087 (13)
Pb1—S2^ii	2.945 (13)	2.808 (13)	3.087 (13)
Pb1—S3^i	3.403 (19)	3.13 (2)	3.69 (2)
Pb1—S3^ii	3.398 (19)	3.13 (2)	3.69 (2)
Pb1—S4	2.975 (19)	2.963 (19)	2.985 (19)
Hg1—S2^i	3.159 (12)	3.114 (12)	3.205 (12)
Hg1—S2^ii	3.159 (12)	3.114 (12)	3.205 (12)
Hg1—S3	2.40 (2)	2.40 (2)	2.40 (2)
Hg1—S5	2.43 (2)	2.42 (2)	2.45 (2)
Hg1—S5^iii	3.184 (16)	2.880 (17)	3.501 (17)
Hg1—S5^iv	3.179 (16)	2.880 (17)	3.501 (17)
As1—S1	2.20 (3)	2.19 (3)	2.26 (3)
As1—S3^i	3.287 (13)	3.056 (14)	3.397 (14)
As1—S3^ii	2.308 (16)	2.224 (17)	2.495 (17)
As1—S4^v	3.212 (13)	3.141 (13)	3.316 (13)
As1—S4^vi	2.460 (15)	2.377 (15)	2.518 (15)
As1—S5^vii	3.41 (2)	3.39 (2)	3.44 (2)
As2—S2	2.28 (2)	2.26 (2)	2.32 (2)
As2—S4^v	3.155 (12)	3.080 (12)	3.259 (12)
As2—S4^vi	2.426 (14)	2.342 (14)	2.489 (14)
As2—S5^v	3.239 (14)	3.083 (14)	3.309 (14)
As2—S5^vi	2.328 (17)	2.272 (17)	2.455 (17)
S1—S3	3.37 (3)	3.37 (3)	3.38 (3)
S1—S3^i	3.423 (18)	3.164 (19)	3.695 (19)
S1—S3^ii	3.419 (18)	3.164 (19)	3.695 (19)
S2—S5^v	3.67 (2)	3.47 (3)	3.88 (3)
S2—S5^vi	3.67 (2)	3.47 (3)	3.88 (3)
S4—S5	3.48 (2)	3.48 (2)	3.48 (2)

Symmetry codes: (i) −x₁+1/2, −x₂, x₃+1/2, x₄+1/2; (ii) −x₁+1/2, −x₂+1, x₃+1/2, x₄+1/2; (iii) −x₁+1, x₂−1/2, −x₃+2, −x₄+1/2; (iv) −x₁+1, x₂+1/2, −x₃+2, −x₄+1/2; (v) −x₁+1/2, −x₂, x₃−1/2, x₄+1/2; (vi) −x₁+1/2, −x₂+1, x₃−1/2, x₄+1/2; (vii) x₁−1/2, −x₂+1/2, −x₃+5/2, −x₄.