Daliranite, PbHgAs2S5: determination of the incommensurately modulated structure and revision of the chemical formula (original) (raw)
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.
Supporting information
B-IncStrDB reference: 15062EdDLkO
CCDC references: 1917352; 1917353
Computing details top
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).
Crystal data
| As2HgPbS5 | _D_x = 5.493 Mg m−3 |
|---|---|
| M r = 717.9 | Electron radiation, λ = 0.0335 Å |
| Orthorhombic, P n m a | 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) Å3 | Needle, orange |
| Z = 4 | 0.0002 × 0.0001 × 0.0001 mm |
| F(000) = 1232 |
Data collection
| TEM diffractometer | _R_int = 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/(σ2(F) + 0.0001_F_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 (Å2)
| | x | y | z | _U_iso*/_U_eq | 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 (Å2)
| | _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 | | |
Crystal data
| As2HgPbS5 | F(000) = 1232 |
|---|---|
| M r = 717.9 | _D_x = 5.493 Mg m−3 |
| Orthorhombic, P n m a(00γ)0_s_0† | 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) Å3 | Needle, orange |
| Z = 4 | 0.0002 × 0.0001 × 0.0001 mm |
| † Symmetry operations: (1) _x_1, _x_2, _x_3, _x_4; (2) −_x_1+1/2, −_x_2, _x_3+1/2, _x_4+1/2; (3) −_x_1, _x_2+1/2, −_x_3, −_x_4+1/2; (4) _x_1+1/2, −_x_2+1/2, −_x_3+1/2, −_x_4; (5) −_x_1, −_x_2, −_x_3, −_x_4; (6) _x_1+1/2, _x_2, −_x_3+1/2, −_x_4+1/2; (7) _x_1, −_x_2+1/2, _x_3, _x_4+1/2; (8) −_x_1+1/2, _x_2+1/2, _x_3+1/2, _x_4. |
|---|
Data collection
| TEM diffractometer | _R_int = 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/(σ2(F) + 0.0001_F_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 (Å2)
| | x | y | z | _U_iso*/_U_eq | 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 (Å2)
| | _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—S1i | 3.031 (11) | 2.912 (11) | 3.151 (11) | | Pb1—S1ii | 3.029 (11) | 2.912 (11) | 3.151 (11) | | Pb1—S2i | 2.948 (13) | 2.808 (13) | 3.087 (13) | | Pb1—S2ii | 2.945 (13) | 2.808 (13) | 3.087 (13) | | Pb1—S3i | 3.403 (19) | 3.13 (2) | 3.69 (2) | | Pb1—S3ii | 3.398 (19) | 3.13 (2) | 3.69 (2) | | Pb1—S4 | 2.975 (19) | 2.963 (19) | 2.985 (19) | | Hg1—S2i | 3.159 (12) | 3.114 (12) | 3.205 (12) | | Hg1—S2ii | 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—S5iii | 3.184 (16) | 2.880 (17) | 3.501 (17) | | Hg1—S5iv | 3.179 (16) | 2.880 (17) | 3.501 (17) | | As1—S1 | 2.20 (3) | 2.19 (3) | 2.26 (3) | | As1—S3i | 3.287 (13) | 3.056 (14) | 3.397 (14) | | As1—S3ii | 2.308 (16) | 2.224 (17) | 2.495 (17) | | As1—S4v | 3.212 (13) | 3.141 (13) | 3.316 (13) | | As1—S4vi | 2.460 (15) | 2.377 (15) | 2.518 (15) | | As1—S5vii | 3.41 (2) | 3.39 (2) | 3.44 (2) | | As2—S2 | 2.28 (2) | 2.26 (2) | 2.32 (2) | | As2—S4v | 3.155 (12) | 3.080 (12) | 3.259 (12) | | As2—S4vi | 2.426 (14) | 2.342 (14) | 2.489 (14) | | As2—S5v | 3.239 (14) | 3.083 (14) | 3.309 (14) | | As2—S5vi | 2.328 (17) | 2.272 (17) | 2.455 (17) | | S1—S3 | 3.37 (3) | 3.37 (3) | 3.38 (3) | | S1—S3i | 3.423 (18) | 3.164 (19) | 3.695 (19) | | S1—S3ii | 3.419 (18) | 3.164 (19) | 3.695 (19) | | S2—S5v | 3.67 (2) | 3.47 (3) | 3.88 (3) | | S2—S5vi | 3.67 (2) | 3.47 (3) | 3.88 (3) | | S4—S5 | 3.48 (2) | 3.48 (2) | 3.48 (2) |
Symmetry codes: (i) −_x_1+1/2, −_x_2, _x_3+1/2, _x_4+1/2; (ii) −_x_1+1/2, −_x_2+1, _x_3+1/2, _x_4+1/2; (iii) −_x_1+1, _x_2−1/2, −_x_3+2, −_x_4+1/2; (iv) −_x_1+1, _x_2+1/2, −_x_3+2, −_x_4+1/2; (v) −_x_1+1/2, −_x_2, _x_3−1/2, _x_4+1/2; (vi) −_x_1+1/2, −_x_2+1, _x_3−1/2, _x_4+1/2; (vii) _x_1−1/2, −_x_2+1/2, −_x_3+5/2, −_x_4.