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ISSN: 2052-5206

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

aCenter for Nanotechnology Innovation @NEST, Istituto Italiano di Tecnologia, Piazza S. Silvestro, 12, Pisa, 56127, Italy, bDipartimento di Scienze della Terra, University of Florence, Via La Pira, Firenze, I-50121, Italy, and cDepartment of Chemistry and Physics of Materials, University of Salzburg, Salzburg, Austria
*Correspondence e-mail: mauro.gemmi@iit.it

Edited by M. Dusek, Academy of Sciences of the Czech Republic, Czech Republic (Received 19 March 2019; accepted 20 May 2019; online 22 July 2019)

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.

1. Introduction

Daliranite is a rare sulfosalt species originally discovered at the Carlin-type Zarshouran Au–As deposit north of the town of Takab in the Province of West Aze­rbaijan (Iran). Its formula was determined by Paar et al. (2009[Paar, W. H., Pring, A., Moëlo, Y., Stanley, C. J., Putz, H., Topa, D., Roberts, A. C. & Braithwaite, R. S. W. (2009). Mineral. Mag. 73, 871-881.]) as PbHgAs2S6. Daliranite occurs as matted nests of acicular crystals usually associated with orpiment and quartz (Fig. 1[link]). The characterization of daliranite was quite a challenge because of the fineness of the hair-like crystals (<3 µm) which caused significant problems for both the preparation of suitable polished sections and the determination of the unit-cell parameters. Based on zone-axis electron diffraction patterns, daliranite was reported as monoclinic, with lattice parameters a ≃ 19, b ≃ 4, c ≃ 23 Å and β ≃ 115°, and possible space groups P2, Pm or P2/m. Although the unit cell was confirmed by X-ray powder diffraction, no structure solution was achieved and it remained unknown (Paar et al., 2009[Paar, W. H., Pring, A., Moëlo, Y., Stanley, C. J., Putz, H., Topa, D., Roberts, A. C. & Braithwaite, R. S. W. (2009). Mineral. Mag. 73, 871-881.]). Given its peculiar characteristics, daliranite is a perfect candidate to be tackled using the recent 3D electron diffraction (ED) methods, which allow the collection, in a transmission electron microscope, of single-crystal-like data from coherent domains having the size of just a few hundreds of nanometres (Gemmi et al., 2015[Gemmi, M., La Placa, M. G. I., Galanis, A. S., Rauch, E. F. & Nicolopoulos, S. (2015). J. Appl. Cryst. 48, 718-727.]; Palatinus et al., 2017[Palatinus, L., Gemmi, M. & Klementová, M. (2017). EMU Notes Mineral. 19, 139-181.]; Mugnaioli & Gemmi, 2018[Mugnaioli, E. & Gemmi, M. (2018). Z. Kristallogr. 233, 163-178.]; Mugnaioli & Gorelik, 2019[Mugnaioli, E. & Gorelik, T. E. (2019). Acta Cryst. B75, 550-563.]).

[Figure 1]
Figure 1
Daliranite (orange fibres) in association with orpiment (yellow) on quartz.

Nowadays, 3D ED can be considered to be in an advanced stage of development. It is now possible, by collecting a sequence of ED patterns while tilting the sample around the goniometer axis, to obtain a 3D reconstruction of the reciprocal space of a nanocrystal, from which the unit cell and the crystal symmetry can be directly derived (Kolb et al., 2007[Kolb, U., Gorelik, T. E., Kübel, C., Otten, M. T. & Hubert, D. (2007). Ultramicroscopy, 107, 507-513.], 2008[Kolb, U., Gorelik, T. & Otten, M. T. (2008). Ultramicroscopy, 108, 763-772.]). Thanks to the peculiar geometry of this data collection, the ED intensities extracted from the patterns are quasi-kinematical and can be exploited for solving the crystal structure using standard phasing methods like direct methods (Kolb et al., 2011[Kolb, U., Mugnaioli, E. & Gorelik, T. E. (2011). Cryst. Res. Technol. 46, 542-554.]), charge flipping (Palatinus et al., 2011[Palatinus, L., Klementová, M., Dřínek, V., Jarošová, M. & Petříček, V. (2011). Inorg. Chem. 50, 3743-3751.]) or simulated annealing (Das et al., 2018[Das, P. P., Mugnaioli, E., Nicolopoulos, S., Tossi, C., Gemmi, M., Galanis, A., Borodi, G. & Pop, M. M. (2018). Org. Process Res. Dev. 22, 1365-1372.]). 3D ED methods have been successfully applied in solving new mineral crystal structures. Charoite-90 (Rozhdestvenskaya et al., 2010[Rozhdestvenskaya, I. V., Mugnaioli, E., Czank, M., Depmeier, W., Kolb, U., Reinholdt, A. & Weirich, T. (2010). Mineral. Mag. 74, 159-177.]), charoite-96 (Rozhdestvenskaya et al., 2011[Rozhdestvenskaya, I. V., Mugnaioli, E., Czank, M., Depmeier, W., Kolb, U. & Merlino, S. (2011). Mineral. Mag. 75, 2833-2846.]), sarrabusite (Gemmi et al., 2012[Gemmi, M., Campostrini, I., Demartin, F., Gorelik, T. E. & Gramaccioli, C. M. (2012). Acta Cryst. B68, 15-23.]), widenmannite (Plášil et al., 2014[Plášil, J., Palatinus, L., Rohlíček, J., Houdková, L., Klementová, M., Goliáš, V. & Škácha, P. (2014). Am. Mineral. 99, 276-282.]), karibibite (Colombo et al., 2017[Colombo, F., Mugnaioli, E., Vallcorba, O., García, A., Goñi, A. R. & Rius, J. (2017). Mineral. Mag. 81, 1191-1202.]), denisovite (Rozhdestvenskaya et al., 2017[Rozhdestvenskaya, I. V., Mugnaioli, E., Schowalter, M., Schmidt, M. U., Czank, M., Depmeier, W. & Rosenauer, A. (2017). IUCrJ, 4, 223-242.]) and a still unnamed mineral with presumed composition (S2)1+x[Bi9−xTex(OH)6O8(SO4)2]2 (Capitani et al., 2014[Capitani, G. C., Mugnaioli, E., Rius, J., Gentile, P., Catelani, T., Lucotti, A. & Kolb, U. (2014). Am. Mineral. 99, 500-510.]) are some examples. In experimental petrology 3D ED has been crucial in the identification and structure determination of three new high-pressure phases in the MgO–Al2O3–SiO2–H2O system: HAPY (Gemmi et al., 2011[Gemmi, M., Fischer, J., Merlini, M., Poli, S., Fumagalli, P., Mugnaioli, E. & Kolb, U. (2011). Earth Planet. Sci. Lett. 310, 422-428.]), HYSO and 11.5 Å-phase (Gemmi et al., 2016[Gemmi, M., Merlini, M., Palatinus, L., Fumagalli, P. & Hanfland, M. (2016). Am. Mineral. 101, 2645-2654.]).

Precession-assisted 3D ED of daliranite nanocrystals coming from the holotype material showed that the mineral actually exhibits a modulated structure and a different chemical composition. Here we report the solution of the average crystal structure and a possible (3+1)-model of the modulated structure together with the revision of the chemical formula.

2. Experimental methods

Samples for transmission electron microscopy (TEM) studies were prepared by mild grinding of a group of fibres in an agate mortar. The powder was then suspended in 2-propanol and a drop of the suspension was deposited on a carbon-coated copper grid. ED experiments were carried out on a Zeiss Libra 120 transmission electron microscope operating at 120 kV and equipped with a LaB6 thermionic source and an in-column omega filter. The data collection was performed in precession-assisted ED tomography mode. A sequence of patterns was collected in stepwise mode as reported by Mugnaioli et al. (2009[Mugnaioli, E., Gorelik, T. & Kolb, U. (2009). Ultramicroscopy, 109, 758-765.]), using a parallel beam of ∼150 nm obtained in Köhler illumination by a 5 µm condenser aperture. The electron beam was precessed around a semi-angle of 0.85° by a Nanomegas Digistar P1000 device (Vincent & Midgley, 1994[Vincent, R. & Midgley, P. A. (1994). Ultramicroscopy, 53, 271-282.]). All the patterns were energy-filtered on the zero-loss peak with a slit width of ∼20 eV (Gemmi & Oleynikov, 2013[Gemmi, M. & Oleynikov, P. (2013). Z. Kristallogr. Cryst. Mater. 228, 51-58.]). The tilt step was 1°, for a total angular range of 113°. After each tilt step, the crystal position was tracked in dark-field STEM scanning transmission electron microscopy (STEM) imaging. Diffraction data were recorded by an ASI Timepix single-electron detector (Georgieva et al., 2011[Georgieva, D., Jansen, J., Sikharulidze, I., Jiang, L., Zandbergen, H. W. & Abrahams, J. P. (2011). J. Instrum. 6, C01033.]; Nederlof et al., 2013[Nederlof, I., van Genderen, E., Li, Y.-W. & Abrahams, J. P. (2013). Acta Cryst. D69, 1223-1230.]). Data reduction and analysis of the 3D ED data have been carried out with the program PETS (Palatinus et al., 2011[Palatinus, L., Klementová, M., Dřínek, V., Jarošová, M. & Petříček, V. (2011). Inorg. Chem. 50, 3743-3751.]). The direct methods SIR2014 program (Burla et al., 2015[Burla, M. C., Caliandro, R., Carrozzini, B., Cascarano, G. L., Cuocci, C., Giacovazzo, C., Mallamo, M., Mazzone, A. & Polidori, G. (2015). J. Appl. Cryst. 48, 306-309.]) has been used for structure solution of the average structure, while the modulated model was obtained and refined with JANA2006 (Petříček et al., 2014[Petříček, V., Dušek, M. & Palatinus, L. (2014). Z. Kristallogr. 229, 345-352.]).

3. Results and discussion

3.1. Revision of the unit cell

Preliminary TEM observations showed that daliranite crystals have an acicular morphology with grains several microns long and a few hundreds of nanometres wide [Fig. 2[link](a)]. ED carried out along these needles shows that each is formed by several smaller coherent domains having different crystallographic orientations. The size of these monocrystalline domains is of the order of 100–200 nm only and sometimes they can be observed as isolated rectangular nanoparticles [Fig. 2[link](b)]. 3D ED data collected on these fragments show main and satellite reflections (Fig. 3[link]), which are evidence for a 1D-modulated structure. The modulation is also accompanied by diffuse scattering that connects the satellite reflections (Fig. S1 in the supporting information).

[Figure 2]
Figure 2
High-angular annular dark-field STEM images of (a) an acicular crystal and (b) two rectangular nanocrystals of daliranite.
[Figure 3]
Figure 3
Sections of the reciprocal space of daliranite obtained from a 3D ED data collection on a nanocrystal similar to those reported in Fig. 2[link](b).

The main reflections can be indexed with an orthorhombic cell with a = 21, b = 4.3, c = 9.5 Å and extinction symbol Pn_a. The modulation vector is along c* (q = 00γ) with γ varying in the range between 0.33 and 0.25 from crystal to crystal. Only the first-order satellites are visible. Although the unit-cell values appear different from those given by Paar et al. (2009[Paar, W. H., Pring, A., Moëlo, Y., Stanley, C. J., Putz, H., Topa, D., Roberts, A. C. & Braithwaite, R. S. W. (2009). Mineral. Mag. 73, 871-881.]), a = 19, b = 4, c = 23 Å and β = 115°, if we apply to the latter cell values the transformation matrix |½01/0[{\bar 1}]0/½00| we obtain: a = 20.8, b = 4, c = 9.5 Å and β = 90.6°. The obtained unit cell is almost identical to that found in this study. Indeed, the deviation of the β angle from the ideal value of 90° can be due to diffuse scattering connected with the modulation of the structure.

3.2. Revision of the chemical formula

The average structure of daliranite was solved by direct methods in space group Pnma (Table 1[link]). Unexpectedly, the resulting model corresponded to the stoichiometry PbHgAs2S5, which differs from the literature composition, in that it is less sulfur-rich. The obtained structural formula does not invoke unusual oxidation states (e.g. As5+), nor requires the presence of (S2)2− disulfide groups previously proposed (Paar et al., 2009[Paar, W. H., Pring, A., Moëlo, Y., Stanley, C. J., Putz, H., Topa, D., Roberts, A. C. & Braithwaite, R. S. W. (2009). Mineral. Mag. 73, 871-881.]). The formula is also in agreement with the energy-dispersive X-ray spectroscopy (EDX) analysis performed on the analysed crystals (approximate atomic composition: Pb 10%; Hg 9%; As 24%; S 55%). Furthermore, if we normalize the chemical data reported by Paar et al. (2009[Paar, W. H., Pring, A., Moëlo, Y., Stanley, C. J., Putz, H., Topa, D., Roberts, A. C. & Braithwaite, R. S. W. (2009). Mineral. Mag. 73, 871-881.]) on the basis of nine atoms (present structure solution) we obtain Pb0.87Tl0.01Hg0.94As1.88S5.30, which is not far from PbHgAs2S5 taking into account the difficulty of getting good microprobe chemical data of Hg-bearing minerals due to the presence of cryptocrystalline accessory phases.

Table 1
Experimental details of data collection and refinement for daliranite

For all structures: PbHgAs2S5, Mr = 717.9, Z = 4. Experiments were carried out at room temperature on a crystal of circa 200 × 100 × 100 nm with electron radiation, λ = 0.0335 Å.

  Average structure Modulated structure
Crystal data
Crystal system Orthorhombic Orthorhombic
Space or superspace group Pnma Pnma(00γ)0s0
a, b, c (Å) 21.246 (5), 4.2897 (9), 9.5257 (12) 21.246 (5), 4.2897 (9), 9.5257 (12)
V3) 868.2 (3) 868.2 (3)
Modulation vector   q = 0.262 (2)c*
 
Data collection
No. of independent and observed [I > 3σ(I)] reflections 562, 401 1503, 981
Rint 0.335 0.335
(sin θ/λ)max−1) 0.625 0.625
Range of h, k, l, m h = −20→20, k = −4→3, l = −8→10 h = −20→20, k = −4→3, l = −8→10, m = −1→1
     
Refinement
R[F2 > 2σ(F2)], wR(F2) main reflections 0.244, 0.303 0.249, 0.297
R[F2 > 2σ(F2)], wR(F2) satellite (±1) reflections   0.302, 0.332
S 13.93 10.70
No. of reflections 562 1503
No. of parameters 34 38
(Δ/σ)max 0.0002 0.001
Δρmax, Δρmin (e Å−3) 0.45, −0.40 0.45, −0.40
†Symmetry operations: (1) x1, x2, x3, x4; (2) −x1 + [1\over 2], −x2, x3 + [1\over 2], x4 + [1\over 2]; (3) −x1, x2 + [1\over 2], −x3, −x4 + [1\over 2]; (4) x1 + [1\over 2], −x2 + [1\over 2], −x3 + [1\over 2], −x4; (5) −x1, −x2, −x3, −x4; (6) x1 + [1\over 2], x2, −x3 + [1\over 2], −x4 + [1\over 2]; (7) x1, −x2 + [1\over 2], x3, x4 + [1\over 2]; (8) −x1 + [1\over 2], x2 + [1\over 2], x3 + [1\over 2], x4.

3.3. The average structure

The average structure of daliranite is formed by columns of face-sharing PbS8 bicapped trigonal prisms running along b (Fig. 4[link], left-hand view). These are connected along the c direction with neighbouring columns, forming a zigzag sheet by sharing of S1 vertices (Fig. 4[link], right-hand view). Such sheets are alternated along a by double columns of edge-sharing distorted [2+4]Hg polyhedra. The two shortest Hg—S distances (2.40–2.42 Å, see Table 2[link]) are comparable with those found in cinnabar [i.e. 2.368 Å (Auvray & Genet, 1973[Auvray, P. & Genet, F. (1973). Bull. Soc. Fr. Mineral. Cristallogr. 96, 218-219.])], imiterite [2.376 Å (Guillou et al., 1985[Guillou, J. J., Monthel, J., Picot, P., Pillard, F., Protas, J. & Samama, J. C. (1985). Bull. Minéral. 108, 457-464.])], balkanite [2.366 Å (Biagioni & Bindi, 2017[Biagioni, C. & Bindi, L. (2017). Eur. J. Mineral. 29, 279-285.])], as well as in the lead sulfosalts rouxelite [2.381 Å (Orlandi et al., 2005[Orlandi, P., Meerschaut, A., Moëlo, Y., Palvadeau, P. & Léone, P. (2005). Can. Mineral. 43, 919-933.])] and marrucciite [2.361 and 2.386 Å at Hg1 and Hg2 sites, respectively (Orlandi et al., 2007[Orlandi, P., Moëlo, Y., Campostrini, I. & Meerschaut, A. (2007). Eur. J. Mineral. 19, 267-279.])]. In all these minerals, the Hg linear coordination is perpendicular to the ≃4 Å axis, as in daliranite.

Table 2
Bond lengths in Å for the average and modulated models of daliranite

For the modulated model the average value is given with the min–max range given in brackets.

  Average Modulated
Pb—S1 2.98 (2) 2.982 (17) [2.979 (17)–2.986 (17)]
Pb—S1′ 3.033 (15) 3.031 (11) [2.912 (11)–3.151 (11)]
Pb—S1′′ 3.033 (15) 3.029 (11) [2.912 (11)–3.151 (11)]
Pb—S2 2.94 (2) 2.948 (13) [2.808 (13)–3.087 (13)]
Pb—S2′ 2.94 (2) 2.945 (13) [2.808 (13)–3.087 (13)]
Pb—S3 3.38 (3) 3.403 (19) [3.13 (2)–3.69 (2)]
Pb—S3′ 3.38 (3) 3.398 (19) [3.13 (2)–3.69 (2)]
Pb—S4 2.96 (3) 2.975 (19) [2.963 (19)–2.985 (19)]
     
Hg—S3 2.42 (3) 2.40 (2) [2.40 (2)–2.40 (2)]
Hg—S5 2.40 (3) 2.43 (2) [2.42 (2)–2.45 (2)]
Hg—S5′ 3.18 (2) 3.184 (16) [2.880 (17)–3.501 (17)]
Hg—S5′′ 3.18 (2) 3.179 (16) [2.880 (17)–3.501 (17)]
Hg—S2 3.171 (19) 3.159 (12) [3.114 (12)–3.205 (12)]
Hg—S2′ 3.171 (19) 3.159 (12) [3.114 (12)–3.205 (12)]
     
As1—S1 2.21 (4) 2.20 (3) [2.19 (3)–2.26 (3)]
As1—S3 2.42 (3) 2.308 (16) [2.224 (17)–2.495 (17)]
As1—S4 2.48 (2) 2.460 (15) [2.377 (15)–2.518 (15)]
As2—S2 2.29 (4) 2.28 (2) [2.26 (2)–2.32 (2)]
As2—S4 2.43 (2) 2.426 (14) [2.342 (14)–2.489 (14)]
As2—S5 2.43 (2) 2.328 (17) [2.272 (17)–2.455 (17)]
[Figure 4]
Figure 4
Daliranite average structure. Half-coloured spheres represent half-occupied As sites [picture obtained using the VESTA software (Momma & Izumi, 2011[Momma, K. & Izumi, F. (2011). J. Appl. Cryst. 44, 1272-1276.])].

As it is typical in sulfosalts, As atoms are coordinated by three S atoms and occupy a vertex of trigonal AsS3 pyramids which, in daliranite, share one vertex (S4) to form (As2S5)4− dimeric anion groups. By sharing all their S vertices, such dimers laterally staple the Pb and Hg columns together.

In the average Pnma model, all atoms are localized on the mirror plane perpendicular to b, with the exception of the As atoms, which are shifted circa 0.45 Å off the m plane and disordered, giving rise to two half-occupied sites. This results in quite reasonable As—S distances. However the S—As—S angles are quite distorted, spanning the range 92°–108°. The presence of two partially occupied As sites could indicate some disorder along the ∼4 Å periodicity. The unit cell of most SnS-archetype- and PbS-archetype-based sulfosalts is characterized by such a periodicity that can be commonly found doubled, giving rise to 8 Å commensurate superstructures. Recently Bindi et al. (2017[Bindi, L., Petříček, V., Biagioni, C., Plášil, J. & Moëlo, Y. (2017). Acta Cryst. B73, 369-376.]) have shown that incommensurability in sulfosalts could be much more frequent than previously thought owing to a potentially very small departure from the commensurate values of the modulation. However, daliranite shows incommensurate modulation along the c axis (9.5 Å periodicity), which suggests the presence of some ordering in the occupation of the As sites.

3.4. The modulated structure

In order to shed light on the mechanisms behind the observed modulation, we integrated the satellite reflections from a crystal with q = 0.263c* and analysed the complete data set with a superspace approach using JANA2006. The reflection conditions detected for satellites are: 0klm: k + l = 2n; h0lm: m = 2n; hk00: h = 2n (see Fig. 3[link]), which are consistent with the (3+1)D superspace group Pnma(00γ)0s0 (superspace group 62.1.9.2). The structural model was solved and refined in this superspace group, which constrains all the modulation functions to have non-zero components only along x2 (corresponding to the b direction in real space) (Fig. 5[link]). All atoms are affected by the modulation: As ions are best modelled with a crenel function (Petříček et al., 2016[Petříček, V., Eigner, V., Dušek, M. & Cejchan, A. (2016). Z. Kristallogr. 231, 301-312.]), describing the alternated occupancy of the two possible disordered sites generated by the mirror normal to b. Consequently, all the other atoms are also shifted off their average special positions on the m plane. The positional modulation of Pb, Hg and S atoms can be described by harmonic waves with amplitudes ranging from circa 0.1 Å for S4 to circa 0.4 Å for Pb (Fig. 6[link]).

[Figure 5]
Figure 5
Fobs Fourier maps of the (3+1)D superspace around selected atoms, projected on the x2x4 planes. Horizontal axes display x2 fractional coordinates (y coordinates) and vertical axes correspond to x4; the contours are in arbitrary units and, in kinematic approximation, represent the intensity of the electrostatic potential. The fitted atomic modulation functions, represented as continuous white lines, show how the modulation causes the atoms to displace from their average special position on the mirror plane, represented as a dashed yellow line.
[Figure 6]
Figure 6
Displacement from the average y positions for Pb, Hg and S atoms as a function of the phase of the modulation, t.

The mechanism triggering the modulation is the possibility for each As to form the trigonal pyramid by bonding alternatively two S atoms that can be either above or below the m plane perpendicular to b, depending on which of the two symmetry-equivalent split As sites is occupied. By focusing our attention on As1, if we call these two split sites As1 and As1′, we can observe that As1 is occupied for half of the modulation period, while As1′ is occupied for the second half (see Fig. 4[link], Figs. S2 and S3). When occupied, As1 bonds three S atoms (S1, S3, S4) and is significantly far from S3′ and S4′ atoms (the symmetry-generated positions of S3, S4), which are bonded to the As1′ site instead. S1 is always at bonding distance in both configurations, acting like a pivot atom (Fig. 7[link] and Table 2[link]). The same occurs for the As2 site, bonding with S2, S4 and S5, and its symmetry-related As2′, bonding with S2, S4′ and S5′.

[Figure 7]
Figure 7
Interatomic distances for As1 and its symmetry-equivalent As1′ (generated by the m plane perpendicular to b), as a function of the phase of the modulation, t.

As mentioned above, the modulation vector has the same direction but different components in different crystals, and the one described above is incommensurate with respect to the basic cell. In order to visualize the structure, an approximant can be represented, in P1 symmetry, using a supercell of the kind a × b × nc, where n is an integer ≥ 1/γ (Fig. 8[link]).

[Figure 8]
Figure 8
Arrangement of the (As2S5)4− groups (represented as vertex-sharing trigonal pyramids) within a portion of size 2a × 2b × 5c unit cells. (a) Average disordered structure, both orientations of the disordered pyramids are possible at every position. (b) A portion of the incommensurately modulated structure of size 2a × 2b × 5c unit cells. The differently coloured (As2S5)4− groups correspond to configurations where the two different As positions are alternatively occupied, showing pyramids pointing up or down with respect to the plane of the picture.

4. Conclusions

The case of daliranite presented here is a clear example of how a complex incommensurate structure cannot be identified as such when the crystalline domains are too small for conventional single-crystal diffraction methods. The lack of a suitable 3D diffraction method prevented the previous authors (e.g. Paar et al., 2009[Paar, W. H., Pring, A., Moëlo, Y., Stanley, C. J., Putz, H., Topa, D., Roberts, A. C. & Braithwaite, R. S. W. (2009). Mineral. Mag. 73, 871-881.]) from (i) identifying the real stoichiometry of the mineral, (ii) understanding the real driving forces causing the appearance of the observed satellite reflections and (iii) understanding the actual global adjustments of the structural framework.

3D ED instead is a single-crystal diffraction technique suitable for nanocrystalline domains that can be coupled with EDX analysis information from the same domains. In the case of daliranite this meant a clear identification of the unknown mineral from other unavoidable spurious phases present in the sample and a correct determination of its unit cell and stoichiometry. Although the structure is disordered, as proven by the diffuse scattering along the modulation, the small lateral size of the 3D ED beam allowed us to probe regions where the ordered domains are dominant. Thus, besides the actual detection of the modulation, the satellite reflection intensities can be reliably integrated and successfully employed for structure determination in superspace.

The availability of a single-crystal diffraction technique at the nanometre scale will progressively change the way we tackle new crystallographic problems, opening the possibility that at this scale the crystals are different from what we expected.

Supporting information


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).

(average) top
Crystal data top
As2HgPbS5Dx = 5.493 Mg m3
Mr = 717.9Electron radiation, λ = 0.0335 Å
Orthorhombic, PnmaCell parameters from 2033 reflections
a = 21.246 (5) Åθ = 0.1–1.2°
b = 4.2897 (9) ŵ = 0 mm1
c = 9.5257 (12) ÅT = 298 K
V = 868.2 (3) Å3Needle, orange
Z = 40.0002 × 0.0001 × 0.0001 mm
F(000) = 1232
Data collection top
TEM
diffractometer
Rint = 0.335
Radiation source: LaB6θmax = 1.2°, θmin = 0.1°
10451 measured reflectionsh = 2020
562 independent reflectionsk = 43
401 reflections with I > 3σ(I)l = 810
Refinement top
Refinement on F0 restraints
R[F2 > 2σ(F2)] = 0.2440 constraints
wR(F2) = 0.303Weighting scheme based on measured s.u.'s w = 1/(σ2(F) + 0.0001F2)
S = 13.93(Δ/σ)max = 0.0002
562 reflectionsΔρmax = 0.45 e Å3
34 parametersΔρmin = 0.40 e Å3
Special details top

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

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Pb10.2886 (7)0.251.3368 (8)0.083 (6)
Hg10.4150 (6)0.250.9831 (7)0.065 (5)
As10.1286 (13)0.356 (3)1.1428 (18)0.030 (6)*0.5
As20.0526 (12)0.356 (3)0.8089 (16)0.019 (6)*0.5
S10.2233 (15)0.251.060 (2)0.034 (7)*
S20.1437 (15)0.250.690 (2)0.036 (7)*
S30.3337 (16)0.250.805 (2)0.042 (7)*
S40.4132 (13)0.251.4762 (19)0.019 (6)*
S50.4954 (15)0.251.160 (2)0.040 (7)*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Pb10.137 (16)0.101 (8)0.011 (5)00.0023320
Hg10.118 (14)0.069 (6)0.009 (5)00.0016520
Geometric parameters (Å, º) top
Pb1—S12.982 (17)
Pb1—S1—S2177.9
(modulated) top
Crystal data top
As2HgPbS5F(000) = 1232
Mr = 717.9Dx = 5.493 Mg m3
Orthorhombic, Pnma(00γ)0s0†Electron radiation, λ = 0.0335 Å
q = 0.262(2)c*Cell parameters from 10451 reflections
a = 21.246 (5) Åθ = 0.1–1.2°
b = 4.2897 (9) ŵ = 0 mm1
c = 9.5257 (12) ÅT = 298 K
V = 868.2 (3) Å3Needle, orange
Z = 40.0002 × 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 top
TEM
diffractometer
Rint = 0.335
Radiation source: LaB6θmax = 1.2°, θmin = 0.1°
10451 measured reflectionsh = 2020
1503 independent reflectionsk = 43
981 reflections with I > 3σ(I)l = 810
Refinement top
Refinement on F0 restraints
R[F2 > 2σ(F2)] = 0.2720 constraints
wR(F2) = 0.310Weighting scheme based on measured s.u.'s w = 1/(σ2(F) + 0.0001F2)
S = 10.70(Δ/σ)max = 0.001
1503 reflectionsΔρmax = 0.45 e Å3
38 parametersΔρmin = 0.40 e Å3
Special details top

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

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Pb10.2885 (5)0.251.3367 (5)0.061 (4)
Hg10.4149 (5)0.250.9835 (5)0.063 (4)
As10.1285 (8)0.371 (2)1.1430 (11)0.031 (3)*0.5
As20.0517 (7)0.365 (2)0.8082 (10)0.027 (3)*0.5
S10.2236 (10)0.251.0596 (15)0.027 (4)*
S20.1430 (9)0.250.6898 (14)0.019 (4)*
S30.3344 (11)0.250.8066 (15)0.026 (4)*
S40.4134 (8)0.251.4756 (12)0.007 (4)*
S50.4962 (10)0.251.1610 (15)0.030 (5)*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Pb10.132 (11)0.033 (4)0.018 (3)00.003 (4)0
Hg10.122 (10)0.060 (4)0.006 (3)00.002 (3)0
Bond lengths (Å) top
AverageMinimumMaximum
Pb1—S12.982 (17)2.979 (17)2.986 (17)
Pb1—S1i3.031 (11)2.912 (11)3.151 (11)
Pb1—S1ii3.029 (11)2.912 (11)3.151 (11)
Pb1—S2i2.948 (13)2.808 (13)3.087 (13)
Pb1—S2ii2.945 (13)2.808 (13)3.087 (13)
Pb1—S3i3.403 (19)3.13 (2)3.69 (2)
Pb1—S3ii3.398 (19)3.13 (2)3.69 (2)
Pb1—S42.975 (19)2.963 (19)2.985 (19)
Hg1—S2i3.159 (12)3.114 (12)3.205 (12)
Hg1—S2ii3.159 (12)3.114 (12)3.205 (12)
Hg1—S32.40 (2)2.40 (2)2.40 (2)
Hg1—S52.43 (2)2.42 (2)2.45 (2)
Hg1—S5iii3.184 (16)2.880 (17)3.501 (17)
Hg1—S5iv3.179 (16)2.880 (17)3.501 (17)
As1—S12.20 (3)2.19 (3)2.26 (3)
As1—S3i3.287 (13)3.056 (14)3.397 (14)
As1—S3ii2.308 (16)2.224 (17)2.495 (17)
As1—S4v3.212 (13)3.141 (13)3.316 (13)
As1—S4vi2.460 (15)2.377 (15)2.518 (15)
As1—S5vii3.41 (2)3.39 (2)3.44 (2)
As2—S22.28 (2)2.26 (2)2.32 (2)
As2—S4v3.155 (12)3.080 (12)3.259 (12)
As2—S4vi2.426 (14)2.342 (14)2.489 (14)
As2—S5v3.239 (14)3.083 (14)3.309 (14)
As2—S5vi2.328 (17)2.272 (17)2.455 (17)
S1—S33.37 (3)3.37 (3)3.38 (3)
S1—S3i3.423 (18)3.164 (19)3.695 (19)
S1—S3ii3.419 (18)3.164 (19)3.695 (19)
S2—S5v3.67 (2)3.47 (3)3.88 (3)
S2—S5vi3.67 (2)3.47 (3)3.88 (3)
S4—S53.48 (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, x21/2, x3+2, x4+1/2; (iv) x1+1, x2+1/2, x3+2, x4+1/2; (v) x1+1/2, x2, x31/2, x4+1/2; (vi) x1+1/2, x2+1, x31/2, x4+1/2; (vii) x11/2, x2+1/2, x3+5/2, x4.
 

Funding information

MG and AL would like to acknowledge Regione Toscana for funding the purchase of the Timepix single-electron detector through Felix project (Por CREO FESR 2014–2020 action). LB thanks MIUR-PRIN2017, project "TEOREM deciphering geological processes using Terrestrial and Extraterrestrial ORE Minerals", prot. 2017AK8C32.

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