Powder diffraction

Powder X-ray diffraction data of argentopearceite were recorded at room temperature using a Bruker D8 Advance diffractometer equipped with a solid-state LynxEye detector and secondary monochromator producing CuKα radiation housed at the Department of Mineralogy and Petrology, National Museum, Prague. The instrument was operated at 40 kV and 40 mA. To minimise the background, the powdered samples were placed on the surface of a flat silicon wafer. The powder pattern was collected in the Bragg–Brentano geometry in the range 3–70°2θ, step size 0.01° and counting time of 20 s per step (total duration of the experiment was c. 30 hours). The positions and intensities of diffractions were found and refined using the Pearson VII profile-shape function of the ZDS program package (Ondruš, Reference Ondruš1993); data are given in Table 3. The differences between intensities observed for the samples from Mikulov and Moldava samples and those calculated on the basis of the refined structural model are related to the preferred orientation and other textural effects. Unit-cell parameters were refined by the least-squares program of Burnham (Reference Burnham1962) for trigonal space group P321 (#150) as follows – Mikulov: a = 14.8934(18), c = 12.339(2) Å, V = 2370.3(6) ų and Z = 4; Moldava: a = 14.8741(16), c = 12.318(2) Å and V = 2360.1(5) ų. The c:a ratio calculated from unit-cell parameters is 0.8285 (Mikulov) and 0.8282 (Moldava).

Table 3. Powder X-ray diffraction data (d in Å) for argentopearceite from Mikulov and Moldava; the six strongest diffractions are reported in bold

I _calc* - relative intensity calculated using the software PowderCell2.3 (Kraus and Nolze, Reference Kraus and Nolze1996) on the basis of the structural model given in Tables 4 and 5.

Single-crystal X-ray diffraction (SCXRD)

Single-crystal diffraction data of argentopearceite were collected from the holotype specimen from Mikulov at room temperature on an Oxford Diffraction Gemini diffractometer equipped with a standard sealed X-ray tube (graphite monochromatised MoKα radiation, λ = 0.71073 Å) and an Atlas S2 CCD detector. The raw data reduction was done using CrysAlisPro Version 1.171.39.46 software (Rigaku, 2019). The data were corrected for Lorentz factor, polarisation effect and absorption (multi-scan, ABSPACK scaling algorithm; Rigaku, 2019). The crystal structure of argentopearceite was solved from the diffraction data using the SHELXT program (Sheldrick, Reference Sheldrick2015) and refined using the Jana2020 software (Petříček et al., Reference Petříček, Palatinus, Plášil and Dušek2023). The crystal was modelled as a four-fold twin due to metric merohedry twinning (trigonal<hexagonal; diffraction type II; Petříček et al., Reference Petříček, Dušek and Plášil2016). We employed the third-order anharmonic Gram–Charlier development (see, e.g. Volkov et al., Reference Volkov, Charkin, Firsova, Aksenov and Bubnova2023) to describe the Debye-Waller factors for some of the Ag atoms that behave strongly anharmonically in the structure studied. The refined values were checked for significance (shift vs. error). The use of the Gram–Charlier development and corresponding data handling and refinement were discussed recently by Plášil et al. (Reference Plášil, Sejkora, Dolníček, Petříček, Désor, Majzlan, Gross, Möhn and Schürmann2024). The Wilson’s correction was applied during the refinement, preventing the statistical bias in the least-squares refinement (Wilson, Reference Wilson1976). Details of data collection and refinement are given in Table 4. Fractional atomic coordinates and equivalent isotropic displacement parameters are reported in Table 5 and Table 6 reports selected bond distances. Further details of the data collection, crystallographic parameters, and the fit statistics are given within the crystallographic information files provided as Supplementary material. The Vesta program (Momma and Izumi, Reference Momma and Izumi2011) was used to plot the electron density and the isosurface for atomic displacement parameters (ADPs) of the Ag atoms, all other structrure drawings were done using the Diamond4 program (Crystal Impact). For charge distribution analysis and other polyhedral-concerning calculations (Table 7), the program ECoN21 (Ilinca, Reference Ilinca2022) was used.

Table 4. Summary of data collection and refinement for argentopearceite-T2ac from Mikulov

Table 5. Atom positions, occupancy factors and displacement parameters (in Ų; equivalent or isotropic – marked with *) for the structure of argentopearceite-T2ac from Mikulov

Table 6. Selected interatomic distances (in Å) and polyhedral measures for argentopearceite-T2ac structure from Mikulov

Symmetry codes: (i) y, x, –z; (ii) –y+1, x–y+1, z; (iii) –x+y, –x+1, z; (iv) x–y, –y+1, –z; (v) –y, x–y, z; (vi) –x+y, –x, z; (vii) –x, –x+y, –z; (viii) –x+y+1, –x+1, z; (ix) y, x, –z+1; (x) –x+1, –x+y+1, –z+1; (xi) x–y, –y, –z+1; (xii) –y+1, x–y, z; (xiii) –x, –x+y, –z+1; (xiv) x–y, –y+1, –z+1.

Table 7. Charge-distribution analysis, bond-valence sums, ECoN and EDEV* for the structure of argentopearceite-T2ac from Mikulov

Notes: parentheses: () = contribution to the charge <0.1; [] = contribution to the charge < 0.01. CN – coordination number; ECoN – effective coordination number; EDEV – deviation of ECoN from the constrained coordination number (i.e. determined by the ligands with non-zero weight bonds concerning the charge distribution); QX – charge received by cations; qx/QX – ratio of formal charge of cation/QX; BVS – bond-valence sum – a sum of bond-valences (bond-strengths) received by the cation

* Taken from Ilinca (Reference Ilinca2022)

Crystal structure

Argentopearceite from Mikulov is trigonal, space group P321 (No. 150), with a = 14.8583(5) Å and c = 12.3038(5) Å. Thus, it is a Ag end-member of the pearceite-T2ac structure type. The crystal structure of argentopearceite contains two distinct As(Sb) sites (one of them on the three-fold axis of symmetry), twelve distinct Ag sites, and ten S positions. Ag10 is (practically) in a special position, as is S9; selected special coordinates occur also for S6, S7, and S10.

As in other pearceite–polybasite homeotypes, the crystal structure of argentopearceite is divided into two well-defined layers, called A and B (after Bindi et al., Reference Bindi, Evain and Menchetti2006), of almost identical thickness (when measured on well-populated boundary levels composed of anions), which differ, however, in the character of their cation populations. One of them is populated by As³⁺ and Ag (A layer) (Fig. 3a), which are placed ‘under’ the boundary sulfur sheets, with lone electron pairs of As orientated towards its more sparsely populated median sulfur sheet. The other layer lacks the lone-electron pair elements and is populated by ‘subsurface’ silver sheets. The rest of the sulfur occurs between these silver sheets, together with two characteristic cation positions, Ag11 (site occupancy Ag_0.81) and Ag12 (site occupancy Ag_0.66), which are in the median plane of the layer (Fig. 3a). Both positions were refined as pure silver sites, which is in agreement with the chemical analysis. This succinctly describes the distribution of atoms in the B layer; however, it contains a rich assortment of coordinations and coordination polyhedra in both layer types. Equally, it contains several cation–cation interactions and at least some signs of silver mobility.

Figure 3. The crystal structure of argentopearceite. (a) The view of the A and B layers. A layer: Ag – dark grey, As/Sb – green, S – yellow. B layer: Ag11 and Ag12 – dark blue, rest of Ag atoms – grey, S – yellow. (b) A layer: S9-centered Ag₆S octahedra (Ag1, Ag2, Ag4) (turquoise), As/Sb in green colour, corresponding AsS₃ pyramids (orientations not differentiated, blue). B layer: Ag-centred Ag12 distorted trigonal antiprisms (blue), Ag-centred Ag12 square antiprisms (plum), the interconnecting S8-centered Ag₆S octahedra (3× Ag8, 3× Ag5) (light blue).

For further description, we shall use the concept of anion-centred coordination polyhedra, for the A layer in combination with the AsS₃ pyramids (Fig. 3a,b). This concept yields a better-organised description of the layered architecture and its principal elements. It resembles the approach Withers et al. (Reference Withers, Norén, Welberry, Bindi, Evain and Menchetti2008) used, although it differs in definitions of some of these elements. Among other reasons, differences exist because Withers et al. (Reference Withers, Norén, Welberry, Bindi, Evain and Menchetti2008) described the pearceite Tac polytype and we deal with the T2ac polytype. Structural differences between these two polytypes (Bindi et al., Reference Bindi, Evain and Menchetti2007a) are more pronounced than typically assumed.

A layer

The As–Ag layer (Figs 3a,b, 4a) has all AsS₃ coordination pyramids (As–S for As1 is equal to 2.231 Å; for As2 they are 2.257, 2.233 and 2.249 Å) orientated with lone-electron pairs inwards, towards its median plane, and their pyramid bases are parallel to (0001). The simplest and most important observation is that the Ag atoms present in this layer (Ag1, Ag2, and Ag4) together form octahedral Ag₆ clusters, with S9 in their centres. The average of the Ag–S9 bonds is 2.474 Å. Silver, which surrounds the S9 site, forms Ag–S bonds towards the vertices of the surrounding AsS₃ pyramids. A similar octahedral Ag₆ configuration is formed by the (six symmetrically related) Ag3 atoms, constituting an octahedron in the 0,0,z positions. The average Ag3–S10 bond is 2.422 Å, an average of 2.168, 2.434 and 2.663 Å; distances resulting from the split character of S10.

The peculiar behaviour of the S-centred Ag3–S10 cluster does not appear to result only from overall deprivation in space and might also reflect the local situation in the Ag12–S6–(Ag3)₃–S10–(Ag3)₃–S6 column (Fig. 5). The other Ag–S bonds (2.38–2.52 Å) are of the usual length. In the Cu-containing pearceite-Tac, Withers et al. (Reference Withers, Norén, Welberry, Bindi, Evain and Menchetti2008) assume that the positional disorder of the analogue of our S10, results from statistical (Ag, Cu) occupancies of the surrounding octahedral ligands to the central sulfur atom and subsequent satisfaction of bond valences. However, the ligands (all Ag3) were refined as pure silver in the present case. Interestingly, the Ag3–S10 configurations occur only as a minority among the other, configurationally simple types of anion-centred octahedra with S9 in their centres. In contrast, in the Tac structure, they are the only type of anion-centred octahedron in the A layer.

The alternative description of this layer is of equal crystal-chemical importance. All Ag sites (Ag1, Ag2 and Ag4) form 6-winged ‘spinners’, with the central S9 atom (Fig. 4b), as well as all peripheral S atoms, situated within their own structural (0001) A layer. They remind us of the spinners observed in the structure of tetrahedrite isotypes (Makovicky, Reference Makovicky2021). However, the orientation of AgS₃ triangles is different, resulting in the (‘approximate’) spinner bar 3-symmetry. The bond to the central S9 sulfur of the spinner is, in most cases, just slightly shorter than the rest of the Ag–S bonds. The Ag–Ag distances (based on static Ag atoms) are in the range 3.02–4.10 Å, excluding the presence of cation–cation bonds in this layer, and suggesting at the same time that the above octahedral arrangements of silver atoms are a result of general crystal-chemical convenience (satisfying a triangular bonding scheme for Ag) and not of the Ag–Ag bonding. The Ag–Ag distances between spinners are 4.048 Å, and spinner arm edges (S–S distances) measure ∼3.9–4.8 Å. Spinners formed by Ag3 bear signs of the S10 splitting.

Figure 4. The A layer from the crystal structure of argentopearceite. (a) S9-centred SAg₆ polyhedra (turquoise) and projections of the AsS₃ trigonal pyramids (indigo and blue). Viewed along [0001]. (b) An alternative description of the layer: clusters of six AgS₃ propellers, each sharing a central S9 atom.

A side-view of A+B layers indicates that the Ag–S bonds that interconnect the A and B layers originate at the Ag atoms in the ‘Ag-only’ B layer and not in the Ag–As layer. For example, Ag5 has a rather short bond (2.503 Å) directed to S1 from the opposing A layer.

B layer

The As-free B layer can be interpreted as a mosaic of four different coordination polyhedra: two different clusters based on cation–cation bonds and two anion-centred coordination polyhedra which interconnect them (Fig. 6). This scheme of ‘inverted polyhedra’ offers the simplest description for the B layer. The cluster based on the central Ag12 atom has six Ag7 ligands at 2.696 Å and forms a distorted trigonal prism (Fig. 6). These silver atoms are separated by distances of 3.007 Å, and 2× 3.954 Å from one another. The second-nearest Ag atoms to Ag12 are the Ag8 atoms, at a distance of only 3.698 Å from the central Ag12. The Ag12 polyhedron is situated at x = y = 0 and z = 0.5. The other metal cluster is situated at (0.52,0,½) and equivalent positions. Remarkably, it is a distorted square antiprism around Ag11, with only four short cation–cation contacts, arranged according to the ‘horizontal’ two-fold rotation operation: 2× 2.742 Å to Ag10 and 2× 2.852 Å to Ag9 in the form of a disphenoid. Distances from Ag11 to the remaining antiprism corners are longer: 2.972 Å to Ag5, and 3.095 Å to Ag8.

Both cation clusters are topped by single S atoms from both the +c and –c sides. The Ag11–S5 distance is 2.307 Å, and the Ag12–S6 distance is somewhat shorter, 2.226 Å. Both these sulfurs are bonded to the cations at the top corners of the (anti)prisms. The above-mentioned Ag12-based (anti)prism is composed of only Ag7 atoms, and the topping S6–Ag7 bonds are 2.416 Å long. In the Ag11 case, the topping S5 has bond distances from 2.440 Å to 2.756 Å, in agreement with the trapezoidal form of the (0001) faces of the cluster.

Three Ag11 clusters in one B layer are separated only by an octahedral anion-centred cluster of S7, coordinated by three Ag5 and three Ag8 atoms. There are three 2.527 Å bonds S8–Ag8 and three 2.782 Å bonds to Ag5 present; the Ag5–Ag11 distance is 3.645 and 3.710 Å, whereas the Ag5–Ag5 distances are 3.547 Å and the Ag8–Ag8 distances are longer, 3.955 Å. Clearly, none of the cation–cation interaction mechanisms seen in the surrounding antiprisms ‘spill over’ into this polyhedron, and some of the Ag–S distances might even be somewhat longer, perhaps stretched by the requirements of the surrounding polyhedra.

The S7-centred polyhedron is complicated, and these polyhedra leave small unfilled gaps that stretch between adjacent Ag11- and Ag12-based polyhedra (Fig. 6). Four of the Ag ligands to S7 have Ag–S distances between 2.43 and 2.67 Å, whereas the other four have 2.83 Å to 3.45 Å. This polyhedron essentially separates the Ag11-centred clusters from the adjacent Ag12-centred clusters.

An ordered layer-to-layer match of individual configurations is observed across the layer sequence; they form a sort of columnar sequence (for instance, see Fig. 5). In the stacking arrangement inspected along the [0001] direction, the S8-centred octahedra follow one set of AsS₃ pyramids; the other set of pyramids overlaps with the S7 polyhedra in a less-centred fashion. Pyramids of As2 alternate with intermediate S8-based octahedra, leaving a considerable cavity for the lone electron pair of As2 (the As2–S1 distance is 4.288 Å, As2–Ag2 is 3.559 Å, and As2–As2’ is equal to 4.840 Å). However, the pyramidal placement along the c axis and their orientation alternates. Selected centres of false As rings in the As-containing layer (i.e. the S10-centered Ag3 octahedra) overlap with the Ag11-centred trigonal (anti)prisms, whereas the S9-octahedra (Ag1, Ag2, Ag4) with the square Ag12-centred square antiprisms along the c direction. In this way, in the two latter cases, the cation–cation bonded clusters become separated from one another across the layer sequence.

Figure 5. The column (module) of Ag–S–Ag clusters in the structure of argentopearceite that involves a positionally disordered S10 site.

Figure 6. The B layer fragment from the crystal structure of argentopearceite with Ag-centred polyhedra (Ag12 trigonal prism, Ag11 square antiprism, and two types of S-centred polyhedra: S8-centred octahedron (light blue) and S7-centred irregular polyhedron with Ag6 atoms staggered oppositely to each other – faces indicated by the yellow solid lines).

Anharmonic approach to the description of atomic displacement parameters of Ag

It has been well documented (Evain et al., Reference Evain, Bindi and Menchetti2006; Bindi et al., Reference Bindi, Voudouris and Spry2013, Reference Bindi, Stanley and Spry2015a, Reference Bindi, Topa and Frank2015b) that while refining the structure of pearceite–polybasite homeotypic family of minerals using the conventional harmonic approach to the atomic displacement parameters, one will obtain only incomplete information about the behaviour/motion of silver atoms as they are quite mobile in these structures at room temperature. There is always a lot of significant residual electron density in the Fourier-difference maps associated with Ag atoms using a simple harmonic refinement and this is also a valid statement for argentopearceite (6.02 e^–/ų – harmonic vs. 3.67 e^–/ų – anharmonic). We used up to the 3^rd-order anharmonic Gram–Charlier tensors for the description of Debye-Waller factors of Ag atoms implemented in Jana2020. This approach significantly improved the model-to-data fit and a drop in R-values of ∼3%. The use of the higher orders of the Gram–Charlier development is, of course, possible, but questionable regarding the data quality and the nature of the structure (ten corresponding atoms for which the use of the higher order might be considered – a lot of correlations). Recently, we have discussed this topic in the paper describing the use of the Gram–Charlier development to refine the crystal structure of the mineral theuerdankite, Ag₃(AsO₄) (Plášil et al., Reference Plášil, Sejkora, Dolníček, Petříček, Désor, Majzlan, Gross, Möhn and Schürmann2024). The final R-values reached by the refinement, including the anharmonic approach to the ADPs of the Ag atoms (Fig. 7) were R ₁ = 0.0773, wR ₂ = 0.1340 for 6594 reflections with [I > 3σ(I) (GOF = 2.78; largest peak in difference-Fourier electron density was 1.98 e^–/ų).

Figure 7. Non-harmonic joint probability density functions isosurfaces of Ag atoms within the top of the B layer and adhering (interacting) atoms from the A layer in the structure of argentopearceite at room temperature. The size of the S atoms is arbitrary. The isosurface level of the 3D maps is 0.08 Å^–3.

The principal conclusion about the behaviour of silver atoms in the structure of argentopearceite at room temperature is that, with the possible (questionable) exception of the Ag6, Ag9 and Ag10 sites, the displacement parameters of silver atoms indicate more or less fixed cation sites, with a degree and orientation of anisotropy following the shape of their coordination polyhedron and not just the longer occupied portions of the possible diffusion path.

Most remarkable are the shapes of ADPs described by the joint probability density function Ag11 and Ag12. Both are very flat discs (Fig. 8) with a roughly circular outline. A disc of Ag12 is actually thinner than that of Ag11. These strange configurations combine with more pronounced displacement ellipsoids of Ag5 and Ag10 (for Ag11), and Ag6 and Ag7 (for Ag12). This is observed in all cation–cation interactions in argentopearceite. This can be explained as because the cation–cation distances are strictly maintained and, when the central Ag11 or Ag12 cation assumes different positions (shifts) in its displacement disc, the interacting Ag atoms from the above/below sub-layers have to adjust to preserve the cation–cation bond length. Moreover, both of the central cations can eventually host Cu (concerning a possible solid-solution between argentopearceite and pearceite), and analogous statistical adjustment of corresponding bonded Ag atoms to the differing Ag–Ag, Ag–Cu, as well as Ag–S and Cu–S bond lengths has to take place. That may also explain the strange shape of the Ag11 and Ag12 ADPs.

Figure 8. The Ag-centred clusters (Ag11 and Ag12) with cation–cation bonds and the surrounding region. Green joins between the silver atoms indicate significant cation–cation interactions.

The Ag8 and Ag10 atoms are a part of the cluster based on Ag11. They are among those with strongly developed displacement ellipsoids, which are slightly curved, suggesting a potential common free space within the structure. Such a space, perhaps, can suggest the possible diffusion of Ag at temperatures above room temperature. However, this space and character do not continue towards the remaining silver atoms on the same z level; thus, the free space does not surround the central S7 atom. The other two Ag atoms forming the top plane of the square antiprism, Ag5 and Ag9, display a lower degree of in-plane motion and differ greatly from the dynamic behaviour of Ag8 and Ag10.