Contribution to the crystal chemistry of lead-antimony sulfosalts: systematic Pb-versus-Sb crossed substitution in the plagionite homologous series, Pb2N−1(Pb1−xSbx)2(Sb1−xPbx)2Sb6S13+2N

The plagionite homologous series contains four well-defined members with the general formula Pb1+2NSb8S13+2N : fülöppite (N = 1), plagionite (N = 2), heteromorphite (N = 3), and semseyite (N = 4). The crystal structure of several natural and synthetic samples of fülöppite, plagionite, and semseyite have been refined through single-crystal X-ray diffraction, confirming the systematic Pb-versus-Sb crossed substitution observed previously in semseyite and fülöppite. This crossed substitution takes place mainly in two adjacent cation sites in the middle of the constitutive SnS-type layer. The substitution coefficient x appears variable, even for a given species, with the highest values observed in synthetic fülöppite samples. The developed structural formula of the plagionite homologues can be given as Pb2N−1(Pb1−xSbx)2(Sb1−xPbx)2Sb6S13+2N . In the studied samples, x varies between ∼ 0.10 and 0.40. In the ribbons within the SnS-type layer, (Pb/Sb) mixing can be considered the result of the combination, in a variable ratio, of two cation sequences, i.e. (Sb–Sb–Sb)–Pb–Sb–(. . . ), major in plagionite and semseyite, and (Sb–Sb–Sb)–Sb–Pb–(. . . ), major in fülöppite and, probably, in heteromorphite. The published crystal structure of synthetic “Pb-free fülöppite” is revised according to this approach. It would correspond to a Na derivative, with a proposed structural formula of (Na0.5Sb0.5)(Na0.2Sb0.8)2(Na0.3Sb0.7)2Sb6S15, ideally Na1.5Sb9.5S15. In fülöppite, increasing x induces a flattening of the unit cell along c, with a slight volume decrease. Such a general Pb-versus-Sb crossed substitution would attenuate steric distortions in the middle of the SnS-type layer of the plagionite homologous series. Crystallization kinetics seem the main physical factor that controls such an isochemical substitution. Dedicated to the memory of Dr. Nadejda N. Mozgova (1931–2019), Russian mineralogist of the Institute of Geology of Ore Deposits (IGEM Moscow), specialist of sulfosalt systematics.

A detailed crystal chemical analysis permitted Kohatsu and Wuensch (1974b) to develop a general structural scheme for this group. This study can be considered the basis for the modern definition of the plagionite homologous series, Pb 1+2N Sb 8 S 13+2N , with the following members: fülöppite (N = 1), plagionite (N = 2), heteromorphite (N = 3), and semseyite (N = 4). Takéuchi (1997), as part of his general study of tropochemical cell twinning, gave considerable detail about the crystal chemistry of the plagionite series. Recently, Makovicky (2019) presented this series as an example of a homologous series among sulfosalts.
In nature, this series has very simple chemistry. Fluctuations in the Pb/Sb atomic ratio correspond to microscopic or submicroscopic lamellar syntactic intergrowths (Mozgova and Borodaev, 1972;Moëlo, 1983) visible in crossed polars in reflected light or with SEM imaging. Rarely, arsenic may substitute for antimony (up to ∼ 10 at. %-12 at. % in plagionite from Rujevac, former Yugoslavia; Janković et al., 1977;Moëlo et al., 1983). Other erratic minor components detected by electron microprobe analysis would correspond to impurities. Rayite, (Ag,Tl) 2 Pb 8 Sb 8 S 21 , was defined as an (Ag,Tl)rich derivative of semseyite (Basu et al., 1983) on the basis of its X-ray powder diffraction (XRPD) pattern, but this interpretation was later debated (Roy Choudury et al., 1989;Bente and Meier-Salimi, 1991), and crystal structure data are still lacking.
Re-examination of the original structural data for fülöppite (Nuffield, 1975) led Swinnea et al. (1985) to highlight minor Sb substitution in a Pb site, coupled with the reverse substitution of Pb in an adjacent Sb position. A similar Pb-versus-Sb crossed substitution was obtained on semseyite from Wolfsberg by Matsushita et al. (1997) and recently refined and detailed by Matsushita (2018).
During the systematic study of sulfosalt mineralogy in ore deposits of the Apuan Alps, a new occurrence of plagionite was identified in the baryte + pyrite + iron oxide deposit of the Monte Arsiccio mine (e.g. Costagliola et al., 1990). Its crystal structure study, together with those of other samples of plagionite (natural), fülöppite (natural and synthetic), and semseyite (natural) allowed confirmation that such a Pb/Sb crossed substitution is a general feature of members of the plagionite homologous series. Detailed results are presented here.

Modular description of crystal structures in the plagionite series
Modular analysis constitutes a powerful approach for the bottom-up description of complex crystal structures of lead sulfosalts, taking into account polyhedra connection ac-cording to modules of increasing dimensionality: 0D (finite groups), 1D (chain, ribbon, column), 2D (slab, layer), and 3D (whole structure). Each module can be symbolized by its 3D polyhedra width. For instance, symbol 2/3/∞ would correspond to a ribbon, two-polyhedra thick and three-polyhedra large.
Application of modular analysis to the plagionite series permits five organization levels to be distinguished, from the bottom, i.e. polyhedra around metal or S atoms (level 1 -3D symbol 1/1/1; see the example of the plagionite structure in Cho and Wuensch, 1974), up to the top, i.e. the whole structure (level 5 -dimensionality ∞/∞/∞). Level 4 corresponds to a layered organization (Kohatsu and Wuensch, 1974b), with a single type of layer stacking along c with two orientations according to the binary axis. These layers correspond to diagonal slabs of the SnS archetype (Makovicky, 1989), with a distortion referring more exactly to the TlSbS 2 archetype (Takéuchi, 1997;Matsushita, 2018). Layer width increases with the homologue number N, through the addition of Pb polyhedra, corresponding to the stacking of (4 Sb +N Pb) cations (dimensionality (4 +N )/∞/∞). Layers are connected by an additional Pb atom. Figure 1 represents the layered structure of fülöppite along b (Nuffield, 1975). Projection according to [110] or [110] reveals ribbon stacking within each layer. Each ribbon is two atoms thick, six cations large ( Fig. 1c -four Sb and two Pb, including the Pb atom at the margin -dimensionality 2/6/∞). Projection of a single ribbon perpendicular to its flattening (see Fig. 1c) indicates oblique 2-atom-thick × 2atom-thick rows (Fig. 2), with a finite length of six atoms (level 2 -dimensionality 2/2/6). In a row ([110] direction of PbS archetype), there are two cation sequences, Sb-Sb-Sb-Sb-Pb-Pb and its reverse one. Nevertheless, this approach at level 2 is incomplete. Due to the stereochemical activity of its lone electron pair, trivalent Sb shows a dissymmetric coordination, with three strong Sb-S bonds (i.e. SbS 3 polyhedra with eccentric triangular pyramidal coordination). In the plagionite series, SbS 3 polyhedra coalesce to form finite groups (polymers), which have been described in fülöppite and plagionite by Edenharter and Nowacki (1974) and in heteromorphite and semseyite by Edenharter (1980). These groups are represented in Fig. 3, along with neighbouring Pb atoms. They are symmetric across the layer boundary via 2fold rotation (2-fold axis parallel to b -see projection along b in Fig. 1). Whereas in fülöppite, plagionite, and heteromorphite, all Sb sites are connected in an Sb 8 S m group (Fig. 3ac), in semseyite there is an Sb 6 S 13 group with two isolated SbS 3 polyhedra (Fig. 3d).
Plagionite, heteromorphite, and semseyite present the same cleavage plane according to {112}. It corresponds to the flattening of the ribbons according to (100) PbS . It has not been observed up to now in fülöppite but ought to be present for the same structural reasons.  Projection of the SnS-type, two-atom-thick ribbon of the crystal structure of fülöppite, according to Nuffield (1975). Two symmetric oblique cation rows alternate (1 to 6, and 1 to 6 ), with the sequence Sb-Sb-Sb-Sb-Pb-Pb. Short Sb-S bonds have been highlighted in green.

Fülöppite
Sample F1 is a crystal extracted from an old Romanian specimen from the Dealul Crucii deposit (Baia Mare district; La Sorbonne collection, Paris -now Jussieu collection). It occurs as millimetre-sized automorphic crystals on quartz.
Sample F2 is represented by well-developed synthetic crystals of Pb 3 Sb 8 S 15 obtained by Mozgova et al. (1987) through a hydrothermal process (PbS : Sb 2 S 3 mixture, 1 mol/L H 2 SO 4 ; temperature gradient 270-300 • C; run duration 6 d). Some of them were given to one of us (Yves Moëlo) by Nadejda Mozgova. Sample F3 is represented by rare crystals obtained as a by-product of a hydrothermal synthesis at 200 • C (3 weeks) from a mixture of galena and stibnite, together with the addition of PbCl 2 and FeCl 3 (run XIV-1, duration 3 weeks; Moëlo, 1983). The main product was a chloro-sulfosalt ("Phase Y", ∼ Pb 11 Sb 10 S 23 Cl 4 ; Moëlo, 1979).

Plagionite
Sample P1 is a new occurrence of plagionite discovered at the Monte Arsiccio mine (Apuan Alps, Tuscany, Italy), where this mineral occurs as compact masses or, rarely, as tabular crystals, showing growth features, up to 5 mm in size. Plagionite is associated with extremely thin acicular crystals, from black to reddish in colour, of Tl-bearing chovanite, in fractures of metadolostone from the Sant'Olga level. Electron microprobe analysis of plagionite gave (mean of 15 spot analyses; wt %) Pb 40.40(34), Sb 38.09(22), S 21.37(11), and sum 99.85(52). On the basis of Pb + Sb = 13 atoms per formula unit, the chemical formula of plagionite from Monte Arsiccio is Pb 4.99(2) Sb 8.01(2) S 17.05(2) , in agreement with the ideal formula Pb 5 Sb 8 S 17 .

Semseyite
Sample S1 is an old specimen from the Herja deposit (Baia Mare district, Romania). Its wet analysis (Palache et al., 1944), without minor Ag and Cu and insolubles, gave, on the basis of Pb + Sb = 21 atoms per formula unit, Pb 8.99 Sb 8.01 S 21.95 .
Sample S2 is centimetric massive semseyite embedded in quartz, collected in the dumps from La Rodde mine (Ally municipality, Haute-Loire department, French Massif Central; Roger, 1969). It comes from the Saint-Paul Pb-Sb quartz-baryte vein of Liassic age (Marcoux and Bril, 1986), deposited at a low temperature (∼ 100-150 • C; Bril, 1982). Semseyite was the main ore mineral of this deposit.

Single-crystal X-ray diffraction study
Single-crystal X-ray diffraction data for the studied samples were collected using a Bruker Smart Breeze diffractometer, equipped with an air-cooled CCD detector and graphite-monochromatized Mo Kα radiation. The detectorto-crystal working distance was set at 50 mm. Data were corrected for Lorentz-polarization factors, absorption, and background, using the package of software APEX3 (Bruker AXS Inc., 2016). The crystal structure of plagionite homologues was refined using SHELXL-2018(Sheldrick, 2015, starting from the atomic coordinates given by Edenharter and Nowacki (1974), Cho and Wuensch (1974), and Matsushita (2018) for fülöppite, plagionite, and semseyite, respectively. Scattering curves for neutral atoms were taken from the International Tables for Crystallography (Wilson, 1992). Details of data collections and refinements are given in Table 1. Atom coordinates for synthetic Pb 3 Sb 8 S 15 (sample F2), plagionite from Monte Arsiccio (sample P1), and semseyite from Herja (sample S1) are given in Table 2. Files in Crystallographic Information File format for all the studied samples are available in the Supplement.
In the first crystal structure studies, only pure Sb and Pb sites were taken into account (see Fig. 3). During the study of a "Pb-free fülöppite", Swinnea et al. (1985) re-examined the data of Nuffield (1975) on natural fülöppite and revealed a Pb-versus-Sb crossed substitution between neighbouring Pb(2) and Sb(3) sites, with occupancies (Pb 0.825 Sb 0.175 ) and (Sb 0.865 Pb 0.145 ), respectively. A similar result, with a weaker Pb/Sb substitution, was obtained for semseyite by Matsushita (2018) in Pb(5) and Sb(1), with occupancies (Pb 0.95 Sb 0.05 ) and (Sb 0.95 Pb 0.05 ), respectively.
In synthetic fülöppite, the Pb/Sb substitution is very pronounced, up to ∼ 40 at. %. In all fülöppite samples, the refinement also reveals an Sb substitution in a Pb1 site, correlated to a Pb substitution in the two neighbouring Sb6 sites (connected to Pb1 site via two S5 sites). Although very weak in natural fülöppite (x = 0.02 in Pb1), this substitution is more pronounced in synthetic samples (x = 0.04 for F2, 0.10 for F3). It corresponds to a secondary crossed substitution: Figure 4 represents the cation distribution within a ribbon for synthetic Pb 3 Sb 8 S 15 (sample F2). While weakly mixed (Pb,Sb)1 and (Sb,Pb)6 form isolated pairs, two (Pb,Sb)3 and two (Sb,Pb)5 strongly mixed sites form a lozenge, separated from neighbouring lozenges by two Sb6 sites. Figure 5 shows the cation distribution for plagionite from Monte Arsiccio (sample P1). Here lozenges with pairs of mixed (Pb,Sb)7 and (Sb,Pb)5 sites form a continuous file along the ribbon axis. In semseyite, lozenges with pairs of mixed (Pb,Sb)8 and (Sb,Pb)9 sites are separated by two Pb7 sites (Fig. 6), which play the same role as the Sb6 pair in fülöppite. Table 6 compares unit-cell parameters for plagionite and semseyite. In semseyite, unit-cell data are very homogeneous. In plagionite, the unit cell measured for the sample P2 from Wolfsberg is very close to that measured by Cho and Wuensch (1974) on a crystal from the same deposit. Unit cells of samples P3 from Lepuix and P1 from Monte Arsiccio are also similar.

Relationship with unit-cell data
The three natural samples of fülöppite have very close unit-cell parameters (Table 7). They come from the same ore deposit of Dealul Crucii. Nevertheless, taking into account the two synthetic samples, there is a significant increase in a and b intra-layer parameters (∼ 0.5 %) with an increasing Pb/Sb crossed-substitution coefficient x, while the layer stacking (c · sin β) is shortened (∼ 1 % - Table 7). It corre-  sponds to a flattening of the unit cell along c indicated by the increase in the ratio (a · b)/(c · sin β) (about 2 % from F1 to F3). Thus, the measure of this ratio is a way to estimate the crossed-substitution coefficient x. Selecting the new data obtained with the same apparatus (F1, F2, and F3), there is also a slight decrease in the unit-cell volume. Figure 7 compares the lozenge geometry of the [(Pb,Sb)3] 2 [(Sb,Pb)5] 2 groups in fülöppite (sample F2), considering the main and minor substitutions, i.e. (Pb3) 2 (Sb5) 2 and (Sb3) 2 (Pb5) 2 , respectively. The minor lozenge is compressed along c relatively to the major lozenge, as indicated by the values of their angles and diagonal lengths. Clearly, this distortion is the crystal chemical factor that controls the unit-cell flattening with an increasing x coefficient. For steric reasons, it is possible that a given layer contains Table 3. Pb-versus-Sb distribution (SOF), average bond distances <Me-S>, and cation bond valences (BVs) in the studied samples of fülöppite. For the sake of comparison, cation distribution in fülöppite from Baia Mare (Edenharter and Nowacki, 1974) and synthetic Na derivative of fülöppite (Swinnea et al., 1985)   only one type of lozenge, i.e. exclusively (Pb3) 2 (Sb5) 2 or (Sb3) 2 (Pb5) 2 groups. The resulting crystal structure would thus correspond to a disordered interstratification of these two types of layer. Another way to measure x is to compare the calculated XRPD of the three fülöppite samples of the present study, to see if there are some significant changes in the relative intensities of some main diffractions. On the basis of 100 for the intensity I of the 114 reflection at 3.87 Å, there is a significant I decrease for 112 and 331 reflections and, inversely, a significant I increase for 130 and 225 reflections (Table 8). Figure 8 represents the variation in the ratios A/B = I (112)/I (130) and C/D = I (331)/I (225) with x according to this table. The two continuous lines represent the interpolated curves between measured values of A/B and C/D ratios, while the two tie lines correspond to the extrapolated curves obtained starting from the crystal structure of the F1 sample, with x varying from 0 to 0.50. Table 5. Lead-versus-Sb distribution (SOF), average bond distances (<Me-S>), and cation bond valences (BVs) in the studied samples of semseyite. For the sake of comparison, cation distribution of semseyite from Wolfsberg after Matsushita (2018) Table 6. Relationships between unit-cell geometry and Pb/Sb crossed-substitution coefficient x in plagionite and semseyite. Samples classified according to increasing (a · b)/(c · sin β) ratio.   Kohatsu and Wuensch (1974b). 3 Cho and Wuensch (1974).
The tie line relative to the ratio C/D is in good accordance with the interpolated curve, while the A/B tie line presents a significant shift relative to the interpolated curve. The best equations are the two straight lines established on the basis of the A/B and C/D values of F1 and F2: (1) A/B = −0.0234 x + 1.852 and (2) C/D = −0.0074 x + 1.307.
In semseyite, like in fülöppite, with increasing x the unitcell volume decreases, while (a · b)/(c · sin β) increases. In plagionite (Table 6b), x values are very close, which does not permit the relationships between the variations in x, unit-cell volume, and (a · b)/(c · sin β) to be established.
5 The case of Pb-free fülöppite Swinnea et al. (1985) synthesized a Pb-free fülöppite at 250 • C in a saturated Na 2 CO 3 solution, with an ideal formula Sb 10 S 15 , implying the occurrence of vacancy ( ) in several Sb positions. The proposed structural formula is (Sb 0.58 0.42 )(Sb 0.852 0.148 ) 2 (Sb 0.773 0.227 ) 2 Sb 6 S 15 , corresponding to Sb 9.83 S 15 , ideally Sb 10 S 15 (it would be a stibnite dimorph). Re-examination of structural data as well as synthesis conditions brings one of us (Moëlo, unpublished data) to consider this compound a Na derivative of fülöppite (briefly mentioned in Makovicky, 1989). On the one hand, this compound was obtained in a hydrothermal synthesis with a high Na concentration; on the other hand, bond- Table 7. Relationships between unit-cell geometry and Pb/Sb crossed-substitution coefficient x in fülöppite. Samples classified according to increasing (a · b)/(c · sinβ) ratio.  Edenharter and Nowacki (1974). b Nuffield (1975). c Na-fülöppite; Swinnea et al. (1985). d Pb derivation.    valence calculations give bad valence sums in partially occupied Sb positions. In ideal fülöppite, Pb 3 Sb 8 S 15 , the replacement of Pb through the heterovalent substitution 2Pb 2+ = Na + + Sb 3+ would give the formula (Na 0.5 Sb 0.5 ) 3 Sb 8 S 15 , i.e. Na 1.5 Sb 9.5 S 15 .
In Pb-free fülöppite, the position Sb6 has a SOF = 0.58, corresponding to 29.6 electrons (e − ). A mixed site with 0.5 Na and 0.5 Sb corresponds to (11 × 0.5) + (51 × 0.5) = 31 e − , in quite good agreement with the measured electron density. For Sb3 (SOF = 0.852) and Sb5 (SOF = 0.773), one obtains a total of 82.9 e − . This ought to correspond to a mixture of 0.5 Na and 1.5 Sb, that is, a total of (11 × 0.5) + (51 × 1.5) = 82 e − . Here also the agreement is very good. Calculation of the partitioning of Na and Sb between Sb3 and Sb5 positions gives the site populations (Sb 0.81 Na 0.19 ) and (Sb 0.71 Na 0.29 ) for Sb3 and Sb5, respectively. The developed ideal structural formula becomes (Na 0.5 Sb 0.5 )(Na 0.2 Sb 0.8 ) 2 (Na 0.3 Sb 0.7 ) 2 Sb 6 S 15 = Na 1.5 Sb 9.5 S 15 , as proposed above. This new structural model is shown in Fig. 8. For this structure model, bond-valence calculation according to Brese and O'Keeffe (1991) gives for the cations (1.5 Na + 9.5 Sb) a total of 29.4 vu (valence units), against 27.9 vu for the structure solution of Swinnea et al. (1985;ideal total 30 vu).
For comparison with fülöppite, the derivation of the formula of Na-fülöppite through the substitution Na + + Sb 3+ = 2 Pb 2+ gives the new formula Pb(Sb 0.6 Pb 0.4 ) 2 (Pb 0.6 Sb 0.4 ) 2 Sb 6 S 15 , which is very similar Figure 9. Proposed distribution of Na/Sb mixed sites in the structure of Pb-free fülöppite of Swinnea et al. (1985). to the formula of the synthetic fülöppite studied in this work (sample F3). It corresponds to the row sequence Sb-Sb-Sb-(Pb 0.6 Sb 0.4 )-(Sb 0.6 Pb 0.4 )-Pb (Table 3).
The actual formula of Pb-free fülöppite appears to be Na 1.5 Sb 9.5 S 15 (or Na 3 Sb 19 S 30 ). It is a new Na-poor member of the pseudo-binary Na 2 S-Sb 2 S 3 system, together with NaSbS 2 (a dimorph pair; Olivier-Fourcade et al., 1978) and Na 3 SbS 3 (Sommer and Hope, 1977;Pompe and Pfitzner, 2013). Mozgova et al. (1987) detected the presence of hydrogen as (HS) − or (OH) − in synthetic fülöppite through NMR study. Due to the synthesis conditions (pH ∼ 1.5), it is probable that H + substitutes in the crystal structure in a similar way to Na + , i.e. in the sense that 2Pb 2+ = H + + Sb 3+ .
resolved structures will reveal modulations due to long-range ordering along c of two types of layers, as suggested here for fülöppite. The use of transmission electron microscopy (HRTEM) may be decisive for this purpose.
It would be interesting to synthesize Pb-free fülöppite by dry synthesis in the Na 2 S-Sb 2 S 3 system, in order to confirm and refine its structure. This would permit the characterization of its physical properties, taking into account the recent interest of parent NaSbS 2 as a solar absorber material (Sun and Singh, 2017). In addition, it is possible that Na enters as traces in the structures of natural members of the plagionite series, in relationship to the NaCl concentration of hydrothermal solutions. Similarly, NMR study of hydrogen as traces may help to measure the pH of these solutions.
Data availability. Crystallographic Information Files (CIFs) of the studied crystal structures are available in the Supplement.
Author contributions. CB carried out the single-crystal data collection. Both the authors analysed the results and wrote the manuscript.
Competing interests. The authors declare that they have no conflict of interest.