The Crystal Chemistry of Rathite Based on New Electron-Microprobe Data and Single-Crystal Structure Refinements : The Role of Thallium

Crystal-structure refinements in space group P21/c were performed on five grains of rathite with different types and degrees of thallium, silver, and antimony substitutions, as well as quantitative electron-microprobe analyses of more than 800 different rathite samples. The results of these studies both enlarged and clarified the complex spectrum of cation substitutions and the crystal chemistry of rathite. The [Tl+ + As3+]↔ 2Pb2+ scheme of substitution acts at the structural sites Pb1, Pb2, and Me6, the [Ag+ + As3+]↔ 2Pb2+ substitution at Me5, and the Sb-for-As substitution at the Me3 site only. The homogeneity range of rathite was determined to be unusually large, ranging from very Tl-poor compositions (0.16 wt%; refined single-crystal unit-cell parameters: a = 8.471(2), b = 7.926(2), c = 25.186(5) Å, β = 100.58(3)◦, V = 1662.4(6) Å3) to very Tl-rich compositions (11.78 wt%; a = 8.521(2), b = 8.005(2), c = 25.031(5) Å, β = 100.56(3)◦, V = 1678.4(6) Å3). The Ag content is only slightly variable (3.1 wt%–4.1 wt%) with a mean value of 3.6 wt%. The Sb content is strongly variable (0.20 wt%–7.71 wt%) and not correlated with the Tl content. With increasing Tl content (0.16 wt%–11.78 wt%), a clear increase of the unit-cell parameters a, b, and V, and a slight decrease of c is observed, although this is somewhat masked by the randomly variable Sb content. The revised general formula of rathite may be written as AgxTlyPb16−2(x+y)As16+x+y−zSbzS40 (with 1.6 < x < 2, 0 < y < 3, 0 < z < 3.5). Based on Pb–S bond lengths, polyhedral characteristics and Pb-site bond-valence sums, we conclude that the Pb1 site is more affected by Tl substitution than the Pb2 site. When Tl substitution reaches values above 13 wt% (or 3 apfu), a new phase (“SR”), belonging to the rahite group, appears as lamellar exsolution intergrowths with Tl-rich rathite (11.78 wt%). Rathite is found only in the Lengenbach and Reckibach deposits, Binntal, Canton Wallis, Switzerland.

As part of an indepth and long-term study of the sulphosalt mineralogy of the Lengenbach deposit by the first author since 2013, the present paper deals with the crystal chemistry of rathite and aims to provide an understanding of the observed substitutional schemes on the basis of numerous electron microprobe datasets and a larger number of single-crystal structure refinements of samples from the Lengenbach and Reckibach occurrences.

Examined Material, Appearance, and Optical Properties
Euhedral crystals and massive sulphosalt accumulations (patches) of the sartorite homologs from the world-famous Lengenbach deposit (e.g., Graeser et al. [20] and references therein) and the Reckibach sulphosalt occurrence (Cannon et al. [21]) were obtained from the collection of the Natural History Museum, Vienna, and the Natural History Museum, Basel, as well as from private collections of Horst Geuer (Germany), Frank Keutsch (USA), the second author (Austria), Thomas Raber (Germany), Phillippe Roth (Switzerland), and Ralph Cannon (Germany).These samples were collected or acquired in the time range between 1816 and 2017.
Our studies show that rathite is commonly intimately intergrown with sartorite, baumhauerite, liveingite, and dufrénoysite, but also occurs as larger, single-phase homogenous grains.Macroscopically, the mineral is always blackish (independent of the Tl content), with metallic to dull luster.In reflected light, the color of rathite is greyish-white with strong anisotropy.No twin lamellae were observed in the structurally studied fragments, but twinning was partly observed in other fragments and may be present in other samples.Representative back-scattered electron and optical images of rathite grains analysed by EPMA are shown in Figures 1-3: homogeneous rathite grains (aggregates) with low and high Tl content are shown in Figure 1, of Tl-rich rathite with exsolved lamellae of a Tl-richer rathite-type phase "SR" (for details see below) in Figure 2 and of Sb-bearing rathites from Reckibach and Lengenbach in Figure 3.
exsolved lamellae of a Tl-richer rathite-type phase "SR" (for details see below) in Figure 2 and of Sb-bearing rathites from Reckibach and Lengenbach in Figure 3.   1; 11.78 wt% Tl) and a possibly new, still Tl-richer species, "SR" (dark grey phase, rath10 in Table 1; 13.25 wt% Tl).Note that the small fragment in the (b') optical image shows twin lamellae.exsolved lamellae of a Tl-richer rathite-type phase "SR" (for details see below) in Figure 2 and of Sb-bearing rathites from Reckibach and Lengenbach in Figure 3.   1; 11.78 wt% Tl) and a possibly new, still Tl-richer species, "SR" (dark grey phase, rath10 in Table 1; 13.25 wt% Tl).Note that the small fragment in the (b') optical image shows twin lamellae.1; 11.78 wt% Tl) and a possibly new, still Tl-richer species, "SR" (dark grey phase, rath10 in Table 1; 13.25 wt% Tl).Note that the small fragment in the (b') optical image shows twin lamellae.

Chemical Data
Up to twenty separate sulphosalt grains, depending on quantity of available material in a given sample, were mechanically extracted from the dolomite-hosted sulphosalt aggregates or crystals and subsequently embedded in an epoxy-mount, polished, studied in reflected light, examined by qualitative back-scattered electron (BSE) images and energy dispersive spectrometry (EDS) analyses) and quantitative wave-length dispersive spectrometry (WDS) electron microprobe analyses.This procedure was separately applied to a large number of samples.
The formula calculations for the sartorite homologue order Ncalc, described by Makovicky and Topa [13], are designed to identify the minerals of the family from the results of electron microprobe investigations, and are used here to select all point analyses representative for rathite and rathite-related phases with N = 4.More than 2700 point analyses, of more than 800 samples containing rathite, with calculated homologue number Ncalc ranging between 3.9 and 4.1, and with a good charge balance (calculated from at % values) ranging between -2.5 and +2.5, were selected and represent the best analytical data base of rathite compositions at present.The entire content of the database is plotted in the (As + Sb) − (Ag + Tl) − Pb ternary diagram (Figure 4) as a grey background and gives a first hint of the chemical variations.

Chemical Data
Up to twenty separate sulphosalt grains, depending on quantity of available material in a given sample, were mechanically extracted from the dolomite-hosted sulphosalt aggregates or crystals and subsequently embedded in an epoxy-mount, polished, studied in reflected light, examined by qualitative back-scattered electron (BSE) images and energy dispersive spectrometry (EDS) analyses) and quantitative wave-length dispersive spectrometry (WDS) electron microprobe analyses.This procedure was separately applied to a large number of samples.
The formula calculations for the sartorite homologue order N calc , described by Makovicky and Topa [13], are designed to identify the minerals of the family from the results of electron microprobe investigations, and are used here to select all point analyses representative for rathite and rathite-related phases with N = 4.More than 2700 point analyses, of more than 800 samples containing rathite, with calculated homologue number N calc ranging between 3.9 and 4.1, and with a good charge balance (calculated from at % values) ranging between -2.5 and +2.5, were selected and represent the best analytical data base of rathite compositions at present.The entire content of the database is plotted in the (As + Sb) − (Ag + Tl) − Pb ternary diagram (Figure 4) as a grey background and gives a first hint of the chemical variations.sulphide ternary plot (at %).The grey dots show all 2700 spot analyses, while samples rath1 to rath9 are those also characterized by crystal-structure refinements.Most of the analyses belong to the rath3-rath5 interval (1.58 wt%-5.36wt% Tl).Low-Tl (rath1, typical of Reckibach samples) and high-Tl (rath9 and rath10) are very rarely encountered compositions.
The representative mean chemical compositions of rathite with different degree of (Ag + + As 3+ )-for-2Pb 2+ , (Tl + + As 3+ )-for-2Pb 2+ and Sb-for-As substitutions (some used for subsequent crystal-structure studies), are presented in Tables 2 and 3, whereas individual points of the first group of samples (used for the structural studies) are plotted in different colours in the ternary diagram of Figure 4.The range of Ag, Tl, and Sb variations found are considerably larger than those reported by Berlepsch et al. [2].The degree of Ag and Tl substitutions (Agsubst and Tlsubst) are calculated with formulae given by Makovicky and Topa [13].The Agsubst value varies between 43.4 and 47.9, whereas the Tlsubst value shows a large variation between 0.5 and 41.9, with strong implications for the crystal chemistry and range of compositional variability of rathite.sulphide ternary plot (at %).The grey dots show all 2700 spot analyses, while samples rath1 to rath9 are those also characterized by crystal-structure refinements.Most of the analyses belong to the rath3-rath5 interval (1.58 wt%-5.36wt% Tl).Low-Tl (rath1, typical of Reckibach samples) and high-Tl (rath9 and rath10) are very rarely encountered compositions.
The representative mean chemical compositions of rathite with different degree of (Ag + + As 3+ )-for-2Pb 2+ , (Tl + + As 3+ )-for-2Pb 2+ and Sb-for-As substitutions (some used for subsequent crystal-structure studies), are presented in Tables 2 and 3, whereas individual points of the first group of samples (used for the structural studies) are plotted in different colours in the ternary diagram of Figure 4.The range of Ag, Tl, and Sb variations found are considerably larger than those reported by Berlepsch et al. [2].The degree of Ag and Tl substitutions (Ag subst and Tl subst ) are calculated with formulae given by Makovicky and Topa [13].The Ag subst value varies between 43.4 and 47.9, whereas the Tl subst value shows a large variation between 0.5 and 41.9, with strong implications for the crystal chemistry and range of compositional variability of rathite.The empirical formulae of the chemically most different rathite compositions (based on 72 atoms per formula unit (apfu), 32Me + 40S) are presented in the footnote of Tables 2 and 3  The binary plots a, b, c, d in Figure 5, based on apfu, depict the correlations of (Ag + Tl) vs. Pb, (Ag + Tl) vs. (As + Sb), Tl vs. Ag, and Sb vs. As, respectively, and allowed to determine the range of variations and a revised general formula of rathite: Ag x Tl y Pb 16−2(x+y) As 16+x+y−z Sb z S 40 (with 1.6 < x < 2, 0 < y < 3, 0 < z < 3.5).An Ag-free natural rathite does not exist, in agreement with studies of the system PbS-As 2 S 3 between 250 and 750 • C (Kutolglu [22]), although synthetic "rathite" (insufficiently characterized) was observed in an earlier, hydrothermal study of this system (Rösch and Hellner [23]).The conclusion of Berlepsch et al. [2] that the presence of Ag in the crystal structure of rathite is essential for this mineral, agrees with the Kutolglu study.The empirical formulae of the chemically most different rathite compositions (based on 72 atoms per formula unit (apfu), 32Me + 40S) are presented in the footnote of Tables 2 and 3 and demonstrate a limited Ag substitution combined with large Tl and Sb substitutions ranging between Ag1.70Tl0.04Pb12.47(As15.88Sb1.75)Σ17.63S40.17(Tl-poorest sample) to Ag1.76Tl2.91Pb6.67(As19.77Sb0.90)Σ20.66S39.99(Tl-richest sample) and Ag1.82Tl0.80Pb10.79(As14.88Sb3.43)Σ18.31S40.28(Sb-richest sample).
The binary plots a, b, c, d in Figure 5, based on apfu, depict the correlations of (Ag + Tl) vs. Pb, (Ag + Tl) vs. (As + Sb), Tl vs. Ag, and Sb vs. As, respectively, and allowed to determine the range of variations and a revised general formula of rathite: AgxTlyPb16−2(x+y)As16+x+y−zSbzS40 (with 1.6 < x < 2, 0 < y < 3, 0 < z < 3.5).An Ag-free natural rathite does not exist, in agreement with studies of the system PbS-As2S3 between 250 and 750 °C (Kutolglu [22]), although synthetic "rathite" (insufficiently characterized) was observed in an earlier, hydrothermal study of this system (Rösch and Hellner [23]).The conclusion of Berlepsch et al. [2] that the presence of Ag in the crystal structure of rathite is essential for this mineral, agrees with the Kutolglu study.In Lengenbach, the Sb content of rathite, sartorite, baumhauerite, liveingite, and dufrénoysite generally ranges between 0 wt% and ~2 wt% Sb.An unusually high Sb content in rathite (5 wt%-7 wt%) is found normally in samples coming from the Reckibach deposit, except for a single sample from Lengenbach (Table 3).A conspicuous Sb content in rathite was pointed out by Baumhauer [1].
EPMA studies revealed a specific limit to the Tl content in rathite.The back-scattered images in Figure 2 show two aggregates of mixed exsolution lamellae of the Tl-richest rathite (bright grey phase, rath9 in Table 2; 11.78 wt% Tl) and a possibly new, still Tl-richer species, still under investigation, here designated "SR" (dark-grey phase, rath10 in Table 2; 13.25 wt% Tl).The empirical formula of phase "SR" is Ag1.84Tl3.24Pb5.62(As20.05Sb1.44)Σ21.49S39.81,with Ncalc = 3.9, which clearly indicates its membership of the rathite group.Note the small gap between the chemical compositions of rath9 and phase "SR" (rath10), in the ternary plot of Figure 4 and binary plots of Figure 5, where all data In Lengenbach, the Sb content of rathite, sartorite, baumhauerite, liveingite, and dufrénoysite generally ranges between 0 wt% and ~2 wt% Sb.An unusually high Sb content in rathite (5 wt%-7 wt%) is found normally in samples coming from the Reckibach deposit, except for a single sample from Lengenbach (Table 3).A conspicuous Sb content in rathite was pointed out by Baumhauer [1].
EPMA studies revealed a specific limit to the Tl content in rathite.The back-scattered images in Figure 2 show two aggregates of mixed exsolution lamellae of the Tl-richest rathite (bright grey phase, rath9 in Table 2; 11.78 wt% Tl) and a possibly new, still Tl-richer species, still under investigation, here designated "SR" (dark-grey phase, rath10 in Table 2; 13.25 wt% Tl).The empirical formula of phase "SR" is Ag 1.84 Tl 3.24 Pb 5.62 (As 20.05 Sb 1.44 ) Σ21.49 S 39.81 , with N calc = 3.9, which clearly indicates its membership of the rathite group.Note the small gap between the chemical compositions of rath9 and phase "SR" (rath10), in the ternary plot of Figure 4 and binary plots of Figure 5, where all data are considered.The meaning and importance of that are discussed later, in connection with the results of crystal structures and crystal chemistry of the studied rathite samples.

Crystallography
Single-crystal studies were performed on a total of eight rathite fragments, mechanically extracted after quantitative electron microprobe analysis, from samples containing the groups mentioned in Table 2.All fragments were found to show good diffracting quality; no twinning or other anomalies were noted.We were so far unable to obtain structural information for phase "SR" due to the thinness of its exsolution lamellae, but the search for suitable fragments is still ongoing.
Single-crystal X-ray diffraction data were collected for all samples except rath9 on a Bruker SMART APEX CCD-three-circle-diffractometer at the University of Salzburg.Intensity data were collected with graphite-monochromatised MoKα X-radiation (50 kV, 30 mA) using SMART software (Bruker AXS [24]).The crystal-to-detector distance was set to 60 mm for all rathite crystals.The detector was positioned at -28 • 2θ using an ω-scan mode strategy at four different φ positions (0 • , 90 • , 180 • , and 270 • ).In total, 630 frames with ∆ω = 0.3 • were acquired for each run, with a 40 s/frame time of acquisition.Intensity data were integrated using SAINT software (Bruker AXS [25]).The semiempirical absorption correction based on pseudo ω scans was done with XPREP software (Bruker AXS [26]).Sample rath9 (and three other samples not reported here) were measured at the University of Vienna using a Nonius KappaCCD single-crystal diffractometer (graphite-monochromatised MoKα X-radiation, 50 kV, 30 mA; crystal-to-detector distance 30 mm, 1126 frames, 330 s/frame) that was equipped with a 300 µm diameter capillary-optics collimator to provide increased resolution.The data were processed with the Nonius program suite DENZO-SMN and corrected for Lorentz, polarization, background, and by multiscan absorption correction (Otwinowski and Minor [27]), absorption effects.
The centrosymmetric space group P2 1 /n proposed for all fragments by XPREP was chosen in accordance with systematic extinctions and intensity statistics and was afterward transformed in P2 1 /c standard settings.Rathite structures with different Tl content were solved by direct methods (SHELXS-97; Sheldrick [28]), which revealed most of the atom positions.The crystal-structure model and atom-site labeling scheme of Berlepsch et al. [2] were used as starting points for subsequent refinements.Occupancies of split sites were assigned based on geometric features and chemical considerations based on EPMA data.Between about 20 and 50 "bad" reflections (from a total of about 2300 to 6000 reflections) were omitted in order to "sharpen" the obtained models and to improve the distinguishing of the split sites; in the case of rath9 four of the omitted reflections were blocked by the beam stop.We checked that this omission did not seriously affect our models.Taking in account that Pb and Tl cannot be distinguished in X-ray diffraction experiments, no attempt to localize Tl in the structure refinement was made.Based on refinements for low-Sb samples (rath4 and rath3), the distinction between Ag and Sb was possible and found to be in accordance with the Berlepsch et al. [2] model.
Out of the eight studied crystals, we selected five (samples rath1, rath3, rath4, rath7, and rath9) that best represent a series of increasing Tl contents.Details on data collection and results of the structure refinement of these samples are given in Table 4, unit-cell dimensions are compared in Table 5, fractional atomic coordinates and anisotropic atomic displacement parameters of rath1 (Tl-poorest) and rath9 (Tl-richest) are compiled in Tables 6 and 7, and a comparison of corresponding site occupancies is given in Table 8, while Tables 9 and 10 give selected bond lengths for rath1 and rath9.
Table 4. Crystal data and summary of parameters describing data collection and refinement for five rathite fragments with different Tl contents and Pb:As ratios (rath1, rath3, rath4, rath7, and rath9).The full set of data is accessible via the CIF files freely available online as Supplementary Material linked to this article.Supplementary tables of fractional atomic coordinates, anisotropic atomic displacement parameters, bond lengths, and polyhedron characteristics for samples rath3, rath4, rath5 (partly recalculated from [2]), and rath7 are available online (Tables S1-S3, respectively).
The single-crystal diffraction data of all studied rathites indicated, independent of the individual Tl contents, a monoclinic cell, with space group P2 1 /c and a~8.5, b~8, c~25 Å, β~100.6 • .The small but conspicuous changes in unit-cell parameters are shown in Table 4.A clear increase of a, b, and V, and a slight decrease of c with increasing Tl content are masked somewhat by a random variation of the Sb content.The asymmetric unit in the crystal structure of rathite contains eight cation sites and ten sulphur sites.The rathite structure model of Berlepsch et al. [2] consists of two fully occupied Pb sites, three fully occupied As sites, and three mixed split positions Me3 (As 0.735 ,Sb 0.265 ), Me5 (As 0.526 ,Ag 0.474 ), and Me6 (Pb 0.739 ,As 0.261 ).Our refinement results, compared with those of Berlepsch et al. [2] are presented in Table 6. Figure 6 depicts the crystal structure of rath1 (a) and rath9 (b), projected along the a = 8.4 Å axis.The 18 independent sites form a layer (L 1 or L 2 in Figure 6a) four coordination polyhedra long and two polyhedra thick, based on an SnS-like archetype, built by six (mainly) As-centered coordination polyhedra (CN = 5-7) with a crankshaft arrangement of short As-S bonds, and terminating with two Pb-centred tricapped trigonal coordination prisms (CN = 9) at one end.Two such identical layers, symmetry related by inversion centers in rathite, form a tightly bonded double layer (ribbon), and the adjacent parallel double layers are separated by the lone-electron pair micelle.Along the a and b axes, the infinite rows of ribbons form a (001) slab, related by the 2 1 screw axis and the c glide plane to the next one.The dark-green ribbon of rath1 is Pb-rich due to the 0.961 Pb occupancy of the Me6 site and the light-green ribbon of rath9 is As-rich due to the 0.576 As occupancy of the Me6 site.4.1.Crystal Chemistry

Pb Sites
Thallium is supposed to enter into the structure of rathite (as in the sartorite family) on the Pb sites and investigations of those sites reveal the Tl role.Figure 7 shows the coordination polyhedra of [9] Pb1 and [9] Pb2 sharing the S1, S2, and S6 sulphur ligands.The S5, S6, S7, and S8 sulphur ligands are close to the Me3, Me5, and Me6 sites, and the Pb-S bond lengths are slightly affected by the different substitution at these Me sites.The incorporation of Tl on the two Pb sites, Pb1 and Pb2, is expressed by an increase of the (Pb,Tl)-S bond lengths that is positively correlated with the Tl content (Figure 8, Tables 9 and 10).For the samples with high Tl content (above 5 wt%), the first two short (Pb,Tl)-S bond lengths for Pb1 and Pb2 are better separated in comparison with the corresponding bond lengths in the low-Tl samples, thus indicating that Pb1 incorporates more Tl than Pb2.As shown in Tables 11-13, this incorporation is also reflected by the polyhedron characteristics, as defined in IVTON (Balić Žunić and Vicković [29]; Makovicky and Balić Žunić [30]): radius rs in Å of a circumscribed sphere least-squares fitted to the coordination polyhedron, the volume distortion υ, the 'volume-based' eccentricity ECCV, the volume in Å 3 of the circumscribed sphere, the volume in Å 3 of coordination polyhedron, the average bond distance and the standard deviation of the bond distance all increase with increasing Tl content, while the bond-valence sum notably decreases.The incorporation of Tl on the two Pb sites, Pb1 and Pb2, is expressed by an increase of the (Pb,Tl)-S bond lengths that is positively correlated with the Tl content (Figure 8, Tables 9 and 10).For the samples with high Tl content (above 5 wt%), the first two short (Pb,Tl)-S bond lengths for Pb1 and Pb2 are better separated in comparison with the corresponding bond lengths in the low-Tl samples, thus indicating that Pb1 incorporates more Tl than Pb2.The incorporation of Tl on the two Pb sites, Pb1 and Pb2, is expressed by an increase of the (Pb,Tl)-S bond lengths that is positively correlated with the Tl content (Figure 8, Tables 9 and 10).For the samples with high Tl content (above 5 wt%), the first two short (Pb,Tl)-S bond lengths for Pb1 and Pb2 are better separated in comparison with the corresponding bond lengths in the low-Tl samples, thus indicating that Pb1 incorporates more Tl than Pb2.As shown in Tables 11-13, this incorporation is also reflected by the polyhedron characteristics, as defined in IVTON (Balić Žunić and Vicković [29]; Makovicky and Balić Žunić [30]): radius rs in Å of a circumscribed sphere least-squares fitted to the coordination polyhedron, the volume distortion υ, the 'volume-based' eccentricity ECCV, the volume in Å 3 of the circumscribed sphere, the volume in Å 3 of coordination polyhedron, the average bond distance and the standard deviation of the bond distance all increase with increasing Tl content, while the bond-valence sum notably decreases.As shown in Tables 11-13, this incorporation is also reflected by the polyhedron characteristics, as defined in IVTON (Balić Žunić and Vicković [29]; Makovicky and Balić Žunić [30]): radius r s in Å of a circumscribed sphere least-squares fitted to the coordination polyhedron, the volume distortion υ, the 'volume-based' eccentricity ECC V , the volume in Å 3 of the circumscribed sphere, the volume in Å 3 of coordination polyhedron, the average bond distance and the standard deviation of the bond distance all increase with increasing Tl content, while the bond-valence sum notably decreases.The As sites behave differently in rathite.The As-S bond lengths (Tables 9 and 10) of the As1, As2, and A4 sites comprise regular three short (2.2-2.37 Å) and two long (2.9-3.4Å) distances, typical for pure As sites (CN = 5) and indicate that As1, As2, and As4 sites are unaffected by the observed substitutions.
The Ag substitution in rathite occurs on the Me5 site that is split into an Me5b site (As) and a Me5a site (Ag), with a fairly constant ratio of roughly 1:1, also reflected by the fairly constant Ag contents in all chemically analyzed samples (3.1 wt%-4.1 wt%, mean 3.6 wt%).This substitution feature is explained by the fixed location of the Ag atom within the ribbon, as is also observed for other sartorite-group members, such as argentobaumhauerite [31] and argentoliveingite [32], in both of which, however, the Ag site is fully occupied.
Sb substitution is seemingly only affecting the Me3 site.In the Sb-richest, structurally studied sample (rath1), the occupancy of this (then split) site is Me3a = As0.532(9) and Me3b = Sb0.468(9).The left side of the binary plot of Sb vs.As in Figure 5d depicts the linear decrease of As with increasing Sb due to direct Sb-for-As substitution, whereas the right side expresses the increase of As due to the Ag and Tl substitutions.
Since our EPMA data revealed even Sb-richer samples (with up to 7.71 wt% Sb), for which currently no crystal-structure refinements are available, these might theoretically represent a new mineral species with Sb dominant on the Me3 site (according to the current IMA rules on the definition of new mineral species).However, we cannot exclude that minor Sb might also be present on the Me5b (As) subsite of the split Ag/As Me5 site.

Crankshaft Chains
Another way to visualize the differences between the structures of rath1 and rath9 is the analysis of the crankshaft chains (alternating short-long bond distribution present in the highly covalent structures), as an unbroken or fragmented chain of short Me-S bonds.The crankshaft chains of the tightly bonded double SnS-like layer ribbon in rath1 and rath2 (Figure 9b 1 ,b 2 ) and their chemistries are compared with the one of dufrénoysite (Figure 9a).
To achieve that, three unit-cell broad ribbons along the 8.4 Å axis, oriented with the Pb-dominated layer for dufrénoysite on the left side, are sliced in two, 90 • clockwise-rotated layers (L 1 and L 2 ), and placed on the left and right sides of each ribbon (Figure 9).The short As-S bonds are shown in orange color, while the Sb-S short bonds are indicated in yellow color.For each ribbon, the length and direction of the crankshaft chains are indicated.The L 2 SnS-layer of dufrénoysite shows an unbroken four-polyhedra crankshaft chain of As.All other ribbons additionally possess one-or two-polyhedra fragmented crankshaft chains beside the unbroken three-polyhedra chain.
One can distinguish parallel and almost perpendicular directions of the chain directions between the left and right sides of the layers in each ribbon (thick black lines in Figure 9).In the centrosymmetric structures of rathite (exemplified by rath1 and rath9) individual SnS-like layers (L 1 and L 2 ) of the tightly bonded double layer are symmetry related by inversion centers and their direction is parallel to each other, a feature not seen in the acentric structure of dufrénoysite, where the direction are perpendicular to each other.

Phase "SR"
The phase "SR" (rath10) forms thin exsolution lamellae (~2 micron thick, dark in BSE images) with the Tl-richest rathite rath9 (bright in BSE images), in two separate grains coming from different samples, with almost the same chemistry (Figure 2a,b and Table 1).The presence of two kinds of lamellae implies two distinct phases with different chemistries and structures.The exsolved intergrowths between the phase "SR" and rath9 may have formed during cooling of a previously stable, homogeneous higher-temperature Tl-rich phase.
The chemical composition of "SR" differs from that of rath9, but due to the thinness of the lamellae (measured with fully focused beam) an accurate determination of its composition and its range is difficult to achieve.For rath9 a homogenous grain was used for chemistry and structure determination (Figure 1b, Table 2).The calculated homolog order Ncalc is 3.9 for "SR", indicating a close relationship with rathite and the existence of a periodicity based on a ..44.. sequence (as in rathite).The degree of Ag and Sb substitution in "SR" is equivalent to that in rathite, but the degree of Tl substitution is 16% higher than in rath9.

Phase "SR"
The phase "SR" (rath10) forms thin exsolution lamellae (~2 micron thick, dark in BSE images) with the Tl-richest rathite rath9 (bright in BSE images), in two separate grains coming from different samples, with almost the same chemistry (Figure 2a,b and Table 1).The presence of two kinds of lamellae implies two distinct phases with different chemistries and structures.The exsolved intergrowths between the phase "SR" and rath9 may have formed during cooling of a previously stable, homogeneous higher-temperature Tl-rich phase.
The chemical composition of "SR" differs from that of rath9, but due to the thinness of the lamellae (measured with fully focused beam) an accurate determination of its composition and its range is difficult to achieve.For rath9 a homogenous grain was used for chemistry and structure determination (Figure 1b, Table 2).The calculated homolog order N calc is 3.9 for "SR", indicating a close relationship with rathite and the existence of a periodicity based on a ..44.. sequence (as in rathite).The degree of

Figure 2 .
Figure 2. Representative backscattered electron images and corresponding reflected-light photographs (crossed polars) of two aggregates (a,b) showing mixed exsolution lamellae of the Tl-richest rathite (bright grey phase, rath9 in Table1; 11.78 wt% Tl) and a possibly new, still Tl-richer species, "SR" (dark grey phase, rath10 in Table1; 13.25 wt% Tl).Note that the small fragment in the (b') optical image shows twin lamellae.

Figure 2 .
Figure 2. Representative backscattered electron images and corresponding reflected-light photographs (crossed polars) of two aggregates (a,b) showing mixed exsolution lamellae of the Tl-richest rathite (bright grey phase, rath9 in Table1; 11.78 wt% Tl) and a possibly new, still Tl-richer species, "SR" (dark grey phase, rath10 in Table1; 13.25 wt% Tl).Note that the small fragment in the (b') optical image shows twin lamellae.

Figure 2 .
Figure 2. Representative backscattered electron images and corresponding reflected-light photographs (crossed polars) of two aggregates (a,b) showing mixed exsolution lamellae of the Tl-richest rathite (bright grey phase, rath9 in Table1; 11.78 wt% Tl) and a possibly new, still Tl-richer species, "SR" (dark grey phase, rath10 in Table1; 13.25 wt% Tl).Note that the small fragment in the (b') optical image shows twin lamellae.

Figure 5 .
Figure 5. Binary plots (a-d) are based on apfu values of rathite and depict the correlations of (Ag + Tl) vs. Pb, (Ag + Tl) vs. (As + Sb), Tl vs. Ag, and Sb vs. As, respectively.Binary plots c and d clearly indicate the range of variations for Tl, Ag, and Sb.

Figure 5 .
Figure 5. Binary plots (a-d) are based on apfu values of rathite and depict the correlations of (Ag + Tl) vs. Pb, (Ag + Tl) vs. (As + Sb), Tl vs. Ag, and Sb vs. As, respectively.Binary plots c and d clearly indicate the range of variations for Tl, Ag, and Sb.

Figure 6 .
Figure 6.Crystal structures of (a, top) rath1 (Tl-poorest) and (b, bottom) rath9 (Tl-richest), in a projection along the a = 8.4 Å axis and including a comparison of their Me3, Me5, and M6 split and mixed sites.White circles represent sulphur sites, blue ones (Pb,Tl) sites, cyan As sites, green the single half-occupied Ag site, red the single partially occupied Sb site, and light blue the single partially occupied Pb site.The dark-green (a) and light-green (b) ribbons in rath1 and rath9 emphasize their different chemistry, high Pb and high As, respectively.The equivalent SnS-like layers L1 and L2 are indicated with red boxes in (a).

Figure 6 .
Figure 6.Crystal structures of (a, top) rath1 (Tl-poorest) and (b, bottom) rath9 (Tl-richest), in a projection along the a = 8.4 Å axis and including a comparison of their Me3, Me5, and M6 split and mixed sites.White circles represent sulphur sites, blue ones (Pb,Tl) sites, cyan As sites, green the single half-occupied Ag site, red the single partially occupied Sb site, and light blue the single partially occupied Pb site.The dark-green (a) and light-green (b) ribbons in rath1 and rath9 emphasize their different chemistry, high Pb and high As, respectively.The equivalent SnS-like layers L 1 and L 2 are indicated with red boxes in (a).

Figure 8 .
Figure 8. Pb-S bond-length variation for Pb1 (circles) and Pb2 (diamonds) sites in the structurally investigated rathite samples as a function of their thallium substitution.

Figure 8 .
Figure 8. Pb-S bond-length variation for Pb1 (circles) and Pb2 (diamonds) sites in the structurally investigated rathite samples as a function of their thallium substitution.

Figure 8 .
Figure 8. Pb-S bond-length variation for Pb1 (circles) and Pb2 (diamonds) sites in the structurally investigated rathite samples as a function of their thallium substitution.

Figure 9 .
Figure 9.Comparison of the asymmetric (a) dufrénoysite and centrosymmetric (b1) rath1 (Tl-poorest) and (b2) rath9 (Tl-richest) N = 4 double-layer ribbons (three unit-cells along the a = 8.4 Å axis) and their opposing surfaces at the left and right, of the Sn-S like layers (L1 and L2) in the crystal structures of dufrénoysite and rathite.The short As-S bonds are orange colored, and the directions and lengths of the crankshaft chains are indicated by straight black lines.The ┴ symbols and || indicate the almost perpendicular and parallel directions of the crankshaft chains for L1 and L2.The unit-cell dimension along a is indicated as broken lines; site labels are also given.Color coding as in Figure 6.

Figure 9 .
Figure 9.Comparison of the asymmetric (a) dufrénoysite and centrosymmetric (b 1 ) rath1 (Tl-poorest) and (b 2 ) rath9 (Tl-richest) N = 4 double-layer ribbons (three unit-cells along the a = 8.4 Å axis) and their opposing surfaces at the left and right, of the Sn-S like layers (L 1 and L 2 ) in the crystal structures of dufrénoysite and rathite.The short As-S bonds are orange colored, and the directions and lengths of the crankshaft chains are indicated by straight black lines.The symbols ⊥ and || indicate the almost perpendicular and parallel directions of the crankshaft chains for L 1 and L 2 .The unit-cell dimension along a is indicated as broken lines; site labels are also given.Color coding as in Figure 6.

Table 2 .
Chemical-analytical data and derived chemical and structural parameters for the studied rathite samples (all from Lengenbach), ordered according to increasing Tl contents.

Table 5 .
[2]t-cell dimensions of the five studied rathite samples compared with that of the Berlepsch et al.[2]sample (rath5).Corresponding Tl, Ag, and Sb wt% values are also tabulated to show their influence.

Table 8 .
Comparison of site occupancies and measured Tl contents of the studied rathite samples.

Table 12 .
Polyhedron characteristics for atoms in sample rath9 (for explanation of header numbers see Table11).

Table 13 .
Comparison of occcupancies and polyhedron characteristics of the Pb1 and Pb2 sites (CN = 9) in the studied rathite samples.