Sulfur vacancies in fahlores from the Ag-Pb–Zn Mangazeyskoye ore deposit (Sakha, Russia)

Abstract

Fahlores from the epithermal Mangazeyskoye Ag-Pb–Zn ore deposit (Sakha, Russia) typically occur in rhythmically zoned crystals. In contrast to typical (Ag,Cu)₁₀(Fe,Zn)₂Sb₄S₁₃ fahlores, up to about 2.6 of the 13 sulfur atoms in the formula unit may be vacant and many of them have Ag/(Ag + Cu) ratios substantially above those established for (Ag,Cu)₁₀(Fe,Zn)₂Sb₄S₁₃ fahlores coexisting with miargyrite, pyrargyrite, and sphalerite by experimental, field, and theoretical investigations. The charge balance inequalities consequent on the removal of sulfur are compensated by metallization of the nominally Ag⁺ and Cu⁺ ions in the octahedral metal clusters that are formed by the removal of S²⁻ from the octahedral site at the center and corners of the unit cell of fahlore (space group I $\overline{4 }$ 3 m, Z = 2). The development of these vacancies leads to an effective ionic charge of [${(\mathrm{Ag},\mathrm{Cu})}_{6}^{\left(6-2*\mathrm{vac}\right)+}$] for these octahedral clusters, resulting in an intrinsic limit on sulfur vacancies of 3 per formula unit (pfu). The increases in the Ag/(Ag + Cu) ratio of some of the Mangazeyskoye fahlores relative to those defined for (Ag,Cu)₁₀(Fe,Zn)₂Sb₄S₁₃ fahlores are readily attributed to the lowering of the activities of Ag₁₀Zn₂Sb₄S₁₃ and Ag₁₀Fe₂Sb₄S₁₃ components in fahlore by sulfur vacancies. This results in expansion of the field of fahlore stability relative to that given by the fahlore breakdown reaction Ag₁₀Zn₂Sb₄S₁₃ (fahlore) = AgSbS₂ (miargyrite) + 3 Ag₃SbS₃ (pyrargyrite) + 2 ZnS (sphalerite) for (Ag,Cu)₁₀(Fe,Zn)₂Sb₄S₁₃ fahlores. A preliminary analysis demonstrates that the increased Ag/(Ag + Cu) ratios observed in the Mangazeyskoye fahlores relative to those defined for (Ag,Cu)₁₀(Fe,Zn)₂Sb₄S₁₃ fahlores are due to sulfur vacancies being almost exclusively in the octahedral sulfur site where the vacancy for sulfur substitution appears to be approximately ideal. However, it appears that a maximum in Ag/(Ag + Cu) ratios is reached around one pfu, and, to a first approximation, does not appear to increase with further increase in contents. This latter inference suggests that the for S (◻(S)_-1) substitution on tetrahedral sulfur sites may be highly nonideal. When properly calibrated for sulfur fugacity based on experimental, spectroscopic, and theoretical studies, reactions such as

$${\text{Ag}}_{{{1}0}} {\text{Zn}}_{{2}} {\text{Sb}}_{{4}} {\text{S}}_{{{13}}} = {\text{Ag}}_{{{1}0}} {\text{Zn}}_{{2}} {\text{Sb}}_{{4}} {\text{S}}_{{{12}}}{\square}^{{{\text{OCT}}}} \, + \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} {\text{ S}}_{{2}}$$

and

$${\text{Ag}}_{{{1}0}} {\text{Zn}}_{{2}} {\text{Sb}}_{{4}} \left( {{\text{S}}_{{{11, \square}}} } \right)^{{{\text{TET}}}} {\text{S}}\, = \,{\text{Ag}}_{{{1}0}} {\text{Zn}}_{{2}} {\text{Sb}}_{{4}} {\text{S}}_{{{12}}}{\square}^{{{\text{OCT}}}}$$

will afford fahlore to serve as a petrogenetic indicator of sulfur fugacity in low-sulfidation environments. Until such calibrations are developed, the fahlore Ag/(Ag + Cu) ratios may nonetheless be used to define relative sulfur fugacities in rhythmically zoned fahlores from ore deposits such as Mangazeyskoye.

Introduction

Fahlore (tetrahedrite group minerals)¹ is a natural solid solution that is the most common economic ore mineral of silver in Ag–Pb–Zn and bonanza Ag-Au deposits (Sack and Loucks 1985). It has recently been found that fahlore can exhibit high-thermoelectric performance and serve as highly efficient thermoelectric materials for waste heat recovery applications (e.g., Fan et al. 2013). These features of fahlore cause unrelenting interest in it among researchers. Its crystal chemical composition typically approximates the simple stoichiometry ~ ^III(Ag⁺, Cu⁺)₆ ^IV((Cu⁺, Ag⁺)_2/3(Zn²⁺, Fe²⁺)_1/3)₆ ^III(Sb³⁺, As³⁺)₄ ^IV(S²⁻, Se²⁻)₁₂ ^VI(S²⁻, Se²⁻_,^◻) (space group I $\overline{4 }$ 3 m, Z = 2), the sulfur vacancy-free varieties corresponding to an ideal crystal structure with 208 valance electrons per unit cell and full occupancy of the 6 trigonal-planar (TRG), 6 tetrahedral (TET), and 4 semimetal (SM) sites in the l3-sulfur formula unit (e.g., Pauling and Neuman 1934; Wuensch 1964; Johnson and Jeanloz 1983; Biagioni et al. 2020). Pauling and Neuman (1934) reappraised Machatschki’s (1928) solution of the crystal structure, interpreting it as a "complex defect derivative" of the sphalerite structure. Wuensch (1964) and Wuensch et al. (1966) clearly indicate that Pauling and Neuman's interpretation, still prevalent in current mineralogical literature, is at best misleading. The concept that the fahlore crystal structure is a framework analogous to sodalite has been suggested (Belov and Pobedimskaya 1973; Johnson et al. 1988). Synthetic fahlores in the Cu-Sb-S, Cu-As-S, Fe-Cu-Sb-S and Fe-Cu-As-S systems show considerable variation in the number of atoms per formula unit (that is, the number of atoms per 13 sulfurs). For example, the compositional field in the Cu-Sb-S system lies within the range Cu₁₂Sb₄S₁₃ − Cu₁₄Sb₄S₁₃ − Cu₁₂Sb_4.67S₁₃ (Tatsuka and Morimoto 1977; Makovicky and Skinner 1978). Although the chemical compositions of synthetic analogues of fahlores typically deviate from the simple stoichiometric formula, their crystal structures have been considered to have the same space group symmetry, I $\overline{4 }$ 3 m. The results of electron microprobe analysis of natural fahlore are not always satisfactorily converted to a simple stoichiometric formula (Lyubimtseva et al. 2018). Thus, there is a paradox when the data on the chemical composition and crystal structure of the mineral do not agree. This effect is especially enhanced if we turn to silver-containing fahlores.

Several recent studies of the stoichiometry and cell dimensions of Ag-rich compositions of the complex sphalerite derivative structure fahlore have recognized new approved endmembers and assigned them new names (e.g., Ag₁₀(Zn,Fe)₂Sb₄S₁₃, “rozhdestvenskayaite”; Ag₆Cu₄(Fe,Zn)₂Sb₄S₁₃, “argentotetrahedrite”; Ag₆Ag₄(Fe,Zn)₂-As₄S₁₃, “zvêstovite”; Welch et al. 2018; Sejkora et al. 2021a) and have also recognized their additional hypothetical Fe, Zn, and Hg endmembers (Biagioni et al. 2020; Sejkora et al. 2021b, 2022; Wu et al. 2021), and Zn and Fe endmembers components of “kenoargentotetrahedrite”, in which the sulfur in octahedral coordination by Cu and Ag at the corners and center of the unit cell is vacant or absent, Ag₆Cu₄(Fe,Zn)₂Sb₄S₁₂, (e.g., Moëlo et al. 2008; Biagioni et al. 2020; Qu et al. 2021). These studies conclude that the cell edges of Sb-fahlores with 13 sulfur atoms in their formula increase linearly between Cu and Ag endmembers and that the decrease in cell edges that is observed in some natural fahlores with Ag/(Ag + Cu) greater than about 0.4 is due to substitution of vacancies for sulfur in the octahedrally coordinated site (e.g., Riley 1974; Balitskaya et al. 1989; Rozhdestvenskaya et al. 1993). However, Ebel (1993) synthesized a (Ag_0.73,Cu_0.27)₁₀Zn₂Sb₄S₁₃ fahlore at 400 °C with a cell edge dimension of 10.7867 ± 0.004 angstroms on quenching, consistent with the linear trend of increasing cell edge with Ag/(Ag + Cu) ratio established in the synthesis experiments of Pattrick and Hall (1983) and that of rozhdestvenskayaite (Welch et al. 2018, their Fig. 2), but this fahlore exhibited a contraction in its cell edge to 10.6283 ± 0.007 angstroms when annealed at 150 °C for 891 h (cf., Sack and Ebel 2006, Fig. 43). We had initially assumed that the cell edge of Ebel’s fahlore might come to closely approach the trends of the collapsing cell edges of Riley (1974), Balitskaya et al. (1989) and Rozhdestvenskaya et al. (1993), but then realized that a close approach of their cell edges was improbable on the traditional cell edge versus Ag or Ag/(Ag + Cu) diagram, because we would be comparing a sulfur vacancy-free fahlore with sulfur vacancy-bearing fahlores (e.g., the average sulfur vacancy content of the 12 fahlores examined by Balitskaya et al. (1989) is 0.572 ± 0.344 pfu when the formulae of their fahlores are calculated on a 16 metal + semi-metal basis). Clearly the traditional two-dimensional representation of cell edge versus Ag or Ag/(Ag + Cu) diagram is a canard, as, at a minimum, the cell edge lengths of Sb fahlores are a function of Ag or Ag/(Ag + Cu) and sulfur vacancy contents at a given temperature, and therefore a three-dimensional representation of these quantities should be contoured for annealing temperature (i.e., a four-dimensional representation is required).

In addition, the thermodynamic quantity for Fe-Zn exchange between (Cu,Ag)₁₀(Fe,Zn)₂Sb₄S₁₃ fahlores and (Zn,Fe)S sphalerites, RTln[(${X}_{\mathrm{Fe}}^{\mathrm{Fah}}$/${X}_{\mathrm{Zn}}^{\mathrm{Fah}}$)^.(${a}_{\mathrm{ZnS}}^{\mathrm{Sph}}$/${a}_{\mathrm{FeS}}^{\mathrm{Sph}}$)] (where a is activity), is not a linear function of Ag/(Ag + Cu) in fahlore at a given ${X}_{\mathrm{ZnS}}^{\mathrm{Sph}}$/${X}_{\mathrm{FeS}}^{\mathrm{Sph}}$ ratio and temperature (O’Leary and Sack 1987) as this quantity is for Cu₁₀(Fe,Zn)₂(As,Sb)₄S₁₃ fahlores with As/(As + Sb) ratio (Sack and Loucks 1985; O’Leary and Sack 1987). Instead, this quantity has a sigmoid shape with respect to Ag/(Ag + Cu) in fahlore at a given temperature and FeS/ZnS ratio in (Zn,Fe)S sphalerite. It displays both a local maximum and minimum with increasing Ag/(Ag + Cu) ratio. Furthermore, the maxima and minima for varying temperatures and FeS/ZnS ratios in (Zn,Fe)S sphalerite lie respectively above and below the lines defined by the Ag₁₀(Fe,Zn)₂Sb₄S₁₃ and Cu₁₀(Fe,Zn)₂Sb₄S₁₃ endmembers.

To describe these relations O’Leary and Sack (1987) formulated a simple thermodynamic model which makes explicit provision for Ag–Cu ordering between trigonal-planar and tetrahedral sites in (Cu,Ag)₁₀(Fe,Zn)₂Sb₄S₁₃ fahlores. They discovered that all calibrations of this model that complied with their constraints on this Zn-Fe exchange reaction required that Ag changes its preference for trigonal-planar to tetrahedral sites with increasing Ag/(Ag + Cu) ratio. They also discovered that all viable calibrations of this model required that there are low-temperature (T < 200 °C) miscibility gaps in (Cu,Ag)₁₀(Fe,Zn)₂Sb₄S₁₃ fahlores. This latter prediction was subsequently confirmed by the discovery of such miscibility gaps in fahlores from multiple ore deposits (e.g., Sack et al. 2003, Fig. 1 here; Chinchilla et al. 2016, Fig. 16; Zhai et al. 2019, Fig. 11 and Fig. 1 here; Alves et al. 2022, Fig. 8b; Zhai 2022, Figs. 4b, 5).

Fig. 1

Modified from Sack (2005)

Isotherms for the molar Ag/(Ag + Cu) and Zn/(Zn + Fe) ratios of (Cu,Ag)₁₀(Fe,Zn)₂Sb₄S₁₃ fahlores in the miargyrite + pyrargyrite + sphalerite assemblage calculated by Sack (2005, solid curves) compared with fahlore data of Lynch (1989a) and Sack et al. (2003) from mines in the Keno Hill mining district indicated in the legend in the upper right corner, and the data for primary fahlores from the Biangiadajuan Ag-Pb-Zn deposit (Inner Mongolia, China) reported by Zhai et al. (2019). The larger symbols in the legend in the upper right corner represent the average Ag/(Ag + Cu) and Zn/(Zn + Fe) ratios for high-Ag fahlores from mines in the Keno Hill Ag-Pb-Zn district reported by Lynch (1989a). Six out of eight of these average compositions have molar Ag/(Ag + Cu) and Zn/(Zn + Fe) ratios which yield temperatures from the calibration of Sack (2005, solid curves) between the 250 and 310 °C established for the main stage of mineralization from fluid inclusions in quartz and siderite by Lynch (1989b). Average Ag/(Ag + Cu) and Zn/(Zn + Fe) ratios of fahlores from the Homestake, Onek, Sadie and Husky mines reported by Lynch (1989a) are not displayed individually, because the ores containing them exhibit significant evidence of retrograde re-equilibration as reflected by significant concentrations of epithermal minerals and have fahlores with a collective average of Ag/(Ag + Cu) and Zn/(Zn + Fe) ratios, 0.367 ± 0.090 and 0.244 ± 0.159, in accord with a temperature of about 170 °C, as deduced from the calibration displayed in this figure. The large black diamond represents this collective average and the lines emanating from it indicate its associated 1σ error bars. Smaller symbols represent Ag/(Ag + Cu) and Zn/(Zn + Fe) ratios from portions of a grain of fahlore from the Husky mine which appears to have undergone unmixing reported by Sack et al. (2003), a grain in which homogeneous regions (open circles) are intermixed with regions which appear to be the result of unmixing of these homogeneous regions into Ag-rich and Ag-poor compositions (filled circles). This composite grain is in an assemblage containing stephanite (T < 197 °C, Keighin and Honea 1969); microprobe analyses from the homogeneous regions of the grain (open circles) and Ag-rich unmixed portions of the grain are enclosed by red polygons and blue and yellow arrows indicate the sense of unmixing of homogeneous portions of the grain into relatively Ag-rich and Ag-poor compositions (both represented by filled black circles). These points are further clarified by an expansion of the composition field for fahlores with Ag/(Ag + Cu) and Zn/(Zn + Fe) ratios between 0.4 and 0.6 and between 0.0 and 0.2, respectively, that appears to the right of the main figure. It is noteworthy that the Ag-rich and Ag-poor compositions agree with the calculated miscibility gaps of Sack (2005) for a temperature of about 170 °C, a temperature in accord with the presence of stephanite in the Husky Mine assemblage. The inflections in the 200 °C and 170 °C isotherms calculated by Sack (2005) reflect the close approach to the critical temperature of fahlore and the emergence of the subcritical two fahlore miscibility gap, respectively. Green crosses represent Ag/(Ag + Cu) and Zn/(Zn + Fe) ratios and 1σ uncertainties of primary fahlores from the Biangiadajuan Ag-Pb–Zn deposit (Inner Mongolia, China) reported by Zhai et al. (2019). Previous fluid inclusion studies (Wang 2014; Ruan et al. 2015) indicate that the temperatures for Ag-dominant sulfosalt formation where between ~ 160 – 250 °C and < 150 °C for final calcite formation. These temperatures are in accord with those inferred from the Ag/(Ag + Cu) – Zn/(Zn + Fe) isotherms for (Cu,Ag)₁₀(Fe,Zn)₂Sb₄S₁₃ fahlores by Sack (2005). The Ag/(Ag + Cu) – Zn/(Zn + Fe) ratios of the Biangiadajuan fahlores are also consistent with the miscibility gap relations inferred by Sack (2005, 2017) for these temperatures. Dots and 1σ error bars on the vertical axis for Zn/(Zn + Fe) = 1.00 represent means and standard deviations of molar Ag/(Ag + Cu) ratios of (Cu,Ag)₁₀Zn₂Sb₄S₁₃ fahlores at 200, 300, and 400 °C determined in the experiments of Ebel and Sack (1994).

In addition to satisfy the scientific method, the inferences about the structural role of Ag in (Cu,Ag)₁₀(Fe,Zn)₂Sb₄S₁₃ fahlores of O’Leary and Sack (1987) are consistent with the principles of thermodynamics and statistical mechanics, as they predict that Ag and Cu will become increasingly disordered between trigonal-planar and tetrahedral sites with increasing temperature, and thus will trend toward linear volume—composition relations with increasing temperature. This sharply contrasts with the “universally” agreed upon assumption of the sulfide mineralogical community who pronounce, for example, that “substitution by Ag, is universally assumed to start in the triangular sites and spill over into tetrahedral sites only when the former are (nearly) filled” (Makovicky 2006, p. 54). Clearly, the results of Ebel (1993) demonstrate that the linear trend of cell edge lengths established by the synthesis experiments of Pattrick and Hall (1983) and Ebel (1993), and that of Ag₁₀Zn₂Sb₄S₁₃ (rozhdestvenskayaite) determined by Welch et al. (2018), may only be appropriate for temperatures of about 400 °C, because the results of the annealing experiment of Ebel (1993) demonstrates that the cell-edge lengths, and hence the ordering of Ag and Cu between trigonal—planer (i.e., triangular) and tetrahedral sites, are strongly temperature dependent, as required by thermodynamics and statistical mechanics. The thermodynamically challenged interpretation that cell edge lengths of (Ag,Cu)₁₀Zn₂Sb₄S₁₃ are linear in Ag/(Ag + Cu) ratios is also perpetuated by Biagioni et al. (2020, their Fig. 2) who depict data of the Shimada and Hirowatari (1972) for natural (Ag,Cu)₁₀(Fe,Zn)₂Sb₄S₁₃ fahlores as if their cell edge lengths are consistent with a roughly linear relationship between Cu and Ag endmembers, despite the fact that Shimada and Hirowatari (1972) only determined cell edge lengths for fahlores with Ag/(Ag + Cu) ratios < 0.4.

The generally accepted assumption that Ag strongly prefers the trigonal-planar site independent of Ag/(Ag + Cu) ratio is also inconsistent with the observed compositions of the binodes of the low-temperature (i.e., T < 200 °C) miscibility gaps in (Cu,Ag)₁₀(Fe,Zn)₂Sb₄S₁₃ fahlores (e.g., Sack et al. 2003, their Table 1; Fig. 1 here). Because Makovicky (2006) and others (e.g., Moëlo et al. 2008; Welch et al. 2018; Biagioni et al. 2020) allege that Ag enters only the trigonal-planar sites until they are completely (or very nearly) full, miscibility gaps between Cu- and Ag-rich fahlores with less than 6 Ag apfu would not achieve the binode compositions observed in nature, unless asymmetric solution parameters describing the nonideality of mixing of Ag and Cu on trigonal—planar sites were of such different magnitude as to be grossly physically implausible (cf. Sack 2021, Fig. 1 and associated discussion).

Finally, a spectacular example in the list of physically implausible interpretations by mineralogical “spectroscopists” is provided by the study of Pring et al. (2008). They conclude that Fe and Zn display a disordered distribution on the metal sublattice of sphalerite based on their analyses of the infrared spectra of a series of natural sphalerites with differing Fe/Zn ratios. In reaching their conclusion they ignored the wealth of experimental data constraining (Zn,Fe)S sphalerite equilibria (cf. subsequent discussion) and literature in solid-state physics (e.g., Furdyna 1988; Twardowksi et al. 1988; Twardowksi 1990) that clearly demonstrate otherwise (e.g., Toulmin et al. 1991). Fortunately, Wright and Gale (2010) performed Ab initio quantum mechanical calculations that demonstrated that Fe–Fe pair formation is favored in dilute Fe sphalerites, there are no energetic barriers to pair or larger cluster formation in more Fe-rich sphalerites (e.g., Balabin and Sack 2000; Osadchii and Gorgbaty 2010) and inferred that infrared spectroscopy may not be able to differentiate between different configurations of Fe and Zn on the metallic sublattice. Unfortunately these definitive findings from first-principle, quantum mechanical calculations have not prevented the continued appearance of models for the thermodynamic properties of (Zn,Fe)S sphalerites based on the assumption of random mixing of Fe and Zn on the metallic sublattice, models which require large excess entropies of mixing to attempt to conform to the experimental phase equilibrium data. These large excess entropies of mixing are in gross violation of the results of the calorimetric study of Pankratz and King (1965), a study which demonstrates conclusively that any excess entropy of mixing is negligible. This state of affairs prompts us to repeat a quote attributed to the late, distinguished metallurgical thermochemist David R. Gaskell (Sack and Ghiorso 2017, p. 838).²

Accordingly, in this study we will attempt to address the issue of vacancy substitutions for sulfur in (Cu,Ag)₁₀(Fe,Zn)₂Sb₄S₁₃ fahlores from the standpoint of phase equilibrium and thermodynamics, rather than relying on the pronouncements of mineralogical “spectroscopists.” An ideal dataset for this undertaking is provided by the petrological and mineral chemical studies of the sulfide ores from the Mangazeyskoye ore deposit. This deposit has fahlores that exhibits vacancies on both the octahedrally and tetrahedrally coordinated sulfur sites, the latter being previously unrecognized in the mineralogical literature. In this analysis we will demonstrate the mechanisms by which sulfur vacancies expand the stability field of fahlore relative to that of sulfur vacancy-free (Cu,Ag)₁₀(Fe,Zn)₂Sb₄S₁₃ fahlores and attempt to outline general conditions that must govern the concentrations of the vacancies replacing sulfur atoms on the octahedrally and tetrahedrally coordinated sites. Finally, we will explore how the sulfur vacancies are related to sulfur fugacity, concluding that fahlore has the potential to be an ideal indicator of sulfur fugacity of the fluids from which it crystallized, once a comprehensive thermodynamic model is formulated and can be calibrated based on experimental, theoretical, and further field studies.

Geology and mineralogy of the Mangazeyskoye ore deposit

Geology

The Mangazeyskoye Ag-Pb-Zn deposit is located about 400 km northeast of Yakutsk-city and 50 km north of the nearest settlement Sebyan-Kyuel’ (65° 43ʹ 05ʺ N and 130° 09ʹ 06ʺ E) in Sakha (Yakutia), Russia. Its exploration history began in the mid-eighteenth century and has had several peaks in interest (Smirnov 1962; Indolev and Nevoisa 1974). About 80 ore bodies have been explored and assayed in the deposit, which covers an area of almost 150 km² (Nekrasov 2017). The deposit consists of several closely spaced (from tens to hundreds of meters) ore zones, each of which was previously considered as a separate mineral deposit (Anikina et al. 2016). The Canadian Silver Bear Resources Company (July 7, 2015) reported indicated reserves of 800 t Ag (the Ag cutoff is 909 g/t) and inferred resources of 2250 t Ag (the Ag cut-off is 457 g/t) within such a Vertikalny zone. The Mangazeyskoye Ag-Pb–Zn deposit is proposed to be a super large one containing forecast resources of 28 kt Ag of high grade (up to 700 g/t Ag) ores (Aristov and Nekrasov 2010; Nekrasov 2017).

The Mangazeyskoye deposit is localized in the western Verkhoyansk Fold–Thrust Belt (VFTB), which extends for 2000 km with a width of 500 km along the northeastern margin of the Siberian craton. The deposit occurs at an intersection of the Nyuektame and North Tirekhtyakh deep-seated faults in thick (up to 9–11 km) Middle Carboniferous to Early Permian clastic sand–shale sequences. The sedimentary rocks have been deformed into NW-trending folds of various shapes and metamorphosed to sericite (muscovite)–chlorite grade greenschist facies. A granodiorite porphyry massif and numerous diorite, quartz-diorite, granodiorite, granodiorite-porphyry, lamprophyre dikes N-S oriented have intruded the clastic rocks. The ore bodies are hosted in sandstones under the screens of siltstone horizons that compose the core and the steep eastern limb of the asymmetric anticline fold. Two fault zones crosscut this anticline under 5°–15° to the strike of rocks. Diagonal normal–strike-slip bedding-plane dislocations accompany these zones, so that the entire system is a strike-slip duplex that controls and hosts ore bodies.

The Mangazeyskoye deposit may be considered an Ag–Pb–Zn vein deposit in clastic sedimentary rocks comparable with the large and well explored deposits of the Kokanee Range (Beaudoin et al. 1992) and Keno Hill (Boyle 1965; Lynch 1989a, b; Sack et al. 2003; Sack and Lichtner 2009, 2010) in Canada, Coeur d’Alene in the United States (White 1998; Fleck et al. 2002; Sack et al. 2002, 2005; Sack and Lichtner 2009, 2010), Freiberg in Germany (Swinkels et al. 2021), and Pŕibram in the Czech Republic (Beaudoin and Sangster 1992). The latter were formed primarily from metamorphic fluids under mesothermal conditions. A recent fluid inclusions and stable isotope study (Anikina et al. 2016) suggests that the Mangazeyskoye Ag–Pb–Zn veins are derivatives of an epithermal–porphyry hydrothermal–magmatic system related to intrusion and crystallization of subvolcanic felsic stocks and involvement of compositionally contrasting H₂O-CO₂-NaCl fluids of magmatic and meteoric origin with salinity of 15.4–0.8 wt % NaCl equiv. Mineral deposition was the result of fluid phase separation (boiling) and mixing at temperatures of 120 to 340 °C under pressures of 0.2–0.5 kbar.

Mineralogy

The ore bodies are cross-cutting veins, veinlets zones, mineralized breccia, and crushing zones, and stockworks that occur only in sandstone strata in the same fault zones. Ore bodies are composed of quartz, carbonates (siderite, ankerite, and calcite), sulfides (pyrite, arsenopyrite, sphalerite, galena, chalcopyrite, stannite), and sulfosalts (fahlore, boulangerite, pyrargyrite, miargyrite, stephanite, owyheeite, diaphorite, andorite, and freieslebenite). Massive coarse-grained, brecciated, banded, and rhythmically zoned fabrics of ores were observed. Textural and structural crosscutting and crushing relationships between mineral aggregates suggest their following depositional sequence: quartz–pyrite–arsenopyrite → quartz–carbonate–sulfide → silver–base-metal mineral assemblages. Quartz–pyrite–arsenopyrite aggregates, containing gersdorffite, wolframite, molybdenite, and Bi minerals, are accompanied by narrow greisen zones. Quartz–carbonate–sulfide aggregates are surrounded by aureoles of silicification and quartz–sericite alterations.

Silver–base-metal aggregates form the closely spaced series of thin quartz–carbonate–sulfide-sulfosalts veinlets containing Ag-rich fahlore (freibergite), boulangerite, Ag-sulfoantimonites, and Ag-Pb-sulfoantimonites. Sulfosalt minerals fill the interstices between quartz and carbonate grains. Their aggregates composed of different minerals are spatially separated and form mutual boundaries when they occur in intimate intergrowths. Such textures are consistent with the inference that they were deposited under similar physical and chemical conditions.

Fahlores occur in quartz–carbonate–sulfide ores (Figs. 2, 3), where they form mutual intergrowths with galena, pyrargyrite, miargyrite, diaphorite, sphalerite, stannite, stephanite, siderite, and arsenopyrite in interstices between quartz and carbonate grains (Fig. 2a, e, f, h, i) or contain inclusions of these minerals (Figs. 2a, d, g, i, 3a). It is often observed that fahlore corrodes quartz grains and forms pseudomorphs along the periphery of crystals (Fig. 2c). The fahlore in the deposit is often represented by zonal heterogeneous aggregates (Figs. 3b, d), which are composed of areas with unclear patchy heterogeneity and oscillatory zoning with complex relationships among themselves. Rhythms with fine oscillations in most cases are confined to the peripheral parts of the fahlore aggregate in contact with quartz.

Fig. 2

Reflective light (a–f, h, i) and BSE (g) images of intergrowths of fahlore with sulfides, sulfosalts, carbonate and quartz at the Mangazeyskoye deposit: (a) Intergrowths of kenoargentotetrahedrite-(Zn) (KAgTd), sphalerite (Sp), galena (Gn) and quartz (Qz and other black). b Intergrowths of kenoargentotetrahedrite-(Zn), sphalerite, galena and stannite (Stn). The stannite-kenoargentotetrahedrite-galena aggregate replaces sphalerite with varying degrees of intensity. In the right part of the photo, the primary collomorphic-zonal texture of sphalerite grains is partially preserved: late minerals form concentrically similar areas between sphalerite relics. c Intergrowths of kenoargentotetrahedrite-(Zn), galena and boulangerite (Blg). Kenoargentotetrahedrite-(Zn) pseudomorphically replaces quartz along the periphery, preserving the original outlines of well-formed faces of quartz crystals. Galena and boulangerite display intimate and thin intergrowths. d Intergrowths of kenoargentotetrahedrite-(Zn), galena, pyrargyrite (Prg) and arsenopyrite (Apy) filling interstices between quartz and carbonate (Carb) grains. Arsenopyrite contains boulangerite needle inclusions and xenomorphic aggregates of kenoargentotetrahedrite-(Zn). e Intergrowths of kenoargentotetrahedrite-(Zn) and galena in interstices between of quartz and carbonate grains. The kenoargentotetrahedrite-galena aggregate contains xenomorphic quartz inclusions with corroded (dissolved) boundaries. f Intergrowths of kenoargentotetrahedrite-(Zn), galena and pyrargyrite in interstices between quartz grains. Galena forms rims around quartz crystals. Quartz retains its primary euhedral form of crystals at contact with galena and pyrargyrite. Kenoargentotetrahedrite-(Zn) corrodes quartz grains. g Fine intergrowth of kenoargentotetrahedrite-(Zn) and galena containing single mineral inclusions of quartz, pyrargyrite and diaphorite (Df) or their intergrowths; sometimes small inclusions of miargyrite occur in such intergrowths. h Intergrowths of kenoargentotetrahedrite-(Zn), galena, pyrargyrite and miargyrite (Mia). i Intergrowths of kenoargentotetrahedrite-(Zn), galena, pyrargyrite, miargyrite and sphalerite in interstices between quartz crystals. White arrows show intergrowths of pyrargyrite in kenoargentotetrahedrite-(Zn) highlighted in areas enclosed with white dotted lines. Circles and associated numbers indicate the location of analyses given in Table 1. Images are from Mg-1 (d, e, g–i), Mg-2 (a), Mg-3 (f, h), Mg-4 (c), and Mg-8 (b) samples.

Fig. 3

BSE images showing textures and intergrowths of heterogeneous-zonal kenoargentotetrahedrite-(Zn) aggregate with sulfide and carbonate filling interstices between quartz grains in the Mangazeyskoye deposit. a Intergrowths of kenoargentotetrahedrite-(Zn) (KAgTd), galena (Gn), sphalerite (Sp), arsenopyrite (Apy), and siderite (Sid). b Heterogeneous kenoargentotetrahedrite-(Zn) aggregate with inclusions of galena, arsenopyrite, and siderite. Kenoargentotetrahedrite-(Zn) aggregate is composed of areas with unclear patchy heterogeneity and oscillatory zoning with complex interrelationships. Rhythms with fine oscillations are confined to the peripheral parts of the aggregate in contact with quartz (Qz). c Heterogeneous siderite aggregates in association with heterogeneous-zonal kenoargentotetrahedrite-(Zn). d An enlarged fragment of heterogeneous-zonal kenoargentotetrahedrite-(Zn). Yellow arrows indicate positions of R-2 EPMA profile. Normal BSE image (a) and BSE images with high contrast (b–d)

Samples and analysis method

Samples

Ore samples containing fahlore and associated sulfides were investigated from a collection of 10 specimens from the Mangazeyskoye deposit. A heterogeneous-zonal aggregate of argentotetrahedrite–kenoargentotetrahedrite-(Zn) was studied in sample Mg-6. This sample is a fragment of the Vasilkovskoye ore body with the highest silver grade in the deposit. It was collected on the northern flank of this ore body, opened by an exploration trench (ditch 165). This sample is matrix-supported inter-mineral breccia: angular fragments of early milky-white and gray quartz, coarse-crystalline carbonate (siderite) up to 2 cm in size infilled with sulfide galena-sulfosalt aggregates and small milled and corrosive quartz and siderite fragments in mineral flour matrix. Small voids (5–80 µm), which are filled with sulfide-sulfosalt (mainly pyrargyrite) aggregates, occur in quartz, less often in carbonate. Sulfides and sulfosalts fill microcracks in quartz and carbonate fragments. The matrix consists of fine-grained quartz, carbonate, galena, and sulfosalts: fahlore, pyrargyrite, miargyrite, and stephanite (rarely). Kenoargentotetrahedrite-(Zn) is found in intimate associations with galena, sphalerite, and other silver sulfosalts in the voids in the quartz-carbonate matrix.

Electron probe microanalysis (EPMA)

Chemical compositions of fahlore grains and zoning aggregates were studied at the Mineral Substances Analysis Laboratory at the Institute of Geology of Ore Deposits, Petrography, Mineralogy, and Geochemistry, Russian Academy of Sciences (IGEM Analytics Center for Collective Use). Microprobe analyses were obtained with a JEOL JXA-8200 SUPERPROBE with five WDS detectors operated at an accelerating voltage of 20 kV, a beam current in the Faraday cylinder of 20 nA, and a beam diameter of 1 μm, counting time of 10–20 s for major elements and 20–40 s for trace elements.

The following X-ray analytical lines: Lα for Sb, Se, Ag, As, Te, Sn; Kα for Zn, S, Cu, Fe; Mα for Hg, Bi, Pb; and Lβ for Cd were used. Synthetic compounds AgSbS₂ (Ag), HgS (Hg), CuFeS₂ (Fe), ZnS (Zn), CdS (Cd), PbS (Pb), Sb₂S₃ (Sb and S), GaAs (As), CdSe (Se), Cu₂FeSnS₄ (Sn) and pure metals Cu, Bi, and Te were used as standards. The measurements are accurate to ± 2% rel. for major elements and ± 3–5% rel. for trace elements. ZAF corrections were calculated using the JEOL software.

Chemical compositions of fahlore were obtained using point analyses of homogenous areas and along a single line perpendicular to the zoning. The assay at points along the profile was identical to the conventional analysis. Points on the profile were selected automatically in the desired direction at a given interval with preservation throughout the X-ray focus along all the profile. The exact position of the profile’s beginning and end was controlled by carbon accumulation from an electron probe. The minimum profile step (1 μm) was determined based on the size of the electron beam scattering region in the studied matrix under the above analysis conditions. A total of 188 microprobe analyses were carried out in the R-2 profile (Fig. 4) in the heterogeneous-zonal aggregate and 108 microprobe analyses were obtained in the other single grains at points.

Fig. 4

BSE image and compositional profiles illustrating heterogeneous-zonal aggregate of argentotetrahedrite-kenoargentotetrahedrite-(Zn) and variations in the S, Ag, Cu, Fe, and Zn contents (apfu) along the R-2 profile from Mg-6 sample (based on 188 microprobe analyses with a step of 1 µm). Point numbers on S content profile correspond to analysis numbers in Table 2. The composition curves for Sb and As are not shown, because they lack fluctuations, since the fahlore is predominately Sb-bearing with negligible As. Other minor elements are also not displayed, because their concentrations are also negligible. It appears that the temperatures of crystallization of fahlores in at least the outer rhythm III of profile R-2 were at epithermal temperatures below those at which solid state diffusion would wipe out the sharp compositional gradients between successive fahlores. This inference is supported by the experimental studies of Sack and Loucks (1985), Sack and Ebel (1993) and others, and by petrologic studies such as those Sack et al. (2002), Sack and Goodell (2002), Chincilla et al. (2016) and Zhai et al. (2019)

Calculation of chemical formula of Ag-rich fahlores

Different approaches to recalculate the chemical formula of minerals belonging to the fahlore group have been described in detail (e.g., Sejkora et al. 2021a, p.721). Normalizations on the basis of Σ(Me⁺  + Me²⁺  + SMe³⁺) = 16 apfu or ΣSMe = 4 apfu are considered the most preferred when calculating the Ag-rich fahlores formula. The most common normalization based on 29 apfu for the general formula can mask some S deficiency. Therefore, when recalculating the formulas for the Ag-rich fahlores of the Mangazeyskoye deposit, normalization on the basis of Σ(Me + SMe) = 16 apfu was employed.

Fahlore chemistry

General description of the chemical composition

Representative microprobe data and calculated coefficients in formulae of fahlore are given in Table 1. The greatest variations in the Ag, Cu, Zn, Fe, and S contents in wt % are: from 17.90 to 43.53 Ag, from 6.25 to 25.51 Cu, from 1.04 to 7.16 Zn, from b.d.l.³ to 5.53 Fe, and from 17.97 to 23.85 S (number of analyses, n = 107). They are nearly a pure antimony member containing from 21.38 to 27.70 wt % Sb, and minor concentration of As from b.d.l. to 1.72 wt %. A single analysis corresponds to Ag-rich tennantite-(Zn)⁴ with 0.44 Sb/(Sb + As) and 0.21 Ag/(Ag + Cu) ratios (see Table 1, analysis 21). The amount of other minor elements usually determined in the samples studied is low, wt %: up to 0.20 Bi, up to 0.77 Sn, up to 0.75 Pb, and up to 0.13 Te. A spectacular feature of some of the fahlores of the deposit is an extremely high Ag content up to ~ 44 wt % (Table 1, analyses 1 and 22), comparable with the highest concentration of this metal (from ≥  ~ 44 wt % to up to ~ 55 wt %) found in fahlores from a few other localities (cf. Welch et al. 2018; Biagioni et al. 2020).

Table 1 Representative microprobe analyses of fahlore, sulfides, and sulfosalts from the Mangazeyskoe deposit

The formulae calculated from the analyses do not usually correspond to the stoichiometric formula (Cu,Ag)₁₀(Fe,Zn)₂(Sb,As)₄S₁₃ generally accepted in mineralogical textbooks. Formulae calculated based on Σ(Cu + Ag + Fe + Zn + Sb + As) = 16 atoms per formula unit (apfu) range from 2.96 to 8.18 Ag, from 1.97 to 7.28 Cu, from 0.30 to 2.04 Zn, from 0 to 1.79 Fe, from 3.19 to 4.25 Sb, from 0 to 0.42 As, and from 10.39 to 13.50 S. The total of ΣMe⁺_{(Cu + Ag)}, ΣMe²⁺_{(Fe + Zn)} and ΣSMe³⁺_{(As + Sb)} varied from 9.35 to 10.61, from 1.61 to 2.72, and from 3.53 to 4.25, respectively, deviating from the stoichiometric values. Such deviation has been found by many researchers but are typically ignored in the mineralogical literature. The most remarkable finding is that the S content does not typical correspond to 13 apfu.

The EPMA studies revealed that fahlores from the Mangazeyskoye deposit belong mainly to the freibergite series with 0.86–1.00 Sb/(Sb + As) ratio and 2.96–7.15 Ag apfu (Table 1, Fig. 5a) and 2 analyses belong to the rozhdestvenskayaite series with a Sb/(Sb + As) ratio of 1.00 and 8.07–8.18 Ag apfu (Table 1, analyses 1 and 22) (Fig. 5a). A solid solution with continuous Zn–Fe and Ag–Cu substitutions exists in this freibergite series: the Zn/(Zn + Fe) ratio varies from 0.14 to 1.00 and the Ag/(Ag + Cu) ratio ranges from 0.30 to 0.69 (Figs. 5a, c). There is no correlation between the Sb/(Sb + As) and Zn/(Zn + Fe) ratios. A relationship between the contents of Ag/(Ag + Cu) and Zn/(Zn + Fe) ratios has also not been established, but it is noteworthy that Fe predominates over Zn in fahlores with highest Ag content (Fig. 5c). It is very important that there is a negative correlation between Ag and S contents (Fig. 5a). Fahlores with a predominance of Zn over Fe prevail in the samples studied.

Fig. 5

Chemical composition of fahlores from the Mangazeyskoye deposit (a, c) and heterogeneous-zonal kenoargentotetrahedrite-(Zn) aggregates along the R-2 profile (b, d). a, b S vs Ag (apfu). Dotted lines show the boundaries between mineral species and series (Biagioni et al. 2020). c, d Ag/(Ag + Cu) vs Zn/(Zn + Fe). Isotherms taken from Sack (2005, Fig. 1 here). Numbers indicate the analyses given in Table 1. It will be subsequently shown that the scatter in Fig. 5a, c is primarily related to sulfur vacancy content and secondarily to temperature. Although the fahlores in the Outer Rhythm III of profile R-2 are clearly outside the epithermal field on Fig. 5d, this inconsistency is readily resolved when the energetic consequences of sulfur vacancies are accounted for (cf. Fig. 9b)

Previously, two generations of fahlore were reported at the Mangazeyskoye deposit (Anikina et al. 2016). The first generation included "tetrahedrite" with an Ag content of less than 6.2 wt % and a Zn/(Zn + Fe) ratio of 0.8–1.0 (according to the new nomenclature it is Ag-rich tetrahedrite-(Zn)), which was found intergrown with galena in quartz–carbonate–sulfide aggregates. The second generation, found in intergrowths with galena, sphalerite, and Ag-sulfosalts, is represented by "freibergite," the composition of which is as follows (wt %): 17.0–50.0 Ag, 0.1–24.8 Cu, 0.0–5.2 Fe, 0.1–7.7 Zn, 23.6–27.9 Sb; Zn/(Zn + Fe) ratio between 0.1 and 1.0, but with Zn predominating over Fe in most analyses. The Sb/(Sb + As), Zn/(Zn + Fe) and Ag/(Ag + Cu) ratios and the absence of correlation between Zn/(Zn + Fe) and Ag/(Ag + Cu) in fahlores obtained in this study are consistent with the data (Anikina et al. 2016). However, sulfur deficiency in the analyses of fahlore of the Mangazeyskoye deposit has not been previously reported.

According to the new nomenclature (Biagioni et al. 2020) five mineral types of Ag-rich fahlores were found in the samples studied. They are kenoargentotetrahedrite–(Zn), kenoargentotetrahedrite–(Fe), argentotetrahedrite–(Fe), argentotetrahedrite–(Zn), and rozhdestvenskayaite-(Fe)⁵ (Fig. 5a, c; Table 1). Kenoargentotetrahedrite–(Zn) greatly predominates over other members of the tetrahedrite group (Fig. 5a, c). However, the discovery of new unapproved members of the tetrahedrite (i.e., fahlore) group, the determination of approved members and separating them from each other does not bring us one iota closer to understanding crystal chemistry and the formation conditions of fahlore in the deposit. This means that the nomenclature of tetrahedrite group minerals approved by the Commission on New Minerals of the International Mineralogical Association is "stillborn," useless and will not be used in the analysis of petrogenesis based on methods of the physical sciences.

Chemical heterogeneity and zoning in aggregates and grains of fahlore

A characteristic property of the samples studied is heterogeneity and zoning in aggregates and grains of fahlore. These are most clearly visible in BSE images: the lighter the mineral, the higher the Ag content, and vice versa, the darker the mineral, the higher the Cu content. In this aggregate, one can distinguish heterogeneous rhythms and rhythms with oscillatory zoning with complex relationships. Rhythms with fine oscillations are in most cases confined to the peripheral parts of the fahlore aggregate in contact with quartz. The heterogeneous-zonal aggregate of fahlore intergrown with galena, sphalerite, arsenopyrite, and zoned siderite was examined with microprobe step-traverse analyses (Fig. 4). The R-2 profile crosses a heterogeneous aggregate of fahlore (Fig. 3d), which differs in pattern (structure) and chemical composition. Rhythm I is distinguished, in which oscillatory zoning with blurred and jagged zone boundaries (pattern resembles a veil) is found in the fahlore; rhythm II with tracery (pattern looks like folds in clothes), possibly consisting of small grains of fahlore with oscillatory zoning; rhythm III, where oscillatory zoning is well manifested with rectilinear sharp boundaries between zones.

It appears that the temperatures of crystallization of fahlores in at least the outer rhythm III of profile R-2, and probably also inner rhythm I and intermediate rhythm II, were at epithermal temperatures below those at which solid state diffusion would wipe out the sharp compositional gradients between successive fahlores. The preservation of the structure of the heterogeneous-zonal aggregate is probably due to the low diffusion rate in the solid at such low temperatures, even in the presence of a hydrothermal fluid. This inference is supported by the experimental studies of Sack and Loucks (1985), Sack and Ebel (1993) and others and by petrologic studies such as those Sack et al. (2002), Sack and Goodell (2002), Chincilla et al. (2016) and Zhai et al. (2019). A low rate of diffusion between Ag and Cu may be due to the peculiarities of the passage of a large Ag cation through the crystal lattice and through intergranular spaces (Butrymowicz et al. 1974). It was shown in Grove et al. (1984) that even at high temperatures, the oscillatory zones found in plagioclase of granodiorite plutons are preserved due to limiting of diffusion on the submicron scale. Preservation of the structure can also be associated with slow fluid seepage through small cavities between grains and along cracks in early mineral aggregates, as well as low dissolution rates of previously deposited minerals (Lyubimtseva et al. 2020).

The results of EPMA studies of this heterogeneous-zonal aggregate showed that they consist of a solid solution of kenoargentotetrahedrite–(Zn) and argentotetrahedrite–(Zn) with 0.99–1.00 Sb/(Sb + As), 0.45–0.57 Ag/(Ag + Cu), and 0.72–0.94 Zn/(Zn + Fe) ratios (Fig. 5b, d; Table 2). The major elements contents (wt %) are variable: 26.28–32.37 Ag, 14.44–18.71 Cu, 4.89–6.72 Zn, 0.37–1.66 Fe, 25.54–26.96 Sb, b.d.l.-0.15 As, and 20.08–21.68 S (n = 188). The wt % of other minor elements are: up to 0.18 Bi, up to 0.16 Cd, up to 0.14 Pb, up to 0.13 Te, up to 0.08 Se, and up to 0.07 Hg. The formula describing this kenoargentotetrahedrite–argentotetrahedrite–(Zn) solid solution is (Ag_4.50–5.68Cu_4.32–5.44)_{Σ9.81–10.02}(Zn_1.41–1.91Fe_0.13–0.56)_{Σ1.93–2.06}(Sb_3.97–4.18As_0-0.04Bi_0-0.02)_{Σ3.99–4.19}S_{11.92–12.60}. As far as we know, this is the first finding of a fahlore solid solution of this composition.

Table 2 Representative microprobe analyses of heterogeneous-zonal argentotetrahedrite-kenoargentotetrahedrite-(Zn) along the R-2 profile (selection from 188 analyses)

Microprobe analyses carried out along the R-2 profile perpendicular to the zoning revealed different compositional regions and different compositional trends (Fig. 4). In the rhythm I, slight fluctuations of Ag and S are observed in the range of 4.95–5.32 apfu around an average of ~ 5.1 apfu and in the range of 12.20–12.49 apfu around an average of ~ 12.3 apfu, respectively, at a distance of 58 µm, and the lowest concentration of Zn is 1.41–1.70 apfu (0.72–0.86 Zn/(Zn + Fe) ratio) (Table 2, analyses 3–45). The rhythm II 83 µm wide is characterized by a low Ag content of 4.50–4.95 apfu and maximum S and Zn are 12.21–12.60 apfu and 1.65–1.91 apfu, respectively (0.83–0.94 Zn/(Zn + Fe) ratio) (Table 2, analyses 59–141). In the rhythm III (Table 2, analyses 144–187), the sharpest jump with fluctuations in the composition is found: an increase in the Ag content from 4.60 (Table 2, analysis 137) to 5.68 apfu (Table 2, analysis 156) and decrease in the S content from 12.59 to 12.11 apfu over a distance of 20 µm. In the rhythm III, minimum S and maximum Ag contents are found: 11.92 apfu (Table 2, analysis 187) and 5.68 apfu (Table 2, analysis 156); Zn varies from 1.52 to 1.70 (0.77 to 0.86 Zn/(Zn + Fe) ratio. The composition of the fahlore from the external rhythm (III) in contact with quartz is closest to the stoichiometric formula Ag₆(Cu₄Zn₂)Sb₄S₁₂ (Biagioni et al. 2020).

It should be emphasized that the Ag content has a strong negative correlation with those of Cu and S over the entire studied interval of the heterogeneous-zonal aggregate. And, of course, there is a negative relationship between oscillations of isomorphic elements Cu and Ag, and Zn and Fe.

Sulfur vacancies

As noted above, the most spectacular feature of fahlores from the Mangazeyskoye deposit are the S deficiencies in the calculated formulae of many of them. The S content does not typically correspond to 13 apfu but is significantly lower, dropping to 10.39 apfu. It has also been established that in the fahlore at the Mangazeyskoye deposit there is a decrease in the amount of S as Ag concentrations increase (Fig. 5a, b). This trend is observed both in the deposit as a whole and in heterogeneous-zonal aggregates. It should also be noted that fahlore coexisting with sulfides in assemblages lacking other Ag-sulfosalts have predominately low sulfur contents (Fig. 5a, analyses 22–27, 29–31).

Sulfur deficiencies calculated from the EPMA suggest that up to two or more vacancies substitute for sulfur in the formula unit (Fig. 6a, b) and this is particularly intriguing, because this would require that vacancies are present on both the tetrahedral and octahedral sites normally occupied by sulfur, despite that the fact they have only been reported substituting for the octahedrally coordinated sulfur (e.g., Moëlo et al. 2008; Welch et al. 2018), and that only Ag₆Cu₄(Fe,Zn)₂Sb₄S₁₂ fahlores, "kenoargentotetrahedrites," are recognized as approved endmember varieties (Biagioni et al. 2020).

Fig. 6

Sulfur vacancies in fahlores (a, c) and in heterogeneous-zonal kenoargentotetrahedrite-(Zn) aggregate (b, d) from the Mangazeyskoye deposit. a, b Ag/(Ag + Cu) versus S-vacancy (pfu). S-vacancy calculated as 13-S (apfu) with S (apfu) calculated from microprobe analyses assuming 16 atoms of metals and semi-metals in the formula unit. c, d Total Charge versus S-vacancy (pfu). The solid line from the origin of the coordinate shows the theoretical slope of + 2 calculated for the assumption that Ag and Cu are monovalent. Colored symbols indicate total charge calculated on this basis whereas pale-pink symbols indicate total charge pfu calculated on the assumption that the charge on the octahedral metal clusters of Ag and Cu formed by removal of S from the site at the comers and center of the unit cell have an average positive charge of (6–2x(number of sulfur vacancies pfu))⁺. For designations of symbols see Fig. 5a. Negative total charges in Fig. 6c may be due to analytical uncertainties, and where both negative vacancy contents and total negative charges are calculated they may be due to inclusions of pyrite or other sulfides whose cations were not analyzed for, or stoichiometric improprieties in fahlores. In addition, since we use the formal valence of Cu and Fe ions of + 1 and + 2 to calculate the total charge, as reported in the third paragraph of the section on Sulfur Vacancies, and they may also have charges of + 2 and + 3, failure to consider the possibility that some of these ions may have these higher charges may also give negative total charges in Fig. 6c

To consider the plausibility of this assertion it is instructive to examine plots of the positive charge excesses versus sulfur vacancies of these fahlores calculated on the assumption that Ag and Cu ions, Fe and Zn ions, As and Sb ions, and S ions have charges of + 1, + 2, and + 3, and − 2 (cf. Fig. 6c, d, colored symbols). The compelling feature of these plots, when microprobe data for fahlores are recalculated on a sixteen metal + semi-metal basis, is that the vast majority of the Mangazeyskoye fahlores are within analytical uncertainty of lines with a slope + 2 with an intercept at the origin. This observation strongly suggests that the octahedral metal clusters created by vacancies on the ^VIS site have variable average charge with sulfur vacancy content, decreasing from + 6 for fahlores with the ideal formula (Ag,Cu)₁₀(Zn,Fe)₂Sb₄S₁₃ to zero for fahlores approximating the (Ag,Cu)₁₀(Zn,Fe)₂Sb₄S₁₀ formula. The positive charge on these clusters would then be (6—two times the number of vacancies per formula unit) or could be represented as [${(\mathrm{Ag},\mathrm{Cu})}_{6}^{\left(6-2*\mathrm{vac}\right)+}$], and this inference is supported by the observation that when the charge on these clusters is computed by this formula the net charge on the formula unit is reduced to zero, consistent with charge balance (cf. Fig. 6c, d, pale pink symbols). This is in complete accord with the conclusion of Welch et al. (2018) and Biagioni et al. (2020) that in fahlores with one vacancy per formula unit the octahedral clusters have a charge of + 4 rather than the + 6 of the ideal formula, but it indicates that the charge on these clusters will continue to decrease with increasing vacancy content. Complete metallization of these clusters would be achieved for fahlores approximating the (Ag,Cu)₁₀(Zn,Fe)₂Sb₄S₁₀ formula with three sulfur vacancies per formula unit, as these octahedral clusters would be fully metallically bonded at this point and would form alloy nanoparticles electrostatically unattached to the fahlore structure. Accordingly, 3 vacancies on sulfur sites per formula unit may be regarded as the intrinsic limit to vacancy content, as any further vacancy substitution for sulfur would violate ionic charge balance and lead to breakdown of the fahlore structure. The fact that Mangazeyskoye fahlores achieve calculated sulfur vacancy contents exceeding 2 pfu is consistent with the inference that the (S)_-1 substitution becomes increasingly energetically unfavorable with vacancy contents > 1 pfu, because it creates octahedral metal clusters that are less bonded by charge to the remaining structure.

Increase of fahlore Ag/(Ag + Cu) ratios due to sulfur vacancies

Despite their frequent coexistence with miargyrite, pyrargyrite, and sphalerite many of the Mangazeyskoye fahlores have Ag/(Ag + Cu) ratios much higher than those established for (Ag,Cu)₁₀(Zn,Fe)₂Sb₄S₁₃ fahlores coexisting with this assemblage (cf. Figure 1). This discrepancy cannot be attributed to temperature, because the temperatures required by the fahlore isotherms for (Ag,Cu)₁₀(Zn,Fe)₂Sb₄S₁₃ fahlores would be unrealistically high (cf. Figs. 5c, d, 9). Alternatively, this discrepancy may be readily explained by the lowering of the chemical potential of Ag₁₀Zn₂Sb₄S₁₃ in fahlore by sulfur vacancies.

A possible method for resolving this discrepancy and estimating crystallization temperatures of Mangazeyskoye fahlores involves comparing the Mangazeyskoye fahlores data arrays with the Ag/(Ag + Cu)—Zn/(Zn + Fe) isotherms for (Ag,Cu)₁₀(Zn,Fe)₂Sb₄S₁₃ fahlores coexisting with miargyrite, pyrargyrite and sphalerite calculated by Sack (2005, Fig. 1 here). The isotherms calculated by Sack (2005) are very tightly constrained for (Cu,Ag)₁₀Zn₂Sb₄S₁₃ fahlores by the 200–400 °C experiments of Ebel and Sack (1994) on the fahlore breakdown reaction.

$${\text{Ag}}_{{{1}0}} {\text{Zn}}_{{2}} {\text{Sb}}_{{4}} {\text{S}}_{{{13}}} \left( {{\text{fahlore}}} \right)\, = \,{\text{AgSbS}}_{{2}} \left( {{\text{miargyrite}}} \right)\, + \,{\text{3 Ag}}_{{3}} {\text{SbS}}_{{3}} \left( {{\text{pyrargyrite}}} \right)\, + \,{\text{2 ZnS}}\left( {{\text{sphalerite}}} \right),$$

(1)

fahlores whose stoichiometry corresponds to that for the ideal stable structure with 208 valence electrons and full occupancy of the 52nd Brillouin zone (e.g., Johnson and Jeanloz 1983; Jeanloz and Johnson 1984). Sack (2005) employed these constraints on the net-transport reaction for Zn-fahlores, constraints on the Gibbs energy of formation of AgSbS₂ miargyrite and Ag₃SbS₃ pyrargyrite from Ag₂S and Sb₂S₃ (Schenck and von der Forst 1939; Schenck et al. 1939; Verduch and Wagner 1957), the calibrations for the Cu-Ag exchange reactions between miargyrite and pyrargyrite, and fahlore and miargyrite:

$${\text{AgSbS}}_{{2}} \left( {{\text{miargyrite}}} \right) + 1/3 {\text{Cu}}_{{3}} {\text{SbS}}_{{3}} \left( {{\text{pyrargyrite}}} \right) \, = 1/3 {\text{Ag}}_{{3}} {\text{SbS}}_{{3}} \left( {{\text{pyrargyrite}}} \right)\, + \,{\text{CuSbS}}_{{2}} \left( {{\text{miargyrite}}} \right)$$

(2)

and.

$$1/10{ } {\text{Ag}}_{{{1}0}} {\text{Zn}}_{{2}} {\text{Sb}}_{{4}} {\text{S}}_{{{13}}} \left( {{\text{fahlore}}} \right)\, + \,{\text{CuSbS}}_{{2}} \left( {{\text{miargyrite}}} \right) \, = 1/10{ } {\text{Cu}}_{{{1}0}} {\text{Zn}}_{{2}} {\text{Sb}}_{{4}} {\text{S}}_{{{13}}} \left( {{\text{fahlore}}} \right)\, + \,{\text{AgSbS}}_{{2}} \left( {{\text{miargyrite}}} \right)$$

(3)

(e.g., Harlov and Sack 1995; Sack 2000) and the thermodynamic solution model for (Ag,Cu)₁₀(Zn,Fe)₂Sb₄S₁₃ fahlores of Sack (1992) to derive an expression for the Gibbs energy of formation of the Ag₁₀Zn₂Sb₄S₁₃ endmember component from the simple sulfides over the 170 – 400 °C temperature range. He then extrapolated these results into the Fe bearing system using these Ag–Cu exchange reactions and the experimental and field constraints on the Fe-Zn exchange reaction between fahlore and (Zn,Fe)S sphalerite.

$$\begin{gathered} 1/2\,{\text{Cu}}_{{{1}0}} {\text{Zn}}_{{2}} {\text{Sb}}_{{4}} {\text{S}}_{{{13}}} \left( {{\text{fahlore}}} \right)\, + \,{\text{FeS}}\left( {{\text{sphalerite}}} \right) \, \hfill \\ \quad = 1/2\,{\text{Cu}}_{{{1}0}} {\text{Fe}}_{{2}} {\text{Sb}}_{{4}} {\text{S}}_{{{13}}} \left( {{\text{fahlore}}} \right)\, + \,{\text{ZnS}}\left( {{\text{sphalerite}}} \right) \hfill \\ \end{gathered}$$

(4)

of Sack and Loucks (1985) and O’Leary and Sack (1987), and the activity—composition relations for sphalerite derived from the statistical mechanical, cluster variation method (CVM) model for (Zn,Fe)S sphalerite of Balabin and Sack (2000), a model whose tenets were confirmed by the first-principle quantum mechanical calculations of Wright and Gale (2010) and are consistent with a plethora of experimental phase equilibrium data (e.g., Arnold 1962; Barton and Toulmin 1966; Boorman et al. 1971; Scott and Barnes 1971; Scott 1973; Lusk and Ford 1978; Balabin and Urusov 1995) and the calorimetric data of Pankratz and King (1965).

The fundamental features of the calculated isotherms for (Ag,Cu)₁₀(Zn,Fe)₂Sb₄S₁₃ fahlores (Fig. 1) have been subsequently confirmed by the results of field studies (e.g., Lynch 1989a; Sack 2002; Sack et al. 2002, 2003; Chinchilla et al. 2016; Zhai et al. 2019; Alves et al. 2022; Zhai 2022), including the existence of the low-temperature (i.e., epithermal) miscibility gaps in these fahlores first predicted by O’Leary and Sack (1987). Accordingly, the apparent high temperatures inferred for the Mangazeyskoye fahlores from this construction (e.g., Fig. 5c, d) are difficult to rationalize, unless we account for both their octahedral and tetrahedral sulfur vacancies. In the absence of constraints on homogeneous equilibria involving these vacancies, detailed knowledge of the energetics associated with metallization of the Ag and Cu atoms surrounding the sites of the octahedral sulfur vacancies (e.g., Welch et al. 2018; Biagioni et al. 2020; this study), and other uncertainties associated with deviations from the formula for the most stable fahlores (e.g., Johnson and Jeanloz 1983; Jeanloz and Johnson 1984), some simplifying assumptions are in order.

To begin with we will assume that the deviations of Ag/(Ag + Cu) ratios (i.e., X₄) of the Mangazeyskoye fahlores from those given by the construction of Sack (2005) are exclusively due to the lowering of the chemical potential of the Ag₁₀Zn₂Sb₂S₁₃ component in the net-transport (i.e., breakdown) reaction of fahlore to miargyrite, pyrargyrite and sphalerite. Here the issue is to what extent the Ag/(Ag + Cu) ratio must be raised, or to what extent the field of fahlore must expand on the Ag/(Ag + Cu)—Zn/(Zn + Fe) diagram at a given temperature and X₂ or Zn/(Zn + Fe) ratio (i.e., Le Chatelier’s principle) to restore the net-transport reaction to equilibrium. To do so in a first approximation, we will ignore the complexities of non-ideality in the vibrational Gibbs energy and of Ag–Cu ordering between trigonal-planar and tetrahedral sites and consider only the ratio of the disordered configurational component of the chemical potential of Ag₁₀Zn₂Sb₄S₁₃ of the sulfur vacancy-free fahlore, RT ln [(X₄^{with no vacancies in fahlore})¹⁰ (X₂)²] with values of X₄ given by the calibration of Sack (2005, Fig. 1 here), and that of the vacancy substituted fahlore assuming it has only ten atoms of Ag + Cu per formula unit, RT ln [(X₄^{with vacancies})¹⁰(X₂)²(${X}_{S}^{IV}$)¹²(${X}_{S}^{VI}$)). At constant temperature and X₂, the ratio of these quantities that will satisfy the condition of equilibrium of the net-transport reaction should be close to.

$$\begin{gathered} 1 = [(X4\;with\;no\ vacancies\;in\ fahlore)^{10} \hfill \\ \quad \quad /((X4\;with\;vacancies)^{10} (X_{S}^{IV} )^{12} (X_{S}^{VI} ))], \hfill \\ \end{gathered}$$

(5)

if we ignore changes in the compositions of miargyrite, pyrargyrite, and sphalerite associated with the different values of X₄. This cannot be strictly correct, as increased X₄ will increase both the Ag/(Ag + Cu) ratios of pyrargyrite and miargyrite due to the Ag–Cu exchange reactions between fahlore and pyrargyrite and fahlore and miargyrite. But because Ag is very strongly concentrated in these minerals relative to fahlore, the positive increases in their mole fractions of Ag₃SbS₃ and AgSbS₂, and hence their chemicals potentials will be negligible, but they will nonetheless result in further, almost imperceptible, expansion of the fahlore stability field on the X₄–X₂ plot. In general, increasing X₄ in fahlore at constant X₂ will increase the Zn/(Zn + Fe) ratio, and hence the chemical potential of ZnS, in coexisting sphalerite due to the incompatibility between Zn and Ag in fahlore expressed by a positive Gibbs energy of the reciprocal reaction:

$${\text{Cu}}_{{{1}0}} {\text{Zn}}_{{2}} {\text{Sb}}_{{4}} {\text{S}}_{{{13}}} \, + \,{\text{Ag}}_{{{1}0}} {\text{Fe}}_{{2}} {\text{Sb}}_{{4}} {\text{S}}_{{{13}}} \, = \,{\text{Cu}}_{{{1}0}} {\text{Fe}}_{{2}} {\text{Sb}}_{{4}} {\text{S}}_{{{13}}} \, + \,{\text{Ag}}_{{{1}0}} {\text{Zn}}_{{2}} {\text{Sb}}_{{4}} {\text{S}}_{{{13}}} ,$$

(6)

but this increase in partitioning of Fe and Zn between fahlore and sphalerite with increasing X₄ is interrupted at intermediate values of X₄ due to a change in Ag–Cu site ordering, a change that is responsible for the low-temperature (i.e., epithermal) miscibility gaps observed in natural fahlores (cf. O’Leary and Sack 1987; Sack 2017). Accordingly, we are forced to rely on the old geochemical adage that “in complex geochemical calculations the errors tend to cancel” (personal communication from H.C. Helgeson to ROS) until experimental, theoretical, and further field studies result in a satisfactory model that is as accurate as that developed for (Ag,Cu)₁₀(Zn,Fe)₂Sb₄S₁₃ fahlores.

We could readily determine the increases in X₄ associated with sulfur vacancy contents, if the conditions of homogeneous equilibrium relating octahedral to tetrahedral sulfur vacancies and the vibrational nonideality associated with these conditions were known. But as they are not known, we are forced to make some assumptions about the distribution of sulfur vacancies between the octahedral sites at the corners and center of the unit cell and the tetrahedral sites. Following conventional mineralogical “wisdom” we will assume that the sulfur vacancies are primarily in the octahedral sites when total sulfur vacancies do not exceed one pfu. In addition, we will make the assumptions that these vacancies are linearly related to the total sulfur vacancies until this limit is reached and that the octahedral vacancies retain the value they have at this limit (x), when total sulfur vacancies exceed it. Utilizing these assumptions, we may then determine what values of x are required to produce differences in X₄ between those established for (Ag,Cu)₁₀(Zn,Fe)₂Sb₄S₁₃ fahlores and the maximum ones determined here.

To do so, it is appropriate to consider the data array defined by Zn-rich fahlores with average X₂ of about 0.95 (cf. Figs. 5c and 8), as the isotherms are tightly constrained for (Ag,Cu)₁₀Zn₂Sb₄S₁₃ fahlores by the experiments of Ebel and Sack (1994) and these fahlores form the most comprehensive array reported here. Assuming a temperature of about 260 °C, the value of X₄ is about 0.39 for X₂ of 0.95 in (Ag,Cu)₁₀(Zn,Fe)₂Sb₄S₁₃ fahlores and this corresponds quite nicely with the low X₄ end of the array, an array which extends to a maximum value of about 0.7 X₄. According to the approximations we are employing this requires a value of x slightly greater than around 0.995 to satisfy the Mangazeyskoye fahlore data (cf. Fig. 8). Noteworthy features of this diagram include the prediction that X₄ is relatively insensitive to total sulfur vacancy content up to about 0.4 vacancies pfu, achieving progressivity steeper dX₄/d slopes until total vacancies approach 1.

Although the approximation given by Eq. (5) appears to provide a reasonable first-order accounting for the functional relationship between X₄ and vacancy contents in fahlores with vacancy contents $\le$ 1 pfu, it needs to be modified for vacancy contents > 1 pfu, as these fahlores do not appear to exhibit increasing X₄ with further increase in vacancy contents (cf. Figure 6a) and there may even be a maximum in X₄ around one vacancy pfu. This observation may be readily accounted for, providing we acknowledge that mixing of tetrahedrally coordinated sulfurs and vacancies may be highly nonideal and attempt to use a strictly regular solution parameter ^IVW_□-S to describe this nonideality. For this assumption an appropriate approximation might be

$${\text{RTln}}\left[ {\left( {X_{{4}}^{{\text{with no vacancies in fahlore}}} } \right)^{{{1}0}} } \right]\, = \,{\text{RTln}}[\left( {X_{{4}}^{{\text{vacancies in fahlore}}} } \right)^{{{1}0}} \left( {{\text{X}}_{{\text{S}}}^{{{\text{IV}}}} } \right)^{{{12}}} \left( {{\text{X}}_{{\text{S}}}^{{{\text{VI}}}} } \right)]\,\, + \,^{{{\text{IV}}}} W_{{\square - {\text{S}}}} \left( {X_{\square}^{{{\text{IV}}}} } \right)^{{2}} ,$$

(7)

which may be written in more compact form as

$$0\, = \,{\text{RTln}}[\left( {X_{{4}}^{{\text{with no vacancies in fahlore}}} } \right)^{{{1}0}} /\left( {\left( {X_{{4}}^{{\text{with vacancies}}} } \right)^{{{1}0}} \left( {{\text{X}}_{{\text{S}}}^{{{\text{IV}}}} } \right)^{{{12}}} \left( {{\text{X}}_{{\text{S}}}^{{{\text{VI}}}} } \right)} \right)]{-}^{{{\text{IV}}}} W_{{{\square}- {\text{S}}}} \left( {X_{\square}^{{{\text{IV}}}} } \right)^{{2}}$$

(8)

Although the dX₄/d$\square$ slope for total  $\square$ > 1 pfu is not well defined by the present data, ^IVW$_\square$_-S must be a positive number (i.e., on the order of 50—100 kJ/gfw) to achieve the zero dX₄/d$\square$ slope shown in Fig. 8, assuming this nonideality can be adequately expressed by a strictly regular solution parameter. But a nonideality of this order is consistent with the fact that substantial replacement of tetrahedrally coordinated sulfurs with vacancies will substantially destabilize the fahlore structure leading to its collapse (i.e., breakdown) with $X_{\square}^\text{IV}$ near the upper limit inferred here ($X_{\square}^\text{IV}$ ~ 0.133) for total vacancies of around 2.6 pfu. Among the minerals that would be produced by the breakdown of the fahlore component (Ag,Cu)₁₀(Fe,Zn)₂Sb₄S₁₀ include sphalerite, miargyrite, chalcopyrite and Ag–Cu metal alloys (e.g. Jian et al 2020), the exact proportions of these minerals being dependent on the Ag//(Ag + Cu) and Zn/(Zn + Fe) ratios of the fahlore breaking down.

Of course this treatment is clearly a simplification, particularly with regards to the adoption of the 10/4/2 (Au,Cu)/(Sb,As)/(Zn,Fe) ratio of the ideal fahlore formula unit. This is not strictly correct as illustrated in Fig. 7b where (Ag + Cu)_10+x = (Sb + As)_4-x and (Zn + Fe) = 2, and – 0.2 < x < 0.4 describes the stoichiometry of the metals and semi-metals of Mangazeyskoye fahlores to a rough approximation and (Sb + As) and (Ag + Cu) vary between about 4 to 3.6, and 10 to 10.4 with increasing  ${\square}$> 1 pfu. Without the ability to assess the energetic consequences of such stoichiometric improprieties (i.e., variations) at this point due to the absence of appropriate experimental investigations, we may only add them to the list of many other issues that need to be addressed (e.g., the energetics of ordering of Ag and Cu atoms between the octahedral metal clusters and those in tetrahedral metal sites, phase boundaries for breakdown of sulfur vacancy substituted fahlores as a function of temperature, etc.) before a comprehensive thermochemical model for sulfur vacancy substituted fahlores may be developed. We do note that it is fortuitous that the 10/4/2 (Au,Cu)/(Sb,As)/(Zn,Fe) ratio of the ideal fahlore formula unit appears to be a close approximation for Mangazeyskoye fahlores with 1 ${\square}$ pfu.

Fig. 7

a (Ag + Cu) apfu versus (Sb + As) apfu of Mangazeyskoye fahlores calculated on a Σ(Me + SMe) = 16 apfu basis. Symbols are identical to those in Fig. 5b Expanded version of a in section enclosed by dotted lines with horizontal and vertical lines with (Ag + Cu) = 10 and (Sb + As) = 4 indicating the stoichiometric coefficients of the metals and semimetals in the ideal fahlore formula unit. Slanted line (Ag + Cu)_10+x = (Sb + As)_4-x has positive x when  sulfur  vacancies > 1 pfu. Numbers indicate the analyses given in Table 1

This analysis can readily be extended to more Fe-rich fahlores by adding to the X₄—X₂ diagram 200 °C and 250 °C contours obtained by solving Eq. (5) for ${\square}$1 pfu and x = 0.995 (e.g., Fig. 9). This exercise suggests that the Mangazeyskoyean fahlores with the maximal Ag/(Ag + Cu) ratios were crystallized at temperatures between about 260° and 230 °C. However, some of the fahlores currently reflect lower temperatures, because some of them plot below such isotherms for (Ag,Cu)₁₀(Fe,Zn)₂Sb₄S₁₃ fahlores, and these lower temperature fahlores have significantly lower sulfur vacancies (cf. Figure 6a). These exceptions are clearly the result of their crystallization at lower temperatures or retrograde exchange with cooling. The latter possibility would not be unexpected particularly in the more Fe-rich fahlores as they are significantly less refractory than Zn-rich fahlores (cf. Sack and Loucks 1985; Sack et al. 2003) and are thus much more susceptible to retrograde exchange with cooling. Whatever the origin of these lower temperature fahlores, temperatures inferred for them from the X₄ -X₂ diagram for (Ag,Cu)₁₀(Fe,Zn)₂Sb₄S₁₃ are in accord with the development of stephanite, a mineral whose maximum thermal stability is 197 °C (Keighin and Honea 1969) and a temperature of about 155 °C calculated from Fe-Zn partitioning between sphalerite and stannite-kesterite of the Mangazeyskoye ore deposit using the calibration of Nakamura and Shima (1982).

Fig. 8

Variation of X₄ (Ag/(Ag + Cu)) with sulfur vacancy content per formula unit for Zn-fahlores with an average X₂ (Zn/(Zn + Fe)) of about 0.95 utilizing the approximation given in the text (Eq. 5) for values of x (mole fractions of vacancies on octahedral sulfur sites at total vacancy content of unity pfu) of 0.975, 0.985 and 0.995. Vertical arrows attached to horizontal lines for X₄ for total vacancy content > 1 pfu indicate that X₄ may be less than the value for total vacancy content = 1 pfu (i.e., X₄ may be a maximum at the total vacancy content = 1 pfu at a given value of x)

The main takeaway from our analysis is that fahlores from low-sulfidation environments have great potential to serve as petrogenetic indicators of sulfur fugacity through reactions such as.

$${\text{Ag}}_{{{1}0}} {\text{Zn}}_{{2}} {\text{Sb}}_{{4}} {\text{S}}_{{{13}}} \, = \,{\text{Ag}}_{{{1}0}} {\text{Zn}}_{{2}} {\text{Sb}}_{{4}} {\text{S}}_{{{12}}}{\square}^{{{\text{OCT}}}} \, + \,\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} {\text{ S}}_{{2}}$$

(9)

and

$${\text{Ag}}_{{{1}0}} {\text{Zn}}_{{2}} {\text{Sb}}_{{4}} {\text{S}}_{{{13}}} \, = \,{\text{Ag}}_{{{1}0}} {\text{Zn}}_{{2}} {\text{Sb}}_{{4}} \left( {{\text{S}}_{{{11, \square}}} } \right)^{{{\text{TET}}}} {\text{S}}\, + \,\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} {\text{ S}}_{{2}}$$

(10)

and the homogeneous reaction given by the difference of these reactions:

$${\text{Ag}}_{{{1}0}} {\text{Zn}}_{{2}} {\text{Sb}}_{{4}} \left( {{\text{S}}_{{{11, \square}}} } \right)^{{{\text{TET}}}} {\text{S}}\, = \,{\text{Ag}}_{{{1}0}} {\text{Zn}}_{{2}} {\text{Sb}}_{{4}} {\text{S}}_{{{12}}}{\square}^{{{\text{OCT}}}}$$

(11)

Of course, quantitative realization of this potential will require experimental determinations of sulfur vacancy concentration as a function of sulfur fugacity and characterization of the vibration non-idealities and atomic configurations associated with vacancy substitutions. Lacking such information variations in X₄ in the Mangazeyskoye fahlores may only be used to define rhythmic variations in the sulfur fugacity of the hydrothermal fluids from which they crystallized.

Discussion

The observations reported here and the simplified analysis conducted to rationalize them suggest that the Mangazeyskoye sulfur vacancy-rich fahlores with the highest Ag/(Ag + Cu) ratios crystallized at temperatures between about 230 and 260 °C. This inference is the result of comparison of ratios of Ag/(Ag + Cu) and Zn/(Zn + Fe) of the most Ag-rich Mangazeyskoye fahlores with values of these ratios in fahlores with vacancy contents near 1 pfu calculated using the crude approximation given by Eq. (5) and the isotherms for (Ag,Cu)₁₀(Zn,Fe)₂Sb₄S₁₃ fahlores coexisting with miargyrite, pyrargyrite, and sphalerite determined by Sack (2005) (cf. Figs. 5c, 8, 9). This inference is consistent with the conclusions of Anikina et al. (2016) that tetrahedrite fahlores belong to the Ag-base metal stage of the sulfide-sulfosalt paragenetic sequence which crystallized over a temperature range of about 125–280 °C. These fahlores were thus produced near the upper temperature limits of this stage, and contrast with fahlores with lower Ag/(Ag + Cu) and vacancy contents (cf. Fig. 6a, b) which indicate lower equilibration/crystallization temperatures depending on Zn/(Zn + Fe) ratio of fahlore. Lower temperatures within this temperature range are also supported by Zn-Fe partitioning between sphalerite and stannite-kesterite and the occasional presence of stephanite in Mangazeyskoye assemblages. Based on the calibration of Nakamura and Shima (1982) a sphalerite + stannite-kesterite assemblage shown in Fig. 2b represents a temperature of about 155 °C (cf. Shimizu and Shikazono 1985) and stephanite indicates T < 197 °C, as this is the maximum temperature of its stability (Keighin and Honea 1969). And, of course, the variations of vacancy contents in rhythmically zoned fahlores from the Mangazeyskoye ore deposit are indicative of pronounced variations and repetitions in the temperatures and sulfur fugacities in the fluids from which they crystallized. Although an adequate thermodynamic model for sulfur vacancy substituted fahlores is presently unavailable to quantity the sulfur fugacity’s of the parental fluids, such fahlores may be used to define their relative sulfur fugacity’s and temporal variations. Such variations are apparent in the heterogeneous-zonal aggregate of argentotetrahedrite–kenoargentotetrahedrite-(Zn) fahlore (Figs. 3d, 4) where the average vacancy contents of the fahlores are highest the outermost layers (RIII), lowest in the intermediate layers (RII) and intermediate in the core (RI). The average sulfur fugacity’s of the fluids from which they crystallized were lowest for RIII, highest for RII and intermediate for RI fahlores, if the temperatures of crystallization of these fahlores were similar.

Fig. 9

Molar Ag/(Ag + Cu) and Zn/(Zn + Fe) ratios of fahlores (a) from the Mangazeyskoye deposit and (b) from the heterogeneous-zonal kenoargentotetrahedrite-(Zn) aggregates along the R-2 profile compared with the isotherms for (Cu,Ag)₁₀(Fe,Zn)₂Sb₄S₁₃ fahlores in the miargyrite + pyrargyrite + sphalerite assemblage (gray curves, Sack 2005, Fig. 1 here) and those for (Cu,Ag)₁₀(Fe,Zn)₂Sb₄S₁₂ fahlores (a) at 200 and 250 °C and (b) at 170, 200 and 250 °C calculated with the approximation given by Eq. (5) with x = 0.995 (red dotted curves)

Further quantification will not be possible without the development of a reliable thermodynamic model for sulfur vacancy substituted fahlores. This will certainly be a formidable task, as such a model has not even been formulated, would require the calibration of substantially more parameters than those required for (Ag,Cu)₁₀(Zn,Fe)₂(As,Sb)₄S₁₃ fahlores (e.g., Sack 2017) and there are presently virtually no experimental constraints to do such a calibration. Such a development would also require that the assumption about the structural role of Ag in fahlore of the mineralogical community be revisited to conform with the precepts of thermodynamics and statistical mechanics and be consistent with the observation that low-temperature (< 200 °C) miscibility gaps exist in natural fahlores that closely approximate the (Ag,Cu)₁₀(Zn,Fe)₂Sb₄S₁₃ formula (e.gSack et al. 2003; Chinchilla et al. 2016; Sack 2017; Zhai et al. 2019; Alves et al. 2022; Zhai 2022). This reassessment might begin with examination of the temperature dependence of the cell edge lengths of synthetic Ag-rich fahlores as a function of annealing temperature, paralleling the studies of Ebel (1993) for (Ag_0.73,Cu_0.27)₁₀Zn₂Sb₄S₁₃ fahlore and Barton and Toulmin (1966) for Zn-Fe-S sphalerites (cf. Balabin and Sack 2000, their Fig. 6). And, of course, such a model will have to quantify the effects of the nature and compositions of octahedral Ag–Cu clusters centered on the vacated S^VI sites on the configurational entropy and vibrational energy and other thermodynamic properties and correctly predict the existence and compositions of the binodes of the low temperature miscibility gaps. It is also obvious that hydrothermal and/or sealed silica tube experiments at varying temperatures and sulfur fugacity’s will be required to constrain sulfur vacancy forming and homogeneous reactions (9–11). Completion of these exercises should lead more realistic (i.e., lower f_S2) bounds on the stability field of fahlore at a given temperature than those currently calculated on an assumed 13 sulfur stoichiometry.

Despite these uncertainties, the present analysis clearly demonstrates that vacancies substitute for tetrahedrally coordinated sulfurs in fahlores in low sulfidation environments, and this ${\square}$(S^IV)_-1 substitution must be substantially more nonideal than the ${\square}$ (S^VI)_-1 substitution to account for the apparent maximum in Ag/(Ag + Cu) ratios in fahlores near 1${\square}$ pfu (cf. Figures 6a, b). For  ${\square}$ < 1 pfu the ${\square}$(S^VI)_-1 substitution may be substantially ideal, given that a change in the charge of the octahedral metal clusters from + 6 to + 4 is accomplished by increasing metallic bonding between nearest neighbor metal atoms. But metallization of Ag and Cu ions in the octahedral clusters becomes more energetically difficult with vacancy contents ${\square}$  > 1 pfu, as this requires charge imbalances over greater distances and would lead to the production of Ag–Cu alloy nanoparticles (e.g., Jian et al. 2020) rattling around in the structure fully electrostatically unattached at the intrinsic limit of 3 sulfur vacancies pfu. It is therefore unlikely that the intrinsic limit of three sulfur vacancies pfu is ever achieved in natural fahlores, even when they break down to assemblages containing metals. And the fact that the Mangazeyskoye fahlores appear to have a limit of greater than 2 vacancies substituting for S lends credibility to the assumption that Ag₁₀Zn₂Sb₄S₁₂${\square}$^OCT and Ag₁₀Zn₂Sb₄ (S_11,${\square}$)^TETS^OCT will be sufficient to serve as endmember fahlore vacancy components in a thermodynamic analysis.

Conclusions

Fahlores from the Mangazeyskoye Ag-Pb-Zn ore deposit have sulfur contents between about 13 and 10.4 atoms per formula unit (apfu) calculated from EPMA on the assumption that there are 16 metals and semi-metals atoms in the formula unit. Assuming the charges on the metals Ag and Cu are + 1, those on the metals Zn and Fe are + 2, those on the semimetals Sb and As are + 3 and that of S is − 2, these fahlores lie along lines of charge versus sulfur vacancy content with a slope of + 2 and zero intercept within analytical uncertainty. Accordingly, if an ionic model is assumed, the charge on the octahedral Ag and Cu clusters formed by vacating the sulfur sites at the corners and center of the fahlore unit cell (Z = 2) must be reduced from the nominal value of + 6 to that given by the formula (+ 6 – 2 n${\square}$) if charge balance is to be preserved. This implies that the absolute intrinsic limit on vacancies that may substitute for sulfur is three pfu, as this would lead to full metallization of Ag and Cu atoms in these clusters, producing alloy nanoparticles electrostatically unattached to the remaining fahlore structure. The greater Ag/(Ag + Cu) ratios of the sulfur vacancy-rich Mangazeyskoye fahlores than those of (Ag,Cu)₁₀(Zn,Fe)₂Sb₄S₁₃ fahlores in equilibrium with miargyrite, pyrargyrite and sphalerite may be accounted for by equating approximations for the configurational portions of the chemical potential of Ag₁₀Zn₂Sb₄S₁₃ in (Ag,Cu)₁₀(Zn,Fe)₂Sb₄S₁₃ and vacancy substituted fahlores. Satisfactory agreement is achieved providing sulfur vacancies are nearly all on the octahedrally coordinated sulfur site when there are less than 1 sulfur vacancy pfu, and it is assumed that Mangazeyskoye fahlores with vacancy concentrations near this limit and with maximal value of Ag/(Ag + Cu) crystallized at temperatures between about 230 and 260 °C. This inference is consistent with the observations of Anikina et al. (2016) that Mangazeyskoye fahlores crystallized in the third of three depositional successions that were deposited in the 120–340 °C temperature range of petrogenesis. But some of the vacancy-poor Mangazeyskoye fahlores crystallized at temperatures nearer to the lower portion of this temperature range of petrogenesis, as reflected by their Ag/(Ag + Cu) ratios, the temperature of about 155 °C calculated from Fe-Zn partitioning for a sphalerite + stannite-kesterite assemblage using the calibration of Nakamura and Shima (1982) and the occasional presence of minerals such as stephanite (T < 197 °C, Keighin and Honea 1969) in fahlore-bearing assemblages.