The High Pressure Behavior of Galenobismutite, PbBi2S4

: High-pressure single-crystal synchrotron X-ray di ﬀ raction data for galenobismutite, PbBi 2 S 4 collected up to 20.9 GPa, were ﬁtted by a third-order Birch-Murnaghan equation of state, as suggested by a F E - f E plot, yielding V 0 = 697.4(8) Å 3 , K 0 = 51(1) GPa and K ’ = 5.0(2). The axial moduli were M 0a = 115(7) GPa and M a ’ = 28(2) for the a axis, M 0b = 162(3) GPa and M b ’ = 8(3) for the b axis, M 0c = 142(8) GPa and M c ’ = 26(2) for the c axis, with reﬁned values of a 0 , b 0 , c 0 equal to 11.791(7) Å, 14.540(6) Å 4.076(3) Å, respectively, and a ratio equal to M 0a :M 0b :M 0c = 1.55:1:1.79. The main structural changes on compression were the M2 and M3 (occupied by Bi, Pb) movements toward the centers of their respective trigonal prism bodies and M3 changes towards CN8. The M1 site, occupied solely by Bi, regularizes the octahedral form with CN6. The eccentricities of all cation sites decreased with compression testifying for a decrease in stereochemical expression of lone electron pairs. Galenobismutite is isostructural with calcium ferrite CaFe 2 O 4 , the suggested high pressure structure can host Na and Al in the lower mantle. The study indicates that pressure enables the incorporation of other elements in this structure, increasing its potential signiﬁcance for mantle mineralogy.


Introduction
Galenobismutite PbBi 2 S 4 is a Bi-sulfosalt usually found in hydrothermal veins or associated with fumarolic deposits [1,2]. Like other Bi-minerals, it has an important role in the reconstruction of the formation of ore deposits as it is sensitive to physical-chemical fluctuations and can constrain the genesis of ore.
Chemical substitution of Sb for Bi and Fe for Pb are common in gelenobismutite. It is illustrated by galenobismutite from Beiya porphyry-and skarn-type deposits that contain Sb up to 0.39% and Fe up to 0.42% [10]. Selenium can replace sulfur in galenobismutite. In galenobismutite from Vulcano Island  [19]; (c) NaAlSiO4 at room pressure [16]; (d) NaAlSiO4 at 35 GPa [20].

High Pressure Experiments
The HP synchrotron single-crystal X-ray diffraction experiments were carried out at ID-15B beamline at ESRF (Grenoble) dedicated to the determination of structural properties of solids at high pressure using angle-dispersive-diffraction with diamond anvil cells. A membrane-type Diamond Anvil Cell with an opening angle of +/−32 degrees, equipped with 600 µm diamond culets was used. Helium was used as a pressure transmitting medium. According to Singh [24] helium is superior in ensuring near to hydrostatic conditions at pressures of 20 GPa or over compared to argon.
Ruby sphere was loaded as a fluorescent P calibrant together with the galenobismutite sample (80 × 10 × 20 µm 3 ) in the 300 µm hole in the center of a pre-indented stainless steel gasket of 80 µm thickness. Pressure was measured before and after each data collection.
The sample-to-detector distance was 279.88 mm and calibrated, along with the wavelength, using Si standard and Fit2D software [25]. The same synthetic sample of galenobismutite used in Olsen et al 2007 was selected to collect the present set of measurements, to avoid differences in compressibility ascribable to different chemical compositions in the samples.
The X-ray beam was monochromatized to a wavelength of 0.41125 Å and focused down to 10×10 µm area. Data were collected with a DAC rotating 64° around the ω-axis (from −32 to +32°) with angular step of 0.5° and counting time of 1s per step. The scattered radiation was collected by a MAR555 flat panel detector, with 430 × 350 mm (555mm diagonal) active area.

High Pressure Experiments
The HP synchrotron single-crystal X-ray diffraction experiments were carried out at ID-15B beamline at ESRF (Grenoble) dedicated to the determination of structural properties of solids at high pressure using angle-dispersive-diffraction with diamond anvil cells. A membrane-type Diamond Anvil Cell with an opening angle of +/−32 degrees, equipped with 600 µm diamond culets was used. Helium was used as a pressure transmitting medium. According to Singh [24] helium is superior in ensuring near to hydrostatic conditions at pressures of 20 GPa or over compared to argon.
Ruby sphere was loaded as a fluorescent P calibrant together with the galenobismutite sample (80 × 10 × 20 µm 3 ) in the 300 µm hole in the center of a pre-indented stainless steel gasket of 80 µm thickness. Pressure was measured before and after each data collection.
The sample-to-detector distance was 279.88 mm and calibrated, along with the wavelength, using Si standard and Fit2D software [25]. The same synthetic sample of galenobismutite used in Olsen et al 2007 was selected to collect the present set of measurements, to avoid differences in compressibility ascribable to different chemical compositions in the samples.
The X-ray beam was monochromatized to a wavelength of 0.41125 Å and focused down to 10 × 10 µm area. Data were collected with a DAC rotating 64 • around the ω-axis (from −32 to +32 • ) Crystals 2019, 9, 210 4 of 18 with angular step of 0.5 • and counting time of 1s per step. The scattered radiation was collected by a MAR555 flat panel detector, with 430 × 350 mm (555mm diagonal) active area.
The extraction and correction of the intensity data, merging of reflections, and the refinements of the crystal lattice parameters were done by means of the CrysAlis software (Agilent technologies) [26]. Measurements were performed at different pressures from 0.5 to 20.9 GPa on increasing pressure, and at 16.43, 8.12, and 2.1 GPa on decreasing pressure to evaluate the reversibility and hysteresis phenomena of structural changes. The absorption correction was applied by means of ABSORB-7 software [27].

Compressibility
The evolution of the unit-cell of galenobismutite with pressure is reported in Figure 2 and in Table 1. The behavior of the cell parameters shows no discontinuities in the investigated pressure range and indicates that no phase transition occurs in galenobismutite structure up to 20.9 GPa. The volume-pressure data were fitted with a third-order Birch-Murnaghan equations-of-state, using the EOSFIT7-GUI software [29], as suggested by f E -F E , namely the "Eulerian finite strain" versus "normalized stress" plot [30] were in good agreement with the values obtained from the f E -F E plot [30]. The intercept value and the slope obtained by a linear regression give F E0 and K' values equal to 51(1) GPa and 4.8 (8), respectively.
The evolution of the unit-cell of galenobismutite with pressure is reported in Figure 2 and in Table 1. The behavior of the cell parameters shows no discontinuities in the investigated pressure range and indicates that no phase transition occurs in galenobismutite structure up to 20.9 GPa. The volume-pressure data were fitted with a third-order Birch-Murnaghan equations-of-state, using the EOSFIT7-GUI software [29], as suggested by fE-FE ,namely the "Eulerian finite strain" versus "normalized stress" plot [30], (Figure 3). The third order Birch-Murnaghan Equation of State (EoS) fit yields V0 = 697.4(8) Å 3 , K0 = 51(1) GPa and K' = 5.0(2). The bulk modulus and the first derivative values were in good agreement with the values obtained from the fE-FE plot [30]. The intercept value and the slope obtained by a linear regression give FE0 and K' values equal to 51(1) GPa and 4.8(8), respectively.  EOSFIT7-GUI software [29], as suggested by fE-FE ,namely the "Eulerian finite strain" versus "normalized stress" plot [30], (Figure 3). The third order Birch-Murnaghan Equation of State (EoS) fit yields V0 = 697.4(8) Å 3 , K0 = 51(1) GPa and K' = 5.0(2). The bulk modulus and the first derivative values were in good agreement with the values obtained from the fE-FE plot [30]. The intercept value and the slope obtained by a linear regression give FE0 and K' values equal to 51(1) GPa and 4.8(8), respectively.   Density of galenobismutite changed from 7.243 g/cm 3 at 0.5 GPa to 9.029 g/cm 3 at 20.9 GPa, with an increase of about 22% in the investigated pressure range.
To compare the present data with those of other sulfides of metalloids from literature (galena [31], bismuthinite [32], stibnite [33], chalcostibite [34], lillianite [35], heyrovskyite [36], berthierite [37]) a K' vs K 0 plot was elaborated (Figure 4). In the plot, the confidence ellipses at 90 and 68 % of confidence level for the present data and those reported by Olsen et al. [21] are shown. In order to allow a more direct comparison of K 0 and K' calculated with the two data sets and to evaluate if the observed differences were due to the different pressure range, we also calculated K 0 and K' restricting our data to the same pressure range investigated by Olsen et al [21]. We observed a strong negative correlation between K' and K 0 in agreement with the data presented by Olsen et al. [21]. However, the ellipsoides for the two data sets did not overlap, even if they are quite close. The reason might be that the results of Olsen et al. [21] were biased by an unequal distribution of pressures at which the data were measured.  GPa (solid black line) as well as with data limited at 8.8 GPa (stippled black line). Confidence ellipse at 90% for Olsen et al. [21] data is also shown (stippled blue line). (Figure 4), PbS, before the phase transition, were very close to those observed for galenobismutite. On the other hand, K0 for bismuthinite, Bi2S3, were significantly lower ( Figure 4). Olsen et al. [21] suggested an empirical relation between the bulk modulus of galenobismutite and those of PbS and Bi2S3 corresponding to the proportion of Bi and Pb in galenobismutite: KPbBi2S4 = (2KBi2S3 + KPbS)/3. Although this relation holds approximately for the data from the previous study, the present corrected data for galenobismutite does not support this observation. We can conclude that a simple relation between a bulk modulus for a complex composition cannot be derived straightforwardly from the bulk moduli of its simpler constituents [38] even if they contain the same general structural modules (like in sulfosalts). Obviously, a more complex cooperative mechanism between the structural modules should be involved [39]. For sulfosalts it is important to take into account that they contain cations with active lone electron pairs (LEPs), which can strongly affect the polyhedral distortion, and the overall structural compressibility to different extents. Sb 3+ LEP's stereochemical activity is generally higher than that of Bi 3+ , evaluated from the measurements of the eccentricity of Sb and Bi polyhedra at room pressure conditions, which show larger difference in interatomic Sb-S distances compared to Bi-S ones. Under high pressure, the . Bulk Moulus (K 0 ) vs its pressure derivative (K') for different sulfides. Confidence ellipses at 90% of confidence level are reported for K 0 and K' calculated with the present data collected up to 20.9 GPa (solid black line) as well as with data limited at 8.8 GPa (stippled black line). Confidence ellipse at 90% for Olsen et al. [21] data is also shown (stippled blue line). K 0 and K' values for galena (Figure 4), PbS, before the phase transition, were very close to those observed for galenobismutite. On the other hand, K 0 for bismuthinite, Bi 2 S 3 , were significantly lower ( Figure 4). Olsen et al. [21] suggested an empirical relation between the bulk modulus of galenobismutite and those of PbS and Bi 2 S 3 corresponding to the proportion of Bi and Pb in galenobismutite: K PbBi2S4 = (2KBi 2 S 3 + KPbS)/3. Although this relation holds approximately for the data from the previous study, the present corrected data for galenobismutite does not support this observation. We can conclude that a simple relation between a bulk modulus for a complex composition cannot be derived straightforwardly from the bulk moduli of its simpler constituents [38] even if they contain the same general structural modules (like in sulfosalts). Obviously, a more complex cooperative mechanism between the structural modules should be involved [39]. For sulfosalts it is important to take into account that they contain cations with active lone electron pairs (LEPs), which can strongly affect the polyhedral distortion, and the overall structural compressibility to different extents. Sb 3+ LEP's stereochemical activity is generally higher than that of Bi 3+ , evaluated from the measurements of the eccentricity of Sb and Bi polyhedra at room pressure conditions, which show larger difference in interatomic Sb-S distances compared to Bi-S ones. Under high pressure, the polyhedra become more regular and the eccentricity reduces more rapidly for Sb 3+ polyhedra with respect to those of Bi 3+ , because the longest interatomic contacts in atomic coordinations generally compress faster than the shortest ones. As a consequence, Sb sulfosalts have bulk moduli lower than the corresponding Bi sulfosalts, as illustrated by the isomorphic chalcostibite-emplectite series [34].

K0 and K' values for galena
Pb 2+ also contains a LEP, but it is generally less expressed than that of Bi 3+ . LEP of Pb 2+ is even fully suppressed in several structures, like in galena or the earlier mentioned PbSc 2 S 4 . To the best of our knowledge the only observed regular coordination of Bi 3+ is the octahedral coordination in the mineral kupcikite, Cu 4 Bi 5 S 10 [40,41]. It is interesting that the pressure can force coordinations with suppressed LEP to a structure with highly expressed stereochemical activity through phase transition [35,36,42].
Very few theoretical calculations provide an analysis of the relation between electronic structure, lone electron pairs and structural geometrical parameters. Olsen et al 2011 [43], by using SIESTA DFT code considered the effect of pressure in Bi 2 S 3 and compared the theoretical with experimental data. Their data on the effective Bi s-p hydridization support the origin of the stereochemically active lone pair and its evolution with pressure increases.
A comparison of the bulk modulus of galenobismutite to those of CF type structures shows much larger differences. Dubrovinsky et al. [20] reported the CF type NaAlSiO 4 bulk modulus measured up 40 GPa. Their data gave a very high bulk modulus of 220 GPa and its pressure derivative was equal to 4.1(1), similar to the values measured for other compounds with a calcium ferrite structure. For example, the value of K 0 , with K' fixed to 4, of MgAl 2 O 4 measured by Yutani et al. [44] was 241(1) GPa, whereas K 0 measured for Fe 3 O 4 by Haavik et al. [45] was 202(7) GPa, with K' equal to 4. The general rule, suggested by Anderson et al. [46], KV = constant, where V represents the molar volume (36.58cm 3 /mol for NaAlSiO 4 , 36.13 cm 3 /mol for MgAl 2 O 4 and 41.89 cm 3 /mol for Fe 3 O 4 ), seems to be followed by this group of calcium ferrite structures [20]. In comparison, galenobismutite has a higher molar volume (105.0 cm 3 /mol) but, at the same time, a much lower bulk modulus, resulting in a violation of the Anderson's relation. This is most probably due to a large difference in chemistry, influenced by both cation and anion electronic configurations and especially by the presence of cation LEPs in galenobismutite.

Structural Evolution with Pressure
The M1, M2 and M3 polyhedral evolution with pressure was analyzed through changes in bond lengths and polyhedral volumes reported in Table 3. Figures 5 and 6 show the changes of bond distances and volumes with pressure. The bulk moduli of M1, M2 and M3 polyhedra, calculated as the reciprocals of linear compressibilities are 114 (3) GPa, 86(2) GPa and 84(2) GPa, respectively. The values agree with the general relationship suggested by Finger and Hazen [14], which relates the polyhedral bulk moduli to inverse of the mean cation-anion distances for several oxides, silicates as well as sulfides and selenides and several other types of compounds. Figures 5 and 6 show the changes of bond distances and volumes with pressure. The bulk moduli of M1, M2 and M3 polyhedra, calculated as the reciprocals of linear compressibilities are 114 (3) GPa, 86(2) GPa and 84(2) GPa, respectively. The values agree with the general relationship suggested by Finger and Hazen [14], which relates the polyhedral bulk moduli to inverse of the mean cation-anion distances for several oxides, silicates as well as sulfides and selenides and several other types of compounds.   The distortion parameters of the coordination polyhedra can give an additional insight in the compressibility behavior of atomic coordinations. Figure 7 shows the development of the eccentricities, asphericities and shape distortions (or volume distortions [47]). For M3 we calculated the parameters for both CN7 and CN8, because of its specific character. The eccentricities of all coordinations decreased continuously with pressure but much faster for M2 and M3 than for M1. After 4 GPa M1 reached the most eccentric coordination in spite of its smallest CN. It is interesting that the eccentricity of M3 related to only the closest seven S atoms levels off after 12 GPa and does not show further changes with pressure. However, for CN8 it continued to decrease, due to a continuous approach of the eight S atom. The asphericities showed much smaller changes with pressure. Note that M1 from the start had negligible asphericity, meaning that all six S atoms fit practically perfectly to a common sphere. It is interesting that the asphericity of the M3 coordination for CN7 actually increased with pressure, in spite of a constant decrease in asphericity calculated for CN8. It must, however, be noted that the asphericity for CN8 was significantly higher. The shape distortion, which shows the departure of the arrangement of ligands compared to an ideal polyhedron, shows an increase with pressure for all coordination polyhedra. The parameters are in all cases calculated compared to the ideal polyhedron which shows the smallest VS/VP ratio for a given CN, where VS and VP are the volumes of the circumscribed sphere and the polyhedron, respectively. For CN6 this is the regular octahedron, for CN7 the regular pentagonal bipyramid and for CN8 the "maximum volume" bisdisphenoid. Compared to the latter two, an ideal monocapped trigonal prism would have a "shape distortion" of 0.159, and an ideal bicapped trigonal prism would The distortion parameters of the coordination polyhedra can give an additional insight in the compressibility behavior of atomic coordinations. Figure 7 shows the development of the eccentricities, asphericities and shape distortions (or volume distortions [47]). For M3 we calculated the parameters for both CN7 and CN8, because of its specific character. The eccentricities of all coordinations decreased continuously with pressure but much faster for M2 and M3 than for M1. After 4 GPa M1 reached the most eccentric coordination in spite of its smallest CN. It is interesting that the eccentricity of M3 related to only the closest seven S atoms levels off after 12 GPa and does not show further changes with pressure. However, for CN8 it continued to decrease, due to a continuous approach of the eight S atom. The asphericities showed much smaller changes with pressure. Note that M1 from the start had negligible asphericity, meaning that all six S atoms fit practically perfectly to a common sphere. It is interesting that the asphericity of the M3 coordination for CN7 actually increased with pressure, in spite of a constant decrease in asphericity calculated for CN8. It must, however, be noted that the asphericity for CN8 was significantly higher. The shape distortion, which shows the departure of the arrangement of ligands compared to an ideal polyhedron, shows an increase with pressure for all coordination polyhedra. The parameters are in all cases calculated compared to the ideal polyhedron which shows the smallest V S /V P ratio for a given CN, where V S and V P are the volumes of the circumscribed sphere and the polyhedron, respectively. For CN6 this is the regular octahedron, for CN7 the regular pentagonal bipyramid and for CN8 the "maximum volume" bisdisphenoid. Compared to the latter two, an ideal monocapped trigonal prism would have a "shape distortion" of 0.159, and an ideal bicapped trigonal prism would have a "shape distortion" of 0.073. In this respect, the values calculated for M2 and M3 (both for CN7 and for CN8) are actually a sign of approaching the shapes closer to ideal monocapped, respectively bicapped trigonal prism. M1, however, departed more from an ideal octahedron shape with increasing pressure.
The orientation and expression of a LEP can be calculated from the relative positions of the central atom in a coordination and the centroid of the ligand arrangement [48]. The black spheres in Figure 8 have their centers in centroids of coordinations, thus, they illustrate the orientations and the expressions of the LEPs of cations.

Discussion and Conclusion
The comparison of data collected at different pressures on galenobismutite allows the following conclusions: a) The structural evolution is completely reversible with pressure increase up to 20.9 GPa. The same values were measured increasing and decreasing the pressure and the same equation of state is measured by using values collected increasing or decreasing pressure. No evidence of hysteresis in the changes were observed, meaning that the changes are completely elastic. b) The change in atomic coordinations bring the M3 coordination polyhedron closer to the shape observed in other members of the CF structural family (from CN7+1 to CN8  Taking into account the changes in bond distances and distortion parameters plus the global aspects of the crystal structure, the changes that occur in galenobismutite under increasing pressure can be summarized as follows: The main change is that both M2 and M3 atoms move towards the centers of the bodies of respective trigonal prisms. It can be visually verified by comparing the crystal structures at 1 bar and 20.9 GPa, as represented in Figure 8, and by checking the development of the bond lengths, as in Figure 5. Here, the atoms making the body of the trigonal prism were two S3 atoms, two S2 atoms plus S3 and S1 for M2. Note that bond distances to these six S atoms showed a merging tendency with increasing pressure. The distance to the capping S4 atom decreased with a much lower gradient than the ones to two S2 plus S1 atom (that are longer at 1 bar) and actually became the longest one from 12 GPa on. In the case of M3, two S2, two S1 and two S3 atoms formed the prism body and one can observe the same tendency of merging the bond distances up to approximately 10 GPa; above this pressure they became the shortest bond distances in the coordination polyhedron. It is true that the longest distance to one of the capping S4 atoms had a significant decrease during the whole measurement range, but with a gradient that was similar to the one of the two S3 atoms belonging to prism body. On the contrary, the distance to the other S4 capping atom actually slightly increased under compression. This all testifies also in this case that M3 moves inside the body of the trigonal prism with a consequence that it also moves away from the closest capping S4 atom. As the distance to the other one largely decreases due to its approach to the prism body, the two distances to the capping S atoms show a merging tendency and we can assume that the coordination's character changes from the 7+1 type towards the real CN8, becoming a more regular bicapped trigonal prism (also confirmed by the values of the shape distortion in Figure 7c).
The changes in the M1 coordination were very small compared to M2 and M3. The eccentricity of this site changed very little (Figure 7a) as the difference between the three shortest and three longest bonds remained almost the same (Figure 5a). There was actually a slight but constant increase in the distortion of the octahedral shape (Figure 7c). The main change in this coordination is due to the polyhedral accommodation to the contraction of the b axis that had the largest compressibility (Figures 2 and 8a). The expression of the LEP of M1 slightly changed, but its orientation, seen from the atomic nucleus, changed more significantly from the diagonal one, oriented towards the space between the two neighboring M1 coordinations, to a direction along the b axis (Figure 8b). The changes in the expression of LEPs of M2 and M3 were more significant and their orientations changed to directions closer to the M2-capping S and M3-most distant capping S, in accordance to the movement of M2 and M3 towards the centers of their respective trigonal prisms.

Discussion and Conclusion
The comparison of data collected at different pressures on galenobismutite allows the following conclusions: (a) The structural evolution is completely reversible with pressure increase up to 20.9 GPa. The same values were measured increasing and decreasing the pressure and the same equation of state is measured by using values collected increasing or decreasing pressure. No evidence of hysteresis in the changes were observed, meaning that the changes are completely elastic. (b) The change in atomic coordinations bring the M3 coordination polyhedron closer to the shape observed in other members of the CF structural family (from CN7+1 to CN8). However, unlike other CF crystal structures, M2 keeps and even equalizes its seven-fold coordination with increasing pressure. This emphasizes the specific character of galenobismutite in this structural family. We suggest that the main reason is a comparatively large size of the M2 cation, comparable to that of the M3, unlike the other examples of CF structures, where M2 is significantly smaller than M3. (c) The structure remains stable at very high pressures (up to 20 GPa) notwithstanding the moderate bulk modulus, at least under the structural point of view, since there are no incompatible distances up to 20.9 GPa. All sulfur-sulfur distances, which could indicate instability of the structure, remained quite large with the shortest S3-S4 distance equal to 3.140 Å. (d) Calcium ferrite structure type reveals enough flexibility in incorporating various element combinations through the example of galenobismutite. Thus, not only Al and Na, incompatible in the periclase or perovskite crystal structures under the lower mantle conditions, can be considered to prefer this structure type, but it might incorporate also some other important or less abundant elements or combinations of elements.