**3. Results**

## *3.1. 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 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) Å3, 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.

**Figure 2.** Evolution of the unit cell volume and *a*, *b*, *c* lattice parameters normalized to the values at room conditions as a function of pressure (GPa), fitted by a third-order Birch-Murnaghan EoS. Olsen et al. [21] data are shown by stippled lines and triangles for comparison.

**Figure 3.** Evolution of the Eulerian finite strain *fE* versus the "normalized stress" *FE*. The solid line is the weighted linear fit of the data for *V*, *a*, *b* and *c* lattice parameters.

The lattice parameter moduli, calculated using a third-order Birch-Murnaghan equation of state, were for the axis M0a = 115(7) GPa and Ma' = 28(2), for the b axis M0b = 162(3) GPa and Mb' = 8(3), for the c axis M0c = 142(8) GPa and Mc' = 26(2), with refined values of a0 11.791(7) Å, b0 = 14.540(6) Å, c0 = 4.076(3) Å, respectively. Since the results gave large differences in M' parameters, the lattice parameter moduli were calculated using the second order Birch-Murnaghan equation of state, fixing M' to 12 in order to evaluate the anisotropic behavior. The results of this fitting give M0a 191 (9) GPa with a0 equal to 11.74 (2) Å, M0b = 123(5) GPa with b0 equal to 14.96 (2) Å and M0c = 226 (10) GPa with c0 equal to 4.058(6) Å. The compressional anisotropy of crystallographic axes, showed that b and c

were the most and the least compressible lattice parameters, respectively, with the anisotropic ratio M0a:M0b:M0c = 1.55:1:1.84.

Density of galenobismutite changed from 7.243 g/cm<sup>3</sup> at 0.5 GPa to 9.029 g/cm<sup>3</sup> 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 K0 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 K0 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 K0 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 K0 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.

**Figure 4.** Bulk Moulus (K0) *vs* its pressure derivative (K') for different sulfides. Confidence ellipses at 90% of confidence level are reported for *K*<sup>0</sup> 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).

K0 and K' values for galena (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: K*PbBi*2*S4* = (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. Sb3<sup>+</sup> LEP's stereochemical activity is generally higher than that of Bi3<sup>+</sup>, 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 Sb3<sup>+</sup> polyhedra with respect to those of Bi3+, 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].

Pb2<sup>+</sup> also contains a LEP, but it is generally less expressed than that of Bi3<sup>+</sup>. LEP of Pb2<sup>+</sup> is even fully suppressed in several structures, like in galena or the earlier mentioned PbSc2S4. To the best of our knowledge the only observed regular coordination of Bi3<sup>+</sup> is the octahedral coordination in the mineral kupcikite, Cu4Bi5S10 [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 Bi2S3 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 NaAlSiO4 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 K0, with K' fixed to 4, of MgAl2O4 measured by Yutani et al. [44] was 241(1) GPa, whereas K0 measured for Fe3O4 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 (36.58cm3/mol for NaAlSiO4, 36.13 cm<sup>3</sup>/mol for MgAl2O4 and 41.89 cm3/mol for Fe3O4), seems to be followed by this group of calcium ferrite structures [20]. In comparison, galenobismutite has a higher molar volume (105.0 cm3/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.
