*3.2. 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.

**Figure 5.** Evolution of the bond distances with pressure for M1 (**a**), M2 (**b**), M3(**c**) polyhedra.

**Figure 6.** Variation of polyhedral volume for M1 (**a**), M2 (**b**), M3 (**c**) polyhedra with pressure.

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 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.

**Figure 7.** Asphericity (**a**), Eccentricity (**b**) and shape distortion (**c**) evolution with pressure for M1, M2, and M3 polyhedra.

**Figure 8.** Galenobismutite at room pressure (**a**) and at 20.9 GPa (**b**). Black spheres are centered on centroids of coordinations and indicate the orientations of M1, M2 and M3 lone electron pairs.

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.
