Pyrite

3.2 Structural optimisation and working surfaces

3.2.1 Pyrite

Figure 3.8: Total energy against k-points mesh for ZnS structure.

Figure 3.9: Bulk unit cell of FeS2

Table 3.1: Structural parameters of optimised bulk FeS2 compared with experimental values.

Property Value (Å) Population Literature (Å)

Unit cell length(a=b=c) 5.414 5.406^a

Fe–S bond 2.560 0.35 2.23–2.30^a

Fe-Fe bond 3.827 - 3.808

S–S bond 2.196 0.22 2.14–2.17^a

a [68],

The Pyrite (FeS2) structure crystallises in the cubic system with space group Pa3, as shown in Figure 3.9. It possesses a lattice constant of 5.414 Å and one cell contains four FeS2 units. The cation Fe²⁺ is in octahedral coordination with six dianions (S22–) while each anion is tetrahedrally coordinated to three Fe ions and one other anion.

We note that our calculated results are consistent with the experimental values (<1%

difference), suggesting the reliability of the approach employed in this study. Fe-S coordination has equivalent six bonds with the lengths of 2.560 Å, while S–S and Fe- Fe have lengths of 2.196 Å and 3.827 Å, respectively. Moreover, we noted that the octahedral Fe-Fe share a common corner. Goodenough [69] reported that the interactions between two octahedral cations will be cation-anion-cation interactions if

the two octahedra share a common corner but cation-cation interactions if the two octahedra share a common edge. The Mulliken bond population result shows values of 0.22 and 0.34 for the S–S interactions and Fe–S, respectively. The population in the Fe–S region is greater than that in the S–S region, indicating stronger covalent interaction between Fe and S atoms

Table 3.2: Calculated and experimental surface energies (J/m²) for pyrite mineral.

MI Value

(J/m²)

Literature (J/m²) [70]

100 1.04 1.06

110 1.68 1.68

111 1.40 1.40

210 1.66 1.50

In Table 3.2 we present the calculated and experimental surface energies for the pyrite mineral. The surface energy we calculated according to equation 2.13. Similarly, to the lattice constant and population value, we note a good agreement between our calculated and experimental results. The lower the surface energy, the more stable is the surface. We note that the (100) terminated surface is the most stable, followed by the (111), (210) and (110), respectively. Furthermore, we note that the order of stability obtained in this work matches with the data in the literature. It is worth noting that the DFT treatment of surfaces in this study is more rigorous, and the predicted surface energies are more stable. This was also based on the report that during the first stage of flotation where mineral particles are crushed, the minerals will mainly cleave along surfaces that have large inter-planar spacing and few inter-planar bonds, usually low- index surfaces with low surface energies under dry conditions [71].

Since the surface free energy of FeS2 can be expressed as a function of the Wulff- constructions facets, the obtained construction should also be related to the three- dimensional equilibrium shapes of FeS2. The exposed surfaces are labelled accordingly. In Figure 3.12 we show that the shape of the FeS2 crystal is a truncated octahedron, covered by the (100) and (111) surfaces. Furthermore, the (100) terminating the apices of the octahedron has higher surface ratio than (111) at the

surface of the octahedron. There is no significant change in structure for the most stable surface before and after optimisation (see Figure 3.11). There is no visible appearance of other surfaces. On this basis, the (100) terminated surface will be used as the pyrite working surface. A side-on view of a 15-layer, 2x2 supercell of the pyrite working surface and a top-down-net of the same are shown in Figure 3.11.

Figure 3.10: Wulff construction of FeS2 surfaces

Figure 3.11: Pyrite FeS₂ (100) surface: (a) Before being relaxed and (b) Fully being relaxed. The electron density of pyrite (100) surfaces: (c) unrelaxed and (d) relaxed.

(a)

(c)

(b)

(d)

Figure 3.12: Water adsorbed on the FeS2 (100) surface

Before the reagent adsorption, water molecules were placed on the FeS2 (100) surfaces to investigate the effect of water on the surface properties. The optimised geometry configurations are shown in Figure 3.12. To discuss the influence of water adsorption on the surface properties of FeS2, the bond populations and lengths and Mulliken charges between FeS2 atoms are listed in Table 3.3 to Table 3.4.

Table 3.3: Pyrite Mulliken bonding population of atoms in the absence and in the presence of H2O molecule(s) on the surface.

Bond Population length

FeS₂(100)

In the absence of water

molecule

S3 - Fe1 0.48 2.176

S4 – Fe1 0.51 2.219

S3 - Fe2 0.52 2.221

S5 - Fe2 0.49 2.164

In the presence of water

molecule

S3 - Fe1 0.54 2.244

S4 – Fe1 0.49 2.181

S3 - Fe2 0.45 2.201

S5 - Fe2 0.44 2.241

We note that the Mulliken atomic charges populations on the FeS2 surfaces layers before and after H2O absorption are different. The charge of Fe1 atom increases from 0.07e to 0.15e, while the charge of Fe2 reduces from 0.07e to 0.02e, indicating Fe1 becomes more positive and Fe2 more negative. On the other hand, we note that the charges of S1 and S2 become more negative. This shows that the Fe atoms lose electrons while S atoms gain more after the adsorption of the water molecule.

Table 3.4: Mulliken charge populations before and after H2O adsorption on the pyrite surface (s, p and d are the orbitals).

s p d total q/e

FeS₂(100)

In the absence of water molecule

Fe1 0.34 0.44 7.14 7.93 0.07

S1 1.86 4.25 0 6.1 -0.1

S2 1.82 4.2 0 6.02 -0.02

Fe2 0.35 0.44 7.14 7.93 0.07

S1 1.82 4.2 0 6.02 -0.02

S2 1.86 4.25 0 6.1 -0.1

In the presence of water molecule

Fe1 0.33 0.43 7.09 7.85 0.15

S1 1.85 4.29 0 6.15 -0.15

S2 1.84 4.32 0 6.16 -0.16

Fe2 0.35 0.49 7.14 7.98 0.02

S1 1.81 4.17 0 5.98 0.02

S2 1.84 4.3 0 6.15 -0.15

For FeS2, the atomic relaxation on the top layer of the surface is not very remarkable.

However, it is worth noting that the displacement of surface atoms is greater after the surface atoms were reacted with the H2O molecule, i.e., Fe1, Fe2, S1 and S2, is much greater than that of the other surface atoms.

We note that the S4 – Fe1, S3 - Fe2 and S5 - Fe2 bond population decrease after water adsorption, while it increases between the S3 - Fe1 bond. This indicates that

water adsorption generally reduces the covalent bonding between Fe and S atoms in FeS2.