Pyrite (FeS2) forms NaCl-type crystals with Fe2+ ions occupying the positions of Na+, and S2 2- ions — Inorganic Chemistry — Solid State Chemistry Question
Pyrite (FeS2) Crystals
Pyrite (FeS2) forms NaCl-type crystals with Fe2+ ions occupying the positions of Na+, and S2 2- ions occupying the positions of the Cl– ions. The directions of the S-S bonds are alternating body-diagonal.
5.1 Fe is octahedrally coordinated by sulfur atoms. What is the coordination of the sulfur atoms?
Model Answer
The sulphur atoms are coordinated by one sulphur atom and three Fe2+ ions in a distorted tetrahedral arrangement.
The density (ρ) of an ideal pyrite crystal is 5.011 g cm–3.
5.2 Calculate the lattice constant of the smallest cubic unit cell.
Model Answer
The smallest unit cell with a lattice constant of a0 contains 4 Fe and 8 S atoms. This leads to
ρ = (4 M(Fe) + 8 M(S)) / (NA a0^3) = 5.011 g cm-3
From this equation we obtain a0 = 541.8 pm.
It has been found that the lattice constant does not depend on the stoichiometry of the crystal, i.e., the lattice remains stable if the y in the formula FeSy deviates slightly from 2 within a small range (1.95 – 2.05).
5.3 Find the equation which gives the dependence of the density on y, assuming that only the iron content varies. Find a similar equation for the case when only the S content varies.
Model Answer
For varying iron content the calculations can be done as follows:
One mole of the crystal contains 8 mol S and 8/y mol Fe. Hence the relationship between the density of the crystal and the composition in the case of varying iron content is:
ρ = (8/y M(Fe) + 8 M(S)) / (NA a0^3) = 2.679/y + 4.667 g cm–3
For varying S content: one mole of the crystal contains 4 mol Fe and 4y mol S. Thus the dependence of density on y is:
ρ = (4 M(Fe) + 4y M(S)) / (NA a0^3) = 2.332 + 1.339y g cm–3
5.4 Plot the two curves in the same y – ρ coordinate system. Identify the following regions in the graphs: vacancies (Fe, or S deficiencies), interstitials (Fe, or S excess), perfect lattice.
In a natural pyrite sample it was found that only 99 % of the iron positions are occupied, and 1 % additional sulfur atoms are in interstitial positions.
5.5 Calculate the composition of the crystal. Find the corresponding point in the previously constructed y – ρ diagram.
Model Answer
In the unit cell of the natural pyrite sample, there is 4 × 0.99 = 3.96 mol Fe and 8 × 1.01 = 8.08 mol S. This gives y = 8.08 / 3.96 = 2.04. This is within the region where the unit cell parameter does not depend on the composition; therefore the density can be calculated from the available data.
ρ = (3.96 M(Fe) + 8.08 M(S)) / (NA a0^3) = 5.014 g cm–3
The (2.04, 5.014) point is given in the previous figure.