Iron sulfide (FeS) may form a crystal structure that consists of an HCP arrangement of \(\mathrm{S}^{2-}\) ions. (a) Which type of interstitial site will the \(\mathrm{Fe}^{2+}\) ions occupy? (b) What fraction of these available interstitial sites will be occupied by \(\mathrm{Fe}^{2+}\) ions?

The hexagonal close-packed (HCP) structure is a highly efficient way of arranging spherical atoms or ions in a crystalline solid. Imagine stacking layers of spheres in a way that the spheres in one layer nestle into the spaces of the layer below, much like how oranges are stacked in a grocery store. In the HCP structure, each atom touches six atoms in its own layer, three in the layer above, and three in the layer below.

Due to this arrangement, HCP offers very little empty space and is found in metals like magnesium and titanium, and as seen in the exercise, ionic compounds like iron sulfide (FeS). The unique geometry of HCP also results in two main types of interstitial sites, tetrahedral and octahedral, which provide 'homes' for smaller atoms or ions amidst the larger lattice formed by the spherical ions or atoms.

Within the compact structure of hexagonal close packing, the interstitial sites are the nooks where atoms smaller than the main HCP constituents can fit. These sites are categorized as tetrahedral and octahedral based on the arrangement of surrounding atoms.

Tetrahedral Sites

Imagine four atoms or ions that form a sort of 'pyramid' with a triangular base; this is the tetrahedral site. There are two of these sites associated with each atom in an HCP structure, lending potential spaces for smaller cations to maintain the crystal's stability and neutrality.

Octahedral Sites

On the other side, the octahedral site is coordinated by six atoms or ions, shaping like an octahedron – a structure with eight faces. In the exercise, iron ions (Fe²⁺) were considered for these sites due to their charge and size fit. Each atom has one octahedral site associated with it, and in FeS, the Fe²⁺ ions fully occupy these sites to maintain charge balance and spatial harmony within the crystal lattice.

In ionic crystals, the structure is determined by the electrostatic attractions between cations and anions, promoting the formation of a repeating pattern that minimizes energy and maximizes stability. In our exercise, iron sulfide (FeS) forms such a structure, with the negatively charged sulfide ions (S²⁻) creating a hexagonal pattern and the positively charged iron ions (Fe²⁺) filling the octahedral interstitial sites.

The beauty of these structures lies in their predictability. An optimal ratio of cations to anions leads to a definite filling pattern of the interstitial sites, which is essential to predicting properties like electrical conductivity, magnetism, and strength. For FeS, the crystal achieves stability with a 1:1 stoichiometric ratio, fully occupying the available interstitial sites. This knowledge helps chemists and material scientists tailor materials for specific applications, exploiting the orderly nature of these ionic compounds.