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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?

Short Answer

Expert verified
Answer: The Fe虏鈦 ions will occupy the octahedral interstitial sites in the HCP arrangement of S虏鈦 ions, and the fraction of available interstitial sites occupied by Fe虏鈦 ions will be 1, or 100% of available sites.

Step by step solution

01

Review Hexagonal Close-Packed (HCP) Structure

In the HCP structure, atoms (in this case, S虏鈦 ions) occupy the vertices of hexagonal layers, where there are two types of interstitial sites: tetrahedral (T) and octahedral (O) sites. Tetrahedral sites exist between four ions forming a tetrahedron, and octahedral sites occur between six ions forming an octahedron. In HCP, there are 2 tetrahedral sites per ion and 1 octahedral site per ion.
02

Determine the Interstitial Site Occupied by Fe虏鈦 Ions

Since the Fe虏鈦 ions need to stabilize the S虏鈦 ions, we must consider the ionic sizes and charges. The Fe虏鈦 ion has a smaller size than the S虏鈦 ion. However, they have a higher positive charge than the negative charge on the S虏鈦 ion. Therefore, the Fe虏鈦 ions prefer to occupy octahedral sites in the HCP structure, as the octahedral sites provide better charge stabilization for the S虏鈦 ions due to closer proximity.
03

Calculate the Fraction of Occupied Octahedral Sites

Now, we need to find the fraction of available octahedral sites that will be occupied by Fe虏鈦 ions. In the HCP structure, there is 1 octahedral site per ion. So, the total number of available octahedral sites will be the same as the number of S虏鈦 ions present, which is 1 site per S虏鈦 ion. The FeS compound has a 1:1 ratio of Fe虏鈦 and S虏鈦 ions. This means that 1 Fe虏鈦 ion is present for every S虏鈦 ion. As mentioned earlier, the Fe虏鈦 ions will occupy the octahedral sites. So every octahedral site available will have a corresponding Fe虏鈦 ion. Therefore, the fraction of octahedral sites occupied by Fe虏鈦 ions will be 1 (or 100% of the available space). (a) The Fe虏鈦 ions will occupy the octahedral interstitial sites in the HCP arrangement of S虏鈦 ions. (b) The fraction of available interstitial sites occupied by Fe虏鈦 ions will be 1, or 100% of available sites.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Hexagonal Close-Packed Structure
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.
Octahedral and Tetrahedral Sites
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 鈥 a structure with eight faces. In the exercise, iron ions (Fe虏鈦) 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 Fe虏鈦 ions fully occupy these sites to maintain charge balance and spatial harmony within the crystal lattice.
Ionic Crystal Structures
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 (S虏鈦) creating a hexagonal pattern and the positively charged iron ions (Fe虏鈦) 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.

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