Question

In which of the following pairs the cations occupy same type of site (a) Zinc blende, \(\mathrm{Na}_{2} \mathrm{O}\) (b) \(\mathrm{NaCl}, \mathrm{CsCl}\) (c) \(\mathrm{Na}_{2} \mathrm{O}, \mathrm{CaF}_{2}\) (d) \(\mathrm{CsBr}, \mathrm{ZnS}\)

Short answer

Pair (a) Zinc blende and \( \mathrm{Na}_{2}\mathrm{O} \) have cations occupying tetrahedral sites.

Step-by-step solution

Identify Crystal Structures

Understand the crystal structures involved in each pair: Zinc blende (ZnS) has a face-centered cubic structure where cations occupy tetrahedral sites; \( \mathrm{Na}_{2}\mathrm{O} \) has an antifluorite structure where \( \mathrm{Na}^+ \) ions also occupy tetrahedral sites. \( \mathrm{NaCl} \) structure involves octahedral sites, similar to \( \mathrm{CsCl} \) though they are different structurally due to the larger cesium ion altering the arrangement. \( \mathrm{CaF}_{2} \) has an inverse fluorite structure with calcium ions occupying cubic sites. \( \mathrm{CsBr} \) has a similar structure to \( \mathrm{CsCl} \) due to similar ionic sizes. Compare these characteristics for each pair.

Analyze Each Pair

Evaluate the site occupancy for cations for each pair: (a) Both Zinc blende and \( \mathrm{Na}_{2}\mathrm{O} \) have cations occupying tetrahedral sites. (b) In \( \mathrm{NaCl} \) and \( \mathrm{CsCl} \), the cations occupy octahedral sites, though with different arrangements. (c) In \( \mathrm{Na}_{2}\mathrm{O} \), cations occupy tetrahedral sites, whereas in \( \mathrm{CaF}_{2} \), they occupy cubic sites. (d) \( \mathrm{CsBr} \) and \( \mathrm{ZnS} \) do not share similar cation occupancy.

Select the Correct Pair

Based on the analysis, the correct pair where cations occupy the same type of site is pair (a), Zinc blende and \( \mathrm{Na}_{2}\mathrm{O} \), as both involve tetrahedral site occupancy for the cations.

Key concepts

Tetrahedral Sites

In crystallography, tetrahedral sites are positions within a crystal lattice that can host cations. In this arrangement, a cation is surrounded by four anions, placed at the corners of a tetrahedron. This setup is common in certain crystalline structures and can significantly influence the properties of the material.

For example, in the zinc blende structure, which is a form of ZnS, the zinc ions occupy these tetrahedral sites. Here, every zinc ion is surrounded by four sulfide ions forming a tetrahedral arrangement. Similarly, in the antifluorite structure of \( \mathrm{Na}_{2}\mathrm{O} \), each sodium ion is surrounded by four oxide ions, again forming a tetrahedral site.

Understanding which ions occupy tetrahedral sites is crucial in predicting the behavior of materials under various conditions such as pressure and temperature. It helps us recognize how these materials might interact chemically or physically with other substances.

Octahedral Sites

Octahedral sites are another vital aspect of crystal structures. These sites occur when a cation is surrounded by six anions at the vertices of an octahedron. This configuration is typical in many mineral deposits and is a significant factor in the material's stability and properties.

Taking the example of the rock salt structure (\( \mathrm{NaCl} \)), the sodium ions are situated in octahedral sites. Here, each sodium ion is coordinated by six chloride ions in an octahedral symmetry. Though \( \mathrm{CsCl} \), or cesium chloride, has a different structural arrangement due to the larger size of cesium ions, both involve cations in octahedral sites.

This arrangement is critical in understanding and predicting the mechanical aspects of materials, such as ionic conductivity and solubility. Recognizing octahedral sites helps in tailoring material characteristics for specific applications.

Cubic Sites

Cubic sites in crystal structures refer to positions in which cations or atoms are equidistant from their surrounding lattice points. This configuration forms a cube-like space within the crystal lattice. It is less common than tetrahedral and octahedral sites but is characteristic of some specific minerals and compounds.

For instance, in the \( \mathrm{CaF}_{2} \) structure known as fluorite, calcium ions occupy cubic sites. In this arrangement, each calcium ion is surrounded by eight fluoride ions arranged at the corners of a cube.

This type of site occupancy is significant in materials that require high ionic mobility, like in certain types of batteries. Understanding which ions occupy these cubic sites allows scientists and engineers to enhance material properties such as ionic conduction, which is crucial for the efficient functioning of solid-state devices.