Problem 45 - A Complete Resource Book in Chemistry for JEE Main

Question

In the zinc blende structure \((\mathrm{ZnS}), \mathrm{S}^{2}\) adopt ccp arrangement and \(\mathrm{Zn}^{2+}\) occupy (a) Alternate tetrahedral sites (b) Octahedral sites (c) Tetrahedral sites (d) Both octahedral and tetrahedral sites

Step-by-Step Solution

Answer

(c) Tetrahedral sites

Step 1: Understanding the structure

The zinc blende (or sphalerite) structure is a classic example of a cubic close-packed (ccp) system where sulfur atoms form the ccp arrangement, creating an organized lattice structure. This arrangement also forms voids or holes in the lattice, specifically tetrahedral and octahedral sites, which can be occupied by cations such as Zn.

Step 2: Identifying types of sites

In a ccp (fcc) lattice, every cube has: 4 tetrahedral sites and 1 octahedral site per atom of the lattice. Since \( ext{S}^{2-} \) ions form the ccp structure, the available sites for \( ext{Zn}^{2+} \) ions include both tetrahedral and octahedral sites.

Step 3: Determining the occupancy of sites by zinc ions

In the zinc blende structure, \( ext{Zn}^{2+} \) ions specifically occupy the tetrahedral sites only. In every zinc blende unit cell, half of the available tetrahedral sites are occupied by \( ext{Zn}^{2+} \) ions.

Key Concepts

Cubic Close-Packed (CCP) System

The cubic close-packed (CCP) system is a method of organizing atoms in a crystalline structure to achieve high density. In the CCP arrangement, also known as the face-centered cubic (FCC) structure, atoms are positioned at each of the eight corners and the centers of all the cube faces. This creates a highly efficient packing, often seen in metals and compounds like the zinc blende structure.
The advantage of a CCP system is its high packing efficiency. It maximizes the number of atoms that can occupy a given volume, ensuring that atoms are closely packed together. This close packing results in a coordination number of 12, meaning each atom is in contact with 12 others. Such a structure is not only robust but also allows for various types of voids that can be occupied by other atoms or ions.
In the case of zinc blende, sulfur atoms form the CCP lattice framework, providing vacant spaces that zinc ions can occupy. This demonstrates how the CCP system efficiently organizes atoms to form a stable and defined crystal lattice.

Tetrahedral and Octahedral Sites

In a cubic close-packed lattice, the arrangement of atoms creates interstitial spaces known as tetrahedral and octahedral sites. These voids are crucial because they allow for the incorporation of different ions and atoms within the crystal structure.

• Tetrahedral Sites: In a CCP lattice, for every atom, there are two tetrahedral sites available. These voids are formed between four atoms positioned at the vertices of a tetrahedron. Tetrahedral sites are smaller and tend to host smaller ions like the Zn²⁺ ions in the zinc blende structure.
• Octahedral Sites: In comparison, each atom provides one octahedral site. These sites are larger than tetrahedral sites and are formed by six atoms creating an octahedron. Although present, octahedral sites remain unoccupied in the zinc blende structure.

In the zinc blende structure, Zn²⁺ ions occupy only half of the available tetrahedral sites. This specific arrangement maximizes the interaction between Zn²⁺ and S^2- ions, stabilizing the crystal structure.

Lattice Structure in Crystals

The lattice structure in crystals is a repeating arrangement of atoms, ions, or molecules in three-dimensional space. This organization forms the fundamental framework of any crystal and dictates its properties. A lattice structure can be visualized as a series of points extending infinitely in all directions.
Understanding lattice structures is crucial for studying solid-state chemistry and materials science. The nature of the lattice determines how atoms interact, how the crystal can deform, and how energies propagate through the material. In crystalline solids like zinc blende:

• The repeating pattern increases structural stability and uniformity.
• It defines the crystal's symmetry, influencing physical properties such as strength and conductivity.
• Knowledge of the lattice structure allows for the prediction and explanation of its chemical reactivity and other characteristics.

In zinc blende, the lattice consists of a CCP arrangement of sulfur atoms with zinc ions filling the tetrahedral voids. This specific interaction between the lattice and the ions ensures the compound's distinctive properties. It exemplifies how lattice structures are integral to a crystal's composition and behavior.