Problem 8 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

In which of the following crystals alternate tetrahedral voids are occupied? (a) \(\mathrm{NaCl}\) (b) \(\mathrm{ZnS}\) (c) \(\mathrm{CaF}_{2}\) (d) \(\mathrm{Na}_{2} \mathrm{O}\)

Step-by-Step Solution

Answer

(b) ZnS

Step 1: Understand Tetrahedral Voids

A crystal structure has different types of voids where smaller atoms or ions can fit. In a face-centered cubic (fcc) packing, for example, tetrahedral voids are formed in spaces surrounded by four atoms or ions.

Step 2: Identify Crystal Structures

Upon reviewing the given options: (a) NaCl has a rock-salt structure where neither tetrahedral nor octahedral voids are alternately occupied. (b) ZnS (Zinc Blende) has a structure wherein atoms adopt a cubic close-packed arrangement and alternate tetrahedral voids are indeed occupied by Zn ions. (c) CaF2 has a fluorite structure where each Ca ion is surrounded by F ions, but not via alternate tetrahedral voids. (d) Na2O has an antifluorite structure that does not involve alternate tetrahedral void occupation.

Step 3: Choose the Correct Crystal

From the analysis, only ZnS fulfills the condition where alternate tetrahedral voids are occupied in its ZnS (Zinc Blende) structure. This is because, in this structure, the Zn ions fill half of the available tetrahedral voids within the face-centered cubic (fcc) packing of sulfur ions.

Key Concepts

Tetrahedral Voids

In crystal structures, voids are essentially empty spaces between atoms. They provide room for smaller atoms or ions to fit snugly within the larger lattice structure. One particularly important kind of void is the tetrahedral void. To visualize this, imagine four atoms positioned in a way that their centers form the vertices of a tetrahedron. The space between these four atoms is what we call a tetrahedral void.

• These voids occur naturally in a face-centered cubic (fcc) or a hexagonal close packing (hcp) arrangement of atoms.
• Each atom in the lattice contributes to forming two tetrahedral voids.

These voids are smaller compared to other types, like octahedral voids. In many crystals, tetrahedral voids are filled by smaller cations if they fit well within the void without disrupting the overall stability of the lattice.

Face-Centered Cubic

The face-centered cubic (fcc) structure, also known as cubic close packing, is a common and highly efficient way for atoms to be arranged in a crystal. This structure is characterized by atoms at each corner of the cube and an additional atom at the center of each face of the cube.

• Fcc structures are tightly packed, maximizing the use of space. This contributes to the minimal energy arrangement, which is stable.
• Because of the high packing efficiency, the fcc lattice supports both tetrahedral and octahedral voids.

Within such a lattice, when ions or smaller atoms occupy tetrahedral voids, they inherently alter the electrical and mechanical properties of the material. This significant change is due to the efficient use of space and the resulting interactions between the ions or atoms.

Zinc Blende Structure

The zinc blende structure, found in compounds like ZnS, is a classic example of a crystal structure where alternate tetrahedral voids are occupied. This structure is known for its cubic close-packed (ccp) arrangement of larger ions.

• In zinc blende (ZnS), the sulfur atoms form the fcc lattice and the zinc atoms occupy half of the tetrahedral voids.
• Each zinc atom is surrounded by four sulfur atoms in a tetrahedral configuration, and vice versa.

This arrangement leads to a balanced and symmetrical structure, which results in specific physical properties:

• The Zn-S bond lengths are consistent, contributing to the stability of the crystal.
• It exhibits semiconductor properties, often used in technological applications like photodetectors and LEDs.

The filling of alternate tetrahedral voids is crucial in defining these tightly-linked properties and the replications of properties in similar structures.