Problem 90 - A Complete Resource Book in Chemistry for JEE Main

Question

\(\mathrm{M}_{2} \mathrm{X}\) have a structure closely related to that of fluorite. It is actually reverse of fluorite structure hence called antifluorite structure. In such a structure (a) \(\mathrm{F}^{-}\)ions occupy all the 8 octahedral voids (b) each \(\mathrm{F}^{-}\)is surrounded by \(4 \mathrm{Ca}^{2+}\) in tetrahedral arrangement (c) larger cations occupy the position of \(\mathrm{F}^{-}\)ions and smaller anions that of \(\mathrm{Ca}^{2+}\) ions. (d) smaller cations occupy the position of fluoride ions and larger anions that of \(\mathrm{Ca}^{2+}\) ions

Step-by-Step Solution

Answer

Option (c) is correct.

Step 1: Understanding the Problem

We need to understand the antifluorite structure, which is the inverse of the fluorite (CaF₂) structure. In an antifluorite structure, the positions of cations and anions are reversed compared to fluorite.

Step 2: Structure Analysis

In the antifluorite structure, larger cations occupy the positions where fluoride ions (2- ions in fluorite) would be, and the smaller anions occupy the positions where the larger calcium ions (Ca^{2+}+ ions in fluorite) would be.

Step 3: Evaluating the Options

(a) F^{-}- ions do not occupy octahedral voids in the antifluorite structure; M^{2+}+ cations do. (b) In antifluorite, each X^{2-}- surrounds the smaller cations in a tetrahedral arrangement, whereas the statement incorrectly describes the F^{-}- case. (c) This correctly describes the inversion of roles in antifluorite: larger cations occupy F^{-}- positions, and smaller anions take Ca^{2+}+ positions. (d) This statement is incorrect because it reverses the correct occupancy roles in antifluorite.

Step 4: Final Decision

The correct choice among the options is (c), where larger cations take the positions of F^{-}- ions and smaller anions occupy those of Ca^{2+}+ ions, accurately describing this reversal.

Key Concepts

Fluorite Structure

The fluorite structure is a well-known arrangement in solid-state chemistry. It is characterized by a specific pattern in how cations and anions are arranged.
This structure is prominently observed in calcium fluoride \( \text{CaF}_2 \) where each calcium ion is surrounded by fluorine ions.

• In this arrangement, the \( \text{Ca}^{2+} \) cations are placed at the corners of a cube.
• Meanwhile, the \( \text{F}^{-} \) anions are located at the centers of the tetrahedral-shaped voids.

The result is that each \( \text{Ca}^{2+} \) ion is coordinated to eight \( \text{F}^{-} \) ions, and each \( \text{F}^{-} \) ion is surrounded by four \( \text{Ca}^{2+} \) ions. This structure creates a robust and stable crystal.

Cations and Anions Positions

In crystal structures like fluorite and antifluorite, the positions of cations and anions significantly affect the material's properties.
In a typical fluorite structure:

• The larger cation occupies a position surrounded by several anions.
• The smaller anions fill in the voids around the central cation, creating a lattice structure.

However, in an **antifluorite** structure, these roles are reversed:

• The larger ion, now an anion, occupies positions that were once held by the cations in the fluorite pattern.
• The smaller ions, being cations, fill the voids initially occupied by anions.

This inversion leads to changes in the overall structure, maintaining stability while flipping the locations of ions.

Octahedral and Tetrahedral Voids

Voids in crystals are spaces where atoms do not completely fill the structure, and they come in octahedral and tetrahedral varieties.
In the fluorite structure, tetrahedral voids are of particular interest:

• Tetrahedral voids are smaller spaces surrounded by four atoms. In CaF2, these spaces are filled by fluoride ions.
• Octahedral voids have six surrounding atoms and are present in the planer layer of some crystals.

In an antifluorite structure, the similarity continues, but roles are switched:

• Larger cations occupy what would have been octahedral voids if they were not filled.
• Smaller anions find themselves in the compact spaces of tetrahedral voids.

Understanding these voids is crucial for comprehending the overall spatial arrangement in various crystal structures.

Inversion Roles in Crystal Structures

The concept of inversion in crystal structures, such as the transition from fluorite to antifluorite, provides fascinating insights into crystallography.
Consider the following:

• In a fluorite structure, cations and anions have specific positions dictated by size and charge.
• The inversion to an antifluorite structure involves these ions swapping their respective roles, leading to a "role reversal" in position.

This inversion is more than just a positional swap;

• It demonstrates how similar properties can be retained despite structural changes.
• It affects physical properties, such as conductivity and density, by altering how ions interact within the crystal lattice.

By studying these role inversions, scientists can manipulate material properties, utilizing crystal structures for advanced technological applications.