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

Short answer

(d) Smaller cations occupy the position of fluoride ions and larger anions that of 9Ca^{2+} ions.

Step-by-step solution

Understanding Antifluorite Structure

In an antifluorite structure, the arrangement is the inverse of the fluorite structure. This means that the positions of cations and anions are switched compared to the regular fluorite structure. Fluorite structures typically have cations occupying the face-centered cubic (FCC) lattice positions, while anions occupy tetrahedral sites.

Fluorite Structure Positions

In a standard fluorite structure, the larger cations (9Ca^{2+}) occupy the face-centered cubic positions, and the anions (9F^{-}) fill all the tetrahedral sites within the crystal lattice. This arrangement is reversed in an antifluorite structure.

Antifluorite Reversal

In an antifluorite structure, smaller cations now occupy the positions that anions (9F^{-}) previously held in the fluorite structure, and larger anions take the positions that cations (9Ca^{2+}) occupied. Therefore, the correct depiction matches description (d): smaller cations occupy the position of fluoride ions, and larger anions take the position of 9Ca^{2+}.

Key concepts

Fluorite Structure

The fluorite structure, also commonly known as the calcium fluoride (CaF\(_2\)) structure, is a unique crystalline arrangement. It consists of a face-centered cubic (FCC) lattice where the larger cations occupy the main cubic positions. Meanwhile, the smaller anions fill the tetrahedral sites within the cubic arrangement.

This structure is renowned for its efficient packing of ions, which leads to a high coordination number. In this setup:

• The larger cations, such as Ca\(^{2+}\), are positioned at the corners and face centers of the cubic unit cell.
• The smaller anions, such as F\(^{-}\), are located in all tetrahedral voids, where they are surrounded by four cations.

Thus, in a fluorite structure, each anion is equidistantly placed within a tetrahedral arrangement formed by the surrounding cations, ensuring a balanced, stable structure.

Reverse Fluorite

The reverse fluorite structure, often referred to as the antifluorite structure, flips the arrangement seen in regular fluorite structures. Instead of larger cations, it is the larger anions that become central to the crystalline lattice. This reversal is a structural swap where cation and anion positions are exchanged.

In antifluorite structures:

• Smaller cations take the roles originally held by anions in the fluorite setup, occupying the tetrahedral sites.
• Larger anions fill the face-centered cubic positions that were occupied by cations in the fluorite structure.

This interchange leads to a similar geometric framework, but with the positions of ions effectively reversed. Therefore, this structure shows how versatile crystal lattices can be, providing varied ionic arrangements by simply reorganizing the positions of the component ions.

Cation and Anion Positions

The arrangement of cations and anions within a given lattice is crucial for determining the physical properties of a crystalline solid. In both fluorite and antifluorite structures, understanding the specific placements of these ions helps to predict the material's stability and interionic interactions.

In a typical fluorite structure:

• Cations, which are generally larger, occupy face-centered positions, creating the backbone of the crystal's framework.
• Anions fill the spaces between these cations in tetrahedral sites, optimizing the use of space in the lattice.

On the other hand, in the reverse or antifluorite structure:

• The smaller cations move into the tetrahedral positions, which were originally occupied by anions.
• The larger anions take the face-centered cube positions of the earlier cations, illustrating a direct positional switch.

These arrangements are guided by size, charge balance, and the desire to minimize repulsion between similarly charged ions, aiming for maximum stability and order within the crystalline lattice.