Question

\(\mathrm{Na}_{2} \mathrm{O}\) has antifluorite structure. The coordination number of oxide ion is

Short answer

The coordination number of oxide ion in an antifluorite structure is 4.

Step-by-step solution

Understanding the Antifluorite Structure

In the antifluorite structure, the positions of the cations and anions are reversed compared to the fluorite structure. In the fluorite structure, calcium ions occupy the lattice points, and fluoride ions fill the tetrahedral voids. In the antifluorite structure, the oxide ions form a face-centered cubic (FCC) lattice, while the metal cations (such as Na in Na2O) occupy the tetrahedral voids.

Identifying the Coordination Number

Coordination number refers to the number of nearest neighboring atoms or ions immediately surrounding a central atom in a crystal or structure. In the antifluorite structure, since the oxide ions form an FCC lattice, each oxide ion is coordinated to the surrounding sodium ions that occupy the tetrahedral sites.

Counting the Neighboring Ions

In a face-centered cubic structure, each ion in the tetrahedral voids is surrounded by 4 ions in an antifluorite structure. The oxide ion in such a structure is surrounded by four sodium ions, because tetrahedral sites are filled.

Key concepts

Coordination Number

In any crystal structure, the coordination number is crucial in determining how the atoms or ions are arranged. Simply put, the coordination number is the number of nearest neighbors that a central atom or ion has. It provides insights into the geometry and stability of the structure.

For example, in the antifluorite structure of \({\mathrm{Na}_2\mathrm{O}}\), the coordination number of an oxide ion is 4. This indicates that each oxide ion is surrounded by four sodium ions. Understanding the coordination number helps to predict the physical properties and behaviors of the material. More neighbors typically mean a more stable structure, due to the stronger interactions.

Oxide Ions

Oxide ions are negatively charged ions, represented as \(\mathrm{O}^{2-}\). These ions play an essential role in determining the structure type of the compound, particularly in structures like antifluorite.

In an antifluorite structure, the oxide ions form a face-centered cubic (FCC) lattice. This implies that the oxide ions are arranged in such a way that each corner and each face center of the cube is occupied by an oxide ion.

The arrangement of these oxide ions is significant because it determines the positions available for the metal cations, which in turn influences the material's properties. Oxide ions provide the negative charge needed to balance the positive charge of metal cations like sodium.

Face-Centered Cubic Lattice

The face-centered cubic (FCC) lattice is one of the most common types of structures in crystallography. In an FCC lattice, atoms or ions are located at each corner and the center of each face of the cube. This arrangement is dense and efficient, maximizing space usage.

In the context of the antifluorite structure of \({\mathrm{Na}_2\mathrm{O}}\), the oxide ions form this FCC lattice.

• Each unit cell contains a face-centered cube of oxide ions, which establishes the framework of the structure.
• This framework then dictates the available voids or spaces where the other ions, specifically the cations, can fit.

This kind of structure contributes to the high coordination number, allowing each oxide ion to be surrounded by multiple cations, thus stabilizing the crystal.

Tetrahedral Voids

Tetrahedral voids are small spaces or gaps in a crystal lattice that are surrounded by four atoms or ions. These voids are significant because they can host smaller ions or atoms in the lattice, enhancing the structural stability.

In the antifluorite structure, such as that of \({\mathrm{Na}_2\mathrm{O}}\), the metal cations (sodium ions) occupy these tetrahedral voids.

• This means each sodium ion is surrounded by four oxide ions, fitting snugly into a space created by the FCC arrangement of oxide ions.
• The occupation of tetrahedral voids by sodium ions leads to each oxide ion having a coordination number of 4, surrounded as it is by four sodium ions.

The filling of these voids is essential for compensating the charge differences and for maintaining a stable crystal structure.