Question

Consider a $fcc$ lattice made of a metal cation (M$^{6+}$) and three oxide anions per unit cell. The resultant structure would have

• A. 3D network of edge shared octahedra
• B. 3D network of corner shared octahedra
• C. 2D network of edge shared octahedra
• D. 2D network of corner shared octahedra
• E. 3D network of face shared octahedra

Hint:

A $MO_3$ stoichiometry in a cubic system typically signifies the $ReO_3$ structural type, which is a hallmark of 3D corner-shared octahedral networks.

Answer 1

The Correct Option is B

Concept: Solid-state framework dimensionality is determined by the sharing of coordination polyhedra within a unit cell.

Step 1: {Identify the stoichiometric ratio.}
The unit cell composition of one metal cation and three oxide anions establishes a $MO_3$ formula.

Step 2: {Determine coordination geometry.}
Each metal center is surrounded by six oxygen atoms, creating an $MO_6$ octahedral coordination environment.

Step 3: {Analyze the sharing mechanism.}
To satisfy the 1:3 ratio, each oxide anion is shared between two adjacent metal octahedra. This specific arrangement constitutes corner-sharing.

Step 4: {Establish dimensionality.}
The sharing occurs across the x, y, and z axes of the cubic lattice, resulting in an infinite 3D framework.