Question

Consider the crystal structure shown in the figure, where black and grey spheres represent atoms of two different elements and \(a\) denotes the lattice constant. The Bravais lattice for this structure is: 

• A. Simple cubic
• B. Face-centered cubic
• C. Body-centered cubic
• D. Triclinic

Hint:

A cubic lattice with atoms at each face center is always an FCC structure. Corner + face-center positions = 4 atoms per unit cell.

Answer 1

The Correct Option is B

Step 1: Observe the structure.
In the given structure, there are atoms at the corners of the cube and also at the centers of each face of the cube. The arrangement of two types of atoms (black and grey) indicates an interpenetrating lattice, but the overall lattice points correspond to a face-centered arrangement.

Step 2: Identify the Bravais lattice.
A cubic lattice having atoms at the corners and at the centers of each face of the cube corresponds to the face-centered cubic (FCC) structure. Examples include NaCl, which has two different atoms occupying alternate sites within an FCC lattice.

Step 3: Conclusion.
Hence, the Bravais lattice of the given crystal is Face-centered cubic.