Question

The shape of the first Brillouin zone of an FCC lattice is?

• A. Tetrahedral
• B. Triagonal
• C. Truncated hexagon
• D. Truncated octahedron

Hint:

The first Brillouin zone of an FCC lattice is a truncated octahedron, which is an important geometric feature used in understanding the electronic properties of FCC crystals. The structure of the Brillouin zone helps predict the behavior of electrons under different conditions.

Answer 1

The Correct Option is D

In solid-state physics, the concept of Brillouin zones is crucial for understanding the behavior of electrons in a crystal lattice. The Brillouin zone is defined as the set of points in reciprocal space that are closer to a given lattice point than to any other.
For an FCC (Face-Centered Cubic) lattice, the first Brillouin zone is obtained by constructing the Wigner-Seitz cell in reciprocal space. The Wigner-Seitz cell is essentially the region of space that is closer to a given lattice point than to any other. For FCC lattices, this shape takes the form of a truncated octahedron.
A truncated octahedron has 6 square faces, 8 hexagonal faces, and 12 edges. It can be thought of as an octahedron (a polyhedron with 8 triangular faces) where the corners have been truncated, resulting in the formation of square faces. This geometry is a key feature of the first Brillouin zone for FCC crystals.
Therefore, the correct shape of the first Brillouin zone of an FCC lattice is a truncated octahedron.