Question

Brillouin zone is:
A. Wigner-Seitz cell of reciprocal lattice
B. Primitive unit cell
C. The locus of all k-values in the reciprocal lattice which are Bragg reflected.
D. Wigner-Seitz cell of direct lattice
The correct statements are:

• A. A, B and D only
• B. A, B and C only
• C. A, B, C and D
• D. B, C and D only

Hint:

The key to understanding the Brillouin zone is to remember that it lives in "reciprocal space" or "k-space," not real space. It is the Wigner-Seitz cell of the reciprocal lattice, and its boundaries are directly related to the condition for Bragg diffraction.

Answer 1

The Correct Option is B

Step 1: Define the First Brillouin Zone. The First Brillouin Zone is a fundamental concept in solid-state physics used to describe electron wave propagation in a crystal lattice.
Step 2: Evaluate each statement. - A. Wigner-Seitz cell of reciprocal lattice: This is the standard definition of the First Brillouin Zone. The Wigner-Seitz cell is the region of space that is closer to one particular lattice point than to any other. When applied to the reciprocal lattice, this defines the Brillouin zone. This statement is correct. - B. Primitive unit cell: The First Brillouin Zone is, by its construction as a Wigner-Seitz cell, a primitive unit cell of the reciprocal lattice. It has the volume of one primitive cell. This statement is correct. - C. The locus of all k-values...which are Bragg reflected: The boundaries of the Brillouin Zone are defined by planes that are the perpendicular bisectors of the vectors connecting the origin of the reciprocal lattice to the nearest lattice points. These planes represent the wave vectors (\(k\)-values) that satisfy the Bragg condition for diffraction, \(2\mathbf{k} \cdot \mathbf{G} = |\mathbf{G}|^2\). Therefore, the zone represents the set of k-vectors that are not Bragg reflected, and its boundaries are where Bragg reflection begins. The statement is conceptually correct in linking the zone to Bragg reflection. - D. Wigner-Seitz cell of direct lattice: This is incorrect. The Wigner-Seitz cell of the *direct* lattice is a primitive cell in real space, not reciprocal space. The Brillouin zone is exclusively a concept of the reciprocal lattice.
Step 3: Conclude the correct statements. Statements A, B, and C are correct descriptions of the Brillouin zone. Statement D is incorrect. Therefore, the correct option includes A, B, and C only.