Question

The reciprocal lattice for a body centered cubic crystal is:

• A. body centered cubic crystal
• B. face centered cubic crystal
• C. simple cubic crystal
• D. diamond structure

Hint:

Remember the reciprocal lattice pairings: SC \(\leftrightarrow\) SC (self-dual), and BCC \(\leftrightarrow\) FCC (dual to each other). This is a common factual question, and knowing this pairing saves you from having to perform the mathematical derivation during an exam.

Answer 1

The Correct Option is B

Step 1: Concept Overview:
The problem requires identifying the reciprocal lattice corresponding to a Body-Centered Cubic (BCC) direct lattice. The reciprocal lattice represents the Fourier transform of the direct lattice.
Step 2: Detailed Explanation:
Solid-state physics establishes a duality between cubic Bravais lattices. The reciprocal lattice is defined by vectors \(\vec{G}\) satisfying \( e^{i\vec{G} \cdot \vec{R}} = 1 \) for all direct lattice vectors \(\vec{R}\).
The established relationships are:


A Simple Cubic (SC) lattice's reciprocal lattice is also Simple Cubic (SC).
A Body-Centered Cubic (BCC) lattice's reciprocal lattice is Face-Centered Cubic (FCC).
A Face-Centered Cubic (FCC) lattice's reciprocal lattice is Body-Centered Cubic (BCC).

Step 3: Conclusion:
Therefore, the reciprocal lattice of a Body-Centered Cubic (BCC) crystal is a Face-Centered Cubic (FCC) crystal.