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: Understanding the Concept:
This question asks to identify the reciprocal lattice corresponding to a direct lattice with a Body-Centered Cubic (BCC) structure. The reciprocal lattice is the Fourier transform of the direct lattice.
Step 2: Detailed Explanation:
In solid-state physics, there is a fundamental duality between the main cubic Bravais lattices. The reciprocal lattice of a given Bravais lattice can be determined by finding the set of all vectors \(\vec{G}\) that satisfy \( e^{i\vec{G} \cdot \vec{R}} = 1 \) for all direct lattice vectors \(\vec{R}\).
The standard results for cubic lattices are:


The reciprocal lattice of a Simple Cubic (SC) lattice is another Simple Cubic (SC) lattice.
The reciprocal lattice of a Body-Centered Cubic (BCC) lattice is a Face-Centered Cubic (FCC) lattice.
The reciprocal lattice of a Face-Centered Cubic (FCC) lattice is a Body-Centered Cubic (BCC) lattice.

Step 3: Final Answer:
Based on this established duality, the reciprocal lattice for a Body-Centered Cubic (BCC) crystal is a Face-Centered Cubic (FCC) crystal.