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GATE 2025 PH – Question 12

Solid State Physics · Elements of crystallography · 1 mark · Multiple choice

Consider a crystal that has a basis of one atom. Its primitive vectors are $\mathbf a_1=a\hat i$, $\mathbf a_2=a\hat j$, $\mathbf a_3=\frac a2(\hat i+\hat j+\hat k)$, where $\hat i,\hat j,\hat k$ are Cartesian unit vectors and $a$ is a positive constant. Which one is the correct option regarding the type of Bravais lattice?

  1. BCC; primitive volume $a^3/2$
  2. FCC; primitive volume $a^3/4$
  3. BCC; primitive volume $a^3/8$
  4. FCC; primitive volume $a^3$

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Show answer and explanation

Correct answer: (A) BCC; primitive volume $a^3/2$

Explanation

The third primitive vector reaches the body center. The scalar triple product is $a^3/2$, as required for BCC.