Question

The direct lattices are given by \(a_1=(\hat{i}+\hat{j}+\hat{k})\), \(a_2=(3\hat{i}-2\hat{k})\), and \(a_3=(4\hat{i}+3\hat{j})\). Find out the reciprocal lattices \(b_1\), \(b_2\), and \(b_3\).

• A. \(b_1=2\pi(3\hat{i}-6\hat{j}+3\hat{k}),\ b_2=2\pi(3\hat{i}-\hat{j}+\hat{k}),\ b_3=2\pi(2\hat{i}-\hat{j}+\hat{k})\)
• B. \(b_1=2\pi(6\hat{i}-8\hat{j}+9\hat{k}),\ b_2=2\pi(3\hat{i}-4\hat{j}+\hat{k}),\ b_3=2\pi(-2\hat{i}+5\hat{j}-3\hat{k})\)
• C. \(b_1=2\pi(6\hat{i}-8\hat{j}+9\hat{k}),\ b_2=2\pi(2\hat{i}-3\hat{j}+3\hat{k}),\ b_3=2\pi(2\hat{i}-\hat{j}+\hat{k})\)
• D. \(b_1=2\pi(3\hat{i}-6\hat{j}+3\hat{k}),\ b_2=2\pi(3\hat{i}-4\hat{j}+4\hat{k}),\ b_3=2\pi(2\hat{i}-\hat{j}+\hat{k})\)

Hint:

Reciprocal lattice vectors are obtained using cross products of the direct lattice vectors.

Answer 1

The Correct Option is B