Question

In an orthorhombic crystal, a lattice plane cuts intercepts of lengths \( 3a \), \( -2b \), and \( 3c/2 \) along three axes. The Miller indices of the plane are:

• A. \( (2 \ 3 \ 4) \)
• B. \( (1 \ 3 \ 4) \)
• C. \( (2 \ 3 \ 4) \)
• D. \( (3 \ 4 \ 2) \)

Hint:

Miller indices are found by taking reciprocals of the intercepts and clearing fractions.

Answer 1

The Correct Option is A

The Miller indices are found by taking reciprocals of the intercepts in terms of lattice constants:
\[ \frac{a}{3a}, \frac{b}{-2b}, \frac{c}{(3c/2)} \] This gives:
\[ \left(\frac{1}{3}, -\frac{1}{2}, \frac{2}{3} \right) \] Multiplying by 6 to clear fractions, we get:
\[ (2, 3, 4) \]