Question

A crystal plane of a lattice intercepts the principal axes \(\overrightarrow𝑎_1, \overrightarrow𝑎_2,\) and  \(\overrightarrow{a_3}\) at 3𝑎₁, 4𝑎₂, and 2𝑎₃, respectively. The Miller indices of the plane are:

• A. (436)
• B. (342)
• C. (634)
• D. (243)

Answer 1

The Correct Option is A

To find the Miller indices of a plane, we take the reciprocal of the intercepts of the plane on the axes and reduce them to the smallest integers.

Given the intercepts at \( 3a_1, 4a_2, 2a_3 \), the reciprocals are:

• \( h = \frac{1}{3} \)
• \( k = \frac{1}{4} \)
• \( l = \frac{1}{2} \)

To remove the fractions, multiply all values by 12 (the least common multiple):

• \( h = 4 \)
• \( k = 3 \)
• \( l = 6 \)

Conclusion:

Thus, the Miller indices of the plane are:

\[ (436) \]

Therefore, the correct answer is (A) (436).