Question

In a cubic crystal, a plane makes intercepts \( 1,2,2 \) on the \( x, y, \) and \( z \) axes respectively. The Miller indices of that plane is

• A. (122)
• B. (121)
• C. (211)
• D. (212)

Hint:

To determine Miller indices, take the reciprocals of the intercepts and convert them into the smallest integer ratio by multiplying with the least common multiple (LCM) of the denominators.

Answer 1

The Correct Option is C

The Miller indices of a plane in a cubic crystal are determined by the following steps: Step 1: Write down the intercepts of the plane on the \( x, y, \) and \( z \) axes: \[ 1, 2, 2. \]

Step 2: Take the reciprocal of each intercept: \[ \frac{1}{1}, \frac{1}{2}, \frac{1}{2}. \]

Step 3: Convert these reciprocals into whole numbers by multiplying each by the least common multiple (LCM) of the denominators. The LCM of 1 and 2 is 2: \[ (2 \times 1, 2 \times \frac{1}{2}, 2 \times \frac{1}{2}) = (2,1,1). \] Thus, the Miller indices of the given plane are: \[ (2, 1, 1). \]