Question

Miller indices for a plane cutting x = a, y = ∞, z = c is:

• A. (1 0 1)
• B. (1 0 0)
• C. (1 1 1)
• D. (0 1 1)

Hint:

Miller indices represent the orientation of a crystal plane. If a plane cuts an axis at a finite distance and is parallel to another axis, the reciprocal of the intercept gives the corresponding Miller index.

Answer 1

The Correct Option is A

Miller indices are used to describe the orientation of a crystal plane in a lattice. The Miller indices are the reciprocals of the fractional intercepts of the plane with the crystallographic axes. For a plane cutting at \( x = a \), \( y = \infty \), and \( z = c \), the Miller indices are calculated by taking the reciprocal of these intercepts.
- The intercept on the \( x \)-axis is \( a \), so the reciprocal is \( \frac{1}{a} \). This gives a Miller index of 1 for the \( x \)-direction.
- The intercept on the \( y \)-axis is infinite, so the reciprocal is zero, leading to a Miller index of 0 for the \( y \)-direction.
- The intercept on the \( z \)-axis is \( c \), so the reciprocal is \( \frac{1}{c} \), giving a Miller index of 1 for the \( z \)-direction.
Thus, the correct Miller indices for this plane are \( (1 0 1) \).