Question

The intercepts of a crystal face on the crystallographic axes are \( \infty a \), \( 2b \), and \( 3c \). Which one of the following is its Miller Index?

• A. \( (032) \)
• B. \( (023) \)
• C. \( (203) \)
• D. \( (320) \)

Hint:

When determining Miller indices, take the reciprocals of the intercepts and express them as the smallest whole numbers.

Answer 1

The Correct Option is A

The Miller Index is determined by the reciprocals of the intercepts of the crystal face along the crystallographic axes, and then converting them into the smallest integers. Given the intercepts \( \infty a \), \( 2b \), and \( 3c \): - The intercept along the \( a \)-axis is infinite, which means it is parallel to the \( a \)-axis, and thus the Miller index for this axis is 0. - The intercept along the \( b \)-axis is \( 2b \), which means the reciprocal is \( \frac{1}{2} \), so the Miller index for this axis is 2. - The intercept along the \( c \)-axis is \( 3c \), which means the reciprocal is \( \frac{1}{3} \), so the Miller index for this axis is 3. Thus, the Miller Index is \( (032) \). Thus, the correct answer is (A) \( (032) \).