Question

The steps involved in determining the Miller indices are:
A. Take the reciprocal of these intercepts.
B. Simplify the fraction.
C. Enclose the obtained numbers into parentheses.
D. Find the intercepts of the plane on the crystallographic axes.
Choose the correct answer from the options given below:

• A. A, D, C, B
• B. A, B, D, C
• C. B, A, D, C
• D. D, A, B, C

Hint:

A useful mnemonic for the Miller indices procedure is "Intercepts \(\rightarrow\) Reciprocal \(\rightarrow\) Clear Fractions \(\rightarrow\) Parentheses". This ensures you always follow the correct order. Remember that an intercept at infinity corresponds to a Miller index of 0.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Miller indices are used in crystallography to identify planes within crystal lattices. The question requires arranging the steps for determining these indices in the correct order.
Step 2: Detailed Explanation:
The Miller indices (hkl) are determined by the following procedure:
1. Find the intercepts: Identify where the plane intersects the x, y, and z crystallographic axes, expressed as multiples of the lattice parameters (\(p a\), \(q b\), \(r c\)). This is step D.
2. Take the reciprocal: Calculate the reciprocals of the numerical coefficients of the intercepts (\(1/p\), \(1/q\), \(1/r\)). If the plane is parallel to an axis, the intercept is considered to be at infinity (\(\infty\)), and its reciprocal is zero. This is step A.
3. Simplify the fraction (Clear fractions): Reduce the reciprocals to the smallest set of integers (h, k, l) by multiplying or dividing by a common factor. This corresponds to step B.
4. Enclose in parentheses: Write the simplified integers within parentheses (hkl) to represent the Miller index of the plane. No commas are used. This corresponds to step C.
Step 3: Final Answer:
The correct sequence of steps is D, A, B, then C.