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 a notation system in crystallography for planes in crystal (Bravais) lattices. The question asks for the correct sequence of steps to determine these indices for a given plane.
Step 2: Detailed Explanation:
The correct procedure for determining Miller indices (hkl) is as follows:
1. Find the intercepts: Determine the points where the plane intersects the crystallographic axes (x, y, z). These intercepts are expressed as multiples of the lattice parameters (e.g., \(p a\), \(q b\), \(r c\)). This corresponds to step D.
2. Take the reciprocal: Take the reciprocals of the numerical parts of the intercepts (\(1/p\), \(1/q\), \(1/r\)). If a plane is parallel to an axis, its intercept is at infinity (\(\infty\)), and the reciprocal is zero. This corresponds to step A.
3. Simplify the fraction (Clear fractions): Multiply or divide the reciprocals by a common factor to reduce them to the smallest set of integers (h, k, l). This corresponds to step B.
4. Enclose in parentheses: Write the resulting integers in parentheses (hkl) without any commas. This is the Miller index of the plane. This corresponds to step C.
Step 3: Final Answer:
The correct sequence of steps is D, then A, then B, and finally C.