Question

The figure below shows a plane PQR in a unit cell. The Miller indices of the plane PQR is: 

• A. \( (432) \)
• B. \( (43\overline{2}) \)
• C. \( (234) \)
• D. \( (\overline{2}34) \)

Hint:

To find Miller indices, take the reciprocals of the intercepts of the plane with the axes, and simplify to integers. Ensure that any fractions are converted to integers by multiplying by appropriate factors. Remember that negative intercepts are represented with a bar over the number.

Answer 1

The Correct Option is B

The Miller indices are determined by the intercepts of the plane with the axes in the unit cell. To find the Miller indices for the plane PQR, follow these steps:
1. Identify the intercepts: From the diagram, the intercepts of the plane with the unit cell are:
- The plane cuts the \( a \)-axis at \( 1/2 \),
- The plane cuts the \( b \)-axis at \( 2/3 \),
- The plane cuts the \( c \)-axis at \( -1 \) (negative intercept).
2. Reciprocal of intercepts: The Miller indices are the reciprocals of these intercepts:
- The reciprocal of \( 1/2 \) is \( 2 \),
- The reciprocal of \( 2/3 \) is \( 3/2 \), which can be written as 3 (since we multiply both the numerator and denominator by 2),
- The reciprocal of \( -1 \) is \( -1 \).
3. Simplify and write in integer form: After finding the reciprocals, the Miller indices are written in their simplest integer form. In this case, the Miller indices of the plane are \( (43\overline{2}) \).
Thus, the correct Miller indices for the plane PQR are \( (43\overline{2}) \), which corresponds to option (B).