Question:
Which one of the following crystallographic planes represent \( (101) \) Miller indices of a cubic unit cell?
Which one of the following crystallographic planes represent \( (101) \) Miller indices of a cubic unit cell?
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To identify crystallographic planes, remember that Miller indices \( (hkl) \) describe the plane's intersections with the unit cell axes. A zero in an index means the plane is parallel to that axis.
Updated On: Dec 12, 2025
- A
- B
- C
- D
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The Correct Option is B
Solution and Explanation
Step 1: Understanding Miller indices.
Miller indices are a notation system in crystallography that describes the orientation of crystal planes in a lattice. The indices are represented as \( (hkl) \), where \( h \), \( k \), and \( l \) are the intercepts of the plane with the axes of the unit cell. The plane \( (101) \) intersects the x-axis at 1, the y-axis at infinity, and the z-axis at 1.
Step 2: Identifying the correct plane.
The \( (101) \) Miller indices represent a plane that intersects the x and z axes but is parallel to the y-axis. Option (A) correctly shows this plane orientation in a cubic unit cell.
Step 3: Conclusion.
Therefore, the correct answer is (A), as it accurately represents the \( (101) \) Miller indices.
Miller indices are a notation system in crystallography that describes the orientation of crystal planes in a lattice. The indices are represented as \( (hkl) \), where \( h \), \( k \), and \( l \) are the intercepts of the plane with the axes of the unit cell. The plane \( (101) \) intersects the x-axis at 1, the y-axis at infinity, and the z-axis at 1.
Step 2: Identifying the correct plane.
The \( (101) \) Miller indices represent a plane that intersects the x and z axes but is parallel to the y-axis. Option (A) correctly shows this plane orientation in a cubic unit cell.
Step 3: Conclusion.
Therefore, the correct answer is (A), as it accurately represents the \( (101) \) Miller indices.
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