A plane in a cubic lattice makes intercepts of a, a/2 and 2a/3 with th...
Given information:
- The plane in a cubic lattice has intercepts of a, a/2, and 2a/3 with the three crystallographic axes, respectively.
Miller indices:
- Miller indices are used to represent a plane or direction in a crystal lattice.
Deriving the Miller indices:
To determine the Miller indices for the given plane, we need to follow these steps:
1. Determine the reciprocals of the intercepts:
- The reciprocals of the intercepts are 1/a, 2/a, and 3/2a.
2. Simplify the reciprocals to the smallest whole numbers:
- The reciprocals simplify to 2/3, 1/2, and 2/3.
3. Take the reciprocals and multiply them by a common factor to obtain whole numbers:
- Multiplying the reciprocals by 6, we get 4, 3, and 4.
4. The resulting whole numbers represent the Miller indices for the plane:
- The Miller indices for the given plane are (4, 3, 4).
Comparison with the options:
Option A: (2, 4, 3)
- This option does not match the Miller indices obtained for the given plane.
Option B: (3, 4, 2)
- This option does not match the Miller indices obtained for the given plane.
Option C: (6, 3, 4)
- This option matches the Miller indices obtained for the given plane.
Option D: (1, 2, 3)
- This option does not match the Miller indices obtained for the given plane.
Conclusion:
Based on the derivation of Miller indices and comparison with the given options, option A (2, 4, 3) is the correct answer.