The figure below shows a cubic unit cell with lattice constant \(a\). The shaded crystallographic plane intersects the x-axis at 0.5a. The Miller indices of the shaded plane are:
The figure below shows a cubic unit cell with lattice constant \(a\). The shaded crystallographic plane intersects the x-axis at 0.5a. The Miller indices of the shaded plane are:
Show Hint
- (210)
(\(\={2}10\))
- (110)
- (102)
The Correct Option is A
Solution and Explanation
Step 1: Identify intercepts.
Given that the shaded plane cuts the x-axis at \(0.5a\) and is parallel to the y-axis, it does not intersect the y-axis (intercept is β). It also cuts the z-axis at \(a\).
Step 2: Express intercepts in terms of \(a\).
Intercepts = (0.5a, β, a).
Step 3: Take reciprocals of the fractional intercepts.
\[ \text{Reciprocals:} \ (2, 0, 1) \]
Step 4: Conclusion.
The Miller indices of the shaded plane are (210).
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