Question

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: 

• A. (210)
• B. (\(\={2}10\))
• C. (110)
• D. (102)

Hint:

To find Miller indices, express intercepts as fractions of lattice constant, take reciprocals, and reduce to the smallest integers. Use a bar for negative intercepts.

Answer 1

The Correct Option is A

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 ∞). It also cuts the z-axis at \(a\). 
 

Step 2: Express intercepts in terms of \(a\). 
Intercepts = (0.5a, ∞, a). 
 

Step 3: Take reciprocals of the fractional intercepts. 
\[ \text{Reciprocals:} \ (2, 0, 1) \] Since the plane cuts the x-axis on the negative side (at -0.5a), we represent it as \(\={2}10\). 
 

Step 4: Conclusion. 
The Miller indices of the shaded plane are \(\={2}10\).