Question

In X-ray diffraction analysis, the condition for BCC crystal where the reflections are allowed is (where h, k, l are Miller indices):

• A. \( h + k + l \text{ is even \)
• B. \( h, k, l \text{ are all odd \)
• C. \( (h + k + l)/4 \text{ is odd \)
• D. \( h^2 + k^2 + l^2 = 0 \)

Hint:

For BCC structures, remember that only those planes for which \( h + k + l \) is even will produce a diffraction peak.

Answer 1

The Correct Option is A

In a Body-Centered Cubic (BCC) crystal structure, the reflection conditions in X-ray diffraction are derived based on structure factor calculations.
The structure factor for BCC is non-zero (i.e., reflections are allowed) only when the sum of the Miller indices \( h + k + l \) is even.
This arises because the BCC unit cell has atoms at positions (0,0,0) and (1/2,1/2,1/2).
The phase difference introduced by the atom at (1/2,1/2,1/2) is: \[ \exp\left[\pi i (h + k + l)\right] = (-1)^{h+k+l} \] So, the structure factor becomes zero (i.e., forbidden reflection) when \( h + k + l \) is odd, and is non-zero (i.e., allowed reflection) when \( h + k + l \) is even.