Question

In an X-ray diffraction pattern, reflections from a BCC crystal will appear only when

• A. h, k, l is all odd
• B. h, k, l is all even
• C. h+k+l is an even number
• D. h+k+l is an odd number

Hint:

FCC and BCC selection rules are most frequently asked in XRD questions.

Answer 1

The Correct Option is C

Concept: For BCC structures, diffraction conditions are governed by the structure factor. In BCC lattices, the basis atoms lead to constructive interference only when: \[ h+k+l = \text{even} \] If the sum is odd, destructive interference occurs and reflection is absent.

Step 1: Understand BCC structure factor rule.
BCC has atoms at: \[ (0,0,0), \left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right) \] This introduces a phase factor: \[ e^{i\pi(h+k+l)} \]

Step 2: Condition for constructive interference.

• If $h+k+l$ is even → phase = +1 → reflection occurs
• If $h+k+l$ is odd → phase = -1 → cancellation Final Answer: \[ \boxed{h+k+l = \text{even}} \]