Question:medium

The BCC lattice has systematic extinction rules where reflections only occur if the sum of the indices is

Show Hint

Remember the systematic reflection rules for common cubic systems:
- BCC: \( h+k+l = \text{even} \)
- FCC: \( h, k, l \) must be all even or all odd (mixed indices are extinct)
- Simple Cubic: All planes can diffract (no systematic extinctions)
Updated On: Jul 3, 2026
  • h+k+l=odd
  • h+k+l=even
  • h+k=l
  • h+l=k
Show Solution

The Correct Option is B

Solution and Explanation

Step 1: Note where the atoms sit.
A BCC cell has atoms at \( (0,0,0) \) and \( (\frac{1}{2},\frac{1}{2},\frac{1}{2}) \), and whether a plane \( (hkl) \) reflects X-rays depends on whether the waves scattered by these two atoms reinforce or cancel each other.

Step 2: Compare the phase from each atom.
The second atom is offset by half a cell in each direction, which brings in a phase factor of \( e^{i\pi(h+k+l)} \) relative to the first atom.

Step 3: Check when the waves add or cancel.
If \( h+k+l \) is even, this factor equals \( +1 \), so the two atoms scatter in phase and reinforce, giving a visible reflection. If \( h+k+l \) is odd, the factor equals \( -1 \), so the waves cancel exactly, and no reflection appears. This is why planes like (100) and (111), with odd index sums, are missing from a BCC pattern while (110) and (200) show up strongly.
So reflections in a BCC lattice only survive when \( h+k+l \) is even, option (B).
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