Question

The sets of planes which can appear in an FCC diffraction pattern is

• A. (100), (110), (111)
• B. (111), (200), (220)
• C. (110), (211), (310)
• D. (100), (200), (210)

Hint:

FCC: all odd or all even condition is the fastest way to identify allowed reflections.

Answer 1

The Correct Option is B

Concept: In FCC crystals, X-ray diffraction follows the structure factor rule, which states that reflections are allowed only when Miller indices are either all odd or all even. Thus, allowed FCC reflections are: \[ (111), (200), (220), (311), (222), \ldots \]

Step 1: Apply FCC selection rule.
For FCC:
• (100) → forbidden (mixed parity)
• (110) → forbidden
• (111) → allowed (all odd)
• (200) → allowed (all even)
• (220) → allowed (all even)

Step 2: Identify correct set.
Only option containing valid FCC reflections is: \[ (111), (200), (220) \] Final Answer: \[ \boxed{(111), (200), (220)} \]