Discussion
The following XRD is recorded for the crystalline solid, having simple cubic crystal structure :
| Peak | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| (hkl) | (100) | (110) | (111) | (200) | (210) | (211) | (220) | (300) |
If this crystal would have been FCC, the following peaks would have missing :
Answer: C
The missing peaks would be A, B, E, F and H.
In a face-centred cubic lattice, reflections appear only when h, k and l are all odd or all even (zero counts as even). Mixed indices give zero structure factor and are absent.
- Allowed: (111) C, (200) D, (220) G.
- Absent: (100) A, (110) B, (210) E, (211) F, (300) H.
Every other option either keeps one of the mixed-index peaks or removes C, D or G, which FCC does show. For comparison, a body-centred lattice keeps only h + k + l even, which would remove A, C, E and H instead.
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