Discussion
For a face centered cubic lattice, the Miller indices for the first Bragg’s peak (smallest Bragg angle) are
Answer: B
The first Bragg peak of a face-centred cubic lattice is the 1 1 1 reflection.
In an fcc lattice, reflections appear only when h, k and l are all odd or all even (zero counting as even); mixed indices are systematically absent. The Bragg angle rises with h2 + k2 + l2, since sin θ = (λ/2a)(h2 + k2 + l2)1/2. The allowed sets in order are 111 (3), 200 (4), 220 (8), and so on, so 111 comes first.
0 0 1 and 1 1 0 have mixed odd and even indices and are absent in fcc. 0 0 2 is allowed, but h2 + k2 + l2 = 4 places it after 111. (In a body-centred lattice, where h + k + l must be even, 110 would come first.)
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