Miller Indices

Physics: Miller indices (hkl): reciprocals of intercepts on a, b, c axes, reduced to integers. (100) = face; (110) = face diagonal; (111) = body diagonal. d-spacing (cubic): d_hkl = a/√(h²+k²+l²). Bragg's law: 2d·sinθ = nλ; for Cu Kα (λ=1.54 Å), Si(111) d=3.135 Å diffracts at 2θ=28.4°. Negative indices written h̄k̄l̄. Equivalent planes {hkl} related by symmetry; zone axis [uvw] satisfies hu+kv+lw=0. (200) has half d-spacing of (100). Selection rules: FCC requires hkl all odd or all even; BCC requires h+k+l even.