Question: Inter planar separation consider a plane hkl in a crystal lattice. (a) Prove that the reciprocal lattice vector G = hb1 + kb 3 is

Inter planar separation consider a plane hkl in a crystal lattice.

(a) Prove that the reciprocal lattice vector G = hb1 + kb3 is perpendicular to this plane.

(b) Prove that the distance between two adjacent parallel planes of the lattice is d(hkl) = 2π/|G|.

(c) Show for a simple cubic lattice that d2 = a2 /(h2 + k2 + l2).

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