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Interplanar separation. Consider a plane hkl in a crystal lattice. (a) Prove that the reciprocal lattice vector G= hb₁ + kb₂ + lb, 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 cubic lattice that d² = a² /(h² +k² +1²).

Interplanar separation. Consider a plane hkl in a crystal lattice. (a) Prove that the reciprocal lattice vector G= hb₁ + kb₂ + lb, 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 cubic lattice that d² = a² /(h² +k² +1²).

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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1. Interplanar separation. Consider a plane hkl in a crystal lattice. (a) Prove that the reciprocal lattice vector G = hb, + kb₂ + lb, 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 cubic lattice that d² = a² /(h² +k² + 1²).
Transcribed Image Text:1. Interplanar separation. Consider a plane hkl in a crystal lattice. (a) Prove that the reciprocal lattice vector G = hb, + kb₂ + lb, 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 cubic lattice that d² = a² /(h² +k² + 1²).
Expert Solution
Step 1

(a)

Write the reciprocal lattice vector.

G=hb1+kb2+lb3

The terms h, k and l are written when intercepts x, y and z axes at x1b1, x2b2 and x3b3 . Then,

x1:x2:x3=1h:1k:1l

 

 

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