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
7th Edition
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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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d2fdd51-a813-4b36-89e9-f9581acfc2ee%2Fdd862c42-802b-4ca2-9ecf-a9d736899dcf%2Ftyl9d28_processed.jpeg&w=3840&q=75)
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
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
(a)
Write the reciprocal lattice vector.
The terms h, k and l are written when intercepts x, y and z axes at . Then,
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