3. Volume of Brillouin zone. Show that the volume of the first Brillouin zone is (27)³/V where V is the volume of a crystal primitive cell. Hint: The volume of a Brillouin zone is equal to the volume of the primitive parallelepiped in Fourier space. Recall the vector identity (cxä)×(axb) = č. (axb)ā.
3. Volume of Brillouin zone. Show that the volume of the first Brillouin zone is (27)³/V where V is the volume of a crystal primitive cell. Hint: The volume of a Brillouin zone is equal to the volume of the primitive parallelepiped in Fourier space. Recall the vector identity (cxä)×(axb) = č. (axb)ā.
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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![3. Volume of Brillouin zone. Show that the volume of the first Brillouin zone is
(27)³/V where Ve is the volume of a crystal primitive cell. Hint: The volume of a
Brillouin zone is equal to the volume of the primitive parallelepiped in Fourier space.
Recall the vector identity (×ā) × (axb) = c.(axb)ā.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d2fdd51-a813-4b36-89e9-f9581acfc2ee%2F3c708af4-4825-44ff-be20-686ace2eed29%2Fohs737v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Volume of Brillouin zone. Show that the volume of the first Brillouin zone is
(27)³/V where Ve is the volume of a crystal primitive cell. Hint: The volume of a
Brillouin zone is equal to the volume of the primitive parallelepiped in Fourier space.
Recall the vector identity (×ā) × (axb) = c.(axb)ā.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
let the volume of the parallelopiped primitive cell :
The reciprocal lattice primitive translation vectors are :
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