Hexagonal space lattice. The primitive translation vectors of the hexagonal space lattice may be taken as a = (3a/2)& + (a/2)ŷ ; az = -(3Pal2)& + (a/2)§ ; az = cz . %3D (a) Show that the volume of the primitive cell is (32/2)a°c. (b) Show that the primitive translations of the reciprocal lattice are b, = (27/3a)& + (2mla)ŷ ; b2 = -(27/32a) + (27/a)ŷ ; b, = (2m/c)2, %3D %3D so that the lattice is its own reciprocal, but with a rotation of axes. (c) Describe and sketch the first Brillouin zone of the hexagonal space lattice.

Hexagonal space lattice. The primitive translation vectors of the hexagonal space lattice may be taken as a = (3a/2)& + (a/2)ŷ ; az = -(3Pal2)& + (a/2)§ ; az = cz . %3D (a) Show that the volume of the primitive cell is (32/2)a°c. (b) Show that the primitive translations of the reciprocal lattice are b, = (27/3a)& + (2mla)ŷ ; b2 = -(27/32a) + (27/a)ŷ ; b, = (2m/c)2, %3D %3D so that the lattice is its own reciprocal, but with a rotation of axes. (c) Describe and sketch the first Brillouin zone of the hexagonal space lattice.

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter9: Moments And Products Of Inertia Of Areas

Section: Chapter Questions

Problem 9.26P: A circular region of radius R/2 is cut out from the circular region of radius R as shown. For what...

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