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.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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Question

Hexagonal space lattice. The primitive translation vectors of the hexagonal space
lattice may be taken as
a = (3Pa/2)& + (a/2)ŷ ;
a2 = -(32a/2)& + (a/2)ŷ ;
az = c2 .
(a) Show that the volume of the primitive cell is (312/2)a°c.
(b) Show that the primitive translations of the reciprocal lattice are
bị = (27/3a)y + (2la)ŷ ;
b, = -(27/312a)âk + (27/a)ŷ ;
bz = (2m/c)2 ,
%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.

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