Hexagonal space lattice the primitive translation vectors of the hexagonal space lattice may be taken as a
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Hexagonal space lattice the primitive translation vectors of the hexagonal space lattice may be taken as
a1 = (31/2 a/2)x + (a/2)y ; a2 = – (31/2 a/2)x + (a/2)y ; a3 = cz
(a) Show that the volume of the primitive cell is (31/2 /2) a2c.
(b) Show that the primitive translations of the reciprocal lattice are
b1 = (2π/31/2 a)x + (2π/a)y ; b2 = – (2π/31/2 a)x + (2π/a) y ; b3 = (2π/c)z,
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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c Six vectors in the reciprocal lattice are shown ...View the full answer
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