The primitive translation vectors of the hexagonal space lattice may be taken as a = (3a/2)...
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The primitive translation vectors of the hexagonal space lattice may be taken as a = (3a/2) + (a/2)ŷ ; a = -(3a/2)& + (a/2)ý ; az = câ . (a) Show that the volume of the primitive cell is (3/2)a*c. (b) Show that the primitive translations of the reciprocal lattice are b (2m/3a)& + (27la)ŷ ; b = -(2m/3a) + (2mla)ŷ ; b, = (2m/c)î , %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. The primitive translation vectors of the hexagonal space lattice may be taken as a = (3a/2) + (a/2)ŷ ; a = -(3a/2)& + (a/2)ý ; az = câ . (a) Show that the volume of the primitive cell is (3/2)a*c. (b) Show that the primitive translations of the reciprocal lattice are b (2m/3a)& + (27la)ŷ ; b = -(2m/3a) + (2mla)ŷ ; b, = (2m/c)î , %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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