2. Hexagonal space lattice. The primitive translation vectors of the hexagonal space lattice may be taken as a3 = cz. a₁

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2 Hexagonal Space Lattice The Primitive Translation Vectors Of The Hexagonal Space Lattice May Be Taken As A3 Cz A 1 (99.79 KiB) Viewed 145 times

2. Hexagonal space lattice. The primitive translation vectors of the hexagonal space lattice may be taken as a3 = cz. a₁ = (3¹/2a/2) + (a/2)ŷ ; a₂ = −(3¹/2a/2) + (a/2)ŷ ; (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/3¹/2²a)x + (2π/a)ŷ ; b₂ = −(2π/3¹a) + (2π/a)ŷ ; 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. b3 = (2π/c)2,