Hexagonal space lattice. The primitive translation vectors of the hexagonal space lattice may be taken as a₁ = (3¹/2²a/2

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Hexagonal Space Lattice The Primitive Translation Vectors Of The Hexagonal Space Lattice May Be Taken As A 3 2 A 2 1 (126.39 KiB) Viewed 10 times

Hexagonal space lattice. The primitive translation vectors of the hexagonal space lattice may be taken as a₁ = (3¹/2²a/2) + (a/2)ŷ ; a₂ -(3¹⁄²a/2)x+ (a/2)ŷ ; (a) Show that the volume of the primitive cell is (3¹/2²/2)a²c. (b) Show that the primitive translations of the reciprocal lattice are b₁ = (2π/3¹/²a)x + (2π/a)ŷ ; b₂ = −(2π/3¹a) + (2π/a)ŷ ; a3 = cz. b3 = (2π/c)2, 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.