# 10 overhead Bravais Miller RL - , 5fold,...

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Crystal lattice must have translation symmetry, repeat units across the lattice ld, 8 ld and higher cannot make crystal lattices 5 fold, 8 fold and higher cannot make crystal lattices http://www.tulane.edu/~sanelson/eens211/introsymmetry.htm

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Crystal lattice? Rohrer, pg30
Wigner Seitz Rohrer, pg44

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Wigner Seitz Primitive Cell he Wigner itz primitive cell of a Bravais lattice is a region in space around a • The Wigner Seitz primitive cell of a Bravais lattice is a region in space around a lattice point that consists of all points in space that are closer to this lattice point than to any other lattice point • Primitive cells can be used to “tile” the entire lattice without overlapping c Primitive cell Tiling of the lattice by the primitive cell b • The volume (3D), area (2D), or length (1D) of a primitive cell can be given in terms of x b a ˆ 1 ˆ the primitive vectors, and is independent of the choice of the primitive vectors a a 1 1 a 1D 2D Example, for the 2D lattice above: x b a ˆ 1 ˆ ˆ r y c a 2 2 1 2   3 2 1 3 . a a a 3D bc a a 2 1 2 y c x b a 2 bc a a 2 1 2 or Slide courtesy of ECE 407, Farhan Rana
Wigner Seitz Primitive Cell l (2D) Example (2D): x b a ˆ 1 y b x b a ˆ ˆ 2 Primitive cell b 2 2 2 2 2 1 2 b a a b

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## This note was uploaded on 03/15/2010 for the course MSE 2060 taught by Professor Liddell during the Spring '09 term at Cornell.

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10 overhead Bravais Miller RL - , 5fold,...

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