EMS162_2010_Lecture3

EMS162_2010_Lecture3 - Lattice + Unit cell Basis Unit Cell...

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1 1/12/2010 EMS 162 - Winter 2010 1 Yayoi Takamura Lattice + Unit cell Lattice Unit Cell Basis b a γ 1/12/2010 EMS 162 - Winter 2010 2 Yayoi Takamura Bravais Lattices
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2 1/12/2010 EMS 162 - Winter 2010 3 Yayoi Takamura Real vs. Reciprocal Space • Real Space • Reciprocal Space a b c c b a a b c a * b * c * c * a * b * h k l H hkl ( hkl ) N hkl N hkl d hkl H hkl hkl hkl d H 1 = 1/12/2010 EMS 162 - Winter 2010 4 Yayoi Takamura Symmetry Elements Rotation Inversion Mirror Translation (x,y,z) (-x, -y, -z) , , + - , + -
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3 1/12/2010 EMS 162 - Winter 2010 5 Yayoi Takamura N=6 Rotation Axes N=2 N=3 N=4 N ° = 360 ϕ Axis is a line perpendicular to the board 1/12/2010 EMS 162 - Winter 2010 6 Yayoi Takamura Rotation Axes N ° = 360 Axis is a line in plane of the board or
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4 1/12/2010 EMS 162 - Winter 2010 7 Yayoi Takamura Pentagons 1/12/2010 EMS 162 - Winter 2010 8 Yayoi Takamura Crystallographic Restriction 1. Consider lattice pts A and A’ separated by distance, t . 2. Perform a rotation upon A to rotate by an angle, α . A new position, B is created from A’.
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This note was uploaded on 05/14/2010 for the course EMS 162 taught by Professor Howitt during the Spring '08 term at UC Davis.

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EMS162_2010_Lecture3 - Lattice + Unit cell Basis Unit Cell...

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