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MS115a Lect 07 10 10 2011

# MS115a Lect 07 10 10 2011 - Formal Crystallography...

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Formal Crystallography Crystalline Periodic arrangement of atoms Pattern is repeated by translation Three translation vectors define: Coordinate system Crystal system Unit cell shape Lattice points Points of identical environment Related by translational symmetry Lattice = array of lattice points a b c α β γ • space filling • defined by 3 vectors • parallelipiped • arbitrary coord system • lattice pts at corners +

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Crystal system Lattices triclinic simple base-centered monoclinic α = 90° Convention: β = 90° instead of α simple base-centered body-centered face-centered orthorhombic α = β = γ = 90° hexagonal γ = 120° c a a rhombohedral (trigonal) α = β = γ(= α29 simple body-centered tetragonal α = β = γ = 90° a = b simple body-centered face-centered cubic (isometric) α = β = γ = 90° a = b = c 6 or 7 crystal systems 14 lattices Can be redefined as a non- primitive hexagonal cell
Crystallographic notation Position: x, y, z fractional coordinates Direction: – x 2 -x 1 , y 2 -y 1 , z 2 -z 1 no magnitude specific: [t u v] family: < t u v a 1 a 2 a 3 x, y, z cubic system (x 1 , y 1 , z 1 ) (x 2 , y 2 , z 2 )

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Specific vs. family square lattice a 1 a 2 specific: [1, 2] family: <1, 2> includes [1 2], [2 1], [1 2],
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MS115a Lect 07 10 10 2011 - Formal Crystallography...

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