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2spp_MEMS_Week8_Symmetry1

2spp_MEMS_Week8_Symmetry1 - MEMS 1054 Week 8 Crystalline...

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1 MEMS 1054 Week 8 - Crystalline State - Symmetry Professor Jörg Wiezorek, PhD, Materials Science and Metallurgy, University of Cambridge, UK, 1994. Symmetry and Crystallography; Point Symmetry Plane Groups Point Groups (Space Groups)
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2 Definitions: Crystal Structure described by its Bravais Lattice Unit Cell and the Motif decorating each lattice point! Symmetry and Crystals => Crystallography Translational symmetry (LRO) of crystals described by the lattice unit cell; The other symmetry elements compatible with the translational LRO of crystals in 3D restrict the number of distinct lattice unit cells to the 14 Bravais Lattices. The point group symmetry properties of the Bravais lattices are described by the locations and compatible combinations of point group symmetry operations (point group symmetry elements). These include … Reflections / mirror planes location described by (hkl), {hkl}; Rotations / rotation axes location described by [uvw], <uvw>; Inversions / inversion points location described by m,n,p; Combinations of reflections with translations / Glide Planes Combinations of rotations with translations / Screw Axes (Compound symmetry elements) Combinations of rotations and inversions / improper rotations (Compound symmetry elements)
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3 Symmetry and Crystals => Crystallography The symmetry properties of the crystals are captured by the Point Group they belong to, described in shorthand by the point group symbols . Combination of the point group symbol with the type of Bravais lattice , i.e., either Primitive (P) or c-centered (C) or body-centered (I) or face- centered (F), provides the internationally accepted and conventionally used Space Group symbols for the crystals. Fm 3 m Im 3 m … e.g. FCC Cu, cF with one Cu per lattice point, has space group or BCC W, cI with one W per lattice point, See International Tables of Crystallography, examples in Appendices of Textbook .
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