symm_handout2 - Going 3D A crystal is a three dimensional...

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A crystal is a three dimensional periodic discontinuum. It consists of identical “bricks” called unit cells, which form a three- dimensional lattice. The unit cell is defined by the axes a , b , and c , and the three angles α , β , γ , which form a right- handed system. α a b c γ β Volume of the unit cell V: V = abc [1-cos 2 α –cos 2 β –cos 2 γ + 2cos 2 α –cos 2 β –cos 2 γ ] ½ Going 3D Courtesy of George M. Sheldrick. Used with permission.
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The unit cell is the smallest unit that can generate the entire crystal structure only by means of translation in three dimensions. Within each unit cell there may be several symmetry related copies of the asymmetric unit but in general those are oriented differently. Even though in the structure of NaCl there is an atom at every corner of the unit cell, such an arrangement is rather rare. If the structure is centro- symmetric, the unit cell is chosen so that its origin lies on an inversion center. Else: conformity with other
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This note was uploaded on 11/27/2011 for the course CHEMICAL E 20.410j taught by Professor Rogerd.kamm during the Spring '03 term at MIT.

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symm_handout2 - Going 3D A crystal is a three dimensional...

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