MCB124 Lecture5 Supplement

MCB124 Lecture5 Supplement - MCB 124 The Concept of...

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Unformatted text preview: MCB 124 The Concept of Building Blocks of Solids Platos five shapes for the elements earth, air, fire and water, have now become the unit cells for the seven crystal systems MCB 124 What is a Crystal? A time invariant regular arrangement of atoms or molecules on a lattice Need to be precise in our use of lattice and motif (basis) in discussions on structure MCB 124 Translation Vectors Hauy (1801) integral molecules Established the concept of building crystals from unit cells Generic Unit Cell c w b v a u t + + = Translation vector ties corner nodes or lattice points in the unit cell MCB 124 Lattice Definitions A crystal structure consists of a 3-D space lattice which is decorated with one or more atoms (basis) Key point : the space lattice is a mathematical construction and does not contain any atoms MCB 124 The Four 2-D Crystal Systems These represent all the unique ways to fill 2-D space with vectors a and b MCB 124 The Seven 3-D Crystal Systems Symmetry Ranking MCB 124 The Fourteen 3-D Bravais Lattices MCB 124 Directions in the Crystal Lattice Need to draw distinction between directions and translation vectors [123] and [246] are the same direction, but a different translation vector MCB 124 Miller Indices Take the intersection with the origin Divide by the unit vectors Take the reciprocal to get rid of infinity Reduce fractions to the smallest integers to give the Miller Indices MCB 124 Examples of Miller Indices Defines the plane for a particular system so we need to know the planes and the crystal lattice ( 29 1 1 1 ( 29 2 2 1 ( 29 1 MCB 124 Families of Planes and Directions { } 1 1 1 1 1 Reduction in symmetry removes degeneracy of the planes MCB 124 Scattering of X-rays by Lattice Planes n d = sin 2 Braggs Law = sin 2 hkl d MCB 124 k-vectors 1 2 = = D I k k Elastic Scattering: MCB 124 k-vectors (2) k 2 sin = sin 2 = Bragg: B B sin 2 = MCB 124...
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This note was uploaded on 11/09/2010 for the course MCB 124 taught by Professor Baldwin during the Spring '09 term at UC Davis.

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MCB124 Lecture5 Supplement - MCB 124 The Concept of...

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