302-pp3 - GY 302: Crystallography & Mineralogy...

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Unformatted text preview: GY 302: Crystallography & Mineralogy GY 302: Crystallography & Mineralogy UNIVERSITY OF SOUTH ALABAMA Lecture 3: Miller Indices & Point Groups Lecture 3: Miller Indices & Point Groups Last Time 1. Rotoinversion 2. Translational Symmetry 3. Bravais Lattices A combination of rotation with a center of inversion. http://www.cartage.org.lb e.g., 4-fold Rotoinversion- This involves rotation of the object by 90 o then inverting through a center. Note that an object possessing a 4- fold rotoinversion axis will have two faces on top and two identical faces upside down on the bottom, if the axis is held in the vertical position. Rotoinversion Translation: Repetition of points by lateral displacement. Consider 2 dimensional translations: a b Unit Mesh or Plane Lattice Symmetry in Crystals Symmetry in Crystals Symmetry in Crystals Symmetry in Crystals The 14 Bravais Lattices Unit Cells NaCl (Halite)-Na +-Cl- Source: www.chm.bris.ac.uk Face-centered isometric crystal Todays Agenda 1. Miller Indices 2. Point Groups (32 of them) 3. Hermann-Mauguin Class Symbols Miller Indices Crystal facies can be identified using a set of coordinates. Miller Indices Crystal facies can be identified using a set of coordinates. The most widely used scheme is that by Miller (Miller Indices ) Miller Indices Crystal facies can be identified using a set of coordinates. The most widely used scheme is that by Miller (Miller Indices ) Miller Indices Consider the plane in pink (a, , ) Miller Indices Consider the plane in pink. Its actually one of an infinite number of parallel planes each a consistent distance from the origin (a, , ) Miller Indices Consider the plane in pink. Its actually one of an infinite number of parallel planes each a consistent distance from the origin e.g., 1a, 2a, 3a (a, , ) 1a 2a 3a Miller Indices (1a, , ) In the x direction, the first plane terminates at point 1a. It continues indefinitely in the y and z directions Miller Indices This plane can be designated (1a, , ) or better yet (1, , ) (1a, , ) Miller Indices Likewise, this plane in yellow can be designated ( , 1, ) And the plane in green can be designated ( , , 1) ( , 1, ) ( , , 1) ( 1, , ) Miller Indices By convention, Miller Indices are reciprocals of the parameters of each crystal face ( , 1, ) ( , , 1) ( 1, , ) Miller Indices...
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302-pp3 - GY 302: Crystallography & Mineralogy...

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