This preview shows pages 1–21. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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., 4fold 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 Facecentered isometric crystal Todays Agenda 1. Miller Indices 2. Point Groups (32 of them) 3. HermannMauguin 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...
View Full
Document
 Spring '11
 Staff

Click to edit the document details