Crystal Systems Unit Cell: Smallest Repetitive Volume with Lattice Pattern
Unit cell plays a crucial role in defining crystal structures and systems, showcasing the intricate atomic arrangements within. Explore crystallographic directions, indices determination, and more within the realm of crystallography.
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Presentation Transcript
Crystal Systems Unit cell: smallest repetitive volume which contains the complete lattice pattern of a crystal. Fig. 3.4, Callister & Rethwisch 8e. a, b, and c are the lattice constants. Chapter 3 - 1
Crystal Structure and Crystal System Q. What is the difference between crystal structure and crystal system? A: A crystal structure is described by both the geometry of, and atomic arrangements within, the unit cell, whereas a crystal system is described only in terms of the unit cell geometry. For example, face-centered cubic and body-centered cubic are crystal structures that belong to the cubic crystal system. Chapter 3 - 2
Crystal Systems & Bravais Lattices Chapter 3 - 3
Point Coordinates Point coordinates for unit cell center are a/2, b/2, c/2 z 111 c Point coordinates for unit cell corner are 111 y 000 b a x Chapter 3 -
Point coordinates for all atom positions for a BCC unit cell Chapter 3 - 5
Crystallographic Directions Algorithm z 1. Vector repositioned (if necessary) to pass through origin. 2. Read off projections in terms of unit cell dimensions a, b, and c 3. Adjust to smallest integer values 4. Enclose in square brackets, no commas [uvw] y x ex:1, 0, => 2, 0, 1 => [201] -1, 1, 1 where overbar represents a negative index [111] => Chapter 3 - 6
Crystallographic Directions OA AO families of directions <uvw> All cell edges: All face diagonals: All body diagonals: Chapter 3 - 7
Problem 3.32 3.32 Determine the indices for the directions shown in the following cubic unit cell: Chapter 3 - 8
