Topic #4 - Unit Cell Geometry I - Directions :Topic #4 - Unit Cell Geometry I - Directions Overview * Properties can vary significantly with direction * Definition & examples of unit cell positions, directions, & nomenclature * Calculation of linear packing density & angles between directions * Examples of property variation with direction Unit Cell Positions * Definition * Examples Unit Cell Directions * Indices * Nomenclature * Families of directions * Linear packing density * Angles between directions Effect of Directions on Processing and Properties * Metals, Polymers, Ceramics, Semiconductors Homework – 4 problems, Reading: Callister 3.8–3.9, 3.11 (5 pg.); Krause, Topic #4 (6 pg.) Topic #5 Cryst. Geom. II Planes – Read Callister 3.10 – 3.12 (8 pg.); Krause, Topic #5 (6 pg.)


Do Unit Cell Directions Affect You? :Do Unit Cell Directions Affect You? Ni superalloy single crystal turbine blades grown along close packed [110] direction allow engines to run more efficiently at high temperature Computer chips are made from silicon wafers sliced from single crystal boules grown along [100] the direction GaAs in lasers in CD players are epitaxially grown by vapor deposition of electro-optically active layers on to GaAs [100] single crystal wafers


Atomic Force Microscopy of Surface Atoms :Atomic Force Microscopy of Surface Atoms Atomic force microscopy of Si single crystal surface and schematic of AFM and actual AFM cantilever and tip AFM of single steps on a palladium single crystal surface and a set of nanogears etched into surface of single crystal Si AFM image of Ga and As atoms on GaAs single crystal surface GaAs that is used in lasers in CD players when electro-optically active layers are epitaxially grown by vapor deposition on GaAs [100] single crystal wafers


Unit Cell Positions :Unit Cell Positions


Indexing Directions :Indexing Directions Indices are given by [u v w], lowest square bracketed [ ] integers Go from origin at 0, 0, 0 to position x, y, z such that x=u, y=v, z=w Given indices > draw direction [0 1 2] Select origin O at 0, 0, 0 OR Choose new O’ & label axes X’ Y’ Z’ Mark coordinates at ½[0 1 2] = 0, ½, 1 Draw direction from O or O’to coordinate Given direction > determine indices [? ? ?] Move tail of direction, if necessary, to new origin O’ Label O’ and new axes X’, Y’, and Z’ Find coordinates from O’ to head of direction x, y, z Reduce multiples, eliminate fractions, put – for – Place square brackets around integers Mistakes 0 0 1_______ , [1,2,3] _______ , [-1 -2 3] _______ , [1/2 2 3]________, [2 4 6]_______


Activity 1 – Drawing & Indexing Directions :Activity 1 – Drawing & Indexing Directions Draw the specified directions in the unit cells below [1 2 2] [1 0 1] [1 1 1] - - - - Determine indices of these unit cell directions


Families of DirectionsActivity 2 – Identify <1 1 1> directions :Families of DirectionsActivity 2 – Identify directions = [ 1 1 1], [ 1 1 1], [ 1 1 1], [ 1 1 1] _ _ _


Linear Density of Atoms :Linear Density of Atoms


Angles Between Directions :Angles Between Directions


Homework – Lecture #4 – Crystal Geometry I - Directions :Homework – Lecture #4 – Crystal Geometry I - Directions 1a. Draw the specified directions in the unit cells below [1 2 2] [1 0 1] [1 1 1] - - - - 1b. Determine indices of these unit cell directions 2. For BCC iron, calculate the linear packing density along [1 0 0], [1 1 0], and [1 1 1] 3. For a cubic unit cell calculate the angle between [ 1 1 1 ] and [ 1 1 1 ] . 4. Native minerals often have shapes and facets that are a manifestation of the crystal structure of the mineral. NaCl or table salt is one of these. Check the internet to see if you can find some more cubic structure minerals and see of any other planes besides the cube faces are present. -