Lecture4

# Lecture4 - Unit cell smallest number of atoms showing...

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Chapter 3 - 1 Crystal Structure Review • Unit cell- smallest number of atoms showing atomic arrangement in a crystal Structur e #atoms/ uc atom position s APF Coord # a Unit cell SC 1 corners 0.52 6 2R cubic BCC 2 corners +middle 0.68 8 4R/√3 cubic FCC 4 corners +face centers 0.74 12 2√2R cubic HCP 6 corners +center +middle 0.74 12 a=2R c=4√(2/ 3)R hexago nal

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Chapter 3 - 2 Polymorphism Two or more distinct crystal structures for the same material (allotropy/polymorphism) titanium , -Ti carbon diamond, graphite BCC FCC BCC 1538ºC 1394ºC 912ºC - Fe - Fe - Fe liquid iron system
Chapter 3 - 3 Crystallographic planes Some directions and planes have a higher density of nodes; these dense planes have an influence on the properties of the crystal: Optical Properties: the velocity of light varies according to the directions - whether the atoms are close or far Adsorption and Reactivity : the adsorption and the chemical reactions are sensitive to the density of nodes Surface Tension : the surface tension of an interface varies according to the density on the surface For all these reasons, it is important to determine the planes and thus to have a notation system.

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Chapter 3 - 4 Point Coordinates-2 The position of any point located within a unit cell may be specified in terms of its coordinates as fractional multiples of the unit cell edge length 3 numbers are used to designate point locations, directions and planes
Chapter 3 - 5 Section 3.8 Point Coordinates Point coordinates for unit cell center are a /2, b /2, c /2 ½½½ Point coordinates for unit cell corner are 111 Translation: integer multiple of lattice constants identical position in another unit cell z x y a b c 000 111 y z 2 c b b

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Chapter 3 - 6 Crystallographic Points •BCC unit cell •Identify coordinates of points in a unit cell x z y A B C D E F G H
Chapter 3 - 7 Crystallographic Directions 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 ] ex: 1, 0, ½ => 2, 0, 1 => [201] -1, 1, 1 families of directions < uvw > z x Algorithm where overbar represents a negative index [ 111] => y

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Lecture4 - Unit cell smallest number of atoms showing...

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