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

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1 Chapter 3 - 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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2 Chapter 3 - Polymorphism Two or more distinct crystal structures for the same material (allotropy/polymorphism) titanium α , β -Ti carbon diamond, graphite BCC FCC BCC 1538ºC 1394ºC 912ºC δ - Fe γ - Fe α - Fe liquid iron system
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3 Chapter 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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4 Chapter 3 - 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
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5 Chapter 3 - Section 3.8 Point Coordinates Point coordinates for unit cell center are a /2, b /2, c /2 ½ ½ ½ 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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6 Chapter 3 - Crystallographic Points BCC unit cell Identify coordinates of points in a unit cell x z y A B C D E F G H
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7 Chapter 3 - Crystallographic Directions 1. Vector repositioned (if necessary) to pass through origin.
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Lecture4 - Unit cell- smallest number of atoms showing...

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