S2hcp,fcc,bcc - Section 1 Metallic Crystalline Structures...

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Section 1 Metallic Crystalline Structures (Smith Chapter 3, skip 3.11) Gasses – no order Liquids – short range order olids ng range order Solids – long range order the order is determined by the type of bonds STRUCTURE PROPERTIES MATE 210 crystalline amorphous
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Structure of Materials How atoms are arranged: o ato s a e a a ged orderly, periodic crystalline random, nonperiodic noncrystalline , amorphous lack of long range order (similar to atom arrangement in liquids) MATE 210 ( g q)
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Crystalline Materials atomic arrangement in solid: • periodic and repeating 3D order •unit cell – smallest repeating structure metals, many ceramics, certain polymers unit cell MATE 210 Fe (BCC) 1 mm = 3.5 x 10 6 unit cells
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unit cell cubic • basic unit or building block of crystal structure • geometry ttice constants: bc hexagonal lattice constants: a, b, c interaxial angles: α, β, γ tetragonal rhombohedral cubic a = b = c α = β = γ = 90° orthorhombic monoclinic 3-types: simple, body centered, face centered MATE 210 7 crystal systems (Smith Table 3.1) triclinic
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Crystal Structure: geometry + atom positions spatial arrangement of atoms, ions, or molecules a b ceramics aCl CC c metals u Al NaCl CsCl ZnS FCC BCC HCP Polymers -ethylene- Cu,Al Cr, Fe Ti,Zn ystalline & amorphous MATE 210 90% of metals crystalline & amorphous
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Crystal structures a ubic Crystal Structures: a a Cubic Crystal Structures: a = lattice constant length of side of unit cell Si – diamond cubic MATE 210 special version of FCC Al (FCC) a = 0.405 nm
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(Al, Cu, Au, Ni, Pb, Pt, Ag) 1. FCC: face-centered cubic # atoms/unit cell = (8 x 1/8) + (6 x ½) = 4 V s / V c atomic packing factor (APF) = volume atoms/volume cell = 0.74 “ close packed” ( ) 2 2 2 4 r a a = + V atoms = x(4/3 3 volume of sphere a r 2 4 = r a 2 2 = 4 x (4/3 π r ) MATE 210 V cell = a 3 = 3 2 16 r Pythagorean theorem
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2. BCC: body-centered cubic (Fe, Cr, Mo, Ta, W, V) # atoms/unit cell = (8 x 1/8) + 1 = 2 atomic packing factor (APF) = ? () ( ) 2 2 2 2 4 a a r + = atoms touch along body diagonal: V s / V c 3 4 r a = a MATE 210 V c = 64 r 3 / 3(3) 1/2 a a 2 a
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3. HCP: hexagonal close-packed (Cd, Mg, Be, Co, Ti, Zn, Y) c d es a a and c axes c/a ~ 1.633 Smith Table 3.4 noncubic symmetry # atoms/unit cell = ? MATE 210 atomic packing factor (APF) = 0.74 close packed ( ) 3 / 3 12 r a c V c =
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Density ρ = mass of atoms/volume of unit cell n = no. atoms/unit cell AW = atomic weight (g/mole) N A = Avogadro’s no. (6.023 x 10 23 atoms/mole) l f it ll V c = volume of unit cell r = atomic radius a = lattice constant of unit cell AW n A C N V ρ Example: Cu crystal structure n = = FCC 4 atoms in unit cell 3 5 g/mol A = r = a (FCC) olume of unit cell: a 3 = 63.5 g/mol 1.28 Å = 1.28 x 10 -8 cm = 2(2) ½ r = 3.62 x 10 -8 cm 75x10 -23 m 3 Avogadro 1811 V c volume of unit cell: a ρ = 4 atoms/unit cell
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This note was uploaded on 09/25/2010 for the course MATE 210 taught by Professor Gary during the Spring '10 term at Aarhus Universitet.

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S2hcp,fcc,bcc - Section 1 Metallic Crystalline Structures...

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