Chapter 3 Part 2 - Atomic Packing Factor (APF) Volume of...

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Atomic Packing Factor (APF) APF = Volume of atoms in unit cell* Volume of unit cell *assume hard spheres • APF for a simple cubic structure = 0.52 APF = a 3 4 3 π (0.5 a ) 3 1 atoms unit cell atom volume unit cell volume Adapted from Fig. 3.23, Callister 7e. close-packed directions a R =0.5 a contains 8 x 1/8 = 1 atom/unit cell 1 Chapter 3 -
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Body Centered Cubic Structure (BCC) • Atoms touch each other along cube diagonals. --Note: All atoms are identical; the center atom is shaded differently only for ease of viewing. 2 Chapter 3 - • Coordination # = 8 Adapted from Fig. 3.2, Callister 7e. (Courtesy P.M. Anderson) ex: Cr, W, Fe ( α ), Tantalum, Molybdenum 2 atoms/unit cell: 1 center + 8 corners x 1/8
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Atomic Packing Factor: BCC 3 Chapter 3 - a APF = 4 3 π (3 a /4) 3 2 atoms unit cell atom volume a 3 unit cell volume length = 4 R = Close-packed directions: 3 a • APF for a body-centered cubic structure = 0.68 a R Adapted from Fig. 3.2(a), Callister 7e. a 2 a 3
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Face Centered Cubic Structure (FCC) Coordination # = 12 Adapted from Fig. 3.1, Callister 7e. • Atoms touch each other along face diagonals. --Note: All atoms are identical; the face-centered atoms are shaded differently only for ease of viewing. ex: Al, Cu, Au, Pb, Ni, Pt, Ag 4 atoms/unit cell: 6 face x 1/2 + 8 corners x 1/8 4 Chapter 3 - (Courtesy P.M. Anderson)
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• APF for a face-centered cubic structure = 0.74 Atomic Packing Factor: FCC maximum achievable APF 5 Chapter 3 - APF = 4 3 π ( 2 a /4) 3 4 atoms unit cell atom volume a 3 unit cell volume Close-packed directions: length = 4 R = 2 a Unit cell contains: 6 x1/2 + 8 x1/8 = 4 atoms/unit cell a 2 a Adapted from Fig. 3.1(a), Callister 7e.
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ANNOUNCEMENTS - 2/1 Reading: Chapter 3 6 Chapter 3 -
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• ABCABC. .. Stacking Sequence 2D Projection FCC Stacking Sequence A sites A Bs i tes B B B B B BB Cs i C C C A • FCC Unit Cell A B C 7 Chapter 3 -
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Hexagonal Close-Packed Structure (HCP) • ABAB. .. Stacking Sequence • 3D Projection Adapted from Fig. 3.3(a), Callister 7e. • 2D Projection Bottom layer Middle layer Top layer c a A sites Bs i tes A sites 6 atoms/unit cell • Coordination # = 12 ex: Cd, Mg, Ti, Zn • APF = 0.74 8 Chapter 3 - c / a = 1.633
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unit cell of diamond structure Reading: Chapter 3 Core Problems: Self-help Problems: 9 Chapter 3 -
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A general Bravais lattice unit cell Core Problems: Self-help Problems: Reading: Chapter 3 10 Chapter 3 -
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NaCl CsCl Core Problems: Self-help Problems: Reading: Chapter 3 FCC-like structure BCC-like structure 11 Chapter 3 -
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Interstial atoms Small atoms insert into interstices with different coordination numbers EX: C, N, O in Fe 12 Chapter 3 -
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Theoretical Density, ρ cell unit of volume Total cell unit in atoms of Mass Density = ρ = V C N A n A ρ = where n = number of atoms/unit cell A = atomic weight V C = Volume of unit cell = a 3 for cubic N A = Avogadro’s number = 6.023 x 10 23 atoms/mol 13 Chapter 3 -
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14 Chapter 3 - Ex: Cr (BCC) A = 52.00 g/mol R = 0.125 nm n = 2 ρ theoretical a = 4 R / 3 = 0.2887 nm ρ actual a R ρ = a 3 52.00 2 atoms unit cell mol g unit cell volume atoms mol 6.023x10 23 Theoretical Density, ρ = 7.18 g/cm 3 = 7.19 g/cm 3
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Densities of Material Classes 15 Chapter 3 - ρ metals > ρ ceramics > ρ polymers Why?
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This note was uploaded on 07/13/2008 for the course MSE 201 taught by Professor Nieh during the Spring '07 term at University of Tennessee.

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Chapter 3 Part 2 - Atomic Packing Factor (APF) Volume of...

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