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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 B sites B B B B B B B C sites 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 B sites 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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