mse03 - Chapter 3 The Structure of Crystalline Solids...

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1 1 Chapter 3 - ISSUES TO ADDRESS. .. • How do atoms assemble into solid structures? (for now, focus on metals) • How does the density of a material depend on its structure? • When do material properties vary with the sample (i.e., part) orientation? Chapter 3: The Structure of Crystalline Solids 2 Chapter 3 - • Non dense, random packing • Dense, ordered packing Dense, ordered packed structures tend to have lower energies. Energy and Packing Energy r typical neighbor bond length typical neighbor bond energy Energy r typical neighbor bond length typical neighbor bond energy
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2 3 Chapter 3 - • atoms pack in periodic, 3D arrays Crystalline materials. .. -metals -many ceramics -some polymers • atoms have no periodic packing Noncrystalline materials. .. -complex structures -rapid cooling crystalline SiO 2 noncrystalline SiO 2 " Amorphous " = Noncrystalline Adapted from Fig. 3.22(b), Callister 7e. Adapted from Fig. 3.22(a), Callister 7e. Materials and Packing Si Oxygen • typical of: • occurs for: 4 Chapter 3 - Section 3.3 – Crystal Systems 7 crystal systems 14 crystal lattices Fig. 3.4, Callister 7e. Unit cell: smallest repetitive volume which contains the complete lattice pattern of a crystal. a, b, and c are the lattice constants
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3 5 Chapter 3 - Section 3.4 – Metallic Crystal Structures • How can we stack metal atoms to minimize empty space? 2-dimensions vs. Now stack these 2-D layers to make 3-D structures 6 Chapter 3 - • Tend to be densely packed. • Reasons for dense packing: - Typically, only one element is present, so all atomic radii are the same. - Metallic bonding is not directional. - Nearest neighbor distances tend to be small in order to lower bond energy. - Electron cloud shields cores from each other • Have the simplest crystal structures. We will examine three such structures. .. Metallic Crystal Structures
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4 7 Chapter 3 - • Rare due to low packing denisty (only Po has this structure) Close-packed directions are cube edges. Coordination # = 6 (# nearest neighbors) (Courtesy P.M. Anderson) Simple Cubic Structure (SC) 8 Chapter 3 - • 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 Atomic Packing Factor (APF) APF = Volume of atoms in unit cell* Volume of unit cell *assume hard spheres Adapted from Fig. 3.23, Callister 7e. close-packed directions a R =0.5 a contains 8 x 1/8 = 1 atom/unit cell
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5 9 Chapter 3 - • Coordination # = 8 Adapted from Fig. 3.2, Callister 7e. (Courtesy P.M. Anderson) • Atoms touch each other along cube diagonals. --Note: All atoms are identical; the center atom is shaded differently only for ease of viewing. Body Centered Cubic Structure (BCC) ex: Cr, W, Fe ( α ), Tantalum, Molybdenum 2 atoms/unit cell: 1 center + 8 corners x 1/8 10 Chapter 3 - Atomic Packing Factor: BCC 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.
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This note was uploaded on 03/18/2010 for the course ME 2580 taught by Professor Vandenbrink during the Spring '08 term at Western Michigan.

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mse03 - Chapter 3 The Structure of Crystalline Solids...

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