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# Material sciece1 lecture 1 part 2

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Dr sama eldek
professor of physics
faculty of Science -Cairo university

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### Material sciece1 lecture 1 part 2

1. 1. Chapter 3: The Structure of Crystalline Solids ISSUES TO ADDRESS... • How do atoms assemble into solid structures? • How does the density of a material depend on its structure? • When do material properties vary with the sample orientation? Chapter 3 - 1
2. 2. After studying this chapter you should be able to do the following: Describe the difference in atomic/molecular structure between crystalline and noncrystalline materials. Draw unit cells for face-centered cubic, body-centered cubic, and hexagonal close-packed crystal structures. Derive the relationships between unit cell edge length and atomic radius for face-centered cubic and body-centered cubic crystal structures. Compute the densities for metals having face-centered cubic and bodycentered cubic crystal structures given their unit cell dimensions. Given three direction index integers, sketch the direction corresponding to these indices within a unit cell. Specify the Miller indices for a plane that has been drawn within a unit cell. Describe how face-centered cubic and hexagonal close-packed crystal structures may be generated by the stacking of close-packed planes of atoms. Distinguish between single crystals and polycrystalline materials. Define isotropy and anisotropy with respect to material properties. Chapter 3 - 2
3. 3. Energy and Packing • Non dense, random packing Energy typical neighbor bond length typical neighbor bond energy • Dense, ordered packing r Energy typical neighbor bond length typical neighbor bond energy r Dense, ordered packed structures tend to have lower energies. Chapter 3 - 3
4. 4. Materials and Packing Crystalline materials... • atoms pack in periodic, 3D arrays • typical of: -metals -many ceramics -some polymers crystalline SiO2 Adapted from Fig. 3.23(a), Callister & Rethwisch 8e. Noncrystalline materials... • atoms have no periodic packing • occurs for: -complex structures -rapid cooling "Amorphous" = Noncrystalline Si Oxygen noncrystalline SiO2 Adapted from Fig. 3.23(b), Callister & Rethwisch 8e. Chapter 3 - 4
5. 5. 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 Chapter 3 - 5
6. 6. Metallic Crystal Structures • 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... Chapter 3 - 6
7. 7. Simple Cubic Structure (SC) • Rare due to low packing density (only Po has this structure) • Close-packed directions are cube edges. • Coordination # = 6 (# nearest neighbors) Click once on image to start animation (Courtesy P.M. Anderson) Chapter 3 - 7
8. 8. Atomic Packing Factor (APF):SC Volume of atoms in unit cell* APF = Volume of unit cell *assume hard spheres • APF for a simple cubic structure = 0.52 atoms unit cell a R=0.5a close-packed directions contains 8 x 1/8 = 1 atom/unit cell Adapted from Fig. 3.24, Callister & Rethwisch 8e. APF = volume atom 4 π (0.5a) 3 1 3 a3 volume unit cell Chapter 3 - 8
9. 9. 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. ex: Cr, W, Fe (α), Tantalum, Molybdenum • Coordination # = 8 Click once on image to start animation (Courtesy P.M. Anderson) Adapted from Fig. 3.2, Callister & Rethwisch 8e. 2 atoms/unit cell: 1 center + 8 corners x 1/8 Chapter 3 - 9
10. 10. Atomic Packing Factor: BCC • APF for a body-centered cubic structure = 0.68 3a a 2a Adapted from Fig. 3.2(a), Callister & Rethwisch 8e. R a Close-packed directions: length = 4R = 3 a atoms volume 4 π ( 3a/4) 3 2 unit cell atom 3 APF = volume a3 unit cell Chapter 3 - 10
11. 11. Face Centered Cubic Structure (FCC) • 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 • Coordination # = 12 Click once on image to start animation (Courtesy P.M. Anderson) Adapted from Fig. 3.1, Callister & Rethwisch 8e. 4 atoms/unit cell: 6 face x 1/2 + 8 corners x 1/8 Chapter 3 - 11
12. 12. Atomic Packing Factor: FCC • APF for a face-centered cubic structure = 0.74 maximum achievable APF 2a a Adapted from Fig. 3.1(a), Callister & Rethwisch 8e. Close-packed directions: length = 4R = 2 a Unit cell contains: 6 x 1/2 + 8 x 1/8 = 4 atoms/unit cell atoms volume 4 3 π ( 2a/4) 4 unit cell atom 3 APF = volume 3 a unit cell Chapter 3 - 12
13. 13. FCC Stacking Sequence • ABCABC... Stacking Sequence • 2D Projection B B C A B B B A sites C C B sites B B C sites • FCC Unit Cell A B C Chapter 3 - 13
14. 14. Hexagonal Close-Packed Structure (HCP) • ABAB... Stacking Sequence • 3D Projection • 2D Projection A sites B sites a Middle layer A sites c Top layer Bottom layer Adapted from Fig. 3.3(a), Callister & Rethwisch 8e. • Coordination # = 12 • APF = 0.74 • c/a = 1.633 6 atoms/unit cell ex: Cd, Mg, Ti, Zn Chapter 3 - 14