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2010-01-25 Chapter 03 Structures Of Crystalline Solids

2010-01-25 Chapter 03 Structures Of Crystalline Solids -...

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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? Isotropy and anisotropy CHAPTER 3: CRYSTAL STRUCTURES & PROPERTIES Why study crystal structures? Properties of some materials are dependent on crystal structures. Mg (density 1.74 g/cc) and beryllium (density 1.85 g/cc) have HCP-Hexagonal Closed Packed crystal structure and they are brittle. Gold (density 19.32 g/cc) and silver (density 10.49 g/cc) have FCC- Face Centered Cubic crystal structure and they are ductile.
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Chapter 3- 2 Non dense, random packing Dense, ordered packing Dense, ordered packed structures tend to have higher magnitude of bond energy. Energy r typical neighbor bond length typical neighbor bond energy Energy r typical neighbor bond length typical neighbor bond energy ENERGY AND PACKING Just for Information
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Chapter 3- atoms pack in periodic, 3D arrays typical of: 3 Crystalline materials... -metals -many ceramics -some polymers atoms have no periodic packing occurs for: Noncrystalline materials... -complex structures -rapid cooling Si Oxygen crystalline SiO 2 noncrystalline SiO 2 " Amorphous " = Noncrystalline Adapted from Fig. 3.18(b), Callister 6e. Adapted from Fig. 3.18(a), Callister 6e. MATERIALS AND PACKING Important -few ceramics -many polymers typical of:
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Chapter 3- 4 tend to be densely packed. have several reasons for dense packing: - 1. Typically, only one element is present, so all atomic radii are same. - 2. Metallic bonding is not-directional. (the magnitude of the bond is equal in all directions around an atom) - 3. Nearest neighbor distances tend to be small in order to lower bond energy. have the simplest crystal structures. We will look at three such structures... METALLIC CRYSTALS
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Crystal structure and Lattice Atoms are assumed as hard spheres. Picture shows many atoms stacked in orderly manner. Crystal structure is the manner in which atoms/ions/molecules are spatially arranged. Sometimes term ‘lattice’ is used in the context of crystal structure. Lattice is 3D array of points coinciding with atom positions.
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CONCEPT OF UNIT CELL Small repeat entities are called unit cells. You can build entire crystal structure using unit cells. Thus unit cells are basic building blocks in crystal structure. Hard Sphere Unit Cell Representation Reduced Sphere Unit cell
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Chapter 3- 5 Rare due to poor packing Close-packed directions are cube edges. Only Po-Polonium has this structure Coordination Number = 6 (number of nearest neighbor atoms) (Courtesy P.M. Anderson) SIMPLE CUBIC STRUCTURE (SC) close-packed directions a R=0.5a Unit Cell (Hard Spheres) Eight Unit Cells in Reduced Sphere Notation
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Vs = volume of atoms in unit cell n = number of atoms per unit cell (This is not coordination number) R = radius of atom (atoms are assumed as spheres) Vc = volume of unit cell For cubic structures, Vc = a 3 a = side of cube c 3 c s V R 3 4 n V V APF
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