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Understanding Closest Packing in Metals: Structures, Density, and Properties

This chapter delves into the packing of uniform, hard spheres in metals to optimize space, termed closest packing. It discusses cubic closest packed (CCP) and hexagonal closest packed (HCP) structures, including their atomic arrangements and calculations for edge lengths and densities. The chapter explains the concept of metallic bonds, highlighting the weak attraction of valence electrons and the resulting malleability and ductility of metals. Additionally, it covers metal alloys, including substitutional and interstitial types, exemplified by brass and steel.

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Understanding Closest Packing in Metals: Structures, Density, and Properties

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  1. Liquids and Solids Chapter 10 – Day 2

  2. Packing in Metals Model: Packing uniform, hard spheres to best use available space. This is called closest packing. Each atom has 12 nearest neighbors.

  3. Cubic closest packed (ccp) structure • Every fourth layer occupies the same vertical position of atoms. • Occurs with face centered cubic unit cells.

  4. Hexagonal closest packed (hcp) structure • Every other layer occupies the same vertical position. • Occurs with body centered packing unit cells.

  5. Density = mass/volume (g/cm3) Density = (# atoms)(atomic mass/avogadro’s #) edge3 Note – Remember it is easier to convert edge to cm before cubing it. Based on unit cell shape what is the edge length? Calculating Density of Closest Packed Solid

  6. Simple Cubic • Edge = 2r • The edge length is 2x the atomic radii of the element.

  7. FCC – Face Centered Cubic • Edge = e2 + e2 = (4r)2 2e2 = (4r)2 e2 = 8r2 e = r√8

  8. BCC – Body Centered Cubic • Edge = (4r)2 = (e√2)2 + e2 3e2 = (4r)2 4r e e√2

  9. Metallic Bonds • How atoms are held together in the solid. • Metals hold onto their valence electrons very weakly. • Think of them as positive ions floating in a sea of electrons.

  10. + + + + + + + + + + + + Sea of Electrons • Electrons are free to move through the solid. • Metals conduct electricity.

  11. Metals are Malleable • Hammered into shape (bend). • Ductile - drawn into wires. • Because of mobile valence electrons

  12. + + + + + + + + + + + + Malleable

  13. + + + + + + + + + + + + Malleable • Electrons allow atoms to slide by but still be attracted.

  14. Metal Alloys • Substitutional Alloy: some metal atoms replaced by others of similar size. • brass = Cu/Zn

  15. Metal Alloys(continued) • Interstitial Alloy: Interstices (holes) in closest packed metal structure are occupied by small atoms. • steel = iron + carbon

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