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Solids

Solids. Ch.13. Solids. Fixed, immobile (so to speak) Symmetry Crystals So what’s the inner order?. Unit Cells. Unit cell = smallest repeating unit containing all symmetry characteristics Unit cell reflects stoichiometry of solid

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Solids

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  1. Solids Ch.13

  2. Solids • Fixed, immobile (so to speak) • Symmetry • Crystals • So what’s the inner order?

  3. Unit Cells • Unit cell = smallest repeating unit containing all symmetry characteristics • Unit cell reflects stoichiometry of solid • Several unit cell types possible, but atoms or ions placed at lattice points or corners of geometric object

  4. Crystal Lattices • 3D unit cells built like legos  • Crystal Lattice = arrangement of units cells • seven 3D units cells found • Simplest = Cubic Unit Cell (equal length edges meeting at 90° angles) • Each face part of 2 cubes • Each edge part of 4 cubes • Each corner part of 8 cubes

  5. Cubic Unit Cell • 3 types: • 1)Primitive or Simple Cubic (SC) • 2) Body-Centered Cubic (BCC) • 3) Face-Centered Cubic (FCC)

  6. Cubic Unit Cell (cont.) • Similarity: • Same ions/atoms/molecules at each corner • Difference: • BCC/FCC have more items at other locations • BCC has same item in center of cube • FCC has same item centered on each side of cube

  7. SC: What do they look like? • BCC: • FCC:

  8. Which metals have which crystal lattices? • Simple cubic: Po • BCC: GI, 3B, 4B, Ba, Ra, Fe • FCC: VIIIB, IB, Al, In, Pb

  9. How many atoms per unit cell? • SC: each atom shared by 8 cubes • 8 corners of cube  1/8 of each corner atom w/in unit cell = 1 net atom/unit cell

  10. More on SC • Each atom touches one another along edge • Thus, each edge = 2r • Coordination number (# of atoms with which each atom is in direct contact) = 6 • Packing efficiency = fraction of volume occupied = 52%

  11. How many atoms per unit cell? (cont.) • BCC: 2 net atoms w/in unit cell (SC + 1 in center) • FCC: 6 faces of cube  ½ atom w/in unit cell = 3 atoms + 1 atom (SC) = 4 net

  12. More on BCC • Each atom does not touch another along edge • However, atoms touch along internal diagonal • Thus, each edge length = 4r/3 • Let’s derive this… • Coordination number (# of atoms with which each atom is in direct contact) = 8 • Central atom touches 8 atoms • Packing efficiency = fraction of volume occupied = 68%

  13. More on FCC • Each atom does not touch another along edge • However, atoms touch along face diagonal • Thus, each edge length = (22)r • Let’s derive this… • Coordination number (# of atoms with which each atom is in direct contact) = 12 • Packing efficiency = fraction of volume occupied = 74%

  14. Problems • Eu is used in TV screens. Eu has a BCC structure. Calculate the radius of a europium atom given a MW = 151.964 g/mol, a density of 5.264 g/cm3. • Iron has a BCC unit cell with a cell dimension of 286.65 pm. The density of iron is 7.874 g/cm3 and its MW = 55.847 g/mol. Calculate Avogadro’s number.

  15. CCP and HCP: Efficiency in Stacking • CCP = Cubic Close-Packing (it’s FCC) • HCP = Hexagonal Close-Packing • 74% packing efficiency

  16. Structures of ionic solids • Take a SC or FCC lattice of larger ions • Place smaller ions in holes w/in lattice • Smallest repeating unit = unit cell

  17. CsCl • SC unit cell • Cs+ in center of cube  Cubic hole • Surrounded by 1 Cl- (in 8 parts) • 1 Cs+ : 1 Cl- • Coordination # = 8 • Why SC and not BCC? • Because ion in center different from lattice pt ions

  18. LiCl • Notice: Li+ has octahedral geometry • Thus, cation in octahedral hole (between 6 ions) • Coordination # = 6 • FCC

  19. NaCl • FCC • Lattice has net 4 Cl-/unit cell • (8x1/8)+(6x1/2) = 4 • 1 Na+ in center of unit cell • 3 Na+ along edges of unit cell • (12x1/4) = 3 • Thus, net total of 4 Na+ ions • Total 4 Cl- : 4 Na+  1:1

  20. Tetrahedral holes • Each ion surrounded by 4 other oppositely-charged ions • Unit cell: 4 of each ion  total 8 ions • Coordination # = 4 • 8 tetrahedral holes in FCC unit cell • 4 by Zn2+ and 4 by S2- • Zn2+ occupies ½ of tetrahedral holes and surrounded by 4 S2- • S2- forms FCC unit cell

  21. ZnS

  22. ZnS

  23. Other Types of Solids: Network Solids • Array of covalently bonded atoms • Graphite, diamond, and silicon • The latter two  sturdy, hard, & high m.p.’s

  24. Graphite and diamond

  25. Other Types of Solids: Amorphous Solids • Glass & plastics • No regular structure • Break in all sorts of shapes • Long range of m.p.’s

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