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### 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
- Several unit cell types possible, but atoms or ions placed at lattice points or corners of geometric object

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

Cubic Unit Cell

- 3 types:
- 1)Primitive or Simple Cubic (SC)
- 2) Body-Centered Cubic (BCC)
- 3) Face-Centered Cubic (FCC)

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

Which metals have which crystal lattices?

- Simple cubic: Po
- BCC: GI, 3B, 4B, Ba, Ra, Fe
- FCC: VIIIB, IB, Al, In, Pb

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

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%

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

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%

More on FCC

- Each atom does not touch another along edge
- However, atoms touch along face diagonal
- Thus, each edge length = (22)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%

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.

CCP and HCP: Efficiency in Stacking

- CCP = Cubic Close-Packing (it’s FCC)
- HCP = Hexagonal Close-Packing
- 74% packing efficiency

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

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

LiCl

- Notice: Li+ has octahedral geometry
- Thus, cation in octahedral hole (between 6 ions)
- Coordination # = 6

- FCC

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

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

Other Types of Solids: Network Solids

- Array of covalently bonded atoms
- Graphite, diamond, and silicon
- The latter two sturdy, hard, & high m.p.’s

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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