Solids

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# Solids - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about ' Solids' - talbot

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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 = (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%
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