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
What do they look like?
• SC:
• BCC:
• FCC:
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 S2S2- forms FCC unit cell
ZnS
ZnS
Other Types of Solids: Network
Solids
• Array of covalently bonded atoms
• Graphite, diamond, and silicon
• The latter two  sturdy, hard, & high
m.p.’s
Graphite and diamond
Other Types of Solids: Amorphous
Solids
• Glass & plastics
• No regular structure
– Break in all sorts of
shapes
• Long range of m.p.’s