Chapter 12: Solids and Modern Materials
How do properties of solids relate to their structures and
bonding?
12.1 Classification of Solids
Metallic solids
Held together by a delocalized “sea” of electrons
Ionic solids
Held together by ionic charges
Covalent-network solids
Held together by extended network of covalent bonds
e.g. diamond
Molecular solids
Held together by intermolecular forces
Polymers
Long chains of atoms; atoms within a chain held
together by covalent bonds. Chains held together by
intermolecular forces
Nanomaterials
Solids with dimensions of crystals ~1-100 nm
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12.2 Structures of solids
Crystalline solids
Atoms, ions, or molecules ordered in a well-defined
arrangement
Have highly regular shapes
Intermolecular forces uniform throughout – melt at
a specific temperature
E.g., crystalline SiO2
Amorphous solids (noncrystalline)
Particles have no regular, orderly structure
Intermolecular forces vary in strength throughout
sample – soften/melt over a range of temperatures
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Examples: rubber, SiO2 glass (shown here)
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Notice: in the crystalline solids, there is a small unit of
atoms that ‘repeats’ throughout the structure
The unit cell is the smallest repeating unit which
shows the symmetry of the entire solid
What is the smallest repeating unit in the
crystalline SiO2 example above?
The unit cell can be used to generate the threedimensional structure of the crystal, or the crystal lattice
12.3 Structures of Metallic Solids
Crystal structures of most metals are simple enough that
we can generate the structure by placing a single atom on
each lattice point
To describe metallic solids, we use three types of cubic
unit cells (we restrict ourselves to the cubic type):
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Primitive cubic: lattice points (atoms) at corners only,
e.g.,
Body-centered cubic (BCC): lattice point at corners &
center of cell, e.g.,
Face-centered cubic (FCC): lattice points at corners &
centers of each face, e.g.,
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What is the net number of particles in each type of unit
cell?
Each unit cell is a part of the total three-dimensional
lattice and is thus shared.....
primitive cubic unit cell
8 corners x 1/8 particle/corner = 1 particle
body-centered cubic unit cell
8 corners x 1/8 particle/corner + 1 center x 1
particle/center = 2 particles
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face-centered cubic unit cell
8 corners x 1/8 particle/corner + 6 faces x 1/2
particle/face = 4 particles
Recall: density is an intensive property of matter – it is
a ratio of extensive properties
Since density doesn’t depend on amount, the density
of a unit cell is the same as the density of a large
sample of substance!
E.g., Cu crystallizes in an FCC unit cell whose edge length
is 3.61 Å. Calculate the density (g/cm3) of Cu metal.
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E.g., Iridium crystallizes in an FCC unit cell that has an
edge length of 3.833 Å. The atom in the center of each
face is in contact with the corner atom.
Calculate the atomic radius of an Ir atom.
Calculate the density (g/cm3) of Ir metal.
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Notice: most metals have simple cubic unit cells with only
one atom at each lattice point
E.g. Ni has the Fcc structure; Na has the Bcc unit
cell.
Structures are pretty easy to think about if we treat
the metal atoms as being:
(a) spherical
(b) all the same size
Notice that the structures adopted by crystalline solids are
those that bring particles in closest contact to maximize
attractive forces......
Which arrangement of particles brings each particle into
contact with the largest number of other particles?
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The structure on the right is called the closest-packed
structure
Each particle is in contact with 6 other particles in
the same layer
Now: how do these layers of spheres stack?
Pretty easy to stack the second layer of spheres
Fit in the depressions on top of the first layer
What about the third layer?
Two ways to orient:
In line with first layer: hexagonal close packing
(hcp)
Not in line with first layer: cubic close packing
(ccp)
Important feature: in either hcp or ccp structures, each
sphere has 12 equidistant neighbors
Each sphere has a coordination number of 12
Now: what about an ionic compound, where we’re packing
‘spheres’ that aren’t the same size (anions and cations)?
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Problems du Jour
An element crystallizes in a BCC lattice. The edge of the
unit cell is 2.86Å and the density of the crystal is 7.92
g/cm3. Calculate the atomic weight of the element.
Indicate the type of crystal (molecular/metallic/covalentnetwork/ionic) that each of the following would form:
CaCO3
Pt
ZrO2 (m.p. 2677oC)
Kr
C6H6
I2
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