Solid - Liquid - Vapor equilibria: phase diagrams
Phase diagram: graphical way to summarize conditions
under which equilibria exist between different states of
matter
Note: any point on a curve in the diagram represents
values for P and T for which two phases exist in
equilibrium
In any one-phase region, P and T are independent of
one another
For any two phases to exist at equilibrium, this is no
longer true – P becomes a function of T
What is the significance of the triple point?
The liquid-vapor line ends at the critical point – does the
solid-liquid line end similarly?
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Phase diagrams for H2O and CO2: Fig 11.27 (text)
Note that the solid-liquid line in the H2O phase diagram
slopes to the left; why?
At 1 atm pressure and room temperature, would CO2
melt or sublime? Why?
E.g., The normal melting and boiling points of Xe are -112oC
and -107oC. The triple point of Xe is -121oC and 282 torr
and its critical temperature and pressure are 16.6oC and
57.6 atm.
Sketch the phase diagram for Xe.
Will Xe(s) float on Xe(l)?
If Xe gas is cooled under an external pressure of 100 torr,
will it undergo condensation or deposition?
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Structures of Solids
How do properties of solids relate to their structures and
bonding?
Types 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
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Amorphous solids (noncrystalline)
Particles have no regular, orderly structure
Intermolecular forces vary in strength throughout
sample – soften/melt over a range of temperatures
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
Three types of cubic unit cells (we restrict ourselves to the
cubic type):
Primitive cubic: lattice points (atoms/ions) at corners only,
e.g.,
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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
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!
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E.g., Cu crystallizes in an FCC unit cell whose edge length
is 3.61 Å. Calculate the density of Cu metal.
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 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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Bonding in solids
Physical properties of solids (e.g. melting point, hardness,
conductivity) depend both on the arrangement of particles
and the attractive forces between them
Molecular solids
Consist of atoms or molecules held together by
intermolecular forces (dipole-dipole, etc.)
Usually soft, low-melting ( < 200oC); poor
conductors
Most substances that are gases or liquids at room
temp form molecular solids, e.g., Ar, H2O
Covalent network solids
Atoms held in networks or chains by covalent bonds
Much harder & higher melting than molecular
solids
e.g., SiO2, graphite, diamond
Ionic solids
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Held together by ionic bonds
Strength of bonds depends upon ionic charges and
radii (remember Coulomb’s law!)
High-melting; poor conductors
Metallic solids
Consist entirely of metal atoms
Bond strength intermediate between dispersion forces
and covalent bonds
e- delocalized throughout entire solid – excellent
conductors (thermal and electrical)
Wide range of hardness and melting point
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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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