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Chapter 13 — Solids
Metallic & Ionic Solids
Chapter 13
The Chemistry of
Solids
Jeffrey Mack
California State University,
Sacramento
Crystal Lattices
Properties of Solids
• Regular 3-D arrangements of equivalent LATTICE
POINTS in space.
• Lattice points define UNIT CELLS
• Unit cells are the smallest repeating internal unit
that has the symmetry characteristic of the solid.
1. Molecules, atoms or
ions locked into a
CRYSTAL LATTICE.
2. Particles are CLOSE
together.
3. These exhibit strong
intermolecular forces
4. Highly ordered, rigid,
incompressible
ZnS, zinc sulfide
Types of Solids
Type:
Examples:
Network Solids
Forces:
Diamond
Ionic Compounds
Metals
Molecular
Network
Amorphous
NaCl, BaCl2, ZnS
Ion-Ion (ionic bonding)
Fr, Al
Metallic
Ice, I2, C12H22O11
Dipole-Dipole ot
Induced Dipoles
Diamond, Graphite
Extended Covalent
bonds
Glass, Coal
Covalent; directional
electron-pair bonds
Graphite
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Chapter 13 — Solids
Cubic Unit Cells
There are 7 basic crystal systems, but we will
only be concerned with CUBIC form here.
All sides
equal length
• 1/8 of each atom on a
corner is within the
cube
•
1/2 of each atom on a
All angles
face is within the cube
are 90 degrees
• 1/4 of each atom on a
side is within the cube
Cubic Unit Cells
Primitive
cubic (PC)
Bodycentered
cubic (BCC)
Facecentered
cubic (FCC)
Cubic Unit Cells
Unit Cells for Metals
Simple Cubic Unit Cell
Atom Packing in Unit Cells
Assumes atoms are hard spheres and that crystals are built by
PACKING these spheres as efficiently as possible.
• Each atom is at a corner of a unit cell and is shared
among 8 unit cells.
• Each edge is shared with 4 cells
• Each face is part of two cells.
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Chapter 13 — Solids
Atom Packing in Unit Cells
Crystal Lattices—Packing of Atoms
or Ions
• FCC is more
efficient than either
BC or PC.
• Leads to layers of
atoms.
Crystal Lattices—Packing of Atoms
or Ions
Atomic Radii
Packing of C60
molecules. They are
arranged at the lattice
points of a FCC
lattice.
Problem:
Problem:
Calcium metal crystallizes in a face-centered cubic unit
cell. The density of the solid is 1.54 g/cm3. What is the
radius of a calcium atom?
Calcium metal crystallizes in a face-centered cubic unit
cell. The density of the solid is 1.54 g/cm3. What is the
radius of a calcium atom?
Unit cell volume:
40.08 g
1 cm3
1 mol Ca
4 Ca atoms
×
×
×
= 1.73 ´ 10–22 cm3
1 mol Ca
1.54 g
unit cell
6.022 ´ 1023 atoms
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Chapter 13 — Solids
Problem:
Problem:
Calcium metal crystallizes in a face-centered cubic unit
cell. The density of the solid is 1.54 g/cm3. What is the
radius of a calcium atom?
Calcium metal crystallizes in a face-centered cubic unit
cell. The density of the solid is 1.54 g/cm3. What is the
radius of a calcium atom?
Unit cell volume:
Unit cell volume:
40.08 g
1 cm3
1 mol Ca
4 Ca atoms
×
×
×
= 1.73 ´ 10–22 cm3
1 mol Ca
1.54 g
unit cell
6.022 ´ 1023 atoms
40.08 g
1 cm3
1 mol Ca
4 Ca atoms
×
×
×
= 1.73 ´ 10–22 cm3
1 mol Ca
1.54 g
unit cell
6.022 ´ 1023 atoms
Unit cell edge length:
Unit cell edge length:
V = 1.73 ´ 10–22 cm3 = (edge length)3
V = 1.73 ´ 10–22 cm3 = (edge length)3
edge length = 3 1.73 ´ 10–22 cm3 = 5.57 ´ 10–8 cm
edge length = 3 1.73 ´ 10–22 cm3 = 5.57 ´ 10–8 cm
face diagonal = 4 radius = 2 × edge length
radius =
Number of Atoms Per Unit Cell
Unit Cell Type
PC
BCC
FCC
2 × (5.57 ´ 10–8 cm)
= 1.97 ´ 10–8 cm = 197 pm
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Atom Sharing at Cube Faces &
Corners
Net Number Atoms
1
2
4
There is 1/8th of an atom
shared in corner.
Two Views of CsCl
• Lattice can be Primitive Cubic lattice of Cl - with Cs+ in hole
• OR a Primitive Cubic of Cs+ with Cl- in hole
• Either arrangement leads to formula of 1 Cs+ and 1 Cl- per
unit cell
There is 1/2 shared at
each face
Rutile, TiO2, crystallizes in a structure characteristic of many
other ionic compounds. How many formula units of TiO 2 are
in the unit cell illustrated here? (The oxide ions marked by an
x are wholly within the cell; the others are in the cell faces.)
8 corner Ti  1/8 =
1 Ti
4 face O  ½ = 2 O
1 internal Ti
= 1 Ti
2 internal O = 2 O
= 2 Ti total
=
4 O total
There are two TiO2 units per unit cell.
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Chapter 13 — Solids
Common Ionic Solids
• Titanium dioxide,
TiO2
• There are 2 net Ti4+
ions and 4 net O2ions per unit cell.
The Sodium Chloride Lattice
Many common salts have Face Centered Cubic
arrangements of anions with cations in octahedral
holes.
Example: NaCl
•FCC lattice of anions:
4 Cl per unit cell
+
•Na in octahedral hole:
1 Na+ at center
+
1 Na (center) + (12 edges • 1/4 Na+ per edge)
= 4 Na+ per unit cell
Octahedral Holes—FCC Lattice
Structure & Formulas of Ionic
Compounds
Salts with formula MX
can have Primitive
Cubic structure.
Salts with formula MX2
or M2X cannot.
NaCl Construction
FCC lattice of Cl- with
Na+ in holes
Na+ in
octahedral
holes
The Sodium Chloride Lattice
Na+ ions are in
OCTAHEDRAL holes in a
face-centered cubic
lattice of Cl ions.
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Chapter 13 — Solids
Comparing NaCl with CsCl
Common Ionic Solids
•
•
• Even though their formulas have one cation
and one anion, the lattices of CsCl and NaCl
are different.
• The different lattices arise from the fact that a
Cs+ ion is much larger than a Na+ ion.
Common Ionic Compounds
• Fluorite or CaF2
• FCC lattice of Ca2+
ions
• This gives 4 net Ca2+
ions.
• F ions in all 8
tetrahedral holes.
• This gives 8 net F
ions.
Bonding in Metals &
Semiconductors
An energy-level
diagram shows
the bonding and
antibonding
molecular orbitals
blending together
into a band of
molecular orbitals.
•
•
Zinc sulfide, ZnS
The S2 ions are in facecentered cubic (FCC) structure.
1/8 of each corner S2½ of each face S2Each Zn2+ is in a hole between
S2-.
The holes are tetrahedral
1 atom in ½ of the holes.
Zn = (4  1) = 4
S = (1/8  8) + (½  6) = 4
Zn:S = 4:4 = 1:1 Therefore the
formula is ZnS
Bonding in Metals &
Semiconductors
• Molecular orbital (MO) theory was introduced in
Chapter 9 to rationalize covalent bonding in
molecules
• MO theory can also be used to describe metallic
bonding.
• Metals can be thought of as a “supermolecule”.
• Metallic bonding is described as delocalized: The
electrons are associated with all the atoms in the
crystal and not with specific bonded atoms.
• This theory of metallic bonding is called band
theory.
Band Theory
Molecular orbitals are constructed from the valence
orbitals on each atom and are delocalized over all the
atoms. When sufficient energy is added, electrons are
excited to the conduction band. (Thermal energy
provides this for metals)
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Chapter 13 — Solids
Band Theory
Classifications of Solids
Solids can be classified on the basis of the
bonds that hold the atoms or molecules
together.
This approach categorizes solids as either:
Molecular orbitals are constructed from the valence orbitals on
each atom and are delocalized over all the atoms. When
sufficient energy is added, electrons are excited to the
conduction band. (Thermal energy provides this for metals)
Molecular Solids
• Molecular solids are characterized by
relatively strong intramolecular bonds
between the atoms that form the molecules
• The intermolecular forces between these
molecules are much weaker than the bonds.
• Because the intermolecular forces are
relatively weak, molecular solids are often
soft substances with low melting points.
• Examples:
I2(s), sugar (C12H22O11) and “Dry Ice”, CO2(s)
Ionic Solids
• Ionic solids are salts, such as NaCl, that are held
together by the strong force of attraction between
ions of opposite charge.
q( + ) × q( -)
F»
r2
• Because this force of attraction depends on the
square of the distance between the positive and
negative charges, the strength of an ionic bond
depends on the radii of the ions that form the solid.
• As these ions become larger, the bond becomes
weaker.
•
•
•
•
molecular
Network (covalent)
ionic
metallic
Network (Covalent) Solids
• In Network solids, conventional chemical bonds
hold the chemical subunits together.
• The bonding between chemical subunits is identical
to that within the subunits resulting in a continuous
network of chemical bonds.
• Two common examples of network solids are
diamond (a form of pure carbon) and quartz (silicon
dioxide).
• In quartz one cannot detect discrete SiO2
molecules. Instead the solid is an extended threedimensional network of ...-Si-O-Si-O-... bonding.
Metallic Solids
• In Molecular, ionic, and covalent solids the electrons in
these are localized within the bonding atoms.
• Metal atoms however don't have enough electrons to fill
their valence shells by sharing electrons with their
immediate neighbors.
• Electrons in the valence shell are therefore shared by
many atoms, instead of just two.
• In effect, the valence electrons are delocalized over
many metal atoms. Because these electrons aren't
tightly bound to individual atoms, they are free to
migrate through the metal. As a result, metals are good
conductors of electricity.
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Chapter 13 — Solids
Bonding in Ionic Compounds:
Lattice Energy
The energy of an ion pair (cation/anion) is described
by Coulombs law:
Uion pair
(n +e - )(n -e + )
=C´
d
n+ = cation charge, n = anion charge
d = distance between ion centers
Lattice Energy
The Lattice Energy of a
salt is dependant upon
the charge and size of
the ions.
Uion pair = C ´
latticeU is the energy of formation of one mole of the
solid crystaline compound from its ions in the gas
phase.
M + (g ) + X - (g ) ® MX (s )
Lattice Energy
(n +e - )(n -e + )
d
Problem:
Calculate the molar enthalpy of formation,
fH°, of solid lithium fluoride from the lattice
energy and following thermochemical data.
Calculation of lattice energy via the Born–Haber cycle, an
application of Hess’s law.
Problem:
Problem:
Calculate the molar enthalpy of formation,
fH°, of solid lithium fluoride from the lattice
energy and following thermochemical data.
Calculate the molar enthalpy of formation,
fH°, of solid lithium fluoride from the lattice
energy and following thermochemical data.
Solution: Approach this problem using Hess’s Law.
You need to find the enthalpy for the reaction:
Start by drawing the Born-Haber cycle for the reaction:
Li(s) + ½ F2(g)  LiF(s)
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Chapter 13 — Solids
Problem:
Problem:
Calculate the molar enthalpy of formation,
fH°, of solid lithium fluoride from the lattice
energy and following thermochemical data.
Calculate the molar enthalpy of formation,
fH°, of solid lithium fluoride from the lattice
energy and following thermochemical data.
Start by drawing the Born-Haber cycle for the reaction:
Using Hess’s Law, the enthalpy of formation is found
by:
+
F(g)
Li+(g)
F(g)
+
Li+(g)
subH
Li(s)
subH
Do
+
½ F2(g)

LiF(s)
Li(s)
fHo
Do
+
½ F2(g)

LiF(s)
= subH + I1 + Do + EA + latticeU
Phase Changes Involving Solids
Problem:
Calculate the molar enthalpy of formation,
fH°, of solid lithium fluoride from the lattice
energy and following thermochemical data.
fHo
F(g)
Li(g)
F(g)
Li(g)
EA
IE
EA
IE
= subH + IE + Do + EA + latticeU
Li(s)  Li(g)
Li(g)  Li+(g) + e–
½ F2(g)  F(g)
F(g) + e–  F–(g)
Li+(g) + F–(g)  LiF(s)
∆subH°
IE
Do
EA
∆latticeU
= +159.37 kJ/mol
= +520. kJ/mol
= +78.99 kJ/mol
= –328.0 kJ/mol
= –1037 kJ/mol
fH° =
= –607 kJ/mol
Enthalpies of Fusion Are a Function
of Intermolecular Forces
Melting: Conversion of Solid into Liquid
The melting point of a solid is the temperature at which
the lattice collapses into a liquid. Like any phase change,
melting requires energy, called the enthalpy of fusion.
Energy absorbed as heat on melting = enthalpy of fusion
fusionH (kJ/mol)
Energy evolved as heat on freezing = enthalpy of
crystallization
fusionH (kJ/mol)
Enthalpies of fusion can range from just a few thousand
joules per mole to many thousands of joules per mole.
Phase Changes Involving Solids
• Sublimation: Conversion of Solid into
Vapor
• Molecules can escape directly from the solid
to the gas phase by sublimation
• Solid → Gas Energy required as heat =
sublimationH
• Sublimation, like fusion and evaporation, is
an endothermic process.
• The energy required as heat is called the
enthalpy of sublimation.
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Chapter 13 — Solids
Transitions Between Phases: Phase
Diagrams
Sublimation
Sublimation entails the conversion of a solid directly to its
vapor. Here, iodine (I2) sublimes when warmed.
Phase diagrams are used to illustrate the relationship between
phases of matter and the pressure and temperature.
Phase Diagram for Water
Liquid phase
Phase Equilibria—Water
Solid-liquid
Gas-Liquid
Solid phase
Gas phase
Gas-Solid
Triple Point—Water
Phases Diagrams: Water
T(˚C) P(mmHg)
At the TRIPLE POINT all three
phases are in equilibrium.
Normal boil point (at 1atm):
100
760
Normal freeze point (at 1atm):
0
760
Triple point:
0.0098
4.58
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Chapter 13 — Solids
Phases Diagrams: Water
• Water has its maximum
density at 4 °C, in the
liquid phase.
• Most substances have
a maximum density in
the solid phase.
• Hydrogen bonding
accounts for water’s
deviation from normal
behavior.
Phases Diagrams: Water
• At constant
temp, an
increase in
pressure can
bring about a
phase change
from solid to
liquid!
• This occurs when
the blade of an
ice skate runs on
the ice.
Ice skaters actually ride on a film of water, not the ice!
CO2 Phases
Separate
phases
Increasing
pressure
More
pressure
Supercritical
CO2
Phases Diagram: Water
• At constant temp,
an increase in
pressure can
bring about a
phase change
from solid to
liquid!
CO2 Phase Diagram
• Notice the CO2 has a forward slope of the solid/liquid
boundary.
• This is seen because CO2 does not exhibit hydrogen
bonding.