Chapter 3: Crystal Binding (Bonding)
Overview & Survey of Bonding Types
What kinds of forces hold the atoms together in a
solid? That is, What is their physical origin??
Interatomic Bonding (or Binding)
Each bonding mechanism between the atoms in a
solid is a result of the electrostatic interactions
between the nuclei & the electrons.
• The differing bond strengths & differing bond types
are determined by the electronic structures of the
atoms involved.
• The existence of a stable bonding arrangement
implies that the spatial configuration of positive ion
cores & outer electrons has a smaller
Quantum Mechanical Total Energy
than any other configuration of these particles (including
infinite separation of the atoms).
• In a particular solid, the energy difference
of the configuration of atoms compared
with that of the isolated atoms is called
The Cohesive Energy
• Cohesive Energies in solids range from
~ 0.1 eV/atom for solids with only the
weak Van der Waals interaction to
~ 7 eV/atom or greater in some covalent &
some ionic compounds & some metals.
Table 3.1: Cohesive Energies of Elemental Solids
Table 3.2: Melting Points of Elemental Solids
Table 3.3:
Isothermal Bulk Moduli & Compressibilities of Elemental Solids
Interaction Energies Between Atoms
• The energy of a crystal is lower than that of the free
atoms by an amount equal to the energy required to
pull the crystal apart into a set of free atoms.
• This is called the crystal Binding (Cohesive) Energy.
Example
Crystalline NaCl is much more stable than a
collection of free Na & Cl atoms (see figure):
Cl
+
Na
Crystalline
NaCl
• For a pair of atoms, a typical
potential energy curve V(R) as a
function of interatomic separation V(R)
R looks qualitatively as shown.
The force is
0
 R0
Repulsive
R
F(R) = - (dV/dR).
At equlibrium, the repulsive part
of the force exactly equals the
attractive part. The V(R) curve
has a minimum at equilibrium R
2
distance R0: At R0, F(R0) = 0.
Attractive
R1
R = R 1 + R2
• For R > R0, V(R) increases gradually with increasing R.
V(R)  0 as R  ∞
The force F(R) is attractive in this region.
• For R < R0: V(R) increases rapidly with decreasing R.
V(R)  ∞ as R  0
The force F(R) is replusive in this region.
• The potential energy V of either atom is given by:
V= Sum of an Attractive Term which decreases
with increasing separation & a Repulsive Term
which increases with decreasing separation.
Mathematically, V has the general empirical form (R  r):
a
b
V (r )  m  n
r
r
• V(r) = Net potential energy of interaction as a function of r
r = Distance between atoms, ions, or molecules
a, b = Proportionality constants
m, n = Constants characteristic of bond type & structure type.
Types of Bonding Mechanisms
• As discussed in our Quantum Mechanics review, it is conventional
to classify the bonds between atoms into different categories:
1. Van der Waals
2. Ionic
3. Covalent
4. Metallic
5. Hydrogen
“Secondary”
Bonding
Special Case of
Van der Waals
Bonding
• Of course, as we’ve said,
All bonding is a consequence of the
electrostatic interaction between nuclei &
electrons obeying Schrödinger’s equation.
Types of Bonding Mechanisms
Van der Waals Bonding
Chemists often call it London Bonding
Sometimes, it is called Van der Waals-London Bonding
Johannes D. van der Waals
Fritz London
(1837-1923)
(1900-1954)
Studied intermolecular forces in VPT
relationships in liquids & gases.
Studied intermolecular
induced-dipole interactions.
Van der Waals Bondıng
Van der Waals Bonding is Very weak!
• Typically its strength is ~ 0.2 eV/atom.
It is most important in interactions
between neutral atoms or molecules.
• The cause of these weak attractive
forces is the fact that the lattice
vibrations result in slight charge
separations between the electrons & the
nuclei.
Van der Waals Bondıng
• The cause of these weak attractive forces is the
fact that the lattice vibrations result in slight charge
separations between the electrons & the nuclei.
• Thus, (oscillating) Electric Dipoles are
induced on each atom. These dipoles
attract each other.
• The “larger” an atom is, the easier it is to
polarize (to form a dipole). So, Van der
Waal's Forces are stronger between
“large” atoms than between “small” atoms.
• Van der Waals (London) Bonding is very weak in
comparison to all other bonding types. This effect is
present in most bonds, but other effects usually are
much, much larger than it. Exceptions are bonds
between Noble or Rare Gas atoms (with completely
filled valence electron shells). This type of bonding is
important between any neutral molecules.
• Dipole-dipole interactions occur between the
induced dipoles.
Van der Waals Bonds are weak bonds formed by the
attraction of fluctuating dipoles between (e.g., atoms of the
noble gases). Van der Waals bonds are non-directional.
Solid Neon
LINK
The Van der Waals Force
• Produces Bonding Energies ~ 0.2 eV or smaller.
(very, very weak!) These can be even of the order
of the thermal vibrational energy at T = 300 K or
kBT ~ 0.026 eV
Examples: Solids formed from Inert Gas atoms
Near neighbor Ar atoms
Ar
+ Ar -
Ar
+ Ar -
Lattice vibration
induced dipoles on
near neighbor Ar sites.
 There are electric dipole-dipole interactions
between induced dipoles on neighboring Ar sites.
Van der Waals Forces
(or London “Dispersion” Forces)
• Electrons on one atom are attracted
to the nucleus on a neighboring
atom, creating an “instantaneous”
dipole on the 1st atom. That dipole
induces an instantaneous dipole on the
2nd atom. The 2 induced dipoles then
attract each other.
• These forces are proportional to the
polarizability of the atom. This
property is a measure of the ease with
which the electron “cloud” can be
deformed. The polarizability is
approximately proportional to the
number of electrons in the molecule.
Table 3.4: Properties of Solids of Inert Gas Atoms
Ionıc Bondıng
Ionic Bonding is caused by the
Electrostatic Attraction between positively
& negatively charged ions
(usually non-metal atoms & metal atoms).
• The ions are produced by a transfer of
electrons between two atoms with a large
difference in electro-negativities.
• All ionic compounds are crystalline solids at
room temperature.
• NaCl & CsCl are typical examples of
ionically bonded solids.
Ionıc Bondıng
• Atoms of the metallic elements (e.g.
Na, Cs, ..) have weak ionization potentials.
– That is, they easily give up one or more of their
outer valence electrons to become
Positive Ions.
• Atoms of some other elements have
strong electron affinities (unfilled orbitals in
their valence electron shells).
– That is, they can easily “steal” electrons from
other atoms to form
Negative ions.
Example: NaCl
• Na Atoms have a weak ionization potential.
– That is, they easily give up one of their outer valence electrons
to become positive ions.
• Cl Atoms have a strong electron affinity (unfilled orbital
in the valence electron shells).
– That is, they can easily “steal” electrons from other atoms (like
Na) to form negative ions.
Na
Cl
Example: NaCl
• Notice that when a sodium (Na) atom loses its one
valence electron it gets “smaller” in size, while the
chlorine (Cl) grows larger when it gains an additional
valence electron. After the reaction takes place, the
charged Na+ and Cl- ions are held together by
electrostatic forces, thus forming an ionic bond.
• There must also be Repulsive Forces between Ions.
• When Na+ & Cl- ions approach each other close enough
that their electron orbitals begin to overlap, the electrons
begin to repel each other because of the Repulsive
Electrostatic Force. Of course, the closer together the
ions are, the greater the Repulsive Force.
• The Pauli Exclusion Principle also plays an important role
in the repulsive force. To prevent a violation of this principle,
the potential energy of the system increases very rapidly.
Electronegativity Table for Some Elements.
Table continued above right!
As already discussed, the difference
in electronegativities of the atoms
involved in a bond is an indication
whether one member is more
attractive to electrons & so if an
ionic bond will form. Looking at a
table of electronegativities, such as
this one. will help to determine this.
Electronegativity: The tendency of an atom to
attract electrons to itself when chemically combined
with another element.
Periodic
Table
The halogen group has the highest electronegativity of the families.
The first period has the highest electronegativity. Noble gases do not
have electronegativity as the valence shell is already full.
Table 3.5: Ionization Energies
Table 3.6: Electron Affinities of Negative Ions
Table 3.7: Properties of Alkali Halide
Crystals with the NaCl Structure
Ionic Materials
Property
Explanation
Melting Point,
Boiling Point
Melting & boiling points of ionic compounds are high
because a large thermal energy is required to separate
the ions which are bound by strong electrical forces.
Electrical
Conductivity
Solid ionic compounds do not conduct electricity when
a potential is applied because there are no mobile
charged particles. No free electrons causes the ions to be
firmly bound and cannot carry charge by moving.
Hardness
Brittleness
Most ionic compounds are hard; their crystal surfaces
are not easily scratched. This is because the ions are
bound strongly to the lattice & aren't easily displaced.
Most ionic compounds are brittle; crystals shatter if it is
distorted. This happens because distortion cause ions of
like charges to come close together & sharply repel.