Chapter 3. Crystal Binding
Energy of a crystal and crystal binding
Cohesive energy of
Molecular crystals
Ionic crystals
Metallic crystals
Elasticity
What causes matter to exist in
three different forms?
If the intermolecular forces are strong, at
relatively higher temperatures a compound
could exist as a solid or a liquid. The
temperature of matter is directly related to
the kinetic energy of the molecules or
particles making up the matter. This is given
by the kinetic molecular theory (KMT) matter
applies to all phases of matter, gas, liquid
and solid.
Inter-particle forces
•
•
•
•
•
•
London Dispersion or Van der Waals
Ionic bond
Covalent bond
Hydrogen Bonding
Dipole-dipole
Metallic bond
1
London Dispersion-Van der Waals
Forces
These forces are the weakest of all
intermolecular attractions and occur in nonpolar molecules.
The London dispersion forces results from
instantaneous shifts of electron cloud of
non-polar molecules.
These shifts in electron cloud create
instantaneous dipoles with very short
lifetime.
A weaker attractive force results because of
the short lived dipole attractions between
two molecules. Non-polar molecules such as
H2 and N2 can be cooled to liquids at very
low temperature due to the existence of
London Dispersion forces.
Crystals of inert gases
Temporary dipole moments
The weakest possible bond is that
between non-polar molecules and
noble gas atoms (He, Ne, Kr, Ar, Xe,
and Ra). These have closed electronic
structures - and at first sight should not
form bonds. For He this is almost true:
the gas condenses at 4.2 K, and the
liquid freezes only at 0.95 K at a
pressure of 26 atm. The interaction
between neutral particles is best
described by the van der Waals London interaction.
Cohesive Energies of Elements
2
Van der Waals Interaction
In the van der Waals interaction, the long range
cohesive potential results from the electrostatic
attraction between two mutually induced electric
dipoles. Its dependence on the separation r between
two molecules has the form and α is the polarizability
of the molecule
U12 (r) = - B/ r 6
Repulsive term
• Repulsive interaction
Repulsive Interaction:Pauli
Exclusion Principle
• Two electrons can not have their
quantum numbers equal
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Lennard-Jones potential
These two attractive and repulsive terms are
combined in the Lennard-Jones potential
Ionic Crystals: Ionic Bonding
Atoms whose atomic structure only deviates by one or
two electrons from a closed outer shell, may easily
lose or gain electrons to become a stable charged ion.
For example
Na: (1s2 2s2 2p6 3p2 3p6) 4s1 loses its outer 4s electron
to become
Na+: (1s2 2s2 2p6 3p2 3p6) which has the stable Ne
electronic structure
Similarly
F: 1s2 2s2 2p6 3p2 3p5 gains an electron to become
F-: (1s2 2s2 2p6 3p2 3p6)
Two such ions will be attracted by a Coulomb force, with
a binding energy
Coulomb’s Model
where e = charge on an electron = 1.602 x 10-19 C
ε0 = permittivity of vacuum = 8.854 x 10-12 C2J-1m-1
ZA = charge on ion A
ZB = charge on ion B
d = separation of ion centers
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Ionic Interaction
• Two such ions will be attracted by a Coulomb
force, with a binding energy
• where r0 is the equilibrium separation of the ions
and q+ and q- are the charges of the positive
and negative ions respectively. The repulsive
term UR(r) is a short range interaction
• Repulsive interaction ← Pauli exclusion principle
Cohesive Energy
Coulombic Attractions and
Repulsions in the Ionic Crystals
A=
5
Madelung Constant
Calculation
Madelung Constant (A)
Lattice Energy
• The Lattice energy, U, is the amount of
energy required to separate a mole of
the solid (s) into a
• gas (g) of its ions.
6
Born_Haber Cycle
• Energy Considerations in Ionic Structures
7
Energy and ionic bond formation
Na+(s) + Cl(g)
+496 kJ(I.E.)
-349 kJ (E.A.)
Na+(s) + Cl-(g)
Na(g) + Cl(g)
Na(g) + 1/2 Cl2(g)
+121 kJ(1/2 B.D.E.)
Na(s) + 1/2 Cl2(g)
+92 kJ(S.E.)
-771 kJ (L.E.)
-411 kJ(∆Hf)
NaCl(s)
Born-Lande Model:
• This modes include repulsions due to
overlap of electron electron clouds of ions.
εo = permitivity of free space
• A = Madelung Constant
• ro = sum of the ionic radii
• n = average born exponet depend on the
electron configuration
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Lattice energy
• The higher
the lattice
energy, the
stronger the
attraction
between
ions.
Compound
Compound
LiCl
LiCl
NaCl
NaCl
KCl
KCl
NaBr
NaBr
Na
Na22O
O
Na
Na22SS
MgCl
MgCl22
MgO
MgO
Lattice
Latticeenergy
energy
kJ/mol
kJ/mol
834
834
769
769
701
701
732
732
2481
2481
2192
2192
2326
2326
3795
3795
Lattice Energy
Degree of Covalent Character
Fajan's Rules (Polarization)Polarization will be
increased by:
• 1. High charge and small size of the cation
• 2. High charge and large size of the anion
• 3. An incomplete valence shell electron
configuration
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Trends in Melting Points
Silver Halides
• Compound
•
AgF
•
AgCl
•
AgBr
•
AgI
M.P. oC
435
455
430
553
Dipole-Dipole Intermolecular
Forces.
This include the attraction between all polar
molecules through the dipoles (except F-H, O-H
and N-H dipoles) dipolar covalent bond formed
by unequal sharing of electrons of bonds in a
molecule. A molecule can be non-polar even
though it may have polar covalent bond because
of the symmetry of the molecular structure
canceling the dipoles. Therefore, there are no
dipole-dipole interactions in non-polar
molecules.
Molecular Structure and Bonding
Bonding Theories
1. Lewis Theory
2. VSEPR Theory
3. Valence Bond theory (with hybridization)
4. Molecular Orbital Theory (molecular orbitals)
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Bonding in Covalent (net-work)
Crystals
•
•
•
•
•
•
Si, Ge, C
Share electrons, overlap of electrons
Directionality
Tetrahedral bond
→1S22S12P3 → hybridization
exchange interaction ←spin dependent
Coulomb energy
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Hydrogen Bonding
Three special cases of stronger dipole-dipole
interactions resulting from F-H, O-H and N-H
dipolar covalent bond are called hydrogen
bonding. This is because F, O and N have the
largest electronegativities among other
elements. Hydrogen bonding (between O-H and
O-H dipoles) in water allows water to exist as a
liquid at room temperature. N-H dipole in
proteins allows the formation of doubles helix
structure in DNA and other complex structures
found in living cells.
Hydrogen bonding in HF2-
F-
H+
F-
Bonding Models for Metals
• Bonding Models for Metals
• Molecular orbital bands
• Band Theory of Bonding in Solids
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Metallic Bonding
• Metals are held together by delocalized bonds
formed from the atomic orbitals of all the atoms
in the lattice.
• The idea that the molecular orbitals of the band
of energy levels are spread or delocalized over
the atoms of the piece of metal accounts for
bonding in metallic solids.
Bonding Models for Metals
Band Theory of Bonding in Solids
Bonding in solids such as metals,
insulators and semiconductors may be
understood most effectively by an
expansion of simple MO theory to
assemblages of scores of atoms
Linear Combination of Atomic Orbitals
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Linear Combination of Atomic Orbitals
Types of Materials
• A conductor (which is usually a metal)
is a solid with a partially full band
• An insulator is a solid with a full band
and a large band gap
• A semiconductor is a solid with a full
band and a small band gap
• Element
C
Si
Ge
Sn
Band Gap
5.47 eV
1.12 eV
0.66 eV
0
eV
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Different Types of Atomic
Radii
• In the way they are measured:
• 1 Covalent Radii: Radii based on covalently
liked atoms in covalently bonded molecules.
• 2 van der Waals Radii: Radii based on non
bonded atoms in solids.
• 3 Metallic Radii (12-coordinate):Radii based on
metallic solids.
• 4 Ionic Radii: Radii basesd on bond distances
in ionic solids.
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