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Understanding atomic structure
and arrangement will allow us
to better understand how to
control the microstructure and
properties of materials.
Bohr Model
Electrons display characteristics
of both. Not all observed
phenomena can be explained by
the particle definition of electrons.
Particle theory cannot explain
specific heat, tunnel diodes,
scanning electron microscopes,
etc.
Electrons - Wave or Particle?
• The motion of the electron is
described by mathematics that
describe wave motion
• The energy/position of an electron is
described by a probability distribution
(Fermi-Dirac Statistics)
• Heisenberg Uncertainty Principle: the
closer we know the momentum of the
electron, the larger the uncertainty in
the position of the electron. z p = h
Wave Mechanics
The energy/position of an electron is described by a
probability distribution (Fermi-Dirac Statistics)
The energy/position of an electron is described exactly by
the Bohr particle model
• Electrons are transferred to form a bond
• Often found in compounds composed
of electropositive elements (metals)
and electronegative elements (non-
metals)
Na
Valence +1 Cl
Valence -1
Ionic Bonding
• Bonding Energy: 150-370 Kcal/mol
• Nondirectional Bond - strength of
bond equal in all directions
• Low electrical conductivity - entire
ion must move to conduct electricity
• Transparent, brittle, high melting
temperature
• Examples: NaCl 183 Kcal/mol, LiF
240 Kcal/mol
Ionic Bonding
General Characteristics
Electrons are shared to form a bond
Covalent Bonding
• Bonding Energy: 75-300 Kcal/mol
• Directional Bond - strength of bond is
not equal in all directions
• Low electrical conductivity
• Very hard, high melting temperature
• Examples: Si 84 Kcal/mol, GaAs 75
Kcal/mol, Diamond 170 Kcal/mol
Covalent Bonding
General Characteristics
Metallic Bonding
Valence
electrons form
an electron
cloud for
bonding
• Bonding Energy: 25-200 Kcal/mol
• Nondirectional Bond - strength of
bond is equal in all directions
• Good electrical conductivity - cloud of
electrons are free to move to conduct
electricity
• Ductile, opaque
• Examples: Na 26 Kcal/mol, Al 74
Kcal/mol, Cu 81 Kcal/mol
Metallic Bonding
General Characteristics
Van der Waals Bonding
• Weak secondary bond (<10 Kcal/mol)
• Often bonding force between molecules
• Example - PVC can be deformed by breaking
Van der Waals bonds between the molecules
that have strong covalent bonds
Hydrogen Bonding
• Special type of secondary bond between
some molecules containing H
• Example - bonds between molecules of water
Secondary Bonding
Cohesive Energy
Figure 4.19
Atoms are held together by bonds
that behave like springs
Cohesive energy is a measure of
the strength of the bonds
Bond Stiffness
Coulombic Attractive
Force 1/r2FA
Nuclear Repulsive
Force 1/r10FR
Energy=Force dr
a0
Potential Well Concept Ionic Bonding
distance
Ionic
Covalent
Metallic
Van der Waals
Relative Strength of Bonding Types
Table 4.1
Bond stiffness largely determines the value
of the modulus - E
Modulus of Elasticity
distance
Based on the bond energy curve
shown, determine which material
should be used for the applications
given below.
1) Beam that shows little deflection
under load
2) A crucible to be used at high
temperatures
3) A device designed to sense
temperature changes by changing its
dimension
What Determines Density
Density is mostly dependent on atomic weight
• Metals are dense because their atoms are heavy – iron
has an atomic weight of 56
• Polymers have low densities because they are made of
light atoms – carbon has an atomic weight of 12 while
hydrogen has an atomic weight of 1
The size of atoms and the way in which they are packed
also influence density, but to a much lesser degree
Atomic Packing
Most materials are crystalline – have a regularly
repeating pattern of structural units
Atoms often behave as if they are
hard and spherical
Layer A represents the close-packed
layer – there is no way to pack the atoms
more closely than this
Short-Range Order versus
Long-Range Order
1. No Order
Example: gases where atoms randomly fill whatever space is
available
2. Short-Range Order (SRO)
Example: glasses and many polymers where order only extends
to first nearest neighbors. Also called noncrystalline or
amorphous
3. Long-Range Order (LRO)
Example: atomic order that extends to large distances (> 100
nm) typical of metals and all “crystalline” materials
4. Liquid Crystals
Example: LCD’s where the material can change from amorphous
(SRO) to crystalline (LRO) under stimulus
Figure 4.8
Atomic structures are close-packed in three dimensions
Close-packed hexagonal: ABABAB stacking sequence
Face-centered cubic: ABCABC stacking sequence
Packing fraction for CPH and FCC structures is 0.74 – meaning
spheres occupy 74% of all available space
B and C represent alternative
positions for atoms in the next close-
packed plane
If the next plane of atoms lie in the same
position as the A atoms, the stacking sequence will be ABABAB. If the
next plane instead occupy the depressions marked C, the stacking
sequence will be ABCABC.
Unit Cell
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon
Figure 4.11
Red lines define the cell while spheres represent
individual atoms
Shaded regions represent close or closest packed plane
Face-Centered Cubic Crystal
Body-Centered Cubic Crystal
Close-Packed Hexagonal Crystal
Crystal Lattice
Figure 4.12
Lattice points are the
points at which cell
edges meet
(a): hexagonal cell
(b): cubic cell
(c): cell with different
length edges
Non Close-Packed Structures
Body-centered cubic:
ABABAB packing sequence
Packing fraction = 0.68
Amorphous structure:
Packing fraction ≤ 0.64
Figure 4.9
Figure 4.10
Atomic Packing in Ceramics
Figure 4.13
(a): Hexagonal unit cell with a W-C atom pair associated
with each lattice point
(b): Cubic unit cell with a Si-C atom pair associated with each
lattice point
Atomic Packing in Glasses
Figure 4.14
Amorphous silica is the bases of most glasses
Rapid cooling allows material to maintain amorphous
structure achieved after melting
Atomic Packing
in Polymers
Figure 4.15
Figure 4.16
Polymers have a
carbon-carbon
backbone with
varying side-groups
Figure 4.17
Polymer chains bond to each other through weak hydrogen
bonds
Red lines indicate strong cross-linked carbon-carbon bonds
Polymer Structure
Figure 4.18
(a): No regular repeating pattern of
polymer chains – results in a
glassy or amorphous structure
(b): Regions in which polymer chains
line up and register – forms
crystalline patches
(c): Occasional cross-linking allowing
they polymer to stretch – typical
of elastomers
(d): Heavily cross-linked polymers
exhibit chain sliding – typical of
epoxy
Elastic Moduli of Elastomers
Figure 4.20
Undeformed polymer chains
has high randomness (entropy)
Stretched polymer chains
resemble more of a crystalline
structure and has a lower
entropy
Moduli of elastomers is
generally low and unlike
metals, increases with
temperature
Rule of Mixtures
f volume fraction of material or element A
ρA density of material or element A
ρB density of material or element B
Modifying the modulus and density is most effective when
done at a macro scale such as creating a hybrid rather than
a micro scale such as alloying a metal
Density of solid solution or hybrid material
Composites –
Density and Modulus
Figure 4.21
Polymer matrix composite (PMC)
Ceramic matrix composite (CMC)
Metal matrix composite (MMC)
Modulus can be altered by
combining stiff fibers with a
less-stiff matrix
ρr – density of reinforcement
ρm – density of matrix
Modulus of composite bracketed by two bounds:
• Upper bound: assumes that, on loading, both components strain
by the same amount, like springs in parallel
• Lower Bound: assumes that, on loading, each component carries
the same stress, like springs in series
Figure 4.22
Range of modulus and density properties for composites
with a ceramic reinforcement and polymeric matrix
