Materials Science 4 - Clarkson University

FE-4: Review of materials science for the FE
Part 3: Corrosion, thermal and
electrical properties
• Based on the following:
• ES 260 text:
• FE free Reference Handbook:
• FE review manual:
• Practice problems:
Last revised February 22, 2014 by W.R. Wilcox at Clarkson University.
Thermal properties
• Atoms in a solid vibrate around their equilibrium positions.
• The vibrations increase as temperature is increased.
Heat capacity
• Energy is required to increase the temperature.
• We define the heat capacity at constant pressure as CP = dQ/dT, where
Q is the energy added to the material and T is the temperature.
• If CP is constant, then the amount of energy required for T is Q = CPT.
• The specific heat cP is usually defined as the heat capacity per unit mass,
so that CP is cP multiplied by the mass of the object.
Thermal expansion coefficient
• As temperature increases, the average distance between atoms also
• This causes an increase in the dimensions of the object, e.g. going from
initial length L0 to new length L.
L  L0
• We define the thermal expansion coefficient as  
Thermal conductivity
• If the temperature is raised at the surface of a solid, heat is transferred to the
interior gradually raising the temperature there.
• The rate of heat flow increases as the temperature gradient dT/dx increases.
• We can define the thermal conductivity as k = q/(-dT/dx) where q is the heat
flow per unit area perpendicular to the temperature gradient.
• Thus q = k(-dT/dx) (- sign if q is in x direction; heat flows from high to low T)
• (In the FE manual, the symbol  is used rather than k, and it is called “heat
conductivity” rather than “thermal conductivity.”)
• Three mechanisms for heat transfer in solids:
1. Lattice vibrations. Important with strong bonding, as in diamond.
2. Electron motion. Important when there are many free electrons, e.g. metals
3. Radiation. When the material does not absorb the radiation. Depends on
the material composition, the presence of defects, the temperature and the
wavelength of the radiation. Zero for metals. Sometimes important for
ceramics. This is NOT thermal conduction and it is very difficult, if not
impossible, to calculate.
Electrical Properties
Ohm’s law: V = I R
Resistivity of the specimen is defined as  = RA / l
Conductivity = 1/resistivity
An electric field, E = dV/dx, causes movement of electrons (or sometimes
ions at high temperature). Thus metals are good electrical conductors.
• Resistance to movement of electrons is caused by interaction with the atoms
and with defects such as impurities.
Pure metals at 1 atm
Capacitors and dielectrics
• Charge held by a capacitor is given by q = CV, where C is capacitance
(coulomb/volt = farad) and V is the voltage across the capacitor.
• C =  A/d = o A/d where A is the area of each plate, d is the distance
between plates,  is the permittivity of the dielectric, o is the permittivity of
vacuum (8.85E-12 F/m).
• Relative permittivity (dielectric constant): r = /o > 1.
• Reflects movement of ions in the dielectric due to the applied electric field.
Piezoelectric properties
• Application of a force causes a voltage difference
between the plates.
• Application of a voltage difference causes the
dimensions to change.
• Quartz, barium and lead titanates, lead zirconate,
ammonium dihydrogen phosphate, etc.
• Many applications, e.g.:
– To measure a force or pressure (transducer).
– Create a spark for ignition of gas.
– Used in oscillator circuits; natural frequency depends
on thickness.
– Used in ink-jet printers to form the small drops.
• Oxidation reaction must be coupled
with a reduction reaction, i.e. the
reverse of a reaction above it in this
• For example:
Zn  Zn2+ + 2e2H+ + 2e-  H2
• Fe  Fe2+ + 2eO2 + 2H2O + 4e-  4(OH)• This is the reaction causing rusting
of iron and steel.
• Some materials such
as stainless steel
and aluminum are
corrosion resistant
because they form a
tightly adhering nonporous oxide film.
• Cl- can make this film
ineffective and lead
to general corrosion
of Al and pitting of
stainless steel.
Electronic conduction in solids
• No two electrons can occupy the same quantum state.
• Thus as atoms become closer to form a solid, the outer electron
states broaden to form bands (1 state for each atom).
• In order for electrons to move in an electric field, they must be able to move
into a vacant state.
• At absolute 0 K, all electrons are in the lowest possible states and so cannot
move without addition of energy to raise them to empty levels.
• There are four possibilities:
e.g., Cu
e.g., Mg
• As T is increased, electrons may be excited to higher levels.
• This is easy if the top band has unfilled states, as for Cu.
• It is also easy if the top band is filled but overlaps with an otherwise empty
band, as for Mg.
• If there's a gap, can conduct only if energy moves electron over the gap.
Conduction in semiconductors
• Examples: silicon, germanium, gallium arsenide, some organic compounds.
Many others, providing the basis of modern electronics, solar cells, infrared
sensors, light emitting diodes, etc.
• May be excited by temperature (kT, where k = R/NA is Boltzmann's constant)
or be absorption of a photon (ν, where  is Planck's constant & ν
• Not only may the excited electron move, but also the empty state (hole) left
Semiconductor devices
• Conductivity in semiconductors is more commonly provided by addition of
impurities (dopants), e.g. B and P in Si.
• When a substitutional impurity has an extra valence electron the extra
electron may be free to move in an electric field. Since the current is carried
by negative charges, the semiconductor is called "n-type." P in Si:
• When the "dopant" has one fewer electrons, the missing electron in a
covalent bond is called a "hole." An electron from an adjacent covalent bond
may move into this hole in an electric field. Since the electric current is
carried by what appears to be positive charges, the semiconductor is called
"p-type." For example, B in Si:
Ionization of dopants
• The electron energy level for an impurity is in the band gap. For conduction,
the extra electron in a donor must be excited into the conduction band:
• Much less energy must be added for this than exciting an electron from the
valence band into the conduction band. So may be entirely ionized at room
temperature, thereby giving one conduction electron for each donor atom.
• Similarly, when the energy level for an acceptor is near the valence band, it
may be entirely ionized at room temperature, thereby giving one hole for
each acceptor atom.
• Most semiconductor devices require p-n junctions to function.
From the FE exam handbook
• Eg - Ed is the energy required to
excite an electron from a donor
into the bottom of the
conduction band.
• Ea is the energy required to
excite an electron from the top
of the valence band into an
• The smaller these values, the
more ionization will occur at a
given temeperature.
Maximum dopant solubilities in the FE handbook
Solubility versus T in Si in the literature.
Units are atoms/cm3 = 106 atoms/m3
Solubility of impurities in Si:
Si-B phase diagram at 1 atm
Solubility of B
in solid Si.
Si-As phase diagram at ~40 bar
Solubility of
As in solid Si
Si-P phase diagram at 1 atm
Where is the line for the solubility of P in solid Si versus temperature?