Scientists do stupid looking things sometimes (though not too unsafe if
they made the material carefully enough)
THERMAL EXPANSION
• Materials change size when heating.
L final  L initial
 (Tfinal  Tinitial )
L initial
CTE: coefficient of
thermal expansion (units: 1/K)
Linit
Lfinal
Tinit
Tfinal
Flashback: PROPERTIES FROM BONDING:
Energy versus bond length
• Bond length, r
F
F
r
• Bond energy, Eo
PROPERTIES FROM BONDING: TM
• Melting Temperature, Tm
Tm is larger if Eo is larger.
PROPERTIES FROM BONDING:
Elastic Properties
• Elastic modulus, E
Elastic modulus
F
L
=E
Ao
Lo
E similar to spring constant
• E ~ curvature at ro
Energy
unstretched length
ro
r
E is larger if curvature is larger.
smaller Elastic Modulus
larger Elastic Modulus
PROPERTIES FROM BONDING: CTE or 
• Coefficient of thermal expansion, 
coeff. thermal expansion
L
= (T2-T1)
Lo
•  ~ symmetry at ro
 is larger if Eo is smaller
and very asymmetric.
Atomic positions and vibrations
• The minimum in an atomic energy
vs. interatomic distance curve
yields the near neighbor distance
(bond length).
• The width of the curve is
proportional to the amplitude of
thermal vibrations for an atom.
• If the curve is symmetric, there is
no shift in the average position of
the atom (the center of the thermal
vibrations at any given T).
• The coefficient of thermal
expansion is negligible for
symmetric energy wells.
T3
T2
T0
Thermal Expansion
• If the curve is not symmetric, the average position in
which the atom sits shifts with temperature.
• Bond lengths therefore change (usually get bigger for
increased T).
• Thermal expansion coefficient is nonzero.
THERMAL EXPANSION: COMPARISON
•Thermal expansion
mismatch is a major
problem for design of
everything from
semiconductors to
bridges.
•Particularly an issue
in applications where
temperature changes
greatly (esp. engines).
Why does  generally
decrease with increasing
bond energy?
Selected values from Table 19.1, Callister 6e.
Thermal expansion example
• Example
• An Al wire is 10 m long and is cooled from 38 to -1
degree Celsius. How much change in length will it
experience?
l = l  T

o l
= (10 m) 23.6 x 10
6
(C)
-9.2 mm
(1C  38C)
-1
Heat and Atoms
• Heat causes atoms to vibrate.
• Vibrating in synch is often a low energy configuration
(preferred).
– Generates waves of atomic motion.
– Often called phonons, similar to photons but atomic motion instead of optical
quanta.
THERMAL CONDUCTIVITY
• General: The ability of a material to transfer heat.
• Quantitative:
heat flux
(J/m2-s)
dT temperature
Fick’s First Law
q  k
gradient
dx
k= thermal conductivity (J/m-K-s):
Defines material’s ability to transfer heat.
Atomic view: Electronic and/or Atomic
vibrations in hotter region carry energy
(vibrations) to cooler regions. In a metal,
electrons are free and thus dominate thermal
conductivity. In a ceramic, phonons are more
important.
THERMAL CONDUCTIVITY
• Non-Steady State: dT/dt is not constant.
  2T 
T   T 
T
nd
 k
if
K

f
T


k
Fick
'
s
2
Law



Fick’s Second
2 

t x  x 
t
 x 
Law
THERMAL CONDUCTIVITY
K=kl+ke: Again think about band gaps: metals have lots of free
electrons (ke is large), while ceramics have few (only kl is active).
Selected values from Table 19.1, Callister 6e.
THERMAL CONDUCTIVITY
Good heat conductors are usually good electrical
conductors.
k
 2 k B2
8
2
L

2
.
443

10
(
J


/
K
 s)
2
 T
3e
(Wiedemann & Franz, 1853)
Thermal conductivity changes by 4 orders of magnitude (~25
for electrical conductivity).
Metals & Alloys: free e- pick up energy due to thermal
vibrations of atoms as T increases and lose it when it
decreases.
Insulators (Dielectrics): no free e-. Phonons (lattice vibration
quanta) are created as T increases, eliminated as it
decreases.
THERMAL CONDUCTIVITY
• Thermal conductivity is
temperature dependent.
– Analagous to electron
scattering.
– Usually first decreases with
increasing temperature
• Higher Temp=more
scattering of electrons AND
phonons, thus less transfer
of heat.
– Then increases at still higher
temperatures due to other
processes we haven‘t
considered in this class
(radiative heat transfer—eg. IR
lamps).
THERMAL STRESSES
• Occurs due to:
--uneven heating/cooling
--mismatch in thermal expansion.
• Example Problem
--A brass rod is stress-free at room temperature (20C).
--It is heated up, but prevented from lengthening.
--At what T does the stress reach -172MPa?
Strain (ε) due to ∆T causes a stress (σ) that
depends on the modulus of elasticity (E):
L
T
L
  thermal   (T  To )
Lo
100GPa
20 x 10-6 /C
  E (  thermal )   E (T  To )
-172MPa
Answer: 106C
20C
THERMOELECTRIC COOLING & HEATING
Two different materials are connected at the their ends and
form a loop. One junction is heated up.
There exists a potential difference that is proportional to
the temperature difference between the ends.
dV
Seebeck Coefficien t  S 
( V/K )
dT
THERMOELECTRIC COOLING & HEATING
Reverse of the Seebeck effect is the Peltier Effect.
A direct current flowing through heterojunctions causes one junction
to be cooled and one junction to be heated up.
Lead telluride and or bismuth telluride are typical materials in
thermoelectric devices that are used for heating and refrigeration.
Why does this happen?
When two different electrical conductors are brought
together, e- are transferred from the material with higher
EF to the one with the lower EF until EF (material 1)= EF
(material 2).
Material with smaller EF will be (-) charged. This results in
a contact potential which depends on T.
e- at higher EF are caused by the current to transfer their
energy to the material with lower EF, which in turn heats
up. Material with higher EF loses energy and cools down.
Peltier–Seebeck effect, or the thermoelectric effect, is
the direct conversion of thermal differentials to electric
voltage and vice versa.
The effect for metals and alloys is small, microvolts/K.
For Bi2Te3 or PbTe (semiconductors), it can reach up to
millivolts/K.
Applications: Temperature measurement via
thermocouples (copper/constantan, Cu-45%Ni, chromel,
90%Ni-10%Cr,…); thermoelectric power generators
(used in Siberia and Alaska); thermoelectric
refrigerators; thermal diode in microprocessors to
monitor T in the microprocessors die or in other thermal
sensor or actuators.
THERMOELECTRIC COOLING & HEATING
http://www.sii.co.jp/info/eg/thermic_main.html