1.   (Vfinal – Vinitial)/Vinitial
Thermal Expansion
It is well-known that most materials expand their volume when they are heated.
A measure of this is the Coefficient of Thermal Expansion (CTE) . This is defined by:
  (Vfinal – Vinitial)/Vinitial
In some cases, an expansion in only one dimension happens. In that case, a Coefficient of Linear Expansion (CLE)  is defined by:

2. Properties from Bonding: Energy Versus Bond Length
Bond length, r
Bond energy, Eo

3. PROPERTIES FROM BONDING: TM
Melting Temperature, Tm
Tm is larger if Eo is larger.

4. PROPERTIES FROM BONDING: Elastic Properties
• Elastic modulus, E
E similar to spring constant
• E ~ curvature at ro
E is larger if curvature is larger.

5. PROPERTIES FROM BONDING: CTE or a
• Coefficient of thermal expansion, a
• a ~ symmetry at ro
is larger if Eo is smaller
and very asymmetric.

6. 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. T0 T2 T3
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.

7. 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.

8. THERMAL EXPANSION: COMPARISON
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 a generally decrease with increasing bond energy?
Selected values from Table 19.1, Callister 6e.

9. Thermal expansion 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?
-9.2 mm

10. 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.

11. THERMAL CONDUCTIVITY • Quantitative:
• General: The ability of a material to transfer heat.
• Quantitative:
temperature
gradient
k= thermal conductivity (J/m-K-s):
Defines material’s ability to transfer heat.
heat flux
(J/m2-s)
Fick’s First Law
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.

12. THERMAL CONDUCTIVITY • Non-Steady State: dT/dt is not constant.
Fick’s Second
Law

13. THERMAL CONDUCTIVITY
Selected values from Table 19.1, Callister 6e.

14. Good heat conductors are usually good electrical conductors.
THERMAL CONDUCTIVITY
Good heat conductors are usually good electrical conductors.
(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.

15. 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).

16. THERMAL STRESSES --uneven heating/cooling • Occurs due to:
--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):
-172MPa
100GPa
20 x 10-6 /C
20C
Answer: 106C

17. 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.

18. 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.

19. 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.

20. 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.

21. THERMOELECTRIC COOLING & HEATING