1. CHAPTER 17: THERMAL PROPERTIES
ISSUES TO ADDRESS...
• How does a material respond to heat?
• How do we define and measure...
--heat capacity
--coefficient of thermal expansion
--thermal conductivity
--thermal shock resistance
• How do ceramics, metals, and polymers rank? 1

2. Chapter 17 – Thermal Properties
Motivation
Many applications necessitate a thorough understanding of how materials respond to temperature changes
How does a material respond to heat?
Much of this will be a refresher for you (especially if you have taken/are taking heat transfer)!
End of lecture 1

3. HEAT CAPACITY • General: The ability of a material to absorb heat.
• Quantitative: The energy required to increase the
temperature of the material.
energy input (J/mol)
heat capacity
(J/mol-K)
temperature change (K)
• Two ways to measure heat capacity:
-- Cp : Heat capacity at constant pressure.
-- Cv : Heat capacity at constant volume. 2

4. Vibrational Heat capacity
Chapter 17 – Thermal Properties
Vibrational Heat capacity
In most solids the principal mode of heat absorption is by increasing the vibrational energy of the atoms
Atoms are constantly vibrating at high frequencies
Atomic vibrations are coupled because of bonding
Waves have very high frequencies and short wavelengths, and travel at the velocity of sound
From quantum mechanics – the vibrational energies must have well-defined (quantized) values
A single quantum of vibration energy is called a phonon
Tie to Ch 12 – the thermal scattering of free electrons during conduction is by phonons
End of lecture 1

6. Vibrational contribution
to heat capacity
How does Cv vary with temperature?
The heat capacity is zero at zero 0 K
Strongly nonlinear below the Debye temperature
Plateau above the Debye temperature

7. HEAT CAPACITY VS T • Heat capacity... • Atomic view:
--increases with temperature
--reaches a limiting value of 3R
Adapted from Fig. 19.2, Callister 6e.
• Atomic view:
--Energy is stored as atomic vibrations.
--As T goes up, so does the avg. energy of atomic vibr. 3

8. Chapter 17 – Thermal Properties
Other heat capacity contributions
Other mechanisms for heat absorption are possible, though are usually minor compared to the vibrational contribution
Electronic contribution – electrons increase their KE with heat absorption (do you think this is significant?)
Must be free electrons to contribute to this
Randomization of spins in a ferromagnetic material produces heat at T > Curie temperature
End of lecture 1

9. HEAT CAPACITY: COMPARISON
• Why is cp significantly
larger for polymers?
Selected values from Table 19.1, Callister 6e. 4

10. THERMAL EXPANSION • Materials change size when heating.
coefficient of
thermal expansion (1/K)
• Atomic view: Mean bond length increases with T.
Adapted from Fig. 19.3(a), Callister 6e. (Fig. 19.3(a) adapted from R.M. Rose, L.A. Shepard, and J. Wulff, The Structure and Properties of Materials, Vol. 4, Electronic Properties, John Wiley and Sons, Inc., 1966.) 5

11. Chapter 17 – Thermal Properties
Thermal expansion
How does a sample’s length change upon heating/cooling?
End of lecture 1
lf and lo are the final and initial lengths, al – linear coefficient of thermal expansion al [=] 1/K
Could also express this in terms of volume
Molecular picture – expansion is due to increase in spacing of atoms

12. Asymmetric curvature of the potential well
The shape/depth of the potential well is related to bonding strength – stronger bonds, smaller al
Increase of interatomic separation with increasing T

13. THERMAL EXPANSION: COMPARISON
• Q: Why does a
generally decrease
with increasing
bond energy?
Selected values from Table 19.1, Callister 6e. 6

14. Thermal properties (relate to bonding strength)
Chapter 17 – Thermal Properties
Thermal properties (relate to bonding strength)
Metals: al typically between 5 – 25 x /C
Can make alloys with lower values
Ceramics – low expansion coefficients (0.5–15 x /C); coefficient can be anisotropic
Polymers – can have very high expansion coefficients
End of lecture 1

15. THERMAL CONDUCTIVITY
• General: The ability of a material to transfer heat.
• Quantitative:
temperature
gradient
Similar to Fick’s
first law
heat flux
(J/m2-s)
thermal conductivity (J/m-K-s)
• Atomic view: Atomic vibrations in hotter region carry
energy (vibrations) to cooler regions. 7

16. Chapter 17 – Thermal Properties
Thermal conductivity
Mechanism for transport of heat from high to low temperature domains
q – heat flux (W/m2)
k – thermal conductivity (W/m-K)
Mechanisms of heat conduction
Two contributions: lattice vibration waves (phonons) and free electrons
End of lecture 1

17. Thermal conductivity in metals
Free electron mechanism dominates (k ~ 20 – 400 W/m-K)
Free electrons participate both in thermal and electrical conduction – Wiedemann-Franz law
L is a constant

18. Effect of impurities on thermal conductivity

19. Chapter 17 – Thermal Properties
Ceramics
Very few free electrons … phonon processes dominate the heat conduction process (k ~ 2 – 50 W/m-K)
Amorphous materials have lower thermal conductivities than crystalline solids (why?)
Most ceramics conductivity goes down when temperature increases (why?) But at very high temperature, radiation takes place also
Porosity leads to reduction (dramatic) in thermal conductivity (why?)
Polymers
k is small ~ 0.3 W/m-K
Energy transfer due to vibration and rotation of the chains
k depends on polymer crystallinity
Typically viewed as thermal insulators
End of lecture 1

20. THERMAL CONDUCTIVITY: COMPARISON
Selected values from Table 19.1, Callister 6e. 8

21. Chapter 17 – Thermal Properties
Thermal stresses
Induced as a result of temperature changes
Consider an isotropic solid rod heated or cooled uniformly; no T gradient imposed. However if the axial motion of the rod is restrained, introduces stress (think back to thermal expansion!)
Magnitude of the stress is given by
Stresses caused by temperature gradients:
Heating – compressive stress
Cooling – tensile stress
End of lecture 1

22. EX: THERMAL STRESS • Occurs due to:
--uneven heating/cooling
--mismatch in thermal expansion.
• Example Problem 17.1, p. 724, Callister 2e.
--A brass rod is stress-free at room temperature (20C).
--It is heated up, but prevented from lengthening (ends are kept rigid).
--At what T does the stress reach -172MPa?
100GPa
20 x 10-6 /C
20C
-172MPa
Answer: 106C 9

23. Chapter 17 – Thermal Properties
Thermal shock (brittle materials)
So, change in temperature can cause stress
If these are large enough can have plastic deformation (for metals)
But brittle materials can’t deform plastically!
Brittle materials can fracture due to large temperature changes (thermal shock)
Cooling more problematic – why?
This is a problem because ceramics are very good insulators
How to know when thermal shock can happen – thermal shock resistance parameter
End of lecture 1
High fracture strengths
High thermal conductivities
Low elasticity modulus
Low coeff. thermal expansion

24. THERMAL SHOCK RESISTANCE
• Occurs due to: uneven heating/cooling.
• Ex: Assume top thin layer is rapidly cooled from T1 to T2:
Tension develops at surface
Temperature difference that
can be produced by cooling:
Critical temperature difference
for fracture (set s = sf)
set equal
• Result:
• Large thermal shock resistance when is large. 10

25. THERMAL PROTECTION SYSTEM
• Application:
Space Shuttle Orbiter
Fig. 23.0, Callister 5e. (Fig courtesy the National Aeronautics and Space Administration.
Fig. 19.2W, Callister 6e. (Fig. 19.2W adapted from L.J. Korb, C.A. Morant, R.M. Calland, and C.S. Thatcher, "The Shuttle Orbiter Thermal Protection System", Ceramic Bulletin, No. 11, Nov. 1981, p )
• Silica tiles ( C):
--large scale application
--microstructure:
~90% porosity!
Si fibers
bonded to one
another during
heat treatment.
Fig. 19.3W, Callister 5e. (Fig. 19.3W courtesy the National Aeronautics and Space Administration.
Fig. 19.4W, Callister 5e. (Fig W courtesy Lockheed Aerospace Ceramics
Systems, Sunnyvale, CA.) 11

26. SUMMARY • A material responds to heat by: • Heat capacity:
--increased vibrational energy
--redistribution of this energy to achieve thermal equil.
• Heat capacity:
--energy required to increase a unit mass by a unit T.
--polymers have the largest values.
• Coefficient of thermal expansion:
--the stress-free strain induced by heating by a unit T.
• Thermal conductivity:
--the ability of a material to transfer heat.
--metals have the largest values.
• Thermal shock resistance:
--the ability of a material to be rapidly cooled and not
crack. Maximize sfk/Ea. 12

27. ANNOUNCEMENTS
Reading: Chapter 17 (pdf sent to you by )