1. THERMAL PROPERTIES Heat Capacity
The ability of a material to absorb heat
• Quantitatively: The energy required to produce a unit rise in temperature for one mole of a 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.
Cp usually > Cv
• Heat capacity has units of

2. Dependence of Heat Capacity on Temperature
-- increases with temperature
-- for solids it reaches a limiting value of 3R
R = gas constant 3R
Cv = constant
= 8.31 J/mol-K Cv
Adapted from Fig. 17.2, Callister & Rethwisch 3e.
T (K) q D
Debye temperature
(usually less than T )
room
• From atomic perspective:
-- Energy is stored as atomic vibrations.
-- As temperature increases, the average energy of atomic vibrations increases.

3. Atomic Vibrations
Atomic vibrations are in the form of lattice waves or phonons
Adapted from Fig. 17.1, Callister & Rethwisch 3e.

4. Specific Heat: Comparison
Selected values from Table 17.1, Callister & Rethwisch 3e.
• Polymers
Polypropylene
Polyethylene
Polystyrene
Teflon
cp (J/kg-K)
at room T
• Ceramics
Magnesia (MgO)
Alumina (Al2O3)
Glass
• Metals
Aluminum
Steel
Tungsten
Gold
1925
1850
1170
1050
900
486
138
128
cp (specific heat): (J/kg-K)
Material
940
775
840
Cp (heat capacity): (J/mol-K)
increasing cp

5. Other heat capacity contributions
Electrons absorbing energy by increasing their kinetic energy
Only for free elections
Very small for insulating/semiconducting materials
Randomization of electron spin at some specific temperature
These two factors are (very) small compared to the contribution from the vibrations

6. Thermal Expansion Materials change size when temperature is changed
Tinitial
 initial
Tfinal > Tinitial
Tfinal
 final
linear coefficient of
thermal expansion (1/K or 1/°C)
For isotropic materials
αv = 3αl

7. Atomic Perspective: Thermal Expansion
Thermal expansion arises from an increase in the average distance between the atoms
Symmetric curve:
-- increase temperature, no increase in interatomic separation -- no thermal expansion
Asymmetric curve:
-- increase temperature, increase in interatomic separation -- thermal expansion

8. Coefficient of Thermal Expansion: Comparison
Polypropylene
Polyethylene
Polystyrene
90-150
Teflon
• Polymers
• Ceramics
Magnesia (MgO)
13.5
Alumina (Al2O3)
7.6
Soda-lime glass 9
Silica (cryst. SiO2)
0.4
• Metals
Aluminum
23.6
Steel 12
Tungsten
4.5
Gold
14.2
a (10-6/C) at room T
Material
increasing 
Polymers have larger  values because of weak secondary bonds
• Q: Why does a
generally decrease
with increasing
bond energy?
A: deeper and narrower
energy “trough”

9. Thermal Expansion: Example
Ex: A copper wire 15 m long is cooled from 40 to -9°C. How much change in length will it experience?
Answer: For Cu
rearranging Equation 17.3b

10. Thermal Conductivity The ability of a material to transport heat.
Fourier’s Law
temperature
gradient
heat flux
(J/m2-s)
thermal conductivity (J/m-K-s) T1 T2
T2 > T1 x1 x2
heat flux
• Atomic perspective: Atomic vibrations and free electrons in hotter regions transport energy to cooler regions.

11. Mechanisms of Heat Conduction

12. Thermal Conductivity: Comparison
Energy Transfer Mechanism
Material
k (W/m-K)
increasing k
• Metals
Aluminum
247
atomic vibrations and motion of free electrons
(electron motion is more efficient)
Steel 52
Tungsten
178
Gold
315
• Ceramics
Magnesia (MgO) 38
Alumina (Al2O3) 39
Soda-lime glass
1.7
Silica (cryst. SiO2)
1.4
atomic vibrations
(phonons are primarily responsible)
• Polymers
Polypropylene
0.12
Polyethylene
Polystyrene
0.13
Teflon
0.25
vibration/rotation of chain molecules
Selected values from Table 19.1, Callister & Rethwisch 3e.

13. Thermal Stresses • Occur due to: Thermal stress 
-- restrained thermal expansion/contraction
-- temperature gradients that lead to differential dimensional changes
Thermal stress


14. Example Problem  0  0 D Tf  0 D
-- A brass rod is stress-free at room temperature (20°C).
-- It is heated up, but prevented from lengthening.
-- At what temperature does the stress reach -172 MPa?
Solution: T0
Original conditions
 0 Tf
Step 1: Assume unconstrained thermal expansion
 0 D
Step 2: Compress specimen back to original length
 0  D 14

15. Example Problem (cont.)
 0 
The thermal stress can be directly calculated as
Noting that compress = -thermal and substituting gives
20 x 10-6/°C
Answer: 106°C
100 GPa
20ºC
Rearranging and solving for Tf gives
-172 MPa (since in compression) 15 15

16. Thermal Shock Resistance
• Occurs due to: nonuniform heating/cooling
• Ex: Assume top thin layer is rapidly cooled from T1 to T2 s
rapid quench
resists contraction
tries to contract during cooling T2 T1
Tension develops at surface
Temperature difference that
can be produced by cooling:
Critical temperature difference
for fracture (set s = sf)
set equal •
• Large TSR when is large

17. Summary The thermal properties of materials include: • Heat capacity:
-- energy required to increase a mole of material by a unit T
-- energy is stored as atomic vibrations
• Coefficient of thermal expansion:
-- the size of a material changes with a change in temperature
-- polymers have the largest values
• Thermal conductivity:
-- the ability of a material to transport heat
-- metals have the largest values
• Thermal shock resistance:
-- the ability of a material to be rapidly cooled and not fracture
-- is proportional to

18. Magnetic Properties Generation of a Magnetic Field -- Vacuum
• Created by current through a coil: H I B0
N = total number of turns
 = length of each turn (m)
I = current (ampere)
H = applied magnetic field (ampere-turns/m)
B0 = magnetic flux density in a vacuum (tesla)
• Computation of the applied magnetic field, H:
(A / m)
B0 = 0H
permeability of a vacuum (1.257 x 10-6 Henry/m)
• Computation of the magnetic flux density in a vacuum, B0:

19. Magnetic field vector etc.
Electric field can be defined in terms of the force acting on a charge
Ie, if a charge q at rest is experiencing electric force FE from the electric field E,
FE = qE
where E is electric field.
Magnetic field could be defined in a similar way, if there is a monopole, but there’s none
Instead, we can use the moving charge q with velocity v.
The force acted on the moving charge by a magnetic field B is
FB = qv x B
Then the unit of B is
N / (coulomb m / s) = N/(A m) = T = Tesla

20. Magnetic field vector etc.

21. Finally
B0 = 0H

22. H & B B : magnetic field in the material
From external magnetic field + “internal” magnetic field (magnetization)
Magnetic induction, magnetic flux density
H: “Driving” magnetic influence from external field
Magnetic field strength
In vacuum, B & H are essentially same (up to 0)
H can be defined as
H = B/ 0 - M

23. Generation of a Magnetic Field -- within a Solid Material
• A magnetic field is induced in the material B
B = Magnetic Induction (tesla) inside the material
applied
magnetic field H
B = H
permeability of a solid
current I
• Relative permeability (dimensionless)

24. Generation of a Magnetic Field -- within a Solid Material (cont.)
• Magnetization
M = mH
Magnetic susceptibility (dimensionless)
• B in terms of H and M
B = 0H + 0M
• Combining the above two equations:
B = 0H + 0 mH H B
vacuum cm = 0 cm
> 0
< 0
permeability of a vacuum:
(1.26 x 10-6 Henry/m)
= (1 + m)0H
cm is a measure of a material’s magnetic response relative to a vacuum

25. Origins of Magnetic Moments
• Magnetic moments arise from electron motions and the spins on electrons.
magnetic moments
electron
electron
nucleus
spin
Adapted from Fig. 18.4, Callister & Rethwisch 3e.
electron orbital motion
electron spin
• Net atomic magnetic moment:
-- sum of moments from all electrons.
-- in atom with completely filled shells, there is total cancellation of orbital & spin moments -> cannot be permanently magnetized

26. Types of Magnetism (3) ferromagnetic e.g. Fe3O4, NiFe2O4
(4) ferrimagnetic e.g. ferrite(), Co, Ni, Gd ( cm
as large as
106 !)
B (tesla)
(2) paramagnetic (
e.g., Al, Cr, Mo, Na, Ti, Zr cm
~ 10-4)
vacuum ( cm
= 0)
(1) diamagnetic ( cm
~ -10-5)
e.g., Al2O3, Cu, Au, Si, Ag, Zn
H (ampere-turns/m)
Plot adapted from Fig. 18.6, Callister & Rethwisch 3e. Values and materials from Table 18.2 and discussion in Section 18.4, Callister & Rethwisch 3e.

27. Diamagnetic / Paramagnetic
none
random
No Applied
Magnetic Field (H = 0)
opposing
aligned
Applied
Magnetic Field (H)

28. Ferromagnetism

29. Antiferromagnetism Antiferromagnetism
Another form of magnetic moment coupling between the adjacent atoms/ions
Forms antiparallel alignment of magnetic dipoles
MnO (Manganese Oxide)
O2- ion has no net magnetic moment
Mn2+ has net magnetic moment (due to spin)
They align so that the adjacent ions are antiparallel, resulting in no net magnetic moment overall

30. Ferrimagnetism Like ferromagnets, permanent
Consider the mineral magnetite Fe3O4
Can be written Fe2+O2--(Fe3+)2(O2-)3

31. Effect of temperature
The atomic thermal motion counteract the coupling forces between the atomic dipole moments -> Decrease in saturation magnetization
At Curie temperature Tc, it becomes 0

32. Domains
Domain: small region in ferro/ferrimagnetic solid where there is a alignment along the same direction
Very small, smaller than grain
Magnetization of entire solid is the vector sum of the magnetization of all domains

33. Domains & Hysteresis B does not increase linearly with M Recall B = H
So  changes with H
Initial permeability i.
Starting with initially randomly oriented domain, the domains aligning with the magnetic fields grows
At maximum saturation, a single domain remains.

34. Domains & Hysteresis From saturation, reduce H
The B-H curve does not retraces the original path – HYSTRTERESIS
B decreases “slower” than H and does not become 0 when H = 0 -> remanence (remanent flux density Br)
Single domain rotates
New domain forms
Some domain with original direction remains (remanence)
Can be explained in terms of domain
Resistance to domain wall motion
Hc: coercivity
Magnitude need to make B=0

35. Hysteresis and Permanent Magnetization
• The magnetic hysteresis phenomenon B
Stage 2. Apply H, align domains
Stage 3. Remove H, alignment
remains! => permanent magnet!
Stage 4. Coercivity, HC Negative H needed to demagnitize!
Adapted from Fig , Callister & Rethwisch 3e. H
Stage 5. Apply -H, align domains
Stage 1. Initial (unmagnetized state)
Stage 6. Close the hysteresis loop

36. Hard and Soft Magnetic Materials
Hard magnetic materials:
-- large coercivities
-- used for permanent magnets
-- add particles/voids to
inhibit domain wall motion
-- example: tungsten steel --
Hc = 5900 amp-turn/m) B
Hard
Soft H
Soft magnetic materials:
-- small coercivities
-- used for electric motors
-- example: commercial iron Fe
Adapted from Fig , Callister & Rethwisch 3e. (Fig from K.M. Ralls, T.H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering, John Wiley and Sons, Inc., 1976.) 36 36

37. Superconductivity
Found in 26 metals and hundreds of alloys & compounds
Mercury
Copper (normal)
Fig , Callister & Rethwisch 3e.
4.2 K
TC = critical temperature
= temperature below which material is superconductive

38. Critical Properties of Superconductive Materials
TC = critical temperature - if T > TC not superconducting JC = critical current density - if J > JC not superconducting HC = critical magnetic field - if H > HC not superconducting
Fig , Callister & Rethwisch 3e.

39. Summary
• A magnetic field is produced when a current flows through a wire coil.
• Magnetic induction (B):
-- an internal magnetic field is induced in a material that is situated within an external magnetic field (H).
-- magnetic moments result from electron interactions with the applied magnetic field
• Types of material responses to magnetic fields are:
-- ferrimagnetic and ferromagnetic (large magnetic susceptibilities)
-- paramagnetic (small and positive magnetic susceptibilities)
-- diamagnetic (small and negative magnetic susceptibilities)
• Types of ferrimagnetic and ferromagnetic materials:
-- Hard: large coercivities
-- Soft: small coercivities
• Magnetic storage media:
-- particulate g-Fe2O3 in polymeric film (tape)
-- thin film CoPtCr or CoCrTa (hard drive)

40. ANNOUNCEMENTS
Reading:
Core Problems:
Self-help Problems:

41. (3) Ferromagnetism Saturation magnetization Ms:
Maximum possible magnetization
Magnetization when all the dipoles are mutually aligned with the external field