Review 4,

1
Additional Information for Exam 4

• Covers lectures 26 32 and the associated
  reading assignments
• Arrive 5 minutes before the start of the exam
• Closed-book, closed notes
• Bring
• Calculators (memories cleared)
• Notes on a 3 x 5 card
• Periodic table (handed out in recitation)
• Provided
• Fundamental constants

2
Glassy Materials the Glass Transition
Glassy
Semicrystalline
Crystalline
3
Properties from Engineering Stress-Strain Curves
Callister 6.5

• Elastic modulus
• Yield strength
• Tensile strength
• Strain to failure
• Modulus of resilience
• Modulus of toughness
• Other topics
• Poissons ratio
• True stress, true strain

Callister Fig. 6.11
4
Mechanical Properties of Metals Callister 6.5

• Brittleness vs. ductility in metals, ceramics,
  and polymers

Callister Fig. 6.13
5
Effect of Temperature Glassy vs. Plastic
Callister 16.2

• Effect of temperature in a linear polymer (PMMA)

Tg 4 C TgtTg plasticity? TTg stiffness?
brittleness?
Callister Fig. 16.3
6
Polymer Crystallinity Callister 15.11

• Polymer crystals
• Platelets Bundles Spherulites

Callister Fig. 15.14
Callister Fig. 15.15
7
Mechanical Characteristics of Polymers Callister
16.3

• Macroscopic effects of deformation

Callister Fig. 16.4
Callister Fig. 16.5
8
Defects in Crystalline Solids by Dimension

• Point defects
• vacancies self-interstitials
• impurities (in elemental solids or in compounds)
• substitutional interstitial
• in compounds
• Schottky cation Frenkel anion Frekel
• Line defects dislocations
• edge screw mixed
• Planar defects
• grain boundaries twin boundaries surfaces
• stacking faults
• Volume defects
• pores inclusions

intrinsic defects
9
More on Point Defects

• Intrinsic defects are thermally activated
• e.g., metal vacancies NV NS exp(GV/RT)
• Alternate form NV NS exp(QV/kT) (Callister
  eq. 4.1)
• gives
  probability of an event
• Impurities factors favoring solubility of B in A
• Atomic size ?r/r 15
• Same crystal structure for A and B
• Similar electronegativities ?A ?B 0.6
  (preferably 0.4)
• At least one valence in common

10
Diffusion a Thermally Activated Process
Callister 5.5
intercept_at_T?
slope
on a plot of ln D vs. 1/T
0.0
11
Ficks First Law Callister 5.3
concentration gradient
Always true
eq. 5.3
flux
D diffusion coefficient

• Special case steady state diffusion
• No accumulation or depletion concentrations are
  invariant
• ? concentration gradient and flux are constant in
  time
• Concentration gradient is linear

12
Nonsteady-State Diffusion Callister 5.4

• Conservation of mass what stays there what
  goes in what comes out
• Flux at plane 1 Flux at plane 2
• Accumulation

0 in steady state ? 0 in unsteady state
Ficks second law
13
Thermal Conductivity Callister 20.4

• Fouriers law of cooling
• heat flux W m2
• thermal conductivity W m1 K1
• temperature gradient K m1
• Compare to Ficks first law
• mass flux
• diffusivity
• concentration gradient

14
Diffusion a Thermally Activated Process
Callister 5.5
vacancy diffusion
interstitial diffusion
15
Diffusion a Thermally Activated Process
Callister 5.5
intercept
slope
on a plot of ln D vs. 1/T
16
Interatomic Potential Heat Capacity Callister
20.2
add thermal energy ET ? separation r oscillates
about eqm spacing r0
Callister Figs. 2.8 20.3
17
Heat Capacity Specific Heat Callister 20.2

• Heat capacity amount of energy needed to raise a
  materials temperature by 1 degree, per mole of
  material
• J/mol-K, cal/mol-K
• Specific heat heat capacity per unit mass
• Specific heat J/kg-K, cal/g-K

18
Temperature Dependence of Heat Capacity
Callister 20.2

• Low T CV heat capacity at constant volume
• Only long-wavelength phonons are active (? gt
  atomic spacing)
• At T ?D, the Debye temperature, all phonon
  modes are active
• Above ?D CV ? 3R constant

• ?D is below room T for many solids
• Above ?D, adding heat increases amplitude (not
  number) of phonons

CV ? 3R
Callister Fig. 20.2
19
Thermal Expansion Callister 20.3

• Dimensional changes as a function of temperature
• start (s)
• finish (f)
• Example T2 ? T4

Callister Fig. 20.3
20
Thermal Expansion Callister 20.3

• Linear expansion
• Initial length l0
• Volume expansion
• Initial volume V0

Callister Fig. 20.3
21
Thermal Expansion of Metals Callister Table 20.1
?l ? 15?106 C1
22
Thermal Conductivity Callister 20.4

• Fouriers law of cooling
• heat flux W m2
• thermal conductivity W m1 K1
• temperature gradient K m1
• Compare to Ficks first law
• mass flux
• diffusivity
• concentration gradient

23
Wiedemann-Franz Law Callister 20.4

• In metals
• Conduction electrons are responsible for both
  electrical and thermal conduction
• Metals with high thermal conductivity ? also have
  high electrical conductivity ?
• Wiedemann-Franz Law
• where L is predicted to be a constant for all
  metals

24
Thermal Conductivity of Metals Callister Table
20.1
Metals
2.79
4.05
2.50
? ? 100 Wm1K1
for many metals, L is within 15 of predicted
value
25
Charge, Heat Mass Transport

• Ficks first law
• Fouriers law of cooling
• Ohms law
• current density (charge flux)
• electrical conductivity
• electric field (voltage
  gradient)

OGN eq. 23.4
26
Electrical Conduction Macroscopic View
Callister 19.2

• Current density, conductivity, electric field
• resistance of material
• voltage drop across material
• current through material
• ? Ohms law

?? electrical conductivity ?? electrical
resistivity
Callister Figure 19.1
27
Electrical Conduction Microscopic View
Callister 19.2
? nezµ

• ?? electrical conductivity
• n concentration of charge carriers
• e charge on an electron
• z valence of charge carriers
• µ mobility of charge carriers

?1m1Cm1V1s1 m3 C m2V1s1
a constant
z1 for electrons and holes, 2 for O2 ions,
(1, 2, )

• This expression holds for all substances
• Electrical conductivity varies by gt22 orders of
  magnitude in ordinary materials
• If material has more than one type of charge
  carrier

, because of differences in n and µ
28
Electrical Mobility of Metals Callister 19.8

• Effect of deformation on µ
• Dislocations (regions of deformed material)
  scatter carriers, increasing the electrical
  resistivity by

29
Electron-Hole Pair Formation

• Thermal energy ? some electrons are excited from
  the valence band into the conduction band ?
  conduction electrons
• This leaves an empty state in the valence band
  a hole
• n concn of condn e
• p concn of holes
• Intrinsic semiconductorelectrons and holes
  formin pairs,
• Conductivity

Callister Figure 19.6
30
Electrical Conduction in Intrinsic Semiconductors
Callister 19.10

• Intrinsic semiconductors (no impurities)

Note µe usu. gt µh
Callister example problem 19.1
31
Electrical Conductivity in n-type Semiconductors
Callister 19.10

• If concn of donors Nd gtgt ni, pi then n ?? Nd
  an n-type extrinsic matl

Callister Figure 19.12
32
Electrical Conductivity in p-type Semiconductors
Callister 19.10

• If concn of acceptors Na gtgt ni, pi then p ?? Na
  a p-type extrinsic matl

Callister Figure 19.14
33
Electrical Conductivity in Semiconductors
Callister 19.10

• Can obtain Eg from intrinsic region
• Slope of ln(n) vs. 1/T is Eg/2kB

Callister Fig. 19.16
34
Callister Table 19.1
35
Callister Table 19.2
36
Electrical Conductivity in Insulators Callister
19.15-16

• Ionic materials
• Often electrical insulators low electrical
  conductivity
• Charge carriers can be
• Ions
• Electrons or holes
• Ionic valence
• Mobility based on diffusivity
• Electrical properties of polymers
• Most are insulating
• Conducting polymers as high as

37
Wiedemann-Franz Law Callister 20.4

• In metals
• Conduction electrons are responsible for both
  electrical and thermal conduction
• Metals with high thermal conductivity ? also have
  high electrical conductivity ?
• Wiedemann-Franz Law
• where L is predicted to be a constant for all
  metals

38
Thermal Conductivity of Metals Callister Table
20.1
Metals
2.79
4.05
2.50
? ? 100 Wm1K1
for many metals, L is within 15 of predicted
value
39
Materials Cycle

• Raw materials
• Synthesis
• Engineered materials
• Product design
• Applications
• Waste
• Recycle / reuse
• Solid waste / landfill
• If biodegradable a new natural resource

40
Life Cycle Assessment of a Product
41
What Materials are Recycled?

• Metals
• Lead (Pb) e.g., lead batteries
• Aluminum (Al) e.g., aluminum cans
• Iron/steel (scrap metals)
• Gold, silver, platinum (e.g., contacts in
  electronic devices)
• Rubber and plastics
• PET and polycarbonates e.g., plastic bottles
• Tires
• Synthetic textile fibers
• Glass
• Food containers
• Paper
• Newspapers, cardboard boxes, etc.

42
Ref http//www.icmm.com/gmi_conference/
433BrianWilsonPresentation.pdf
43
Materials Cycle Environmental Considerations

• The earths materials are a closed system, not an
  infinite reservoir
• Each step in the materials cycle consumes energy
• In order of increasing energy consumption
• Reduce amount of material used
• Reuse existing material
• Recycle existing material
• Produce new material from natural resources
• Each step in the materials cycle produces
  byproducts
• Solid waste litter landfills
• Liquid waste water pollution
• Gaseous waste air pollution
• Health impact
• Control of toxic materials (Pb in solders Cr
  volatile organics )

44
Thermodynamics Remelting Aluminum

• Estimate energy needed to remelt 1 kg of aluminum
  cans
• Assumptions
• Cans are pure Al Start at room T
  Remelt at Tm of Al
• Input
• Tm,Al 933 K cP,Al 900 J kg1 K1
  ?Hf,Al 10.5 kJ mol1
• AWAl 26.98 g mol1
• Energy needed to heat solid Al to melting point
  cP,Al(Tm,Al room T)
• Energy needed to melt solid Al at melting point
  ?Hf,Al/AWAl
• Answer

45
Thermodynamics Reduction of Alumina

• Estimate energy needed to extract 1 kg of Al from
  Al2O3
• Assumptions
• T 298 K Process is 100 efficient
• Input
• ?G (given above) AWAl 26.98 g mol1
• Answer

Vs. 961 kJ/kg to remelt used Al 30? as much
energy