1. CHAPTER 11: PHASE TRANSFORMATIONS
ISSUES TO ADDRESS...
• Transforming one phase into another takes time.
• How does the rate of transformation depend on
time and T?
• How can we slow down the transformation so that
we can engineer non-equilibrium structures?
• Are the mechanical properties of non-equilibrium
structures better? 1

2. Phase Transformations
Introduction and Motivation
Microstructure  Processing  Properties
Our previous discussions focused on the equilibrium phase diagrams
These tell you what can happen
Now we will talk about the rates of phase changes to find out what does happen
Why is this important? Many materials are not processed under equilibrium conditions
Heating/cooling rates
End of lecture 1

3. Phase Transformations
A phase transformation is an alteration in the number and/or compositions of the phases present in a material
These are usually not instantaneous processes (hence our interest in rates)
Organize these into 3 categories
Diffusion dependent processes with no change in the composition or number of phases – solidification, allotropic transformations, grain boundary growth, recrystallization
Diffusion dependent process with a change in the number and/or composition of phases – eutectic, eutectoid, peritectic reactions
Diffusionless processes – form metastable states (haven’t seen these yet)
End of lecture 1

4. FRACTION OF TRANSFORMATION
• Fraction transformed depends on time.
Adapted from Fig. 10.1,
Callister 6e.
• Transformation rate depends on T.
Adapted from Fig. 10.2, Callister 6e. (Fig adapted from B.F. Decker and D. Harker, "Recrystallization in Rolled Copper", Trans AIME, 188, 1950, p. 888.)
• r often small: equil not possible! 2

5. Phase Transformations
Kinetics of phase transformations
Phase transformations are not usually instantaneous
Hence from a processing viewpoint their rates are of interest
These transformations have two key events
Nucleation – formation of small clusters (~10’s –100’s of atoms) of the new phase
Growth – little clusters get bigger
End of lecture 1

6. Phase Transformations
Kinetics of phase transformations
Nucleation – two types
Homogeneous nucleation – nuclei of the new phase are formed uniformly throughout the parent or original phase
Heterogeneous nucleation – nuclei of the new phase form preferentially at heterogeneities (surfaces, impurities, etc.)
The energetics (and hence kinetics) of these processes are typically different
The discussion of energetics will use free energies
Remember the Gibbs free energy DG?
DG < 0 for transformation occur spontaneously
End of lecture 1

7. TRANSFORMATIONS & SUPERCOOLING
Adapted from Fig. 9.21,Callister 6e. (Fig adapted from Binary Alloy Phase Diagrams, 2nd ed., Vol. 1, T.B. Massalski (Ed.-in-Chief), ASM International, Materials Park, OH, 1990.)
super
For cooling, transformations are shifted to lower temperatures than indicated by the phase diagram 3 3

8. NUCLEATION AND GROWTH
• Reaction rate is a result of nucleation and growth
of crystals.
Adapted from
Fig. 10.1, Callister 6e.
• Examples: 5

9. Phase Transformations
Nucleation
Homogeneous nucleation – start with simple picture: what is the free energy of a small spherical particle of a solid in a continuous media of the liquid (i.e. solidification)
Two major contributions to the free energy
Free energy difference between the solid and liquid phases (book calls it the volume free energy) DGv
Free energy of the solid-liquid phase boundary
End of lecture 1
Few points: 1) DGv is negative if T < T solidification
2) The surface free energy g is always positive
So,

10. Phase Transformations
Nucleation
Homogeneous nucleation
So what does the plot of DG versus r look like?
There is a clear maximum in DG as a function of r
This size r* has physical meaning
Particles smaller than this will not lead to nuclei
Particles this size or larger will grow (they are called nuclei)
DG* can be thought of as an energy barrier to nucleation
What is the value of DG* ?
End of lecture 1
embryo (r < r*)
nucleus (r > r*)

11. Phase Transformations
Sub into
Original eqn.
Nucleation
Homogeneous nucleation – DG*, r*
Take derivative of DG with respect to r and set it equal to zero!
End of lecture 1
Some observations – DGv is the driving force for nucleation (solidification)
It is a function of temperature!
At the equilibrium melting temperature Tm its value is zero!
Can I relate this to enthalpies? Of course!

12. Phase Transformations
Nucleation
Homogeneous nucleation – DG*, r*
Relations using enthalpy
What do the equations tell you?
Both r* and DG* decrease as T decreases for T < Tm
T2 < T1
End of lecture 1

13. Phase Transformations
Nucleation
Homogeneous nucleation – How many nuclei?
Increase T, fewer nuclei (not immediately clear from this!)
Frequency of attachment (how often do clusters collide and combine) – why is this related to diffusion?
End of lecture 1
Put all this together … the rate of nucleation is …
K3 is the number of atoms on a nucleus surface

14. Phase Transformations
Nucleation
Homogeneous nucleation – rate!
End of lecture 1
Plots clearly show there is an optimal temperature for maximizing the nucleation rate.

15. EUTECTOID TRANSFORMATION RATE ~ DT
• Growth of pearlite from austenite:
Adapted from Fig. 9.13, Callister 6e.
• Reaction rate
increases with
DT.
Adapted from Fig. 10.3, Callister 6e. 4

16. Phase Transformations
Nucleation
Homogeneous nucleation – supercooling
It can turn out that to have appreciable nucleation take place the sample temperature must be well below the equilibrium melting (solidification) temperature
This is called supercooling – the degree of supercooling can be significant!
End of lecture 1

17. TRANSFORMATIONS & SUPERCOOLING
Adapted from Fig. 9.21,Callister 6e. (Fig adapted from Binary Alloy Phase Diagrams, 2nd ed., Vol. 1, T.B. Massalski (Ed.-in-Chief), ASM International, Materials Park, OH, 1990.)
super
For cooling, transformations are shifted to lower temperatures than indicated by the phase diagram 3 3

18. NUCLEATION AND GROWTH
• Reaction rate is a result of nucleation and growth
of crystals.
Adapted from
Fig. 10.1, Callister 6e.
• Examples: 5

20. Phase Transformations
Example Problem 11.1
For the solidification of pure gold, calculate r* and DG* if nucleation is homogeneous. DHf = x 109 J/m3, g = J/m2. Use supercooling value from table 11.1 (230 C)
*Where did the 1064 C come from? That is the melting temperature of gold!
End of lecture 1

21. Phase Transformations
Example Problem 11.1
(b) Now determine the number of Au atoms in a nucleus of critical size. Assume a lattice parameter of nm.
End of lecture 1
How many atoms: 4 x 137 = 548 atoms/critical nucleus

22. Phase Transformations
Nucleation
Heterogeneous nucleation
Following up on the last point, in fact large degrees of supercooling are usually not observed
Why? Turns out you can have heterogeneous nucleation as well
Exactly what it sounds like – the solid nucleates from an interface
Preexisting surface, impurity atom, etc.
Can use similar approach as before to describe energetics of heterogeneous nucleation
End of lecture 1

23. Phase Transformations
Nucleation
Heterogeneous nucleation
Consider a flat surface or interface and a solid particle that nucleates off it
Now there are three interfacial energy terms
Interface-liquid (gIL), solid-liquid (gSL), solid-interface (gSI) (*gSL was the one from before)
If you write a force balance for the surface tension in the plane of the surface you get
End of lecture 1
*Note: there is still a free energy difference between the solid and liquid (next slide)

24. Phase Transformations
Nucleation
Heterogeneous nucleation
Using same approach before to find the maximum Gibbs free energy (and corresponding r) gives
Few points about the equations:
S(q) is only a function of the wetting angle and varies between 0 and 1.
r* is the same as before
The expression for DG* is similar to before (except for the S(q) function)
Note that the expression for the free energy for heterogeneous nucleation is always lower than that for homogeneous nucleation
End of lecture 1

25. Phase Transformations
Nucleation
Heterogeneous nucleation
What does this mean physically? Heterogeneous nucleation is faster than homogeneous nucleation!
The N vs T curve is shifted to higher temperatures for heterogeneous nucleation
End of lecture 1

26. Phase Transformations
Growth
Growth begins once an embryo (or cluster) has exceeded the critical size r* and becomes a stable nucleus
Nucleation still occurs during the growth phase
Growth ceases in a region where particles of the new phase meet
Physical mechanism of growth – long-range diffusion processes
Diffusion in the liquid phase to the growing phase
Since the growth rate is governed by diffusion it can be written in the form
End of lecture 1

27. Phase Transformations
Growth
Few comments based on figure below
Want large grains – solidify the material close to Tm
Want small grains – solidify far below Tm
Cool quickly enough – can form non-equilibrium phases
End of lecture 1

28. Phase Transformations
Kinetics of solid-state transformations
So now you have some idea about the mechanism of solidification
How do you describe the kinetics of this?
Issue 1 – need way to monitor phase transformation
S-shaped or sigmoidal curves are often observed in plots of the fraction of transformation ( y) v log(time)
The mathematical expression is often referred to as the Avrami equation
End of lecture 1
k, n are material specific
Another convention is that the rate of transformation is taken as the time needed for the transformation to proceed halfway (t0.5)

29. Phase Transformations
Kinetics of solid-state transformations
One other point – the kinetics of the transformation depend strongly on T
Now some pictures …
End of lecture 1

30. FRACTION OF TRANSFORMATION
• Fraction transformed depends on time.
Adapted from Fig. 10.1,
Callister 6e.
• Transformation rate depends on T.
Adapted from Fig. 10.2, Callister 6e. (Fig adapted from B.F. Decker and D. Harker, "Recrystallization in Rolled Copper", Trans AIME, 188, 1950, p. 888.)
• r often small: equil not possible! 2

31. Phase Transformations
Metastable versus equilibrium structures
Many ways to induce phase transformations, but temperature is the easiest
You have seen that on the phase diagrams
Additionally, the phase diagrams are based on equilibrium states, but contain no information about the rate equilibrium is achieved
So what? It turns out that in practice the cooling/heating rates to achieve equilibrium states are prohibitively slow
Transformations are shifted to lower temperatures than the phase diagrams indicate
Ex. Iron-carbon eutectoid is shifted by 10 – 20 C below the equilibrium T for normal cooling rates used
End of lecture 1

32. Phase Transformations
Metastable versus equilibrium structures
But there is more
Often the heating and cooling rates are such that one achieves metastable states (i.e. non equilibrium states) that exist between the initial and equilibrium states
This may actually be very desirable
This is why kinetics matter!
End of lecture 1

34. Isothermal Transformation Diagrams
Use these to understand rates of phase transformations
Consider the iron-iron carbide eutectoid reaction
This is a very important reaction in terms of microstructure development in steel – this reaction leads to pearlite formation
This is the isothermal transformation diagram
The isothermal transformation diagram will tell you how fast the pearlite phase forms at a given T
End of lecture 1

35. Isothermal Transformation Diagrams
How do you read these?
There are two solid lines
One indicates the time at which the transformation begins
The indicates when the transformation ends
Dashed line – 50% completed
These are also called time-temperature-transformation (T-T-T) plots
Also note that the initial composition is fixed
in this plot!
End of lecture 1

36. ISOTHERMAL TRANSFORMATION DIAGRAMS
• Fe-C system, Co = 0.77wt%C
• Transformation at T = 675C.
Adapted from Fig. 10.4,Callister 6e.
(Fig adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1977, p. 369.) 6

37. Isothermal Transformation Diagrams
Figure below shows the same plot now with the isothermal heat treatment curve included (at the eutectoid composition)
End of lecture 1

38. PEARLITE MORPHOLOGY Two cases: • Ttransf just below TE
--Larger T: diffusion is faster
--Pearlite is coarser.
• Ttransf well below TE
--Smaller T: diffusion is slower
--Pearlite is finer.
Adapted from Fig (a) and (b),Callister 6e. (Fig from R.M. Ralls et al., An Introduction to Materials Science and Engineering, p. 361, John Wiley and Sons, Inc., New York, 1976.) 8

39. EX: COOLING HISTORY Fe-C SYSTEM
• Eutectoid composition, Co = 0.77wt%C
• Begin at T > 727C
• Rapidly cool to 625C and hold isothermally.
Adapted from Fig. 10.5,Callister 6e.
(Fig adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1997, p. 28.) 7

40. Phase Transformations
Isothermal Transformation Diagrams
Comments about pearlite structure
The thickness ratio of ferrite and cementite layers in pearlite is approximately 8:1
However, the absolute thickness of the layers depends on the cooling profile (what T the isothermal transformation is allowed to occur)
Higher T (closer to eutectoid) – thick layers – coarse pearlite
Lower T (farther from eutectoid) – thin layers – fine pearlite
End of lecture 1

41. Phase Transformations
Isothermal Transformation Diagrams
Bainite
Another microstructure that can form from austenitic transformations (in addition to Pearlite)
Note! Not a different phase, a different microstructure
Bainite is a mixture of ferrite and cementite phases
It forms as needles or plates – domain sizes are much smaller as compared to pearlite
No proeutectoid forms with bainite
End of lecture 1
Structure obtained with electron
microscopy
Bainite:
Needles of ferrite in a matrix of cementite

42. Isothermal Transformation Diagrams
Looking at the isothermal transformation plot a few points
Bainite forms at lower temperatures
Pearlite forms at higher temperatures
These phases form competitively!
Either form one microstructure or the other ( Note: there is no mixture of B+P) on the figure!
Rate of transformation is a
maximum at N
End of lecture 1

43. Isothermal Transformation Diagrams
Spheroidite
Another wrinkle – if I take the materials above containing either pearlite or bainite domains and heat it near the eutectoid temperature (e.g. 973 K) for a sufficiently long period of time, (18-24 h) another microstructure forms … spheroidite
Instead of lamellae (pearlite) or stripes of cementite and ferrite (bainite), here the cementite domains are spherical encapsulated in a ferrite matrix
End of lecture 1

44. Phase Transformations
Isothermal Transformation Diagrams
Spheroidite
How does this happen? It is due to carbon diffusion with no change in the composition/relative amounts of ferrite and cementite
The driving force for this is the reduction of the ferrite-cementite phase boundary area
Final point:
Pearlite, bainite, spheroidite
These are all ferrite/cementite 2-phase solids
The difference? The microstructure – size/shape of the ferrite/cementite domains!
End of lecture 1

45. Phase Transformations
Isothermal Transformation Diagrams
Martensite
Get this when you rapidly cool austenized iron-carbon alloys to low temperatures (e.g. ambient T)
This is a nonequilibrium single-phase solid
Diffusionless transformation of austenite (g on phase diagram)
Transformation product that competes with bainite, pearlite formation
Observe martensite when quenching is fast enough to prevent carbon diffusion
End of lecture 1
Rapid quench
Austenite
(FCC)
Body centered tetragonal (BCT)
Martensite (BCT)

46. Phase Transformations
Isothermal Transformation Diagrams
Martensite
The BCT structure you get is the the original structure elongated
Carbon is still in the interstitial positions – another view is that martensite is supersaturated in carbon
Since this transformation does not involve diffusion it occurs almost instantly
Martensite and other microconstituents can coexist
End of lecture 1
Martensite forms as platelets/needles

47. Phase Transformations
Isothermal Transformation Diagrams
Martensite
Why don’t you see martensite on the phase diagrams?
You do see it on the isothermal transformation diagrams
See martensite lines
Note they are horizontal – why do you think that is?
Transformations like this are called athermal – why? They are only a function of the quenching temperature (the transformation is time independent)
End of lecture 1

48. Isothermal Transformation Diagrams Summary
Ok, time to wake up! – Here is the picture summarizing all this!
End of lecture 1

49. Phase Transformations
Example problem 11.2 – using the figure below, specify the final microstructures obtained from a sample, that is initially at 760 C possessing a homogeneous austenite structure, which is then
Rapidly cooled to 350 C, held at 350 C for 104 s, and then quenched to RT
Rapidly cooled to 250 C, held at 250 C for 102 s, and then quenched to room temperature
Rapidly cooled to 650 C, held at 650 C for 20 s, rapidly cooled to 400 C, held at 400 C for 103 s, and then quenched to RT
End of lecture 1

50. Phase Transformations
Example problem 11.2 – using the figure below, specify the final microstructures obtained from a sample, that is initially at 760 C possessing a homogeneous austenite structure, which is then
Rapidly cooled to 350 C, held at 350 C for 104 s, and then quenched to RT
What is the microstructure?
End of lecture 1
PURE BAINITE

51. Phase Transformations
Example problem 11.2 – using the figure below, specify the final microstructures obtained from a sample, that is initially at 760 C possessing a homogeneous austenite structure, which is then
Rapidly cooled to 250 C, held at 250 C for 102 s, and then quenched to room temperature
What is the microstructure?
End of lecture 1
PURE MARTENSITE

52. Phase Transformations
Example problem 11.2 – using the figure below, specify the final microstructures obtained from a sample, that is initially at 760 C possessing a homogeneous austenite structure, which is then
Rapidly cooled to 650 C, hold at 650 C for 20 s, cool rapidly to 400 C, hold for 103 s, and then quenched to room temperature
What is the microstructure?
End of lecture 1
50/50 Pearlite/Bainite

53. NON-EQUIL TRANSFORMATION PRODUCTS: Fe-C
• Bainite:
--a lathes (strips) with long
rods of Fe3C
--diffusion controlled.
• Isothermal Transf. Diagram
(Adapted from Fig. 10.8, Callister, 6e. (Fig from Metals Handbook, 8th ed.,
Vol. 8, Metallography, Structures, and Phase Diagrams, American Society for Metals, Materials Park, OH, 1973.)
Adapted from Fig. 10.9,Callister 6e.
(Fig adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1997, p. 28.) 9

54. OTHER PRODUCTS: Fe-C SYSTEM (1)
• Spheroidite:
--a crystals with spherical Fe3C
--diffusion dependent.
--heat bainite or pearlite for long times
--reduces interfacial area (driving force)
• Isothermal Transf. Diagram
(Adapted from Fig , Callister, 6e. (Fig copyright United States Steel Corporation, 1971.)
Adapted from Fig. 10.9,Callister 6e.
(Fig adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1997, p. 28.) 10

55. OTHER PRODUCTS: Fe-C SYSTEM (2)
• Martensite:
--g(FCC) to Martensite (BCT)
(Adapted from Fig , Callister, 6e.
• Isothermal Transf. Diagram
(Adapted from Fig , Callister, 6e. (Fig courtesy United States Steel Corporation.)
Adapted from Fig , Callister 6e.
• g to M transformation..
-- is rapid!
-- % transf. depends on T only. 11

56. COOLING EX: Fe-C SYSTEM (1)
Adapted from Fig , Callister 6e. 12

57. COOLING EX: Fe-C SYSTEM (2)
Adapted from Fig , Callister 6e. 13

58. COOLING EX: Fe-C SYSTEM (3)
Adapted from Fig , Callister 6e. 14

59. Phase Transformations
Continuous Cooling Transformation Diagrams
Turns out that isothermal heat treatments are not the most practical (why?)
Continuous cooling is more practical – this means we need to look at things differently
Isothermal transformation diagrams assume T is fixed
Continuous cooling transformation (CCT) diagrams
T is changing, the cooling rate is fixed
Turns out the time required for reaction is longer (why?)
End of lecture 1

60. Continuous Cooling Transformation Diagrams
Comparison between T-T-T and CCT diagrams
Big difference – plots for CCT diagrams you are constantly cooling the sample down instead of holding it at a fixed T!
Does this make sense?
For the slow cooling curves what do I have at the end?
Where is the bainite? Should there be any?
Should there be any martensite?
Note: transformation ceases at the point
of intersection
End of lecture 1

61. Phase Transformations
Continuous Cooling Transformation Diagrams
Comparison between T-T-T and CCT diagrams
Time for the class to talk
Tell me with the T-T-T curves mean
What does the CCT curves mean?
End of lecture 1

62. Phase Transformations
Continuous Cooling Transformation Diagrams
Martensitic transformations
To see martensite need to cool quickly
Trajectory is tangent or to the right of the “nose”
If trajectory does not cross line indicating 100% pearlite formation, get pearlite + martensite, not pearlite + bainite – why?
End of lecture 1
Critical cooling rate: minimum
quenching rate that produces
only martensitic structure

63. Phase Transformations
Continuous Cooling Transformation Diagrams
Full story .. “real steel” vs binary mixtures …
End of lecture 1

64. MECHANICAL PROP: Fe-C SYSTEM (1)
Adapted from Fig. 9.27,Callister
6e. (Fig courtesy Republic Steel Corporation.)
Adapted from Fig. 9.30,Callister 6e. (Fig copyright 1971 by United States Steel Corporation.)
Adapted from Fig , Callister 6e. (Fig based on data from Metals Handbook: Heat Treating, Vol. 4, 9th ed., V. Masseria (Managing Ed.), American Society for Metals, 1981, p. 9.) 15

65. MECHANICAL PROP: Fe-C SYSTEM (2)
Adapted from Fig , Callister 6e. (Fig based on data from Metals Handbook: Heat Treating, Vol. 4, 9th ed., V. Masseria (Managing Ed.), American Society for Metals, 1981, pp. 9 and 17.) 16

66. MECHANICAL PROP: Fe-C SYSTEM (3)
• Fine Pearlite vs Martensite:
Adapted from Fig , Callister 6e. (Fig adapted from Edgar C. Bain, Functions of the Alloying Elements in Steel, American Society for Metals, 1939, p. 36; and R.A. Grange, C.R. Hribal, and L.F. Porter, Metall. Trans. A, Vol. 8A, p )
• Hardness: fine pearlite << martensite. 17

67. TEMPERING MARTENSITE • reduces brittleness of martensite,
• reduces internal stress caused by quenching.
Adapted from Fig , Callister 6e. (Fig adapted from Fig. furnished courtesy of Republic Steel Corporation.)
Adapted from Fig , Callister 6e. (Fig copyright by United States Steel Corporation, 1971.) 18

68. SUMMARY: PROCESSING OPTIONS
Adapted from Fig , Callister 6e. 19

69. Phase Transformations
Precipitation hardening
Turns out you can modify the strength/hardness of some metal alloys by forming a 2nd phase which is small and uniformly dispersed in the original phase
This is done by temperature treatments – called precipitation hardening because the small particles are termed “precipitates”
Can try to understand this using phase diagrams! (We will stick to binary mixtures for simplicity…)
End of lecture 1

70. Phase Transformations
Precipitation hardening – consider a theoretical AB binary mixture
Two requisite features have to be observed in the phase diagram to “have” precipitate hardening
An appreciable maximum solubility of one component in the other (here point M)
End of lecture 1
A solubility limit that rapidly decreases as T decreases
Have both here…

71. Phase Transformations
Precipitation hardening – consider a theoretical AB binary mixture
Have those two points here … this is necessary but not sufficient!
Two-step process to achieve precipitation hardening
Solution heat treatment – heat up alloy to form single solid phase (Co, heat to To). Follow by rapid cooling (to T1) to form a solid solution a phase “supersaturated” in B
End of lecture 1

72. Phase Transformations
Precipitation hardening – consider a theoretical AB binary mixture
Two-step process to achieve precipitation hardening
Solution heat treatment
Precipitation hardening treatment – heat back up to intermediate temperature (T2) in the two phase region so that diffusion becomes appreciable. Form b precipitate phase – final microstructure of b phase (i.e. domain size) depends on T chosen as well as the hold time.
End of lecture 1

73. Phase Transformations
Precipitation hardening – consider a theoretical AB binary mixture
How do mechanical properties depend on precipitation hardening/aging?
End of lecture 1

74. Phase Transformations
Precipitation hardening – microscopic view
Okay, so what preceded was a “macroscopic” view of the process that we rationalized via the phase diagrams
What happens at the microscopic level? – Use Al-Cu as an example (96-4 Al-Cu by weight)
Idea: this is 2-phase < ~500 C
Heat up to get into a phase
Quench
Then heat to induce formation of the q phase as a precipitate
End of lecture 1

75. Phase Transformations
Precipitation hardening – microscopic view
Use Al-Cu as an example (96-4 Al-Cu by weight)
Idea: this is 2-phase < ~500 C
Heat up to get into a phase
Quench
Then heat to induce formation of the q phase as a precipitate
After quench you have a supersaturated in Cu (a)
Heat up, start to form something looks like q phase (q’, q”). These have considerable lattice strain (b)
Eventually form q phase (c)
End of lecture 1

76. Phase Transformations
Precipitation hardening
Few final comments:
Not all alloys are amenable to precipitation hardening
Constraints given previously
Plus: must establish considerable strain at the precipitate-matrix interface to get the desired enhancement in hardness/strength
Good practical example of “precipitate hardening”
Rivets – aluminum alloys
Driven while soft, and age harden at ambient conditions
End of lecture 1

77. PRECIPITATION HARDENING
• Particles impede dislocations.
• Ex: Al-Cu system
• Procedure:
--Pt A: solution heat treat
(get a solid solution)
--Pt B: quench to room temp.
--Pt C: reheat to nucleate
small q crystals within
a crystals.
• Other precipitation
systems:
• Cu-Be
• Cu-Sn
• Mg-Al
Adapted from Fig , Callister 6e. (Fig adapted from J.L. Murray, International Metals Review 30, p.5, 1985.)
Adapted from Fig , Callister 6e. 20

78. PRECIPITATE EFFECT ON TS, %EL
• 2014 Al Alloy:
• TS peaks with
precipitation time.
• Increasing T accelerates
process.
• %EL reaches minimum
with precipitation time.
Adapted from Fig (a) and (b), Callister 6e. (Fig adapted from Metals Handbook: Properties and Selection: Nonferrous Alloys and Pure Metals, Vol. 2, 9th ed., H. Baker (Managing Ed.), American Society for Metals, p. 41.) 21

79. SIMULATION: DISLOCATION MOTION PEAK AGED MATERIAL
--avg. particle size = 64b
--closer spaced particles
efficiently stop dislocations.
Simulation courtesy
of Volker Mohles,
Institut für Materialphysik der Universitåt, Münster, Germany (
uni-munster.de/physik
/MP/mohles/). Used with permission.
Click on image to
begin simulation 22

80. SIMULATION: DISLOCATION MOTION OVERAGED MATERIAL
--avg. particle size = 361b
--more widely spaced
particles not as effective.
Simulation courtesy
of Volker Mohles,
Institut für Materialphysik der Universitåt, Münster, Germany (
uni-munster.de/physik
/MP/mohles/). Used with permission.
Click on image to
begin simulation 23

81. STRENGTHENING STRATEGY 3: PRECIPITATION STRENGTHENING
• Hard precipitates are difficult to shear.
Ex: Ceramics in metals (SiC in Iron or Aluminum).
• Result: 24

82. SIMULATION: PRECIPITATION STRENGTHENING
• View onto slip plane of Nimonic PE16
• Precipitate volume fraction: 10%
• Average precipitate size: 64 b (b = 1 atomic slip distance)
Simulation courtesy of Volker Mohles, Institut für Materialphysik der Universitåt, Münster, Germany (
/MP/mohles/). Used with permission. 25

83. APPLICATION: PRECIPITATION STRENGTHENING
• Internal wing structure on Boeing 767
Adapted from Fig. 11.0, Callister 5e.
(Fig is courtesy of G.H. Narayanan and A.G. Miller, Boeing Commercial Airplane Company.)
• Aluminum is strengthened with precipitates formed
by alloying.
1.5mm
Adapted from Fig , Callister 6e.
(Fig is courtesy of G.H. Narayanan and A.G. Miller, Boeing Commercial Airplane Company.) 26

84. Phase Transformations
Time to finish this little voyage with a discussion of a few things you already know about, and to talk about polymers
Crystallization, melting, and glass transitions in polymers
Ok, you know about two of the three
Crystallization – process by which, upon cooling, an ordered crystalline phase forms from a liquid melt of polymer with a highly random structure
Melting – you know
Glass transition – cool polymer from liquid melt that becomes a non-crystalline solid … becomes rigid but has structural ordering reminiscent of the liquid state
End of lecture 1

85. Phase Transformations
Polymer Crystallization – can describe this using approach described earlier in the chapter (Avrami eqn, etc.)
Molecular picture – chains go from a highly disordered state in the melt to a highly ordered state in the solid upon cooling
But remember, polymers are usually semicrystalline
Have regions of crystalline and amorphous polymer
Polypropylene crystallization kinetics
This plot is normalized
Cannot completely crystallize PP
End of lecture 1

86. Phase Transformations
Polymer Melting – go from a solid  liquid melt as the polymer is heated above some temperature Tm
Few differences between polymers and metals/ceramics
Have a range of melting temperatures – the polymer does not completely melt at one temperature like a molecular compound
Why?
Melting behavior depends on the polymer “history”  how it has been processed
Why would that be the case?
End of lecture 1

87. Phase Transformations
The glass transition – cool from a melt, but get a disordered solid instead of a crystalline solid
Occurs due to reduction of motion of the segments of the polymer chains with decreasing temperature
Upon cooling: liquid  rubbery material  rigid solid
Glass transition temperature (Tg) is when the transformation from a rubbery material to a rigid solid is observed
Why do we care about the glass transition? Observe abrupt changes in material properties at Tg
End of lecture 1

88. Phase Transformations
Tm and Tg are important for polymers – they define the temperature ranges a polymer can be used for applications!
Determine Tm and Tg for polymers by observing the specific volume as a function of temperature
Note differences in the plot for a crystalline solid, glass, and semicrystalline solid!
End of lecture 1

89. Phase Transformations
Factors (some) that influence polymer melting temperatures
Chain stiffness – ease of rotation of bonds along backbone
Molecular weight – generally increase MW Tm increases; but there is a range of Tm values
Degree of chain branching – what would you expect the correlation to be here?
End of lecture 1

90. Phase Transformations
Factors (some) that influence polymer glass transition temperatures
Chain stiffness
Bulky side groups
Polar side groups
Double-chain bonds and aromatic rings
Molecular weight
Crosslinking
In general terms the same things that increase the melting temperature also increase the glass transition temperature
Typically Tg ~ 0.5 – 0.8 Tm (K)
End of lecture 1

91. ANNOUNCEMENTS Reading: Chapter 11
HW # 7:Due Monday, March 19th : 11.2; 11.4;
11.9; 11.12
HW # 8: Due Monday, March 26th : 11.15;
11.20; 11.24; 11.28; 11.32; 11.41; 11.44;
11.D2; 11.D5; 11.D8