1. Dispersion Strengthening and Eutectic Phase Diagrams
Chapter 10 – 4th Edition
Chapter 11 – 5th Edition

2. In the last chapter…
We talked about alloys that form from materials that are completely soluble in each other
We also learned not all materials are completely soluble
In this chapter we’ll talk about what happens when there are multiple solid phases present

3. Dispersion Strengthening
The existence of two or more phases can strengthen a material
When that happens it’s called dispersion strengthening
Matrix – present in large amounts
Precipitate – present in smaller amounts

4. Guidelines Matrix should be soft to provide ductility
Precipitate should be hard to provide strength – more precipitate results in higher strength
Precipitate should be discontinuous
Precipitate
Matrix

5. Guidelines
Smaller, more numerous precipitate particles give higher strength because they interfere with slip
Round particles are better than sharp particles – Sharp particles can initiate a crack
Good
Not so Good

6. Guidelines
Smaller, more numerous precipitate particles give higher strength because they interfere with slip
Round particles are better than sharp particles – Sharp particles can initiate a crack
Good
Not good at all

7. Intermetallic Compounds
Often precipitates are intermetallic compounds – metals that are bonded to each other
Stoichiometric Compounds
Non-stoichiometric Compounds have a range of compositions (often a blend of two or more stoichiometric compounds)

8. 3-Phase Reactions
In order to have a precipitate we must have 2 solid phases
Matrix
Precipitate
There are a number of ways to create these phases – but we are going to look at the following 3-Phase reactions
Eutectic L-> S1 + S (this chapter)
Eutectoid S1 -> S2 + S3 (next chapter)

9. Let’s start with the Eutectic
L → S1 + S2

10. Eutectoid S1 S2 S3
S2 + S3
S1 → S2 + S3

11. The Eutectic Phase Diagram
Temperature
Wt% Y X Y
Liquid a b
Eutectic
Solidus
Solidus
Liquidus
a + L
b + L
Solvus
Solvus
a + b

12. The Eutectic Phase Diagram
Temperature
Wt% Y X Y
Liquid a b
a + L
b + L
a + b
In this portion of the diagram only a 2 phase reaction occurs – similar to what we observed in Chapter 9
The strengthening mechanism is solid solution strengthening

13. Lead – Tin Phase Diagram
Temperature
Wt% Y X Y
Liquid a b
a + L
b + L
a + b Pb Sn
Lead – Tin Phase Diagram
Amount of a
Amount of b Sn

14. Cooling Curve
Liquid
Liquid + a
Temperature a
a + b
Time

15. Solidification of a Lead-Tin Alloy
Lead – Tin Phase Diagram
Lead – Tin Cooling Curve
Liquid
Liquid
Liquid + a
Temperature a
a + L
Temperature a
b + L b
a + b
a + b
Amount of a
Amount of b
Wt% Sn Pb X Sn Y
Time

16. How Does the Solid Form?
We’ll talk in the next chapter about how to manipulate the particle growth to achieve the optimum distribution of the precipitate
Liquid a
L + a
a + b
This alloy is dispersion strengthened

17. Lead – Tin Phase Diagram
Temperature
Wt% Y X Y
Liquid a b
a + L
b + L
a + b Pb Sn
Lead – Tin Phase Diagram
Eutectic
Amount of b
Amount of a Sn

18. Cooling Curve for a Hypoeutectic System
Liquid
Liquid + a
a + b
Temperature
L + a + b
Time

19. Lets not look at how the solid forms just yet – it’s a little complicated
Instead lets look at what happens if your over all composition is the eutectic composition

20. Temperature
Wt% Y X Y
Liquid a b
a + L
b + L
a + b Pb Sn
Lead – Tin Phase Diagram
Eutectic Composition

21. Cooling Curve for a Eutectic System
Plumber’s solder is a eutectic alloy of Pb and Sn.
Why?
Liquid
a + b
L + a + b
Temperature
Low, sharp melting point
Time

22. How Does the Eutectic Solid Form?
Liquid
L + a + b
Eutectic Solids are strong but generally have little ductility

23. Strength of Eutectic Alloys
Each phase is solid solution strengthened
Grain size affects the strength – well inoculated melts have smaller grain size
Interlamellar spacing

24. Cobalt-Carbon Eutectic
Scanning electron microscope image of cobalt-carbon eutectic. There is an irregular arrangement of graphite needles in a cobalt rich-phase matrix.

25. Interlamellar Spacing
The spacing is controlled by how long the grains are allowed to grow
You can limit the spacing by reducing the solidification time – by removing heat faster
Small interlamellar spacing results in high strength
Interlamellar Spacing

26. Lead – Tin Phase Diagram
Temperature
Wt% Y X Y
Liquid a b
a + L
b + L
a + b Pb Sn
Lead – Tin Phase Diagram
Eutectic
Amount of b
Amount of a
Let’s go back to the hypo eutectic composition Sn

27. How does solidification occur in a hypoeutectic system?
L + a + b
Liquid
L + a
Primary Phase is a (Proeutectic)
Eutectic Microconstituent

28. Pb-Sn HypoEutectic Composition
This image is lead-tin solder showing the dark dendrites of primary lead surrounded by Pb-Sn eutectic. Scale bar is 667 micrometers
Used with permission of Ruth I. Schultz Kramer Scientist, Dept. of Materials Science and Engineering, Michigan Technological University

29. Higher magnification of solder showing varying structure of the Pb within the two phase Pb-Sn eutectic, which surrounds the primary lead dendrites. Scale bar is 100 micrometers long. Used with permission of Ruth I. Schultz Kramer Scientist, Dept. of Materials Science and Engineering, Michigan Technological University

30. Lead – Tin Phase Diagram
Temperature
Wt% Y X Y
Liquid a b
a + L
b + L
a + b Pb Sn
Lead – Tin Phase Diagram
Eutectic
As the alloy cools from the eutectic temperature, there is a rearrangement WITHIN each microconstituent of the amount of  and β
Amount of Eutectic Microconstituent
Amount of a existing as the proeutectic or primary microconstituent Sn

31. Lead – Tin Phase Diagram
Temperature
Wt% Y X Y
Liquid a b
a + L
b + L
a + b Pb Sn
Lead – Tin Phase Diagram
As the alloy cools from the eutectic temperature, there is a rearrangement WITHIN each microconstituent of the amount of  and β
Eutectic
The amount of β existing in the eutectic microconstituent changes with temperature
The amount of  existing in the eutectic microconstituent changes with temperature Sn

32. Lead – Tin Phase Diagram
Temperature
Wt% Y X Y
Liquid a b
a + L
b + L
a + b Pb Sn
Lead – Tin Phase Diagram
The PRIMARY microconstituent has no beta at the eutectic temperature, but particles grow within in it as the temperature decreases
Eutectic
Amount of β in the primary phase
Amount of  in the primary phase Sn

33. 50-50 alloy of Pb and Bi - HypoEutectic
Note: This is lead and bismuth – but the idea is the same
Eutectic Microconstituent
Primary – Lead rich phase
Used with permission of Ruth I. Schultz Kramer Scientist, Dept. of Materials Science and Engineering, Michigan Technological University

34. Temperature
Wt% X Y
Liquid a b
a + L
b + L
a + b Pb Sn
Lead – Tin Phase Diagram
Hypereutectic Composition

35. What happens during the solidification of a hypereutectic system?
L + a + b
Liquid
L + b
Primary Phase is b
Eutectic Microconstituent

36. Which is Best? It depends on your design requirements
Eutectic
Hypoeutectic
Hypothetical Alloy
Dispersion Strengthening
Hypereutectic
Solid Solution Strengthening
Strength
Composition

37. Let’s do some calculations
Assume you have an alloy that is
40 wt% Sn
60 wt% Pb
What is the composition at room temperature of the
 (Pb rich) phase?
β (Sn rich) phase?
What fraction of the alloy is ?
β ?
What fraction is
Eutectic microconstituent?
Proeutectic microconstituent?

38. This version of the phase diagram will be easier to use
At room temperature the Pb rich phase is approximately 2% Pb
At room temperature the Pb rich phase is approximately 2% Sn
At room temperature the Sn rich phase is approximately 100% Sn

39. Fraction of each phase
At room temperature the Pb rich phase is approximately 2% Pb 
Fraction Sn rich phase (β)
Fraction Pb rich phase ()

40. Fraction of each microconstituent
At room temperature the Pb rich phase is approximately 2% Pb 
Fraction Proeutectic microconstituent
Fraction Eutectic microconstituent

41. Other Phase Diagrams Containing 3-Phase Reactions
All we’ve looked at are phase diagrams with a eutectic
Remember, a eutectic is a point where L-> a + b
There are lots of other possible 3 phase reactions, and lots of much more complicated phase diagrams

42. 3-Phase Reactions Eutectic L-> S1 + S2 Eutectoid S1 -> S2 + S3
Peritectic S1 + L1 -> S2
Peritectoid S1 + S2 -> S3
Monotectic L1 -> S1 + L2
We will be primarily concerned with Eutectic and Eutectoid Reactions

43. Consider the following hypothetical phase diagram taken from Askeland (pg 270)

44. L1 Monotectic d Eutectic L2 Peritectic g Temperature b Eutectoid a
g + d
L1 + g L2
L1 + L2
L2 + b
L2 + g g b
Temperature
g + b
Eutectoid
a + g a
Peritectoid
a + b
a + m m
m + b X Y

45. Three Component Phase Diagrams
So far we have only looked at 2 component alloys
Three component phase diagrams can be very complicated – they require a three dimensional phase diagram
A 2-D slice can tell us a lot though

46. Z
80 %
60 %
40 %
20 %
Wt% X
80%
60%
40%
20%
20%
40%
60%
80%
Wt % Y
Wt% Z Y X

47. Ternary Phase Diagrams
Used to plot the liquidus
An isothermal plot shows the phases present