1. 2/16/2019 9:54 PM
Chapter 9
Phase Diagrams
Dr. Mohammad Abuhaiba, PE

2. Learning Objectives Isomorphous and eutectic phase diagrams:
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Learning Objectives
Isomorphous and eutectic phase diagrams:
label various phase regions
Label liquidus, solidus, and solvus lines
Given a binary phase diagram at equilibrium, composition of an alloy, its temperature, determine:
phases present
compositions of phases
mass fractions of phase
Dr. Mohammad Abuhaiba, PE

3. 2/16/2019 9:54 PM
Learning Objectives
For some given binary phase diagram upon heating or cooling, locate temperatures & compositions and write reactions of:
Eutectic
Eutectoid
Peritectic
congruent phase transformations
Dr. Mohammad Abuhaiba, PE

4. 2/16/2019 9:54 PM
Learning Objectives
Given composition of an Fe–C alloy containing between & 2.14 wt% C:
Is alloy hypoeutectoid or hypereutectoid?
name proeutectoid phase
compute mass fractions of proeutectoid phase and pearlite
schematic diagram of microstructure at a temperature just below the eutectoid.
Dr. Mohammad Abuhaiba, PE

5. Why Study Phase Diagrams?
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Why Study Phase Diagrams?
Design and control of HT procedures
Strong correlation between microstructure and mechanical properties
Development of microstructure of an alloy is related to the char of its phase diagram
Phase Diagram (PD) provides valuable info about melting, casting, crystallization, and other phenomena
Dr. Mohammad Abuhaiba, PE

6. 2/16/2019 9:54 PM
9.2 Solubility Limit
Dr. Mohammad Abuhaiba, PE

7. 2/16/2019 9:54 PM
9.3 Phases
A phase: a physically distinct and homogenous portion in a material.
Each phase is a homogenous part of total mass and has its own characteristics and properties.
Phase Characteristics:
Same structure or atomic arrangement.
Same composition and properties.
Definite interface between phase and any surrounding or adjoining phases
Two types of alloys:
single phase
multiple phases
Dr. Mohammad Abuhaiba, PE

8. 9.3 Phases Alloying consists of two basic forms:
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9.3 Phases
 Alloying consists of two basic forms:
Solid solutions.
Inter-metallic compounds.
Solid Solutions (SS): solid material in which atoms or ions of elements constituting it are dispersed uniformly.
A SS is not a mixture.
A mixture contains more than one type of phase whose char are retained when mixture is formed.
Components of SS completely dissolve in one another and do not retain their individual char.
Properties are controlled by creating point defects such as substititional and interstitial atoms.
Solute: minor element that is added to solvent, which is the major element.
When the particular crystal structure of solvent is maintained during allying, the alloy is called a Solid Solution.
Dr. Mohammad Abuhaiba, PE

9. 9.6 One Component (Unary) Phase Diagrams
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9.6 One Component (Unary) Phase Diagrams
Dr. Mohammad Abuhaiba, PE

10. 9.7 Binary Isomorphous Systems
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9.7 Binary Isomorphous Systems
A phase diagram (PD) shows the relationships among temperature, composition, and phases present in a particular alloy system under equilibrium conditions.
From PD, we can predict:
how a material will solidify under equilibrium conditions
what phases for diff temp and comp.
Equilibrium means that state of a system remains constant over an indefinite period of time.
Dr. Mohammad Abuhaiba, PE

11. 9.7 Binary Isomorphous Systems
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9.7 Binary Isomorphous Systems
Dr. Mohammad Abuhaiba, PE

12. 9.7 Binary Isomorphous Systems
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9.7 Binary Isomorphous Systems
Only one solid phase forms, the two components in the system display complete solid solubility.
Liquidus temperature.
Solidus temperature.
Freezing range: pure metals and alloys
When temperature of molten metal is reduced to freezing point:
energy of latent heat of solidification is given off while temperature remains constant.
Eventually, solidification is complete and solid metal continues cooling to RT.
Dr. Mohammad Abuhaiba, PE

13. 9.7 Binary Isomorphous Systems
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9.7 Binary Isomorphous Systems
Cooling curve for the solidification of pure metals
Alloys solidify over a range of temperatures
Dr. Mohammad Abuhaiba, PE

14. 9.7 Binary Isomorphous Systems
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9.7 Binary Isomorphous Systems
Dr. Mohammad Abuhaiba, PE

15. 9.8 Interpretation of Phase Diagrams
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9.8 Interpretation of Phase Diagrams
Phases Present
Determination of Phase Compositions
Determination of Phase Amounts
Dr. Mohammad Abuhaiba, PE

16. EXAMPLE PROBLEM 9.1 Derive the lever rule. 2/16/2019 9:54 PM
Dr. Mohammad Abuhaiba, PE

17. 9.8 Interpretation of Phase Diagrams
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9.8 Interpretation of Phase Diagrams
Volume Fractions
Conversion between volume and mass fractions
Dr. Mohammad Abuhaiba, PE

18. 9.9 Development of Microstructure in Isomorphous Alloys
The completely solidified alloy in the phase diagram shown is a solid solution because:
alloying element (Cu, solute atom) is completely dissolved in host metal (Ni, solvent atom),
Each grain has same composition.
atomic radius of Cu is 0.128nm and that of Ni is 0.125nm,
Both elements are of FCC structure; HRRs are obeyed.
Dr. Mohammad Abuhaiba, PE

19. 9.9 Development of Microstructure in Isomorphous Alloys
Two conditions required for growth of solid a:
Growth requires that latent heat of fusion (DHf), which evolves as liquid solidifies, be removed from solid liquid interface.
Unlike the case of pure metals, diffusion must occur so that compositions of solid and liquid phases follow solidus and liquidus curves during cooling. DHf is removed over a range of temperatures so that cooling curves shows a change in slope
Dr. Mohammad Abuhaiba, PE

20. 9.9 Development of Microstructure in Isomorphous Alloys
Figure 9.4 Schematic representation of the development of microstructure during the equilibrium solidification of a 35 wt% Ni–65 wt% Cu alloy.
Dr. Mohammad Abuhaiba, PE

21. 9.9 Development of Microstructure in Isomorphous Alloys
On cooling from liquidus to 1250oC, some Ni atoms must diffuse from 1st solid to new solid, reducing Ni in 1st solid.
Additional Ni atoms diffuse from solidifying liquid to new solid. Meanwhile, Cu atoms have concentrated –by diffusion – into remaining liquid.
The process must continue until we reach solidus temperature, where last liquid to freeze, which contains Cu-28%Ni, solidifies and forms a solid containing Cu-40%Ni.
Dr. Mohammad Abuhaiba, PE

22. 9.9 Development of Microstructure in Isomorphous Alloys
Figure 9.5 Schematic representation of the development of microstructure during the nonequilibrium solidification of a 35 wt% Ni–65 wt% Cu alloy.
Dr. Mohammad Abuhaiba, PE

23. 9.10 Mechanical Properties of Isomorphous Alloys
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9.10 Mechanical Properties of Isomorphous Alloys
Dr. Mohammad Abuhaiba, PE

24. 9.11 Binary Eutectic Systems
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9.11 Binary Eutectic Systems
Dr. Mohammad Abuhaiba, PE

25. 9.11 Binary Eutectic Systems
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9.11 Binary Eutectic Systems
Dr. Mohammad Abuhaiba, PE

26. 2/16/2019 9:54 PM
EXAMPLE PROBLEM 9.2
Determination of Phases Present and Computation of Phase Compositions
For a 40 wt% Sn–60 wt% Pb alloy at 150C,
what phase(s) is (are) present?
What is (are) the composition(s) of the phase(s)?
Dr. Mohammad Abuhaiba, PE

27. 2/16/2019 9:54 PM
EXAMPLE PROBLEM 9.3
Relative Phase Amount Determinations—Mass and Volume Fractions
For the lead–tin alloy in Example Problem 9.2, calculate the relative amount of each phase present in terms of
mass fraction and
volume fraction. At 150C take the densities of Pb and Sn to be and 7.24 g/cm3, respectively.
Dr. Mohammad Abuhaiba, PE

28. 9.12 Development of Microstructure in Eutectic Alloys
Dr. Mohammad Abuhaiba, PE

29. 9.12 Development of Microstructure in Eutectic Alloys
Dr. Mohammad Abuhaiba, PE

30. 9.12 Development of Microstructure in Eutectic Alloys
Dr. Mohammad Abuhaiba, PE

31. 9.12 Development of Microstructure in Eutectic Alloys
Dr. Mohammad Abuhaiba, PE

32. 9.12 Development of Microstructure in Eutectic Alloys
Dr. Mohammad Abuhaiba, PE

33. 9.12 Development of Microstructure in Eutectic Alloys
Dr. Mohammad Abuhaiba, PE

34. 9.13 Equilibrium Diagrams Having Intermediate Phases or Compounds
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9.13 Equilibrium Diagrams Having Intermediate Phases or Compounds
Dr. Mohammad Abuhaiba, PE

35. 9.13 Equilibrium Diagrams Having Intermediate Phases or Compounds
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9.13 Equilibrium Diagrams Having Intermediate Phases or Compounds
Dr. Mohammad Abuhaiba, PE

36. 9.14 Eutectoid and Peritectic Reactions
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9.14 Eutectoid and Peritectic Reactions
Dr. Mohammad Abuhaiba, PE

37. 9.15 Congruent Phase Transformations
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9.15 Congruent Phase Transformations
congruent transformations: Those for which there are no compositional alterations.
allotropic transformations (Sec 3.6)
melting of pure materials.
Incongruent transformations: at least one of the phases will experience a change in composition.
Eutectic and eutectoid reactions
melting of an alloy that belongs to an isomorphous system
Dr. Mohammad Abuhaiba, PE

38. 9.18 The IRON–IRON Carbide (Fe–Fe3C) Phase Diagram
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9.18 The IRON–IRON Carbide (Fe–Fe3C) Phase Diagram
Dr. Mohammad Abuhaiba, PE

39. 9.18 The IRON–IRON Carbide (Fe–Fe3C) Phase Diagram
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9.18 The IRON–IRON Carbide (Fe–Fe3C) Phase Diagram
Dr. Mohammad Abuhaiba, PE

40. 9.19 Development of Microstructure in Iron Carbon Alloys
Dr. Mohammad Abuhaiba, PE

41. 9.19 Development of Microstructure in Iron Carbon Alloys
Dr. Mohammad Abuhaiba, PE

42. 2/16/2019 9:54 PM
9.19 Development of Microstructure in Iron Carbon Alloys Hypo-eutectoid Alloys
Dr. Mohammad Abuhaiba, PE

43. 2/16/2019 9:54 PM
9.19 Development of Microstructure in Iron Carbon Alloys - Hypo-eutectoid Alloys
Dr. Mohammad Abuhaiba, PE

44. 2/16/2019 9:54 PM
9.19 Development of Microstructure in Iron Carbon Alloys - Hyper-eutectoid Alloys
Dr. Mohammad Abuhaiba, PE

45. 2/16/2019 9:54 PM
EXAMPLE PROBLEM 9.4
Determination of Relative Amounts of Ferrite, Cementite, and Pearlite Microconstituents
For a wt% Fe–0.35 wt% C alloy at a temperature just below the eutectoid, determine the following:
The fractions of total ferrite and cementite phases
The fractions of the proeutectoid ferrite and pearlite
The fraction of eutectoid ferrite
Dr. Mohammad Abuhaiba, PE

46. 9.20 The Influence of Other Alloying Elements
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9.20 The Influence of Other Alloying Elements
Dr. Mohammad Abuhaiba, PE

47. 2/16/2019 9:54 PM
Home Work Assignment
1, 6, 11, 16, 21, 26, 32, 39, 44, 49, 54, 59, 65
Dr. Mohammad Abuhaiba, PE