1. Chapter 9
Phase Diagrams

2. Phase Diagram Vocabulary
System
The universe or any part of it.
Phase
A region in the system that has a distinct structure and/or composition
Structure
How the atoms or molecules of the components are physically arranged in space
Composition
The relative amounts of different components
Components
Chemically distinct species, generally pure elements or compounds
Phase Diagram
A graphical representation of the influence of various factors, such as temperature, pressure, and composition on the phases that exist in a system.
Unary System
A system that has only one component
Binary System
A system that has two components – what this course primarily deals with
Ternary System
A system that has three components
Quaternary System
A system that has four components
A, B, C …
Generic names of components
L, α, β,  …
Generic names of phases

3. Unary Phase Diagrams – H2O
1 atmosphere

4. Unary Phase Diagram – Pure Fe

5. Gibbs Phase Rule (Section 9.17)
Tells us how many phases can exist under a given set of circumstances.
P+F=C+2
P = number of phases
F = number of degrees of freedom – number of variables that can be changed independently of all other variables in the system
C=number of components
The number two indicates the ability to change temperature and pressure; these are non-compositional variables that affect the phases.
Modified Gibbs phase rule
Most engineering systems function at a pressure of 1 atmosphere, i.e. we have picked the pressure as one of our degrees of freedom. Therefore,
P+F = C+1

6. Binary Isomorphous System
Two components are completely soluble in each other in both solid and liquid phases
Hume-Rothery’s Rules (Section 4.3 text 7th edition)
Atomic size difference not greater than 15%
Crystal structure is the same for both components
Similar electronegativity (i.e. no ionic bonding)
Elements have a similar valance
Example: Cu-Ni System
rCu = nm rNi = nm
Both have a face centered cubic (fcc) structure
Electronegativity Cu = 0.19; Ni = 0.18
Valance – Cu+ and Cu++; Ni++

7. Cooling Curves during Solidification
Solidification occurs at constant temperature while latent heat of fusion is released

8. Cooling curves for a binary isomorphous alloy
Features:
Solidus – locus of temperatures below which all compositions are solid
Start of solidification during cooling
Liquidus – locus of temperatures above which all compositions are liquid
Start of melting during heating

10. Modified Gibbs Phase Rule
In the liquid or solid phase:
P=1, C=2
P+F=C+1
F=2
Both composition and temperature can be varied while remaining in the liquid or solid phase
In the L+a region
P=2, C=2
F=1
If we pick a temperature, then compositions of L and a are fixed
If we pick a composition, liquidus and solidus temperatures are fixed TL TS

11. Tie Line and Lever Rule At point B both liquid and a are present
WL×R = WS×S WL WS R S

12. Equilibrium Cooling

13. Non-equilibrium cooling results in
Cored structure
Composition variations in the solid phase as layers of decreasing Ni concentration are deposited on previously formed a phase
Solidification point is depressed
Melting point on reheat is lowered
Homogenization or reheating for extended times at temperature below e’

14. Effect on Mechanical Properties
Due to solid solution strengthening, alloys tend to be stronger and less ductile than the pure components.

15. Binary Eutectic System
The two components have limited solid solubility in each other
Solubility varies with temperature
For an alloy with the Eutectic composition the liquid solidifies into two solid phases
Liquid
α (solid solution) + β (solid solution)
Eutectic temperature
Cooling
61.9% Sn
18.3% Sn
97.8% Sn
183ºC

16. Binary Eutectic System
Apply Modified Gibbs Phase Rule
Phases present: L, a and b (P=3)
Components: Pb and Sn (C=2)
P+F=C+1
F=0  no degrees of freedom
Therefore, three phases can coexist in a binary system only at a unique temperature and for unique compositions of the three phases
Upon cooling, there is a temperature arrest during the solidification process (eutectic reaction)

17. Microstructures in the Eutectic System
Depending on the system, eutectic solidification can result in:
Lamellar structure – alternating plates
Rod-like
Particulate

18. Microstructures in the Eutectic System
Solvus Line

19. Microstructures in the Eutectic System

20. Amounts of Phases at different temperatures
At Teutectic + DT
At Teutectic - DT

21. Other Reactions in the Binary System
Upon Cooling the following reactions are also possible
Peritectic L + a  b
Monotectic L1  L2 + a
Eutectoid a  b + g
Peritectoid a + b  g

22. Copper-Zinc System Terminal phases Intermediate phases
Several peritectics
Eutectoid
Two phase regions between any two single phase regions

23. Mg-Pb System Intermediate Compound Mg2Pb Congruently melting Mg2Pb  L
heating

24. Portion of the Ni-Ti System
Congruently melting intermediate phase g
g  L
heating

25. Iron-Carbon System Reactions on cooling Peritectic L + d  g Eutectic
L  g + Fe3C
Eutectoid
g  a + Fe3C
Steel
Cast Iron

26. Iron-Carbon or Iron-Fe3C
In principle, the components of the phase diagram should be iron (Fe) and carbon/graphite (C).
Fe and C form an intermediate compound Fe3C, which is very stable
There isn’t anything of interest at carbon contents greater than 25 at.% or 6.7 wt.% C.
Fe3C is considered to be a component, and the binary phase diagram is drawn using Fe and Fe3C.
Names of phases:
Ferrite - a iron – bcc structure
Austenite – g iron – fcc structure
High temperature d iron – bcc structure
Cementite – Fe3C
Steels have carbon contents <2%, usually <1.2%
Cast irons have carbon contents >2%

27. Phase Transformations in Steels
Eutectoid Composition – 0.76wt% C
Pearlite
Alternating plates (lamellae) of Fe and Fe3C
Austenite  Ferrite Cementite (at 727ºC upon cooling)
0.76wt.%C wt.%C wt.% C

28. Phase Transformations in Steels
Hypoeutectoid composition <0.76 wt% C
Proeutectoid ferrite nucleates and spreads along austenite grain boundaries at T>727ºC
Remaining austenite converts to pearlite during eutectoid transformation

29. Phase Transformations in Steels
Hypereutectoid composition >0.76 wt% C
Proeutectoid cementite nucleates and spreads along austenite grain boundaries at T>727ºC
Remaining austenite converts to pearlite during eutectoid transformation

30. Phase Transformations in Steels
Hypoeutectoid
Hypereutectoid
Proeutectoid ferrite
Pearlite
Proeutectoid cementite

31. Effect of Alloying Elements
Addition of an alloying element increases the number of components in Gibbs Phase Rule.
The additional degree of freedom allows changes in the eutectoid temperature or eutectoid Carbon concentration