1. How to calculate the total amount of  phase (both eutectic and primary)?
Fraction of  phase determined by application of the lever rule across the entire  +  phase field:
W = (Q+R) / (P+Q+R) ( phase)
W = P / (P+Q+R) ( phase)
Show that We * W in e + W` = W
W in e = R/(P+Q+R)

2. Intermediate Phases So far only two solid phases (a and b)
Terminal solid solutions
Some binary systems have intermediate
solid solution phases.
Cu-Zn: a and h are terminal solid solutions, b, b’, g, d, e are intermediate solid solutions.

3. Intermetallic Compounds
precise chemical compositions exist in some systems.
Using the lever rules, intermetallic compounds are treated like any other phase,
They appear as a vertical line.
intermetallic
compound
Two eutectic diagrams: Mg-Mg2Pb and Mg2Pb-Pb. Intermetallic compound Mg2Pb is considered a component.

4. Eutectoid Reactions (I)
Eutectoid (eutectic-like in Greek) reaction similar to eutectic reaction
One solid phase to two new solid phases
Invariant point (the eutectoid) 
Three solid phases in equilibrium
Upon cooling, a solid phase transforms into two other solid phases (   +  below)
Cu-Zn
Eutectoid

5. Eutectoid Reactions (II)
Contains an eutectic reaction
and an eutectoid reaction

6. Peritectic Reactions
Peritectic  solid phase + liquid phase will together form a second solid phase at a particular temperature and composition upon cooling
L +   
Reactions are slow as product phase will form at boundary between two reacting phases separating them
Peritectics are not as common as eutectics and eutectiods. There is one in Fe-C system

7. Congruent Phase Transformations
Congruent transformation  no change in composition
(e.g, allotropic transformation such as a-Fe to g-Fe or melting transitions in pure solids)
Incongruent transformation, at least one phase changes composition (eutectic, eutectoid, peritectic).
Congruent
melting of g
Ni-Ti

8. The Iron–Iron Carbide (Fe–Fe3C) Phase Diagram
Steels: alloys of Iron (Fe) and Carbon (C).
Fe-C phase diagram is complex. Will only consider the steel part of the diagram, up to around 7% Carbon.

9. Phases in Fe–Fe3C Phase Diagram
a-ferrite - solid solution of C in BCC Fe
Stable form of iron at room temperature.
The maximum solubility of C is wt%
Transforms to FCC g-austenite at 912 C
g-austenite - solid solution of C in FCC Fe
The maximum solubility of C is 2.14 wt %.
Transforms to BCC d-ferrite at 1395 C
Is not stable below the eutectic temperature (727  C) unless cooled rapidly (Chapter 10)
d-ferrite solid solution of C in BCC Fe
The same structure as a-ferrite
Stable only at high T, above 1394 C
Melts at 1538 C
Fe3C (iron carbide or cementite)
This intermetallic compound is metastable, it remains as a compound indefinitely at room T, but decomposes (very slowly, within several years) into a-Fe and C (graphite) at C
Fe-C liquid solution

10. Comments on Fe–Fe3C system
C is an interstitial impurity in Fe. It forms a solid solution with a, g, d phases of iron
Maximum solubility in BCC a-ferrite is wt% at727 C. BCC:relatively small interstitial positions
Maximum solubility in FCC austenite is 2.14 wt% at 1147 C - FCC has larger interstitial positions
Mechanical properties: Cementite (Fe3C is hard and brittle: strengthens steels. Mechanical properties also depend on microstructure: how ferrite and cementite are mixed.
Magnetic properties:  -ferrite is magnetic below 768 C, austenite is non-magnetic
Classification. Three types of ferrous alloys:
Iron: < wt % C in a-ferrite at room T
Steels: wt % C (usually < 1 wt % ) a-ferrite + Fe3C at room T (Chapter 12)
Cast iron: wt % (usually < 4.5 wt %)

11. Eutectic and eutectoid reactions in Fe–Fe3C
Eutectic: 4.30 wt% C, 1147 C
L   + Fe3C
Eutectoid: wt%C, 727 C
(0.76 wt% C)   (0.022 wt% C) + Fe3C
Eutectic and Eutectoid reactions are important in heat treatment of steels

12. Microstructure in Iron - Carbon alloys
Microstructure depends on composition (carbon content) and heat treatment.
Assume slow cooling  equilibrium maintained
Microstructure of eutectoid steel (I)

13. Microstructure of eutectoid steel (II)
Pearlite, layered structure of two phases: a-ferrite and cementite (Fe3C)
Alloy of eutectoid composition (0.76 wt % C) Layers formed for same reason as in eutectic: Atomic diffusion of C atoms between ferrite (0.022 wt%) and cementite (6.7 wt%)
Mechanically, properties intermediate to soft, ductile ferrite and hard, brittle cementite.
In the micrograph, the dark areas are Fe3C layers, the light phase is a-ferrite

14. Microstructure of hypoeutectoid steel (I)
Compositions to the left of eutectoid ( wt % C) hypoeutectoid (less than eutectoid -Greek) alloys.
   +    + Fe3C

15. Microstructure of hypoeutectoid steel (II)
Hypoeutectoid contains proeutectoid ferrite formed above eutectoid temperature and eutectoid perlite that contains ferrite and cementite.

16. Microstructure of hypereutectoid steel (I)
Compositions to right of eutectoid ( wt % C) hypereutectoid (more than eutectoid -Greek) alloys    + Fe3C   + Fe3C

17. Microstructure of hypereutectoid steel (II)
Hypereutectoid contains proeutectoid cementite (formed above eutectoid temperature) plus perlite that contains eutectoid ferrite and cementite.

18. How to calculate the relative amounts of proeutectoid phase (a or Fe3C) and pearlite?
Lever rule + tie line that extends from the eutectoid composition (0.75 wt% C) to a – (a + Fe3C) boundary (0.022 wt% C) for hypoeutectoid alloys and to (a + Fe3C) – Fe3C boundary (6.7 wt% C) for hipereutectoid alloys.
Show that We * W in e + W` = W
W in e = R/(P+Q+R)
Fraction of  phase determined by application of lever rule across the entire ( + Fe3C) phase field

19. Example: hypereutectoid alloy, composition C1
Fraction of pearlite:
WP = X / (V+X) = (6.7 – C1) / (6.7 – 0.76)
Fraction of proeutectoid cementite:
WFe3C = V / (V+X) = (C1 – 0.76) / (6.7 – 0.76)

20. Summary Make sure you understand language and concepts: Austenite
Cementite
Component
Congruent transformation
Equilibrium
Eutectic phase
Eutectic reaction
Eutectic structure
Eutectoid reaction
Ferrite
Hypereutectoid alloy
Hypoeutectoid alloy
Intermediate solid solution
Intermetallic compound
Invariant point
Isomorphous
Lever rule
Liquidus line
Metastable
Microconstituent
Pearlite
Peritectic reaction
Phase
Phase diagram
Phase equilibrium
Primary phase
Proeutectoid cementite
Proeutectoid ferrite
Solidus line
Solubility limit
Solvus line
System
Terminal solid solution
Tie line

21. Reading for next class:
Chapter 10: Phase Transformations in Metals
Kinetics of phase transformations
Multiphase Transformations
Phase transformations in Fe-C alloys
Isothermal Transformation Diagrams
Mechanical Behavior
Tempered Martensite
Optional reading (Parts that are not covered / not tested):
10.6 Continuous Cooling Transformation Diagrams