1. Chapter Outline: Phase Diagrams
Microstructure + Phase Transformations
in Multicomponent Systems
Definitions and basic concepts
Phases and microstructure
Binary isomorphous systems (complete solid solubility)
Binary eutectic systems (limited solid solubility)
Binary systems with intermediate phases/compounds
The iron-carbon system (steel and cast iron)
Not tested: The Gibbs Phase Rule

2. Components and Phases Component - chemical species
(Fe + C in steel; H2O + NaCl in salt water).
Binary alloy 2 two components,
Ternary alloy – 3, etc.
Phase – a portion with distinct, uniform physical or chemical characteristics
Single-phase system: Homogeneous.
Two or more phases
Mixture or Heterogeneous system.
e.g. water + ice, separated by a phase boundary
Quaternary alloy…

3. Solubility Limit Solvent - host or major component
Solute - minor component (Chapter 4).
Solubility Limit = maximum amount that can be dissolved in a phase
(e.g. alcohol has unlimited solubility in water, sugar has a limited solubility, oil is insoluble).
Same concepts for solids: Cu and Ni are mutually soluble in any amount (unlimited solid solubility), while C has a limited solubility in Fe.
Ask what is one more difference between C-Fe and Cu-Ni solutions (interstitial vs substitutional)

4. Microstructure
Properties of an alloy depend on proportions of the phases and on how they are arranged at the microscopic level.
Microstructure: number of phases, their proportions, and their arrangements
Microstructure of cast Iron
This is an alloy of iron (Fe) with 4% carbon (C) by weight.
The microstructure has two main constituents. The long pale regions are flakes of graphite. They have a shape similar to the cornflake breakfast
cereal. The background or matrix of the alloy is pearlite. This is a fine mixture of ferrite and iron carbide.
A binary alloy may be
a.a single solid solution
b.two separated, essentially pure components.
c.two separated solid solutions.
d.a chemical compound, together with a solid solution.
Alloy of Fe with 4 wt.% C. There are several phases. The long gray regions are flakes of graphite. The matrix is a fine mixture of BCC Fe and Fe3C compound.
Phase diagrams help understand and predict microstructures

5. Equilibrium and Metastable States
Equilibrium: at constant temperature, pressure and composition system is stable
(Equilibrium is achieved given sufficient time, but that may be very long. )
Metastable: System appears to be stable
Equilibrium  minimum in the free energy.
Under conditions of constant temperature, pressure and composition, change is toward lower free energy.
equilibrium
Stable equilibrium is state with minimum free energy.
Metastable state is a local minimum of free energy.
Free Energy
metastable

6. Phase diagram
Phase diagram - combinations of temperature, pressure or composition for which specific phases exist at equilibrium
H2O: diagram shows temperature and pressure at which ice (solid),water (liquid) and steam (gas) exist.
Both the critical points are shown as red circles. The critical point and the orange line in the ice-one phase space refer to the low-density and
high-density forms of amorphous water (ice). All the solid phases of ice involve the oxygen atoms being hydrogen bonded to four
neighboring oxygen atoms. The high pressure phase lines of ice-ten (X) and ice-eleven (XI) are still subject to experimental verification. Two
different forms of ice-eleven have been described by different research groups: the high-pressure form involves hydrogen atoms equally-spaced
between the oxygen atoms (like ice-ten) whereas the lower pressure low temperature form utilizes the incorporation of hydroxide defect
doping to order the hydrogen bonding of ice 1h. Another ice-ten has been described, being the proton ordered form of ice-six (VI) occurring
below about 110 K. Only hexagonal ice-one (1h), ice-three (III), ice-five (V), ice-six (VI) and ice-seven (VII) can be in equilibrium with liquid water,
whereas all the others ices, including ice-two (II), are not stable in its presence under any conditions of temperature and pressure. Ice-two,
ice-eight (VIII), ice-nine (IX), ice-ten and ice-eleven (both) all possess (ice-nine mainly) ordered hydrogen-bonding whereas in the other ices
the hydrogen-bonding is disordered even down to 0 K, where reachable. Ice-four (IV) and ice-twelve (XII) [81] are both metastable within the
ice-five phase space. Cubic ice (1c) is metastable with respect to hexagonal ice (1h). It is worth noting that the water molecule is stable
throughout the phase space above. Kurt Vonnegut's highly entertaining story concerning an (imaginary) ice-nine, which was capable of
crystallizing all the water in the world [K. Vonnegut, Cat's Cradle, (Penguin, London, 1963) p. 34.], fortunately has no scientific basis (see also IE) as ice-nine, in reality, is a proton ordered form of ice-three, only exists at very low temperatures and high pressures and cannot exist alongside liquid water under any conditions.
Ice 1c is a metastable form of ice that can be formed, by condensation of water vapor, at ambient pressure but low temperatures (less than
-80°C, see Phase Diagram) or by reducing the pressure on high-pressure ices at 77 K. It converts, irreversibly but extremely slowly in the
temperature range K, to hexagonal ice with about 40 J mol-1 heat evolution. It consists of a face centered cubic lattice (Space
group Fd3m) with half the tetrahedral holes filled.

7. Phase diagram
Show what phases exist at equilibrium and what transformations we can expect when we change T, P, or composition
Consider binary alloys only
Pressure constant at one atmosphere.

8. Binary Isomorphous System (I)
Assume Complete Solubility L
 + L 
Three phases :
Liquid (L) , solid + liquid (+L), solid ()
Liquidus line separates liquid from liquid + solid
Solidus line separates solid from liquid + solid

9. Binary Isomorphous Systems (II)
Cu-Ni
Complete solubility occurs because Cu and Ni have the same crystal structure (FCC), similar radii, electronegativity and valence

10. Binary Isomorphous System (III)
One-component: melting occurs at a well-defined temperature.
Multi-component: melting occurs over range of temperatures between solidus and liquidus lines.
Solid and liquid phases are in equilibrium in this temperature range. L
Liquid solution
 + L
Liquid solution +
Crystallites of
Solid solution 
Polycrystal
Solid solution

11. Interpretation of Phase Diagrams
Given:
temperature + composition 
determine
1) Phases present
2) Compositions of phases
3) Relative fractions of phases
Composition in a two phase region:
1. Locate composition and temperature
2. Draw tie line or isotherm
Note intersection with phase boundaries
Read compositions at the intersections
Liquid and solid phases have these compositions

12. The Lever Rule Amounts of each phase in two phase region
Locate composition and temperature
Draw tie line or isotherm
Fraction of a phase = length of tie line to other phase boundary divided by the length of tie line
The lever rule is a mechanical analogy to the mass balance calculation. The tie line in the two-phase region is analogous to a lever balanced on a fulcrum.

13. The Lever Rule
Mass fractions: WL = S / (R+S) = (C- Co) / (C - CL)
W = R / (R+S) = (Co- CL) / (C - CL)

14. Derivation of the lever rule
W and WL are fractions of  and L phases
1) All material is in one phase or the other:
W + WL = 1
2) Composition equal composition in one phase + composition second phase
at given T:
Co = WC + WLCL
3) Solution gives Lever rule.
WL = (C- Co) / (C - CL)
W = (Co- CL) / (C - CL)

15. Phase compositions and amounts. An example.
Co = 35 wt. %, CL = 31.5 wt. %, C = 42.5 wt. %
Mass fractions: WL = (C- Co) / (C - CL) = 0.68
W = (Co- CL) / (C - CL) = 0.32

16. Microstructure in isomorphous alloys Equilibrium (very slow) cooling
Solidification in the solid + liquid phase occurs gradually upon cooling from the liquidus line. The composition of the solid and the liquid change gradually during cooling (as can be determined by the tie-line method.) Nuclei of the solid phase form and they grow to consume all the liquid at the solidus line.