1. Phase Diagram

2. Phase Diagram
A phase in a material is a region that differs in its microstructure and/or composition from another region
Phase diagrams are graphical representations of what phases are present in a materials systems at various temperatures, pressures and compositions [It shows show what phases exist at equilibrium and what phase transformations we can expect when we change one of the parameters of the system (T, P, composition)]
In this chapter, we will discuss phase diagrams for binary alloys only and will assume pressure to be constant at one atmosphere. [Phase diagrams for materials with more than two components are complex and difficult to represent]

3. Phase Equlibria
A system is at equilibrium if its free energy is at minimum under some specified combination of temperature, pressure and composition. [ In other words, this means that the characteristics of the system do not change with time, but persist indefinitely: that is the system is stable]

4. Phase Diagram of Pure Substances
Pure substance exist as solid, liquid and vapor.
Phases are separated by phase boundaries.
Example : Water, Pure Iron.
Different phases coexist at triple point.
Figure 8.2
Figure 8.1
8-3
After W. G. Moffatt, et al., “The Structure and Properties of Materials,” vol I: “Structure,” Wiley, 1965, p.151

5. Gibbs Phase Rule
From thermodynamic considerations, J.W. Gibbs derived an equation that computes the number of phases that can coexist in equilibrium in a chosen system. This equation, called Gibbs Phase Rule is:
P + F = C + 2
where P = number of phases that can coexist in a chosen system
C= number of components in the system
F= degrees of freedom
Usually a component C is an element, compound or solution in the system. F, the degrees of freedom, is the number of variables (pressure, temperature and compositiond)

6. Binary Isomorphous Systems
Mixture of
two systems
Two component
system
Binary alloy
Isomorphous system: Two elements completely soluble in each other in liquid and solid state.
Example: Cu-Ni solution.
8-5
Adapted from “Metals Handbook,” vol. 8, 8th ed., American society of Metals, 1973, p. 294.

7. Binary Isomorphous Systems
Three phase region can be identified on the phase diagram:
Liquid (L) ,
solid + liquid (α +L), solid (α )
Liquidus line separates liquid from liquid + solid
Solidus line separates solid from liquid + solid

8. Binary Isomorphous Systems
Example of isomorphous system:
Cu-Ni (the complete
solubility occurs because both Cu and Ni have the same
crystal structure, FCC, similar radii, electronegativity and
valence).

9. Binary Isomorphous Systems
In one-component system melting occurs at a well-defined melting temperature.
In multi-component systems melting occurs over the range of temperatures, between the solidus and liquidus lines. Solid and liquid phases are in equilibrium in this temperature range.

10. Interpretation of Phase Diagram
For a given temperature and composition we can use phase diagram to determine:
1) The phases that are present
2) Compositions of the phases
3) The relative fractions of the phases
Finding the composition in a two phase region:
1. Locate composition and temperature in diagram
2. In two phase region draw the tie line or isotherm
3. Note intersection with phase boundaries. Read compositions at
the intersections.
The liquid and solid phases have these compositions.

11. The Lever Rule
Finding the amounts of phases (mass fraction) in a two phase region:
1. Locate composition and temperature in diagram
2. In two phase region draw the tie line or isotherm
3. Fraction of a phase is determined by taking the length of the tie line to the phase
boundary for the other phase, and dividing by the total 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.

12. The Lever
Rule

13. Question 1 By referring to the Figure:
Determine the phase(s) that is (are) present and its composition for an alloy of composition 60 wt% Ni – 40 wt% Cu at 1100’C
(b) Determine the phase(s) that is (are) present and its composition for an alloy of composition 35 wt% Ni – 65 wt% Cu at 1250’C

14. Answer 1
 phase is present, having a composition of 60 wt% Ni -40 wt% Cu
(b) The composition of the liquid phase, CL is 31.5 wt% Ni wt% Cu
The composition for the  solid solution phase, C is 42.5 wt% Ni-57.5 wt% Cu

15. Phase Composition and amounts – an example

16. Binary Eutectic Systems alloys with limited solid solubility in each other

17. Binary Eutectic Systems
Three single phase regions
( - solid solution of Ag in Cu
matrix,  = solid solution of Cu in
Ag marix, L - liquid)
Three two-phase regions ( + L,
 +L,  + )
Solvus line separates one solid
solution from a mixture of
solid solutions.
Solvus line shows limit of
solubility

18. Binary Eutectic Systems
Eutectic or invariant point –
Liquid and two solid phases
co-exist in equilibrium at the
eutectic composition CE and
the eutectic temperature TE.
Eutectic isotherm - the horizontal
solidus line at TE.

19. Binary Eutectic Systems
Eutectic reaction – transition between liquid and mixture of two solid phases, ,  +  at eutectic concentration, CE.
The melting point of the eutectic alloy is lower than that of the components (eutectic = easy to melt in Greek).
At most two phases can be in equilibrium within a phase field. Three phases (L, a, b) may be in equilibrium only at a few points along the eutectic isotherm. Single phase regions are separated by 2-phase regions.

20. Binary Eutectic System
Compositions and relative amounts of phases are determined from the same tie lines and lever rule, as for isomorphous alloys

21. Question 2: For a 40 wt% Sn-60 wt% Pb alloy at 150’C (300’F):
What phase(s) is (are) present?
What is (are) the composition(s) of the phases(s)?

22. Answer 2 Both  +  phases coexist
The composition of the  phase corresponds to the tie line intersection with the / ( + ) solvus phase boundary – about 10 wt% Sn- 90 wt% Pb
Similarly, for the  phase, it will have a composition of approximately 98 wt% Sn- 2 wt% Pb