1. CHAPTER 8
Phase
Diagrams 1

2. Phase Diagrams
Phase : A region in a material that differs in structure and function from other regions.
Phase diagrams:
Represents phases present in metal at different conditions (Temperature, pressure and composition).
Indicates equilibrium solid solubility of one element in another.
Indicates temperature range under which solidification occurs.
Indicates temperature at which different phases start to melt.
In materials science the most common phase diagrams involve temperature versus composition.

3. Figure 8.1

4. Microstructure of carbon steel

5. Phase Diagram of Fe 5

6. For pure Iron PT phase diagram, there are 3 separate and distinct solid phases:
alpha (α) Fe delta (δ) Fe gamma (γ) Fe
BCC crystal structure FCC crystal structure
There are 3 triple points in the iron PT phase diagram where 3 different phases coexist:
Liquid, vapor, and delta (δ) Fe
Vapor, delta (δ) Fe, and gamma (γ)Fe
Vapor, gamma (γ) Fe, alpha (α) Fe

7. Gibbs phase rule
Gibbs Phase Rule an equation that computes the number of phases that can coexist in equilibrium in a chosen system P F = C + 2
Where P= no. of phases that coexist in a chosen system
C= no. of components in the system ()
F= degree of freedom ( no. of variables [pressure, temperature, and composition] that can be changed independently without changing the no. of phases in equilibrium in the chosen system)

8. Application of Gibbs phase rule to the PT phase diagram of pure water;
At the triple point; 3 phases coexist in equilibrium, no. of component in the system is one (only water)C=1
Therefore;
P F = C + 2
F =  F=0 (zero degree of freedom)
None of the variables (T, P, composition) can be changed and still keep the 3 phases in balance.

9. Gibbs phase rule
consider a point along the liquid-solid freezing curve; at any point along this line 2 phases will coexist.
P F = C + 2
F =  F=1 (one degree of freedom)
F=1 means there is one variable (T or P) can be changed independently and still maintain a system with 2 coexisting phases. Thus if a particular pressure is specified, there is only one temp. at which both liquid and solid phases can coexist

10. Cooling curves for Pure Metal
Plots of temp. vs time acquired during solidification of a metal and alloys (the metal cools from a temp. at which it is molten through solidification and finally to room temperature). It provides phase diagram information as temperature is lowered.
Thermal arrest
A region of the cooling curve for a pure metal where temperature does not change with time (plateaue) representing the freezing temperature.

11. Fig. The cooling curve for a pure metal
A to B -- cooling of liquid
B– solidification begins
C– solidification ends
C to D – cooling of solid
BC region of thermal arrest OR plateau, the metal in the form of a mixture of solid and liquid phases.
The latent heat keeps the mixture at freezing temp. until complete solidification is achieved. A B C D
Pouring temp
Temp (T)
Time (t)
Freezing temp
(melting point)
Liquid
Liquid+solid
Solid
Cooling under the freezing temp. is required for the formation of solid nuclei

12. Cooling curve for pure iron at a Pressure of 1 atm

13. Copper Nickel Binary Phase Diagram

14. Application of Lever Rule to determine the amount of each phases

15. The lever rule
The lever-rule equations state that to calculate the wt fraction of one phase of a 2 phase mixture (alloy), one must use the segment of the tie line that is on the opposite side of the alloy of the interest and is farthest away from the phase for which the wt fraction is being calculated.
Liquid
Solid
L+ S L S O
Temperature (oC)
Weight fraction of B x

16. The lever-rule equations can be derived by using weight balances.
Summation of fractions =1
Weight balance of B in the alloy

17. The lever-rule equations

18. Sample Problem on Lever rule
Example 1.
A copper-nickel alloy contains 47% Cu and 53% Ni and is at 1300 C.
What is the weight percent of copper in the liquid and the solid phases at this temperature?
What weight percent of this alloy is liquid and what weight percent is solid?

19. Example 2.
Calculate the percent liquid and solid for the Ag-Pd phase diagram shown in Fig. at 12000C and 70 wt % Ag.

20. Example 3.
The temperature of 1 kg of the alloy shown in the figure is lowered slowly until the liquid solution composition is 18 wt% B and the solid solution composition is 66 wt % B. Calculate the amount of each phase.
Answer
Mass of liquid phase = [(66- 50) /(66-18 )] * 1 kg = 333 g
Mass of solid phase = [( )/(66- 18)] * 1 kg = 667g

21. Ternary Phase Diagram
Ternary Phase diagrams are diagrams that represent the equilibrium between the various phases that are formed between three components as a function of temperature

22. Three Dimensional Ternary Phasee

23. Ternary phase diagram using Gibbs Triangle

24. Sample Problem on Ternary Phase Diagram :
What are the compositions of point y and z in the figure ? X y z

25. Binary Eutectic alloy system
Eutectic reaction (in a binary phase diagram):-
A phase transformation in which all the liquid phase transforms on cooling into two solid phase isothermally.
Eutectic temperature:-
The lowest temperature at which the liquid phase can exist when cooled slowly
Eutectic composition:-
The composition of the liquid phase that reacts to form two new solid phases at the eutectic temperature.
Eutectic point:-
The point determined by the eutectic composition and temperature.

26. Binary Peritectic alloy system
Peritectic reaction (in a binary phase diagram):-
A phase transformation in which, upon cooling, a liquid phase combines with a solid phase to produce a new solid phase.

27. Binary Monotectic alloy system
Monotectic reaction (in a binary phase diagram):-
A phase transformation in which, upon cooling, a liquid phase transforms into a solid phase and a new liquid phase (of different composition than the first liquid phase). L1 L2