1. Phase diagrams of pure substances
Engineering Materials
Phase Diagrams
Phase diagrams of pure substances
Phase : a physically homogeneous and distinct portion of
a material system.
Equilibrium : a system is said to be in equilibrium if no macroscopic changes take place with time.
Equilibrium Phase Diagram: a graphical representation of the pressures, temperatures, and compositions for which various phases are stable at equilibrium.
In materials science the most common phase diagrams involve temperature versus composition.

2. Phase digrams of pure substances
Engineering Materials
Phase Diagrams
Phase digrams of pure substances

3. Phase digrams of pure substances
Engineering Materials
Phase Diagrams
Phase digrams of pure substances
In the pressure- temperature (PT) phase diagram of water there exist a triple point at low pressure (4.579 torr) and low temperature ( C) where solid, liquid, and vapor phases of water coexist.
Critical Point At a temperature above the critical temperature, Tc, and a pressure above the critical pressure, Pc, it is no longer possible to distinguish between the gas and liquid phases. At T > Tc and P > Pc the substance is referred to as a super-critical fluid.
Phase equilibrium lines:
vaporization line : Liquid and vapor phases exist along it.
freezing line : Liquid and solid phases exist along it.

4. Phase digrams of pure substances
Engineering Materials
Phase Diagrams
Animation
2-6
Phase digrams of pure substances

5. Phase digrams of pure substances
Engineering Materials
Phase Diagrams
Phase digrams of pure substances
Carbon dioxide pressure-temperature phase diagram showing the triple point and critical point of carbon dioxide

6. Phase digrams of pure substances
Engineering Materials
Phase Diagrams
Phase digrams of pure substances
Pressure- Temperature (PT) phase diagram can be constructed for other pure substances (not only for pure water)
For pure Iron PT phase diagram, there are 3 separate and distinct solid phases:
1. alpha (α) Fe gamma (γ) Fe delta (δ) Fe
Have BCC crystal structure Has FCC crystal structure

7. Engineering Materials
Phase Diagrams

8. Phase digrams of pure substances
Engineering Materials
Phase Diagrams
Phase digrams of pure substances
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

9. Phase Diagrams Gibbs phase rule Engineering Materials
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;
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)

10. Phase Diagrams Gibbs phase rule Engineering Materials
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)
Since none of the variables (T, P, composition) can be changed and still keep the 3 phases in balance, the triple point is called an invariant point.

11. Phase Diagrams Gibbs phase rule Engineering Materials
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

12. Phase Diagrams Gibbs phase rule Engineering Materials
consider a point inside a single phase
P F = C + 2
F =  F=2 (two degree of freedom)
F=2 means there are two variable (T and P) can be changed independently and the system still remain a single phase.
Most binary phase diagrams used in materials science are temperature and composition diagrams in which pressure is kept constant (1 atm). In this case the Gibbs phase rule
P F = C + 1

13. Phase Diagrams Cooling curves Engineering Materials
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.

14. A to B -- cooling of liquid
B– solidification begins
C– solidification ends
C to D – cooling of solid
BC region of thermal arrest OR Plateaue, 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
Fig. The cooling curve for a pure metal

15. Phase Diagrams The lever rule Engineering Materials
the weight percentages of the phases in any two-phase region of a binary phase diagram can be calculated using this rule if equilibrium conditions prevail.
Tie line:
A horizontal working line drawn at a particular temperature between two phase boundaries(in a binary phase diagram) to be used to apply the level rule. Vertical lines are drawn from the intersection of the tie line with the phase boundaries to the horizontal composition line. A vertical line is also drawn from the tie line to the horizontal line at the intersection point of the tie line with the alloy of interest to use with the level rule.

16. Phase Diagrams The lever rule Engineering Materials
To drive the lever-rule equation
consider the binary phase diagram
of two elements A and B that are
completely soluble in each other,
see Fig.
Liquid
Solid
L+ S L S O
Temperature (oC)
Weight fraction of B x
Assume x is the alloy composition and its wt. fr of B is wo at temperature of T.
Draw a tie line (LS) at temp T from liquid line at L to the solid line at S.
At temp. T, the alloy x consists of a mixture of liquid of wl wt. fr. of B and solid of ws wt fr. of B

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

18. The lever-rule equations

19. Phase Diagrams The lever rule Engineering Materials
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

20. Phase Diagrams The lever rule Engineering Materials Example1.
Derive the lever rule for the case shown in Fig. x
Liquid
L+ S O L
Temperature (oC) S
Solid
Weight fraction of B

21. Phase Diagrams The lever rule Engineering Materials Example2.
A copper-nickel alloy contains 47% Cu and 53% Ni and is at 1300 C. Use Fig. X1 and answer the following:
What is the weight percent of copper in the liquid and the solid phases at this temperature?
What weight percent of this allow is liquid and what weight percent is solid?

22. Phase Diagrams The lever rule Engineering Materials Example 3.
Calculate the percent liquid and solid for the Ag- Pd phase diagram showing in Fig. X2 at 1200 C and 70 wt % Ag. Assume Wl=74 without Ag and Ws= 64 without Ag.

23. Binary phase diagram & Ternary phase diagram
Engineering Materials
Phase Diagrams
Binary phase diagram & Ternary phase diagram X y z

24. Binary phase diagram & Ternary phase diagram
Engineering Materials
Phase Diagrams
Binary phase diagram & Ternary phase diagram

25. Binary Eutectic alloy system
Engineering Materials
Phase Diagrams
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 temperature at which a eutectic reaction takes place.
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
Engineering Materials
Phase Diagrams
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
Engineering Materials
Phase Diagrams
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