1. PHASE RULE UNIT -VII

2. CONTENTS INTRODUCTION TERMS INVOLVED IN PHASE RULE PHASE DIAGRAM
ONE- COMPONENT SYSTEM
TWO- COMPONENT SYSTEM
IRON-CARBON PHASE DIAGRAM
HARDENING AND ANNEALING

3. INTRODUCTION
For the study of the behaviour of the heterogeneous systems an important generalisation was put forward by American physicist Willard Gibbs in This generalisation commonly known as ‘phase rule’ is applicable to all heterogeneous systems in equilibrium without any exception. This rule cannot be expressed in words. However ,it may be stated mathematically as follows. F= C-P+2 F= Number of degrees of freedom C= Number of components P= Phases of the system.

4. TERMS INVOLVED IN PHASE RULE
PHASE: Phase is defined as a homogeneous, physically distinct and mechanically seperable portion of system which is seperated from other such parts of the system by definite boundary surfaces. Ex: At freezing point water consists of three phases. Ice Water Water vapour (s) (l) (g)

5. COMPONENT: The smallest number of independent variable constituents, taking part in the state of equilibrium by means of which the composition of each phase can be expressed in the form of chemical equation is known as component. Ex: In the water system all the three phases has same chemical composition H2O. Hence it is one component system.

6. DEGREE OF FREEDOM:
The minimum number of independently variable factors such as temperature, pressure and composition of the phases, which must be arbitrarily specified inorder to represent perfectly the condition of a system is known as degree of freedom.
Ex: In water system no condition need to be specified.
Ice Water Water vapour
(s) (l) (g)
Hence it is zero variant or no degree of freedom.

7. PHASE DIAGRAM
When a system goes from one phase to another without change in chemical composition it is known as phase transition. The different phases of a system may be represented using a phase diagram. Phase diagram is a plot showing the conditions of pressure and temperature under which two or more physical states can exist together in a state of dynamic equilibrium. The diagram consists of 1. Curves 2. Areas or regions 3. The triple point.

8. ONE- COMPONENT SYSTEM WATER SYSTEM
Under normal conditions ‘Water’ is a three phase one component system. The three phases involved are liquid water, ice water, and water vapour. All of them has single chemical entity H2O. Hence water is a one component system.
The phase diagram or P-T graph contains
1. Curves OA,OB,OA’, OC.
2. The areas AOC,AOB,BOC.
The triple point ‘O’.

9. PHASE DIAGRAM

10. The Curves OA,OB,OA’, OC:
These three curves meet at the point ‘O’ and divide the diagram into three areas.
Curve OA- Vapour pressure curve of water.
Water exists as liquid above this curve. Along this curve water and water vapour co-exist. Hence phase P=2
Point A is the critical point where liquid and water vapour are indistinguishable and here P=1.
Curve OB- Sublimation curve of ice.
It is the vapour pressure curve of ice. Water exists as

11. The curve OB terminates at absolute zero(-273oc), where no vapour exists. The degree of freedom is 1,i.e., univarient as one pressure or temperature is seen. Curve OC- Melting point curve. This curve divides the solid ice region from the liquid water region. The slope of OC towards the pressure axis shows that the melting point of ice decreased by increasing pressure. Ice above this curve. Along this curve ice and vapour co-exists in equilibrium. Hence P=2. Areas AOC,AOB,BOC: These areas are the fields of existence of vapour,

12. Liquid and ice phase respectively
Liquid and ice phase respectively. In all these areas one phase and one component is observed. Hence the system is bivariant. F= C-P+2 =1-1+2 = 2 The triple point ‘O’: The curves OA,OB,OC meet at the triple point ‘O’, where all the phases are in equilibrium. This point at 273K or oc and 4.58mm Hg pressure is called Triple point. There are three phases and one component at this point. Hence degree of freedom is non variant or zero variant.

13. F= C-P+2 = = 0 Metastable system or curve OAI : The dotted curve OAI ,a continuation of vapour pressure curve OA, represents the vapour pressure curve of supercooled water. This curve is a metastable system which reverts to the stable system on slight disturbance or by adding a crystal of ice. Metastable vapour pressure of supercooled water is higher than the vapour pressure of ice.

14. TWO- COMPONENT SYSTEM
Systems in which two independent constituents chemical composition of each phase is expressed differently is called two-component system. Ex: Pb-Ag system SILVER- LEAD SYSTEM: Lead-silver system is an example for two component system with four possible phases solid Ag, solid Pb, solution of Ag+Pb and vapour. As the pressure has no effect on equilibrium, condensed phase rule is applicable. F= C-P+1

15. Silver- Lead System

16. Molten silver and molten lead mix together in all proportions resulting in a homogeneous solution. They do not react chemically and consists of four phases.
Solid silver ii solid lead
Silver and lead solution iv vapour
The diagram contains curves OA, OB, and areas AOB, AOD, BOE. Point ‘O’ is the Eutectic point.
Curve OA- Freezing point curve of silver:
Along the curve solid Ag and liquid are in equilibrium. The curve shows the effect on freezing point of Ag on addition of lead in small quantities.

17. Curve OB- Freezing point curve of lead:
Along the curve solid lead and liquid are in equilibrium. The curve shows the effect of addition of silver on the melting point of lead.
Both the curves are univariant.
Areas:
AOB: In this area degrees of freedom is 2. since the liquid solution is not in contact with any solid, these solutions are unsaturated.
All the remaining areas have 2 phases and degree of freedom is one.

18. EUTECTIC POINT ‘O’:
The point at which curves OA and OB intersect is known as eutectic point represented by ‘O’ at the temperature 303oC.
The composition at this point is 2.6% Ag+97.4% and is called eutectic composition.
It’s melting point is lower than any alloy of Ag and Pb.
The degrees of freedom at point ‘O’ is zero.
F=O

19. The Iron-Carbide Phase Diagram
Heat Treatment of Steel

21. Features Reactions Phases present a ferrite Bcc structure
Ferromagnetic
Fairly ductile d
Bcc structure
Paramagnetic
g austenite
Fcc structure
Non-magnetic
ductile
Fe3C cementite
Orthorhombic
Hard
brittle
Reactions
Peritectic L + d = g
Max. solubility of C in ferrite=0.022%
Max. solubility of C in austenite=2.11%
Eutectic L = g + Fe3C
Eutectoid g = a + Fe3C

22. Microstructures a g

23. Steels Classification/Nomenclature
Steel is an interstitial solid solution of carbon in iron.
Theoretically steel has a maximum of 2.11% carbon.
In practice, the amount of carbon rarely exceeds 0.8%
Classification/Nomenclature
AISI 1020:
Last two numbers indicate
Amount of carbon :0.2%C
10 indicates plain carbon steel
AISI 4340: 0.4%C
43 indicates alloy steel
Low carbon steels up to 0.2%C
Medium carbon steels %C
High carbon steels >0.4% C

24. Microstructural changes in steel on cooling for different compositions

25. Eutectoid steel

26. Hypoeutectoid steel

27. Hypereutectoid steel

28. HEAT TREATMENT
Involves the heating and cooling of metals in the solid state
Changes the mechanical properties so the metal can be more useful
Metals can be made harder, stronger and more impact resistant or metals can be made softer and more ductile

29. Heat Treatment Methods (Ferrous Metals)
Hardening
Tempering
Annealing
Normalizing
Case hardening

30. HARDENING
Hardening involves heating a steel to its normalising temperature and cooling (Quenching ) rapidly in a suitable fluid e.g oil, water or air.
Steel is basically an alloy iron and carbon some steels alloys have various other elements in solution. 
  When steel is heated above the upper critical temperature (about 760oC), the iron crystal structure will change to face centered cubic (FCC), and the carbon atoms will migrate into the central position formerly occupied by an iron atom.  

31. This form of red-hot steel is called austentite (γ iron)
This form of red-hot steel is called austentite (γ iron).   If this steel form cools slowly, the iron atoms move back into the cube forcing the carbon atoms back out, resulting in soft steel called pearlite. 

32. ANNEALING Annealing is reheating steel followed by slow cooling.
 It is completed a) to remove internal stress or to soften or b) to refine the crystalline structure (This involves heating to above the upper critical temperature ).
This process is used to remove internal stresses built up as a result of cold working and fabrication processes. 

33. NORMALIZING
Normalizing involves heating the steel to about 40oC above its upper critical limit.  
 The steel is then held at this temperature for a period of time and is then cooled in air.
  The structure produced by this process is pearlite or pearlite in a ferrite matrix (hypoeutectoid) or pearlite in a cementite matrix (hypereutectoid). 

34. CASE HARDENING
The steel rod should now have a hardened outer surface and a flexible, soft interior. The process can be repeated to increase the depth of the hardened surface.

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