Phase Diagrams

Phase diagrams are also known as equilibrium diagrams or constitutional diagrams, these diagrams/maps gives us the relationship between the equilibrium phases in a system as a function of temperature, pressure and composition.

The relationship between equilibrium phases / limits of solubility as a function of temperature, pressure and composition are often depicted in the form of maps. Generally, these maps shows the state corresponding to the minimum gibbs free energy of the system. Such maps are called as equilibrium diagrams or phase diagrams

Use of phase diagram :

1. To predict the temperature at which freezing, or melting begins, or end for any specific composition in an alloy system.
2. To predict the safe temperature of working, or heat treatment and possible heat treatment that can be given to obtain desired properties.
3. To determine the number of phases, type of phases, composition of phases present in an alloy at a given temperature and composition.
4. To calculate the relative amount (or fraction) of phases present in a two phase alloy by using lever rule
5. Help us to predict microstructure on an alloy at a given composition and temerature.

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The phase rule :

The Gibbs phase rule is can be stated as -
\[ \boxed{ F = C - P + 2 } \] where,
F : Degree of freedom
C : Number of components in a system
P : Number of Phases in a system
2 : Additional independent variables i.e., pressure and temperature

For a phase transformation involving condensed phases like solid and liquid, the pressure change can be assumed zero as there is very little change in the pressure. So Gibbs phase rule for condense phases is - \[ \boxed{ F = C - P + 1 } \]
Some important definitions :

1. Phases :
   A phase is a physically-distinct, chemically-homogeneous and mechanically-separable entity. There should be some observable difference in their physical state, composition, crystal strucure or physical properties. For example -
       (a) Ice, water and steam are three different phases.
       (b) Salt in water is a single phase as they mixed at the atomic level
       (c) Oil in water is treated as two phase as there is no atomic level mixing.
       (d) Alpha iron (BCC) and Gamma-iron (FCC) are different phases as they have different crystal structure
   
   
2. Component :
   A component is an independent chemical species that constitute an alloy. It is a stable individual substance describing the chemical composition of the system at a given temperature or pressure. Thsese components can be elements, ions or compounds. For example -
       (a) Ice, water and steam syatem, there is only one component i.e., H₂O
       (b) In Cu-Zn alloys (Brass) , Cu and Zn are the two components
       (c) In carbon steels, Fe and C (graphite) are the two components.But in Fe-C metastable phase diagram we often represent C as Fe₃C as it the metastable chemical species at the room temperature.
   
   
3. Degree of Freedom :
   The degree of freedom refers to the number of independent variable that be changed without changing the stability of that phase. Hence, it represent the total number of external and internal variables that can be changed without changing the phase stability. For example in a binary phase diagrams -
       (a) The transition points in the inverient reactions like eutectic, peritectic etc., have zero DOF.
       (b) The solubility line between two phases like solvus, solidus and liquidus, have one DOF. As only one variable (out of two variables i.e., T or Composition) can be changed independently without affecting the phase stability.
       (c) The two phase region have two DOF (T and Composition), as both can be changed independently without affecting the phase stability.
   
   

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Cooling curves :

Cooling curves are the plot that represent the variation of temperature with time when the material is allowed to cool.

1. Pure Metal :


2. Binary Isomorphous Alloy :


3. Eutectic Alloy :


4. Off-Eutectic Alloy :