1. The Phase Rule

2. The phase rule is an expression of the number of variables and equations that can be used to describe a system in equilibrium. 
In simple terms, the number of variables are the number of chemical components in the system plus the extensive variables, temperature and pressure. 
The number of phases present will depend on the variance or degrees of freedom of the system.  The general form of the phase rule is stated as follows:
F = C P
where F is the number of degrees of freedom or variance of the system.
C is the number of components, as defined above, in the system.
P is the number of phases in equilibrium,

3. In dealing problems of phase equilibrium the phase rule of wilaed Gibbs is exteremly useful.
This states that for solid and liquid system in which temperature and composition are the only significant variables
F = C P
where F is the number of degrees of freedom
C is the number of components,..
P is the number of phases in equilibrium

4. For pure metals C=1
So F=2-P
Hence for a two phase stable and coexist F=0
Therefore no degree of freedom
i.e temperatur can not vary
The solid and liqquid phase coexist at single temperature
i.e melting point

5. In two phase alloy C=2
Hence F=3-P
A single phase i.e P=1 can exist over a range of temperature and composition
In a two phase alloy, where P=2 degree of fredom is 1
i.e solid and liquid phase can exist over a range of temperature.

6. Three phase to coexist P=3
Then F=0, no degree of fredom
Corresponding to eutectic or perotectic point
In conclusion, for binary system
Three phase equlibria are invarient
Two phase equilibria are one variable(T or composition
One phase equilibria have two variables (T and composition)