# Thermal equilibrium diagrams ```Thermal equilibrium diagrams
* Thermal Equilibrium Diagrams is one of the metallurgists
most important &quot;tools&quot; with its aid one can find precisely what
the structure of a given alloy will be at any given temperature,
provided that the alloy has been allowed to reach equilibrium. In
the metallurgical sense, &quot; equilibrium&quot;, refers to the state of
balance which exists between the phases in the structure of any
alloy after a chemical or physical change has taken place.
* When a pure liquid solidifies into a crystalline solid, it does at
a fixed temperature called the freezing point. During the
crystallization process the atoms assume positions according to
some geometrical pattern, and whilst this is taking place, the
latent heat of solidification is given out without any fall in
temperature taking place. A typical cooling curve for a pure
metal is shown in Fig1.
Fig -1- Typical cooling curve of pure metal
Type -1- Two metals completely soluble in the liquid and solid
states.
* When an alloy solidify, it does over a range of temperature
which will depend upon the composition of the alloy. Consider,
for example, a number of alloy of different composition,
containing the two metals A and B which form a series of solid
solutions (see Fig.2)
Fig -2- Thermal equilibrium of solid
solution type using cooling curve
For successive compositions containing different amounts of the
metal A, freezing commences at a1, a2, a3, etc….. and ends at b1,
b2, b3 , etc. Thus if we join all points a1, a2, a3, etc., we shall
obtain a line called the liquids line, indicating the temperature at
which any given alloy in the series will commence to solidify.
Similarly, if we join the points b1, b2, b3 , etc., we have a line
called solidus line, showing the temp, at which any alloy
compositions represent completely homogeneous liquids.
Solidus can be defined as the line below which all represented
alloy compositions of A and B are completely solid.
For temperature and compositions corresponding to the coordinates of points between the two lines both liquid solution
and solid solution can exist together in equilibrium.
Such a system occurs when two metals are soluble in each other
in all proportions in both the liquid and solid states, such as
(Cu+Ni) or (Au+Ag).
There areas of diagrams are called &quot;phase fields&quot; and on
crossing any sloping boundary line from one field to the next,
the number of phases will always change by one.
* At point (Q) Fig -3- in two-phase field both liquid and solid
can exist together, if temperature horizontal is drawn through Q,
the composition of the liquid solution is given by Y and the
composition X.
Q it self represents the overall composition of the mixture.
Composition of solid ( ) = 20 % B + 80 % A
Composition of liquid (L) = 80 % B + 20 % A
* The relative amount of both liquid and solid at Q are given by
the relative lengths Qx , Qy
Amount of liquid
Amount of solid
30
 10%  50%
60
30
( )   100%  50%
60

Example
Find the chemical composition at point (Y) in Fig -4- and the
relative amount of both liquid and solid states.
Solution
At point (y) both (  L ) are exist
- Composition of solid ( ) = 10 % B + 90 % A
- Composition of liquid (L) = 26 % B + 74 % A
- Amount of liquid =
10
 100%  62.5%
16
- Amount of solid ( ) 
6
100%  37.5%
16
```