Phase Diagrams

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Phase Diagram

  • It is also known as equilibrium diagram.

  • The plots showing relations between phases in equilibrium versus composition, pressure and temperature are called phase diagrams.

  • The composition is plotted on X-axis and temperature is plotted on Y-axis at any specified pressure. Pressure is generally taken atmospheric.

    • Water in liquid or vapor state is single phase.

    • Ice floating on water is an example two phase system.




Gibbs Phase rule

The number of degrees of freedom, F (no. of independently variable factors),number of components, C, and number of phases in equilibrium, P, are related by :

  • Gibbs phase rule :


F = C – P + 2

  • Number of external factors = 2 (pressure and temperature).


For metallurgical system, pressure has no appreciable effect on phase equilibrium and hence,

F = C – P + 1

One component system 

  • The simplest phase diagram is the water which is a one component system.

  • It is also known as pressure-temperature or P-T diagram.

  • Two phases exist along each of the three phase boundaries.

  • At low pressure (0.006 atm) and temperature (0.01 °C) all the three phases coexist at a point called triple point.


Water phase diagram is shown in the following figure.

03-Phase-diagrams (1)

Binary Phase diagrams

  • A binary phase is a two component system.

  • Binary phase diagrams are most commonly used in alloy designing.

  • The simplest binary system is the Cu-Ni which exhibits complete solubility in liquid and solid state.


The Cu-Ni equilibrium phase diagram is shown below.

03-Phase-diagrams (2)

  • The line above which the alloy is liquid is called the liquidus line. At temperature just below this line crystals of α solid solution start forming.

  • The line below which solidification completes is called solidus line. Hence, only α solid solution exists at any temperature below the solidus line.

  • The intermediate region between liquidus and solidus lines is the two-phase region where liquid and solid coexist.


It can be noted that the two metals are soluble in each other in the entire range of compositions in both liquid and solid state. This kind of system is known as‘Isomorphous’ system.

There are 5 invariant reactions occurring in binary phase system:

  • Eutectic reaction,

  • Eutectoid reaction,

  • Peritectic reaction,

  • Peritectoid reaction, and

  • Monotectic reaction.


Eutectic Point

When a liquid phase changes into two different solid phases during cooling or two solid phases change into a single liquid phase during heating, this point is known as eutectic point and this temperature is known as eutectic temperature.

In the eutectic system between two metals A and B, two solid solutions, one rich in A (α) and another rich in B (β) form. In addition to liquidus and solidus lines there are two more lines on A and B rich ends which define the solubility limits B in A and A in B respectively. These are called solvus lines.

Three phases (L+ α+ β) coexist at point E. This point is called eutectic point or composition. Left of E is called hypoeutectic whereas right of E is called hypereutectic.

Equation for Eutectic:

03-Phase-diagrams (1)

Phase Diagram characteristic of Eutectic:

03-Phase-diagrams (4)

Eutectoid Point

When a solid phase changes into two solid phases during cooling and vice-versa that point is known as eutectoid point and temperature at this reaction occurs known as Eutectoid temperature.

03-Phase-diagrams (3)

Three phases (L+ α+ β) coexist at point E. This point is called eutectic point or composition. Left of E is called hypoeutectic whereas right of E is called hypereutectic.

Equation for Eutectoid:

03-Phase-diagrams (2)

Phase Diagram characteristic of Eutectoid:

03-Phase-diagrams (5)

Peritectic Point

A binary system when solid and liquid phases changes solid phase on cooling and vice-versa on heating, then state of system is known as peritectic point.

Equation for Peritectic:

03-Phase-diagrams (3)

Phase Diagram characteristic of Periterctic:

03-Phase-diagrams (6)

Peritectoid Point

If a binary phase diagram when two solid phases changes to one solid phase, then state of system is known as peritectoid point.

Equation for Peritectiod:

03-Phase-diagrams (4)

Phase Diagram characteristic of Pertitectoid:

03-Phase-diagrams (7)

Monotectic Point

Another three phase invariant reaction that occurs in some binary system is monotectic reaction in which a liquid transforms to another liquid and a solid. L1→ L2 + α

Equation for Montectic:

03-Phase-diagrams (5)

Phase Diagram characteristic of Monotectic:

03-Phase-diagrams (8)

 



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