Phase Diagrams
A phase is a state of matter with the following characteristics:
• It has the same structure or atomic arrangement
throughout
• It has roughly the same composition and properties
throughout.
• There exists a definite interface between it and its
surroundings or adjoining phases.
A phase diagram is a graphical representation of the phases that are
present in a material at various temperatures and pressures and
compositions.
• It usually describes the equilibrium conditions
• Sometimes non-equilibrium conditions are also shown
when well known.
• It indicates the melting/solidification temperatures of the
constituents
• It indicates the compositions of alloys where solidification
begins and the temperature range over which it occurs.
For a pure substance, the Pressure-Temperature phase diagram
simply tells which forms (solid, liquid, gas) of the material exist
under different P-T conditions.
Phase diagram for water.
General Types of Phase Diagrams
There are two general types of alloys having phase diagrams.
• Substitutional alloys
• Interstitial alloys
Subtitutional alloys have elements, which are incorporated into regular lattice positions
within the unit cell.
An example is Tin and Zinc alloying additions to Copper to form bronze and brass,
respectively
Interstitial alloys have elements, which are incorporated into the interstitial sites of the
unit cell.
An example is carbon in iron to form steel.
interstitial sites of the unit cell.
An example is carbon in iron to form steel.
Gibb’s Phase Rule
Gibb’s phase rule describes the thermodynamic state of a material.
This famous rule is used to determine the number of phases that can
coexist in equilibrium in a given system.
It has the general form: F = C – P + 2
C is the number of components, usually elements or compounds, in
the system.
F is the number of degrees of freedom, or number of variables, such
as temperature, pressure, or composition that are allowed to
change independently without changing the number of phases in
equilibrium.
P is the number of phases present
The constant “2” in the equation implies that both temperature and
pressure are allowed to change.
For the triple point of water:
• One component, i.e., water.
• 3 phases present, i.e. vapor, liquid, and solid.
• F = 1 – 3 + 2 = 0, so this is an invariant point on the
diagram
Most binary phase diagrams used in materials science are
temperature and composition diagrams at a constant 1
atmosphere of pressure.
The constant pressure will reduce the degrees of freedom from “2” in
Gibb’s equation to “1” for a binary phase diagram
Thus, F = C – P + 1.