Dissemination of IT for the Promotion of Materials Science (DoITPoMS)


Phase diagrams 2

The free-energy curves and phase diagrams discussed in Phase Diagrams 1 were all for systems where the solid exists as a solution at all compositions and temperatures. In most real systems this is not the case. This is due to a positive ΔHmix caused by unfavourable interactions between unlike neighbour atoms. As the temperature is reduced the ΔHmix term becomes more significant and the curve turns upward at intermediate compositions, resulting in a curve with two minima and one maximum as described earlier. A common tangent can then be drawn between the two minima showing that the system can reduce its free energy through existing as a mixture of two distinct phases.

The free energy of a system of composition Co can be minimised by existing as a mixture of two solid phases of composition C1 and C2:

Schematic free-energy curve for a mixture of two solid phases

This effect can result in a system which, though single-phase upon solidification, will separate into two solid phases on cooling (e.g. Cr-W).

Another possible result is that the free-energy curve for the liquid will intersect the up turned section of the free-energy curve for the solid before the temperature is high enough to induce the formation of a solid solution. As the temperature is increased, the free-energy curve for the liquid moves downward relative to the solid curve and reaches a position where it is possible to link two parts of the solid free energy curve and one part of the liquid free energy curve with a common tangent. At this temperature three phases are in equilibrium.

Here the system is at the eutectic temperature and three phases can be joined by a common tangent:

Schematic free-energy curves

This is known as the eutectic temperature. At this temperature there will be a composition which solidifies at a single temperature through the co-operative growth of the two solid phases. This is the eutectic composition. It is this composition which will exhibit the lowest melting point for the system.

At temperatures above that of the eutectic there will be two common tangents producing two two-phase regions at the same temperature. The two different solid phases are commonly labeled as α and β

Schematic free-energy curves

Eutectic systems therefore have a liquidus which contains a V to the eutectic point where it meets the eutectic invariant-reaction line.

Here is an example of a eutectic phase diagram. α and β are both solid phases.

Eutectic phase diagram

The two-phase solid region on the phase diagram will consist of a mixture of eutectic and either α or β phase depending on the whether the alloy composition is hypoeutectic or hypereutectic. The constitution of an alloy under equilibrium conditions can be found from its phase diagram. This will be discussed in a later section.