# Why eutectic

1. Feb 26, 2010

### venkypf123

for a given combination of metals phase transformations occurs at a variable temperature which is in between the phase change temperatures of constituting metals except at eutectic combination. why at this combination phase transformation is taking place at a constant temperature? what is the reason?

2. Feb 26, 2010

### Studiot

Not quite sure what you mean by 'variable temperature' but this might help you understand.

Consider a simple two metal ( or other substance) system with metals A and B.

There are only three points on the melting temperature v composition diagram that where a single substance occurs.

These are
Pure A
Pure B
The Eutectic point.

At all other compositions there is more than one substance present. Hence the result is a mixture.

Either Eutectic plus excess A or Eutectic plus excess B.

Elementary physics tells us that

A single pure substance has a well defined single melting point.
A mixture of substances melts over a range of temperature, determined by the components of the mixture.

3. Apr 22, 2010

### Matcon

For simplicity, let's stick to a binary system A-B and qualitatively construct free energy versus composition plots for the system.

A "classic" eutectic occurs when A and B are completely miscible in the liquid state and completely immiscible in the solid state.

Qualitatively, if you plot free energy versus composition, you get a U-shaped curve for the liquid because the lowest free energy occurs when A and B are mixed.

The corresponding curve for the solid state is an inverted U-shape because the lowest free energy occurs in the unmixed state. Forget the curved part for now; the minimum free energy plot for the solid state is a straight line joining the ends of the inverted U. The value of free energy is a "law of mixtures" weighted average of the free energies of pure solid A and pure solid B.

The relative positions of the U-curve and straight line depend on the temperature. At higher temperatures, the liquid state is the more stable, the free energy is lower, so the the U-curve is below the straight line. Conversely, at lower temperatures where the system is solid, the straight line is below the U-curve.

It is now easy to see that there is only one temperature (and one composition) at which the straight line is an exact tangent to the U-curve. At that unique point, the free energy of solid and liquid are the same, so A, B and liquid are at equilibrium. That is your eutectic point: one temperature, one composition.