# Difference between revisions of "Eutectic Point"

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According to Gibbs [[Phase Rule]], at this [[phase transition]], we know that the number of degrees of freedom is | According to Gibbs [[Phase Rule]], at this [[phase transition]], we know that the number of degrees of freedom is | ||

::<math>F=\left( C+2-P \right)=2+2-3=1 </math>. | ::<math>F=\left( C+2-P \right)=2+2-3=1 </math>. | ||

− | There is only one degree of freedom, so if we assume constant pressure (a typical choice), then all three phases can only be in equilibrium at an [[invariant point]] --- the ''eutectic point''! | + | There is only one degree of freedom, so if we assume constant pressure (a typical choice), then all three phases can only be in equilibrium at an [[invariant point]] --- the '''eutectic point'''! This means that once we fix the pressure, the eutectic temperature and composition will be set at one point. |

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## Revision as of 16:41, 5 December 2011

Entry by Emily Redston

Figure 1 shows a common and relatively simple binary phase diagram known as a eutectic phase diagram. A eutectic diagram can be thought of as the intersection of two solid solution diagrams. At the intersection of the two liquidus lines, the melt is in equilibrium with the two solid phases. In other words, a single liquid phase is transformed into two solid phases upon cooling, and the opposite occurs upon heating. This is called a eutectic reaction, and can be written as
- <math> L \rightleftharpoons A + B </math>
According to Gibbs Phase Rule, at this phase transition, we know that the number of degrees of freedom is - <math>F=\left( C+2-P \right)=2+2-3=1 </math>.
There is only one degree of freedom, so if we assume constant pressure (a typical choice), then all three phases can only be in equilibrium at an invariant point --- the |

## References

[1] Spaepen, Frans. *Applied Physics 282: Solids: Structure and Defects*. Harvard University

[2] Haasen, Peter. *Physical Metallurgy*. Cambridge: Cambridge UP, 1996.

[3] Callister, William D. *Materials Science and Engineering: an Introduction*. New York: John Wiley & Sons, 2007.

## Keyword in References

Stretchable Microfluidic Radiofrequency Antennas

See also:

Phase separation in Phases and Phase Diagrams from Lectures for AP225.