# Difference between revisions of "Eutectic Point"

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− | Entry by [[Emily Redston]] | + | Entry by [[Emily Redston]], AP 225, Fall 2011 |

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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'''! This means that once we | + | 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 choose the pressure, the eutectic temperature and composition of each phase is fixed, which we can see in Figure 1 at point E. Also note that the liquid metls at the lowest temperature at the eutectic composition (eutectic means easily melted [3]). |

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See also: | See also: | ||

− | [[ | + | [[Multicomponent phase diagrams#Two-component, liquid/solid phase diagrams|Eutectic point]] in [[Phases and Phase Diagrams]] from [[Main Page#Lectures for AP225|Lectures for AP225]]. |

## Latest revision as of 15:18, 10 December 2011

Entry by Emily Redston, AP 225, Fall 2011

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:

Eutectic point in Phases and Phase Diagrams from Lectures for AP225.