Difference between revisions of "Eutectic Point"

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Entry by [[Emily Redston]]
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Entry by [[Emily Redston]], AP 225, Fall 2011
 
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| [[Image:Phdifig1.gif |thumb| 400px | center| www.tulane.edu/.../geol212/2compphasdiag.html
 
| [[Image:Phdifig1.gif |thumb| 400px | center| www.tulane.edu/.../geol212/2compphasdiag.html
 
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| 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 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
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| 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>
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::<math> L \rightleftharpoons A + B </math>
  
According to Gibbs [[Phase Rule]], we know that the number of degrees of freedom is <math>F=\left( C+2-P \right)=2+2-3=1 </math>. Zero degrees of freedom means that we cannot have a solidification range, and thus the melt must solitify at exactly one point --- the 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  
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::<math>F=\left( C+2-P \right)=2+2-3=1 </math>.  
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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:
  
[[Mixing of liquids -regular solution theory#Phase separation|Phase separation]] in [[Phases and Phase Diagrams]] from [[Main Page#Lectures for AP225|Lectures for AP225]].
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[[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

www.tulane.edu/.../geol212/2compphasdiag.html
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 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]).

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.