Difference between revisions of "Eutectic Point"

From Soft-Matter
Jump to: navigation, search
Line 7: Line 7:
 
| [[Image:Phdifig1.gif |thumb| 400px | center| www.tulane.edu/.../geol212/2compphasdiag.html
 
| [[Image:Phdifig1.gif |thumb| 400px | center| 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 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
+
| 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>
 
::<math> L \rightleftharpoons A + B </math>
Line 13: Line 13:
 
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 set pressure (a typical choice) then we cannot have a solidification range, and thus the melt must solitify at exactly one 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''!  then we cannot have a solidification range, and thus the melt must solitify at exactly one point --- the eutectic point!
 
|-
 
|-
 
|}
 
|}

Revision as of 16:39, 5 December 2011

Entry by Emily Redston

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! then we cannot have a solidification range, and thus the melt must solitify at exactly one point --- the eutectic point!

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.