Editing Eutectic system (section)

=== Alloys ===
The primary strengthening mechanism of the eutectic structure in metals is [[Composite material|composite]] strengthening (See [[strengthening mechanisms of materials]]). This deformation mechanism works through load transfer between the two constituent phases where the more compliant phase transfers stress to the stiffer phase.<ref>{{Cite book |last=Courtney |first=T. H. |title=Mechanical behavior of materials |publisher=McGraw-Hill |year=1990 |edition=2nd |location=New York}}</ref> By taking advantage of the strength of the stiff phase and the ductility of the compliant phase, the overall toughness of the material increases. As the composition is varied to either hypoeutectic or hypereutectic formations, the load transfer mechanism becomes more complex as there is a load transfer between the eutectic phase and the secondary phase as well as the load transfer within the eutectic phase itself.

A second tunable strengthening mechanism of eutectic structures is the spacing of the secondary phase. By changing the spacing of the secondary phase, the fraction of contact between the two phases through shared phase boundaries is also changed. By decreasing the spacing of the eutectic phase, creating a fine eutectic structure, more surface area is shared between the two constituent phases resulting in more effective load transfer.<ref name=":0">{{Cite book |last=Callister |first=W. D. |title=Materials science and engineering : an introduction |year=2010}}</ref> On the micro-scale, the additional boundary area acts as a barrier to [[dislocation]]s further strengthening the material. As a result of this strengthening mechanism, coarse eutectic structures tend to be less stiff but more ductile while fine eutectic structures are stiffer but more brittle.<ref name=":0" /> The spacing of the eutectic phase can be controlled during processing as it is directly related to the cooling rate during solidification of the eutectic structure. For example, for a simple lamellar eutectic structure, the minimal lamellae spacing  is:<ref>{{Cite book |last1=Porter |first1=D. A. |title=Phase transformations in metals and alloys |last2=Easterling |first2=K. E. |last3=Sherif |first3=M. Y. |year=2009}}</ref>

<math>\lambda^*=\frac{2\gamma V_m T_E }{\Delta H * \Delta T_0}</math>

Where  is <math>\gamma</math> is the [[surface energy]] of the two-phase boundary, <math>V_m</math>'' ''is the [[molar volume]] of the eutectic phase, <math>T_E</math>  is the solidification temperature of the eutectic phase, <math>\Delta H</math> is the [[Enthalpy of Formation|enthalpy of formation]] of the eutectic phase, and <math>\Delta T_0</math> is the undercooling of the material. So, by altering the undercooling, and by extension the cooling rate, the minimal achievable spacing of the secondary phase is controlled.

Strengthening metallic eutectic phases to resist deformation at high temperatures (see [[Creep (deformation)|creep deformation]]) is more convoluted as the primary deformation mechanism changes depending on the level of stress applied. At high temperatures where deformation is dominated by dislocation movement, the strengthening from load transfer and secondary phase spacing remain as they continue to resist dislocation motion. At lower strains where Nabarro-Herring creep is dominant, the shape and size of the eutectic phase structure plays a significant role in material deformation as it affects the available boundary area for vacancy diffusion to occur.<ref>{{Cite journal |last1=Wu |first1=T. |last2=Plotkowski |first2=A. |last3=Shyam |first3=A. |last4=Dunand |first4=D.C. |title=Microstructure and creep properties of cast near-eutectic Al-Ce-Ni alloys |journal=Mater. Sci. Eng. A |volume=833 |pages=12}}</ref>