Eutectic solidification

More recent extensions of the theory (see citations in [122]) gave indications that the orientation of the lamellae (under isotropic material parameters) is not necessarily parallel to the growth direction of the front but may be tilted so that the lamellae travel sideways at some specific angles [138]. Finally it was found that the standard model of eutectic solidification has an intrinsic scaling structure [141-147]... 

For an alloy droplet, the post-recalescence solidification involves segregated solidification and eutectic solidification. 619 Droplet cooling in the region (1),(2) and (6) can be calculated directly with the above-described heat transfer model. The nucleation temperature (the achievable undercooling) and the solid fraction evolution during recalescence and post-recalescence solidification need to be determined additionally on the basis of the rapid solidification kinetics. 154 156 ... 

Applying external fields (electric, thermal, eutectic solidification, crystallization, and solvent evaporation etc.) to induce long-range ordering in micro domains with desirable orientation. 

Fig. 4 Schematic representation of control over block copolymer thin film orientation by directional eutectic solidification. The scheme shows control of polystyrene-b-polyethylene (PS-b-PE) block copolymer microdomain orientation through directional crystallization of benzoic acid (BA), (taken from [95])...

Any appearance of secondary phases can be easily taken into account in this approach with the assumption that no back-diffusion is involved. Therefore all transformations can be handled, including the final eutectic solidification. This approach is based on a series of isothermal steps but, as the temperature step size becomes small, it provides results which are almost completely equivalent to those which would be obtained from continuous cooling. 

The eutectically solidified ceramics represent a large group of ceramic systems with microstructures that can be tailored during cooling. Since the eutectic solidification is based on the simultaneous crystallization of two solids from one liquid, many complex arrangements of the eutectic phases have been observed [93]. A schematic representation of a eutectic reaction is as follows ... 

Figure 2 Portion of a hypothetical A-B binary phase diagram showing a simple eutectic solidification reaction. Compositional variations can occur within the liquid during solidification as a result of relative kinetics of growth of solids a and f. In this case, a grows more easily. When dendrites of phase a grow, the remaining liquid solution becomes more B-rich (Ci). f forms in the resulting hypereutectic liquid, causing the liqidd composition to make small oscillations about the initial composition with time (inset). Eventually eutectic solid fills in the spaces around all primary phases.

Rosa CD, Park C, Thomas EL, Lotz B. 2003. Microdomain patterns from directional eutectic solidification and epitaxy. Nature 405 433 437. 

Cast iron a ferrous alloy whieh solidifies with an eutectic solidification reaction, whatever the chemical composition, but normally with a carbon content above 2 %... 

FIGURE 6.37 Minimum lamellar spacing versus temperature as predicted from Equation 6.58 for a eutectic solidification reaction that occurs on cooling below T. Greater undercooling favors a finer lamellar spacing. 

Question Consider the eutectic solidification of a liquid to a + where the volume fraction of the / phase is relatively low. In this case, rather than solidifying in a lamellar structure, the phase may solidify as a series of rods embedded in a matrix of the a phase. Assuming that the rods are evenly spaced in a square array in the a matrix, calculate the critical 0-phase volume fraction (0 ) below which the rodlike morphology is more energetically stable than the lamellar morphology. 

During a eutectic solidification L a + / , if the interfacial energy between the a and / phases is low compared to the liquid-a and liquid-/ interfacial energies, then the a and p phases will prefer to wet each rather than the liquid. Under rapid, directional solidification, this can lead to the coordinated growth of long alternating lamellar or plateletlike formations of the a and / phases. Such lamellar microstructures are common feature of eutectic phase transformations... 

---