Microstructure development  

 
Nucleation and growth behavior, both determine development of microstructure in solidification of alloys. In alloys, nucleation of solid is not an issue since nucleating sites are present. Growth behavior is important.

Growth behavior    
           
The solute redistribution at the solid/liquid interface governs the stability of the solidification front. The solidification begins with the planar solid/liquid interface .During growth the morphological stability of the planer solid/liquid interface is governed by thermal and composition gradients at the interface

In figure 31.4a the variation in composition as a function of distance from the planar solid/liquid interface is depicted. By referring to the phase diagram such as one shown in figure 31.1b, a curve of equilibrium liquidus temperature versus distance from the S/L interface corresponding to figure 31.3a can be determined and such a curve is shown in figure 31.4b and c. (It must be noted that the equilibrium liquidus temperature depends on the solute; as the solute segregates, the liquidus temperature will be lower than when there is no segregation.)

Two conditions are possible based on the actual temperature distribution in the liquid imposed by temperature gradient arising from the heat flow conditions:

Condition 1:  Actual thermal gradient is steeper than equilibrium liquidus temperature at the interface due to the compositional gradient. Under this condition any perturbation developed at the solid/interface will remelt and the planar front will remain stable.

Condition 2:  If, however, actual  thermal gradient is smaller, as shown in figure 31.4c, then the liquid ahead of the interface is supercooled  since the actual temperature ahead of the interface is lower than the equilibrium liquidus temperature. Any perturbation of the plane front can no longer melt but instead will grow. Under these conditions the planar growth is no longer stable, this is due to constitutional super cooling and is responsible for cellular or dendrite solidification.

The compositional gradient for steady state plane front growth can be determined by mass balance consideration at the planar interface to

(5)

                                                                                                                                               
In the equation 5 is the liquidus and solidus temperature difference at composition CO, is the diffusion coefficient of solute in liquid, GL is thermal gradient in the liquid. Several parameters affect the conmstitutional supercooling. Decrease in the imposed temperature gradient increases the tendency for planar solidification.  

In addition to gradient, growth rate is also important. For a given gradient,(G), the growth rate (R) also plays an important role in determining solidification structure. Higher temperature gradient and smaller growth rate I.e. when G/R is large plane front solidification prevails. As G/R decreases, plane front can no longer be stable. Low  G/R   favors dendridic solidification. Solutes with a smaller partition coefficient create conditions for instable plane front solidification, since more solute will be rejected in the liquid.
Thus as the extent of constitutional super cooling ahead of the solid/liquid interface increases, the morphology of interface changes from planar to cellular and to dendrite

References:

David and vitek: solidification and weld microstructure. International materials Review. 1989 vol 34 NO.5.P 213

A. ghosh : principles of secondary processing and casting of steel .