Formation of Cells and Dendrites

2 CELLULAR AND DENDRITIC SOLIDIFICATION 22.2.1 Formation of Cells and Dendrites 

When the liquid/solid interface is unstable according to the criteria discussed in Section 20.3.3, a cellular or dendritic structure is developed. When the degree of instability is relatively low, an array of protuberances develops on the interface as shown in Fig. 20.8a. These protuberances, called cells, advance perpendicular to the interface. Their shapes vary depending upon the type of material, the orientation of the interface, and other factors. For (100) liquid/solid interfaces in cubic metals, equiaxed cells form like those in Fig. 20.86. However, for a (110) interface, the cells take on a corrugated configuration of long hills and furrows. When the degree of 

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Connection between Transport Processes and Solid Microstructure. The formation of cellular and dendritic patterns in the microstructure of binary crystals grown by directional solidification results from interactions of the temperature and concentration fields with the shape of the melt-crystal interface. Tiller et al. (21) first described the mechanism for constitutional supercooling or the microscale instability of a planar melt-crystal interface toward the formation of cells and dendrites. They described a simple system with a constant-temperature gradient G (in Kelvins per centimeter) and a melt that moves only to account for the solidification rate Vg. If the bulk composition of solute is c0 and the solidification is at steady state, then the exponential diffusion layer forms in front of the interface. The elevated concentration (assuming k < 1) in this layer corresponds to the melt that solidifies at a lower temperature, which is given by the phase diagram (Figure 5) as... 

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