Dendrites

Abstract

The word dendrite derives from the Greek word for tree, and means "tree-like". Dendritic growth occurs only when a diffusion process dominates the rate at which the phase transformation proceeds. An extensive study of this mode of growth was carried out by Papapetrou [1]. Dendrites grow into a metastable phase that is either supercooled or supersaturated. The supercooling can be uniform throughout the sample, or it can be a region of constitutional supercooling ahead of an advancing interface in an alloy. 26.2 Conditions for Dendritic GrowthDendritic growth occurs when the interface kinetic processes are rapid, so that a planar growth front is unstable. Essentially what happens is that the growth front sub-divides the metastable phase into regions that are small enough so that diffusion processes can remove the remaining instability.The diffusion process responsible for dendritic growth can be thermal, compositional, or both. In a pure material, where dendrites grow into a supercooled liquid, the dendrites are a result of thermal diffusion. An example is shown in Fig. 26.1.Experimentally, a liquid can be supercooled, and then, when the solid nucleates, the growth is dendritic. Most liquids cannot be supercooled below about 80 % of their melting points. But the latent heat in most materials is large enough to heat them up through about 30 % of their melting points. So in most materials, the latent heat of the freezing process is more than enough to heat an undercooled sample up to the melting point before it is all frozen.Dendritic growth can be very rapid: dendrites have been observed to grow at a rate of 40 m s À1 into supercooled pure nickel.Dendrites can also grow as a result of constitutional supercooling. In this case they grow in an array as shown in Fig. 11.2. The growth proceeds at a rate determined by the rate at which heat is extracted from the sample. This is the usual growth mode in