Dendrite (metal)
A dendrite in metallurgy is a characteristic tree-like structure of crystals growing as molten metal solidifies, the shape produced by faster growth along energetically favourable crystallographic directions.
This dendritic growth has large consequences in regard to material properties.
The requirement is that the liquid (the molten material) be undercooled, aka supercooled, below the freezing point of the solid.
The solid shape begins to express the preferred growth directions of the crystal.
In metallic systems, interface attachment kinetics is usually negligible (for non-negligible cases, see dendrite (crystal)).
The microstructural length scale is determined by the interplay or balance between the surface energy and the temperature gradient (which drives the heat/solute diffusion) in the liquid at the interface.
[1] As solidification proceeds, an increasing number of atoms lose their kinetic energy, making the process exothermic.
For a pure material, latent heat is released at the solid–liquid interface so that the temperature remains constant until the melt has completely solidified.
The growth rate of the resultant crystalline substance will depend on how fast this latent heat can be conducted away.
Generally, if the melt is cooled slowly, nucleation of new crystals will be less than at large undercooling.
Conversely, a rapid cooling cycle with a large undercooling will increase the number of nuclei and thus reduce the size of the resulting dendrites (and often lead to small grains).
One application where dendritic growth and resulting material properties can be seen is the process of welding.
The dendrites are also common in cast products, where they may become visible by etching of a polished specimen.
As dendrites develop further into the liquid metal, they get hotter because they continue to extract heat.
, for a pure material in two dimensions: which is an Allen-Cahn equation with an anisotropic gradient energy coefficient: where
describes the thermodynamic driving force for solidification, which Kobayashi defines for a supercooled melt as: where
When this system is numerically evolved, random noise representing thermal fluctuations is introduced to the interface via the
In order to minimize the effect on properties, grain boundaries are aligned parallel to the dendrites.
This resulted in blades with high strength and creep resistance extending along the length of the casting, giving improved properties compared to the traditionally-cast equivalent.
