User:Lacomj/Dendrite

Dendrite is a term derived from the Greek δένδρον (dendron), meaning "tree" or "treelike". It refers to the treelike patterns that form throughout nature, in situations that may appear at first glance to be completely unrelated. Aside from the obvious branched structures found in plants, dendrites can also be found in neurons, snowflakes, and in the microstructure of many commonly–used materials. The complex branched patterns of dendrites exhibit fractal geometry characteristics, typical of many natural, self-regulated pattern-formation phenomena.

Dendritic Pattern Formation

Ice dendrite formation on a snowflake

At first glance, the natural formation of dendrites throughout nature may appear to be completely coincidental. However, the physical underpinnings of these seemingly–unrelated pattern formation process can have important connections.

In basic terms, the formation of dendritic (treelike) shapes in materials is the result of a competition. During growth (like solidification), some physical phenomena will cause a small bump (protuberance) on the surface of a material to grow and get even bigger. Other physical phenomena will cause such a bump to shrink back and disappear. In nature, these physical phenomena are all present together, which leads to a competition between these opposing tendencies that often results in dendritic growth shapes. The specifics of these physical mechanisms vary, depending on the process.

Example: Dendritic solidification of a pure crystalline material

In the case of the freezing of a pure material from a supercooled liquid state (common in castings), the driving mechanism behind the freezing is that the liquid is below the freezing temperature. However, the surface of the growing solid is in local equilibrium with the liquid fixed at the (higher) melting temperature. This creates a temperature gradient in the liquid that draws latent heat away from the solid, permitting the growth. If any "microscopic bump" were to form on the surface of the solid, it would be sticking out into a colder (than the surface) liquid, which would make it want to freeze (grow) more. On the other hand, any time a bump forms on the surface of the solid, this creates additional surface area, which takes energy. The natural thermodynamic response is to minimize the free energy of the system by reducing the solid-liquid interface area–and this means that the bump will want to shrink back and disappear. This is the central conflict that results in a precarious balance where bumps can sometimes grow, yet are constrained by the stabilizing "forces" of the surface energy, resulting in the ramified branch structures. To further complicate matters, the branches often have preferred growth directions (especially in crystalline materials) that are influenced by anisotropy in the surface energy due to the underlying crystal structure of the material.

In the case of alloys, where multiple components (and/or multiple phases) are present, the process is also influenced by compositional variations in the growth process. In the case of snowflake formation, the dendrites typically grow directly from the vapor phase.

Dendrites in Metallurgy & Materials

A dendrite in metallurgy refers to the tree-like structure of the small that form as molten metal freezes (as in a casting). The details of the shapes of these dendrites can significantly affect the properties of the solidified material. As a result, metallurgists are very interested in understanding and controlling the dendrite formation process in common materials such as aluminum and steel. Development of methods for control of the dendritic microstructure curently serves as a powerful tool in the arsenal of manufacturers of modern metal alloys.

Dendrites are the most commonly found solidification microstructure in alloys. The shapes and sizes of the dendrites that are first formed upon solidification of the liquid metal typically have a profound impact on the material's properties, even after downstream processing. Dendrites that grow slowly will be more blunt, and the branches will be few and large. However, if the metal is cooled rapidly, the dendrites will grow more quickly, and produce a finer branch structure. This branch structure has the effect of establishing the initial grain size scale of the microstructure, which is well-known to affect important properties such as the strength of the material (described by the Hall-Petch relationship).

Dendrites in Geology

Manganese dendrites on a limestone bedding plane from Solnhofen, Germany. Scale in mm.

Example of a dendrite on pyrolusite.

In paleontology, dendritic mineral crystal forms are often mistaken for plant fossils. These pseudofossils form as naturally occurring fissures in the rock are filled by percolating mineral solutions. They form when water rich in manganese and iron flows along fractures and bedding planes between layers of limestone and other rock types, depositing dendritic crystals as the solution flows through. A variety of manganese oxides and hydroxides are involved, including:

birnessite (Na₄Mn₁₄O₂₇·9H₂O)
coronadite (PbMn₈O₁₆)
cryptomelane (KMn₈O₁₆)
hollandite (BaMn₈O₁₆)
romanechite ((Ba,H₂O)Mn₅O₁₀)
todorokite ((Ba,Mn,Mg,Ca,K,Na)₂Mn₃O₁₂·3H₂O) and others.

A three-dimensional form of dendrite develops in fissures in quartz, forming moss agate.