<title> What Are Dendrites?

Dendrites

What Are Dendrites:

A vast amount of the products and devices that we use everyday, everything from aluminum foil and soda cans, to cars, jet engines and computers, are made from metals and alloys. Early in the creation of all these products the metals are in a liquid, or molten state, that freezes to form a solid, just like water freezes to form ice. Now, if you were to look at some just frozen, or freshly solidified metallic alloy with a strong magnifying glass you would see that its structure is not uniform, but is made up of tiny individual crystalline grains. Moreover, If you were able to look even more carefully at the individual grains through a powerful microscope, you would see that each grain is made up from what looks like a bunch of tiny metallic snowflakes crowding and growing into each other. Scientists and engineers call these tiny metallic snowflakes dendrites. The picture to the right shows what a surface cut through a "forest" of dendrites in a metal would look like through a microscope.

The term dendrite comes from the Greek word "dendron", which means a tree. This description is appropriate because we often describe the form and structure of a metallic dendrite as that of a tree (see figure to left), with a main branch or trunk, from which grow side branches, from which grow smaller side branches, and so on, until all the main branches and the side branches grow into each other and there is no room

for any more branches to grow. The figure to the right shows a few dendrites growing out of the surface of a metal. In fact, almost all freshly crystallized alloys are composed of many thousands, or even millions of dendritic crystals all stuck together. What's most important is that the shape, size, and speed of growth of these dendrites are all factors that profoundly influence the final properties of cast and welded metals.

For example, the dendrites affect how hard or soft a material is, how stretchable or springy it behaves, and how much you can bend or stretch it before it breaks. The dendrites also affect both how long and under what environmental conditions you can use an alloy before it wears out or rusts. The dendrites affect whether the material is a good or a poor conductor of electricity. The dendrites even affect how easily you can weld one piece of metal to another, and what's the best way to do the welding. In short, the dendritic pattern formed during solidification profoundly influences a material's mechanical, electrical, and chemical properties.

What Are Doublons:

Only very recently it could be verified that there is another morphology besides the dendritic one in free diffusive and unfacetted crystal growth. This morphology will continue to exist in the case of vanishing crystal anisotropy where the dendrites are unstable, interesting both for theoretical reasons and as a case that appears in growth of nuclei in fluid phase transitions. Handling this problem numerically imposes two fundamental difficulties: tracking the front in following the dynamics of the interface and avoiding numerical anisotropy. In previous approaches a quasistationary approximation has often been used to alleviate the numerical workload by effectively reducing the dimension of the problem by one. In our research at Magdeburg university we pursue an approach not making use of the quasistationary approximation and solving the anisotropy problem. It is adapted from ideas developed by Mueller-Krumbhaar and Ihle (Physical Review E 51, 475 (1995)). Its main feature is to work on several grids rotated with respect to each other and thereby average out the numerical anisotropy. Grid and interface are discretized independently. This allows us to track completely irregular interfacial geometries dynamically. We use this approach to carry out studies for physical situations which are difficult to treat with other numerical approaches and thereby contribute to a fundamental understanding of interesting morphologies inherent to free growth, be it diffusion- or convection-limited. For some further explanation concerning this point of diffusion- and convection-limited crystal growth respectively you might want to have a look at

Crystal Growth and Convection

And if you are interested in computational physics in general also other topics such as simulation with cellular automata (for example traffic flow?) might be interesting for you. Feel free to have a look at my personal homepage. I believe computational physics is a very fascinating and challenging area of research at the moment and certainly will continue to be. Maybe it could also be a challenge for you? If you are curious and are interested in working at the very basics, the formulation of new models, and you if find it fun to exploit the visual capacities of computers to represent your findings for others as well you might want to know more about our work and are welcome to contact us ........................

Heike Emmerich

Last modified: Tue Apr 13 11:04:04 MET DST 1999