Introduction
A vast amount of the products and devices that we use everyday, everything
from aluminum foil and soda cans, to cars and jet engines are made from
metals and alloys. Early in the creation of these products, the metals
are in a liquid, or molten state, that freezes to form a solid, similar
to the way water freezes to form ice. If you were to look at some just
frozen, or freshly solidified metallic alloy with a strong magnifying glass
you would see that its surface 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 tiny metallic pine trees crowding
and growing into each other. These metallic tree-like crystals are called
dendrites. This description is appropriate because metallic dendrites actually
grow analogously in the manner trees grow, with a main branch or trunk,
from which grow side branches, from which grow smaller side branches, eventually
filling all space.
Dendritic growth is a common mode of crystal growth encountered when metals
and alloys solidify under low thermal gradients, as occurs in most casting
and welding processes. Furthermore, in engineering materials, the details
of the dendritic morphology is directly related to various material responses
and properties, such as hot cracking, corrosion resistance, toughness,
and yield strength. Although, the effects of the initial dendritic microstructure
can be modified by subsequent heat treatments, the final material properties
are generally dependent on the details of the original dendritic microstructure.
Thus, the understanding and control of dendritic growth in solidification
processing is crucial in order to achieve desired physical properties in
products created by casting. According to J.S. Langer, writing on dendritic
growth in Physics Today:
"Metallurgists have long sought to predict and control alloy microstructures.
The development of automated, cost effective manufacturing techniques ultimately
depends on the precision with which we can solve this problem in non-equilibrium
pattern formation. In principle, we would like to incorportate fundamental
understanding of microstructures into computer codes that simultaneously
help us design materials with made to order properties and optimise their
manufacturability and performance [Ivantsov,
1947]."
Of more generic interest, perhaps, dendritic growth is also an archetypical
problem in morphogenesis, where a complex pattern evolves from simple starting
conditions. Thus, the physical understanding and mathematical description
of how dendritic patterns evolve during the solidification process are
of interest to scientists and engineers.
In the case of cast alloys that solidify dendritically, the long term goal
is the development of computational methods to elucidate both the microstructure
and chemical microsegragation and the macroscopic end product made up by
the agglomeration of millions of dendritic grains. Then, metallurgical
engineers can understand and control the metal formation process, and thus
be able to make better, less expensive, and more reliable metal products.
This requires detailing physical processes over a scale change of at least
two orders in magnitude. The mesoscopic dendritic grains, which are strongly
influenced by the growth pattern of individual dendrites, are considered
the starting point to the problem of micro-to-macro scale modeling. A full
understanding of the behavior of a single, isolated dendrite represents
an important step in achieving better understanding and control of the
final properties of dendritically solidified materials.
To be sure, remarkable progress has been made recently by numerical simulations
of dendritic patterns employing phase field models, and in simulating the
grain structure of castings. These types of numerical studies contribute
greatly to our understanding of dendritic growth processes and their effect
on cast properties. The immediate goal of research in dendritic growth
is to provide a complete physical and mathematical description of how a
single, isolated, dendrite grows.
Over the years, scientists and engineers have learned a great deal about
how dendritic crystals grow. Now, the growth of dendrites is known to be
controlled by the transport of heat, and/or solute, from the moving solid-liquid
interface into the supercooled melt. Under terrestrial conditions, the
gradient of the melt density near the solid-liquid interface, caused by
the rejection of solutes or latent heat, is acted upon by gravity, resulting
in a buoyancy-induced convective flow affecting all the other energy and
species transport processes occuring in the liquid phase. The gravity induced
convection severely complicates how dendrites grow, making the study of
certain aspects of dendritic growth intractable.
The Isothermal Dendritic Growth Experiment (IDGE), which flew aboard
the space shuttle Columbia (STS-62) in March 1996, was designed, built,
and operated to grow dendrites, and photograph them as they grow from the
molten state over a range of supercooling, while orbiting the earth. On
orbit, the acceleration field that promotes convection is reduced about
one million times from that on earth. The main scientific objective was
to produce data sets of dendritic tip velocities and radii, on orbit, that
will become the scientific benchmark for critically testing phenomenological
and theoretical models. |
