Numerical simulations of solidification processes have experienced a formidable growth during the last decades. As long as transport of heat and species during solidification is only controlled by diffusion the models to describe the distribution of temperature and solute concentration remain relatively tractable. Taking fluid flow into consideration makes, theoretical predictions more difficult, because nonlinear terms appear in the conservation equations describing the coupling between velocity field, heat and mass transfer, and the solidification process.
Serious predictions about the influence of the electromagnetic convection on the solidification require a detailed knowledge about the direction and intensity of the melt flow ahead of the solidification front. Three different flow regimes were recently identified by numerical simulations, namely an initial adjustment phase, an inertial and an oscillatory phase. The latter is characterized by oscillations of toroidal vortices of the secondary flow and the appearance of Taylor-Görtler vortices along the lateral walls.
These numerical predictions were confirmed by first velocity measurements during solidification using the ultrasound Doppler velocimetry (UDV) revealing permanent modifications of the flow structure in the course of the solidification process.
The role of melt convection has been studied during directional solidification of Pb-Sn alloys. The melt was electromagnetically agitated using a rotating magnetic field (RMF).
The forced convection influences significantly the concentration as well the temperature profile ahead of the solidification front. The convective transport of solute reduces the thickness of the solutal boundary layer. The electromagnetic stirring encourages a thermal homogenization of the liquid bulk zone.
Therefore, the magnetic Taylor number Ta appears as a further, fundamental parameter like the cooling rate, the temperature gradient or the alloy composition controlling the level of undercooling and the length of the undercooled region ahead of the solidification front. The effect of the electromagnetic melt agitation can be verified both in the macro- and microstructure. The applied RMF provokes a distinct grain refinement for all considered alloy compositions. Equiaxed growth has shown to be encouraged by a forced convection in the melt.
Therefore, a flow effect can be supposed both on the presence of nuclei in the melt and suitable conditions allowing them to grow in competition with the columnar front. The melt convection during solidification also results into characteristic segregation patterns. Therefore, an optimization of the flow structure is required in order to achieve solidified ingots with an optimal microstructure, particularly composed of fine, equiaxed grains without macrosegregation.
Figure 1 displays a detail of the microstructure obtained from the region where the solidification took place at that moment when the magnetic field was switched on. Dendrites with trunks growing vertically dominate the structure if the forced convection is absent. As soon as the flow comes up, the secondary arms of the dendrites continue to grow towards the approaching flow instead of the primary trunks.
Figure 1: Micrograph showing the transition from parallel to inclined growth of the columnar dendrites cause by theinitiation of the a longitudinal section
Figure 2: Channel-like Segregation inthecentreof RMF-driven convection
Moreover, the mechanism described above is also responsible for macrosegregation effects. Figure 2 shows a larger area of the same longitudinal section as already presented in Figure 1. Once the forced convection was initiated, an enrichment of eutectic alloy was found at the sample axis forming channel-like segregations. This phenomenon is attributed to the secondary flow inside the liquid phase. The vortex just above the mushy zone carries the excess of solute which is rejected ahead of the solidification front towards the middle of the liquid phase resulting in a depletion of tin in the region around the axis of rotation.
For electrically conducting fluids, magnetic fields can be used to support the melts in place of a mechanical container, provide an environmentally friendly yet effective means for melt stirring, and reduce unwanted turbulent flows and fluctuations associated with melt convection. These remarkable effects of magnetic fields on solidifying melts have led to the development of various magnetically assisted solidification technologies for producing metal ingots and semiconductor crystals of superb quality.
The electromagnetic mold or crucible is based on the concept of magnetic support and replaces a mechanical mold or crucible by the Lorentz forces generated by an inductor surrounding the solidifying melt. Support or shape of the melt eliminates the possible contamination of impurities originated from the container. As such, it has become the method of choice for the production of high-purity and low-defect solidification products, whether they are metal-casting ingots or semiconductor single crystals.
Electromagnetic stirring results from a deliberate application of a.c. magnetic fields and allows the melt convection to be generated at locations where most needed. It is applied in the mold region, below-mold region, and in the final stage of solidification during the continuous casting of metals. Both linear and rotary stirring has been applied in the metals industry; rotary stirring has been the only mode used in the semiconductor industry. While electromagnetic stirring in metals has enjoyed a long history, it has just started in the single-crystal growth fields.
Electromagnetic brake or magnetic damping uses the interaction of the melt convection and a d.c. magnetic field to produce an opposing force to the flow motion in the solidifying melt. It has been widely used in both the metal and semiconductor industries to suppress the melt turbulence and flow instabilities. In the metals industry, mainly transverse magnetic fields have been considered with the purpose of slowing down or braking the turbulence of liquid jets issued from the downspout nozzle. In contrast, many different magnetic-field configurations have been explored in the semiconductor industry to damp out the turbulence and flow instabilities or fluctuations associated with melt convection.
The application of magnetic fields has now become widely practiced in the materials industry for the solidification processing of metals and semiconductors and has resulted in improved quality and process control. Ever-increasing global economic competition has created unquenchable demand for better quality, which in turn generates a powerful thrust for improved process design and operation.
Because of different development histories and different quality requirements, metal and semiconductor researchers have different focuses in their research on solidification processing in magnetic fields, though the design principles applied are the same. Metals researchers, while perfecting the current practice, are now exploring the possibility of extending the use of the electromagnetic fields in near-net-shape casting, thin-gauge casting, and other novel casting processes. On the other hand, crystal growers are preoccupied with adapting electromagnetic stirring in semiconductor melts while developing more effective magnetic damping field configurations.
Two examples have been selected here to illustrate the variety and the complexity of the interactions of the fluid flow and the solidification of alloys. In the case of the continuous casting of steel, the main phenomena which explains why the effects of stirring on the formation of the equiaxed zone are likely and may include, the fragmentation of dendrite arms in the columnar front, the coarsening of bits of equiaxed crystals, and eventually the remelting or the re-dissolution of the crystals in superheated regions of the melt. The fragmentation process along the columnar front is controlled by the morphology of the columnar dendrites together with the micro segregation and the capillary pinching.
Heat transfer is thought to have only an indirect effect through the partial control of the dendrite morphology. On the other hand, in the case of freckling during directional solidification, heat transfer conditions have been demonstrated to be critical for the control of the meso and macro segregation due to channeling in the mushy zone, irrespective of what the dendrite arm spacing is. The morphology and size of dendrites in the columnar zone might affect however the occurrence of disoriented grains due to dendrite fragmentation along the fluid flow channels.