Solidification describes the phenomenon of liquids transforming into solids as a result of a decrease in liquid temperature. It occurs in a wide range of industrial processes, including casting and semiconductor single-crystal growth. As liquids undergo solidification, fluid flow and turbulence occur in the solidifying liquid pool and have critical implications to both the solidification-process design and product quality control.
There is extensive research devoted to developing a fundamental understanding of convective flows in solidifying melts and designing effective measures to control and optimize solidification-processing systems in order to obtain solidification products of high quality. One of the very useful methods that have been successfully applied to controlling melt convection in solidification systems is the use of magnetic fields.
Many references from the cast metal literature are known discussing the effect of melt convection during the early stages of solidification on the grain structure. The application of mechanical or electromagnetic stirring, ultrasonic or sonic vibrations promotes the formation of fine, equiaxed grains. However, there has been much speculation about the mechanism of this process.
The prevalent interpretation favoured during the last decades is that the grain refinement results from a fragmentation of primary dendrites. The macrostructure of chill cast ingots generally consists of a columnar and an equiaxed zone. The occurrence and position of the transition between both zones was found to be influenced by casting parameters, including the temperature gradient, and the cooling rate or the probe composition, respectively. As mentioned above fluid flow occurring in the liquid phase was also found to affect the structure and position of the columnar-to-equiaxed transition (CET).
The fact that molten metals are electrically conducting, opens up possibilities to apply the magnetic fields to control the behavior of the melts during solidification and, therefore, to improve product quality. During metal solidification, magnetic fields have been applied to shape the solidifying melts (i.e., electromagnetic molding), stir the melts at desired locations (i.e., electromagnetic stirring), and reduce the melt disturbance or flow irregularities or turbulence (i.e., electromagnetic braking).
The use of the fields has resulted in benefits of improved internal metallurgical structure, reduced inclusions and liquidation, improved uniformity of compositions and mechanical properties, and alleviation of operation constraints.
The use of external magnetic fields is now widespread in the metals and semiconductor industries to control the behavior of the melts during solidification, resulting in improved process performance and better quality products. With an applied magnetic field, a melt may be supported in air whilst being solidified by a well-shaped Lorentz force in place of a mechanical mold to obtain high-purity products.
The field may also be configured to provide an environmentally friendly, yet effective means for melt stirring, which is useful in generating a desired melt mixing patterns during semiconductor crystal growth or producing a strong turbulent shear flow to induce grain refinement effects during metal casting. A direct current (d.c.) magnetic field can also be used to reduce unwanted turbulent flows and fluctuations associated with melt convection during solidification to help eliminate solidification defects. Because molten metals and semiconductor metals are electrically conducting, the same principles apply for the design of magnetically assisted solidification processing systems for both materials.
The details of operational procedures and field control parameters, however, are different because of different technology development history and quality requirements. The attention of metal producers is presently focused on the adaptation of the existing technology to the new generation of casting processes. The semiconductor crystal growers, on the other hand, are actively pursuing electromagnetic stirring while searching for magnetic field configurations that render more effective damping effects in crystal growth.
The basic mechanism by which an applied magnetic field affects the solidifying melt may best be appreciated through the study of the Maxwell stress tensor Tαβ (SI unit) for a macroscopic homogeneous medium
where ε is the electric permittivity, Eα is the αth component of the electric field, µ is the magnetic permeability, Hα is the αth component of the magnetic field, ρ is the density of the fluid, and T is the temperature. The Kroneker delta δαβ takes the value δαβ = 1 if α = β and δαβ = 0 if α ≠ β, where α,β = 1, 2, 3.
In Equation 1, the first (a) and the third terms (c) on the right-hand side represent the electrostatic effects. While electrostatic fields are rarely used during the solidification of conducting fluids, their use in affecting other types of phase-change processes such as boiling and condensation are common.
The magnetic effects come from the remaining two terms (b and d) . The last term (d) represents the force resulting from the change of magnetic properties and has recently found applications in protein single-crystal growth, a rapidly growing area of great economic importance. The major effect of the applied electromagnetic field on metal and semiconductor solidification comes from the other two terms on the right-hand side.
The directional solidification of binary alloys is an example for self-organization and nonequilibrium pattern formation occurring dynamically at the solid-liquid interface. Natural or forced convection occurring in the liquid phase during solidification shows a distinct impact on the kinetics of the solidification process as well as on the resulting macro- and microstructures. The physical mechanism of the interaction between solidification and flow field is only insufficiently understood until now, however, the knowledge about that is of high technological importance.
The application of time varying magnetic fields can be considered as an effective tool to organize a well-defined flow structure in the liquid phase affecting the nucleation and solidification parameters. Once a flow occurs in the liquid melt during solidification, nucleation and grain growth are mainly governed by the convective transport of heat and solute.
The consequences on the structure of solidified ingots are widely discussed in literature primarily covering the application of mechanical or electromagnetic stirring, which promotes the formation of fine, equiaxed grains and promotes the columnar-toequiaxed transition (CET). Also of great importance in these discussions, and not to be ignored, are the occurrence of a forced flow during solidification may cause macrosegregation in cast alloys.