Control of floating-zone crystal growth in high-frequency magnetic field

This work presents a numerical and experimental study of the growth of single intermetallic-compound crystals by the floating-zone method using a radio frequency (RF) heating magnetic field. The quality of the grown crystals depends strongly on the growth conditions, particularly on the shape of solidification front. To obtain single crystals of complex composition, a convex to the melt growth interface is desirable. The shape of the solid-liquid interface can be strongly influenced by the convective heat transport in the melt. There is a number of mechanisms driving the melt convection: differential rotation of the crystal and the seed, buoyancy, thermocapillarity and electromagnetic forces due to the RF heating. The aim of this work is to find out the growth parameters ensuring a desired shape of the crystalization front. The numerical study consists of two major parts - finding of the electromagnetic field induced by the RF-heater coil and the solution of the coupled heat and hydrodynamic problems. For the solution of the electromagnetic problem a novel boundary-integral method is developed. This method involving integration only along the surfaces is easily applicable to complex geometries at arbitrary skin depth. The heat and hydrodynamic problems are solved by a numerical code based on the control volume technique using a triangular finite-element-like mesh adapting to the solid-liquid interfaces. For small-diameter crystals considered here, only the thermocapillary and electromagnetically-driven convections turn out to be significant for the heat transport. Pure heat diffusion is found to result in the interfaces which are slightly convex over most of the diameter except close to the crystal surface where the interface is always concave to the solid phase. Such a form of the interface is determined by the Ohmic dissipation in the skin-layer and the heat radiation from the surface. A part of the produced heat is emitted directly from the liquid zone that makes the surface colder than the underlaying melt. Therefore the interface is concave in the vicinity of the surface. The rest of the heat released in the skinlayer is conducted radially inwards into the melt from where it enters the crystal to be emitted further away from the liquid zone. This inward heat flux is responsible for the central convex part of the interface. The numerical results give evidence that at the minimal length of the liquid zone, electromagnetically-driven convection may be so weak that it has no significant effect on the heat transfer. Strength of the forced convection rapidly increases with the heating power resulting in a concave interface over the whole diameter. Thermocapillary convection is found to be significant at smaller crystal diameters where it can substantially counterbalance the electromagnetically-driven convection in the bulk of the melt. Numerically found interface shapes are compared with experimental results obtained on a model system of Ni crystals.