Effect of static magnetic field on a thermal conductivity measurement of a molten droplet using an electromagnetic levitation technique

Recently, a novel method of measuring the thermophysical properties, particularly thermal conductivity, of high-temperature molten materials using the electromagnetic levitation technique has been developed by Kobatake et al. [H. Kobatake, H. Fukuyama, I. Minato, T. Tsukada, S. Awaji, Noncontact measurement of thermal conductivity of liquid silicon in a static magnetic field, Appl. Phys. Lett. 90 (2007) 094102]; this method is based on a periodic laser-heating method, and entails the superimposing of a static magnetic field to suppress convection in an electromagnetically levitated droplet. In this work, to confirm the fact that a static magnetic field really suppresses convection in a molten silicon droplet in an electromagnetic levitator, numerical simulations of convection in the droplet and periodic laser heating in the presence of convection have been carried out. Here, the convections driven by buoyancy force, thermocapillary force due to the temperature dependence of the surface tension on the melt surface, and electromagnetic force in the droplet were considered. As a result, it was found that applying a static magnetic field of 4 T can suppress convection in a molten silicon droplet enough to measure the real thermal conductivity of molten silicon.     

Effect of static magnetic field on thermal conductivity measurement of a molten Si droplet by an EML technique: Comparison between numerical and experimental results

In order to investigate quantitatively the effect of melt convection in an electromagnetically levitated molten droplet on the thermal conductivity of liquid silicon measured by the electromagnetic levitation (EML) technique superimposed with a static magnetic field, the numerical simulations for melt convection in the droplet and additionally, for the measurement of thermal conductivity were carried out. In addition, the thermal conductivity of molten silicon was measured by the EML technique, and then compared with those obtained numerically. In the numerical simulations of melt convection, the buoyancy force, thermocapillary force due to the temperature dependence of the surface tension on the melt surface, and electromagnetic force in the droplet were considered as the driving forces of convection. As a result, the numerical simulations could sufficiently explain the measurement of thermal conductivity by the EML technique under a static magnetic field. Also, it was suggested that a magnetic field of more than 4 T should be applied to measure the real thermal conductivity of molten silicon by the EML technique.     

MAGNETIC DAMPING OF g-JITTER INDUCED DOUBLE-DIFFUSIVE CONVECTION

This article describes a numerical study of g-jitter driven double-diffusive convective flows and thermal and concentration distributions in binary alloy melt systems subject to an external magnetic field. The study is based on the finite element solution of transient magnetohydrodynamic equations governing the momentum, thermal, and solutal transport in the melt pool. Numerical simulations are conducted using synthesized single- and multi-frequency g-jitter as well as real g-jitter data taken during space flights with or without an applied magnetic field. It is found that for the conditions studied, the main melt flow follows approximately a linear superposition of velocity components induced by individual g-jitter components, regardless of whether a magnetic field exists or not. The flow field is characterized by a recirculating double-diffusive convection loop oscillating in time with a defined frequency equal to that of the driving g-jitter force. An applied magnetic field has little effect on the oscillating recirculating pattern, except around the moment when the flow reverses its direction. The field has no effect on the oscillation period, but it changes the phase angle. It is very effective in suppressing the flow intensity and produces a notable reduction of solute striations and time fluctuations in the melt. For a given magnetic field strength, the magnetic damping effect is more pronounced on the velocity associated with the largest g-jitter component present and/or the g-jitter spiking peaks. A stronger magnetic field is more effective in suppressing the melt convection and also is more helpful in bringing the convection in phase with the g-jitter driving force. The applied field is particularly useful in suppressing the effect of real g-jitter spikes on both flow and solutal distributions. With appropriately selected magnetic fields, the convective flows caused by g-jitter can be reduced sufficiently, and it is possible that diffusion dominates the solutal transport in the melt.     

On the control of solidification using magnetic fields and magnetic field gradients

Solidification from the melt to near net shape is a commonly used manufacturing technique. The fluid flow patterns in the melt affect the quality of the final product. By controlling the flow behavior, the final solidified material can be suitably affected. Most of the magnetic field approaches to melt flow control rely on the application of a constant magnetic field. A constant magnetic field results in the Lorentz force which is used to damp and control the flow. However, simultaneous application of a magnetic gradient results in the Kelvin force along with the Lorentz force. This can be used for better control of the melt flow resulting in higher crystal quality. In the present work, a computational method for the design of solidification of a conducting material is addressed. The control parameter in the design problem is the time history of the imposed magnetic field. A steady, constant magnetic gradient is also maintained during the process. The design problem is posed as an unconstrained optimization problem. The adjoint method for the inverse design of continuum processes is adopted. Examples of designing the time history of the imposed magnetic field for the directional growth of various materials are presented to demonstrate the developed formulation.     

Global simulation of a silicon Czochralski furnace in an axial magnetic field

Control of melt flow in crystal growth process by application of the magnetic field is a practical technique for silicon single crystals. In order to understand the influence of axial magnetic field on the silicon melt flow and oxygen transport in a silicon Czochralski (Cz) furnace, a set of global numerical simulations was conducted using the finite-element method for the magnetic field strength from 0 to 0.3 T, the crystal rotation rates from 0 to 30 rpm and the crucible counter-rotation rates from 0 to −15 rpm. It was assumed that the flow was axisymmetric laminar in both the melt and the gas, the melt was incompressible and a constant temperature was imposed on the outer wall of the Cz furnace. The results indicate significantly different flow patterns, thermal and oxygen concentration fields in the melt pool when a uniform axial magnetic field is applied.     

Effect of pulsed magnetic field on superalloy melt

In order to investigate the magnetic force distribution, flow field distribution and Joule heat distribution under the pulsed magnetic field (PMF), transient numerical simulation was carried out. Results show that the magnetic pressure force appears in the inner of the melt, while the magnetic pull force and the magnetic pressure force appear alternately in the exterior of the melt, which is caused by the skin vortex current. The axial direction magnetic force results in the convection of the melt. The radial direction magnetic force produces vibration of the melt. The vibration will diffuse and superpose to produce the pressure wave. Finally, the fluctuation of the melt is caused by the pressure wave. The Joule heat produced by pulsed magnetic field concentrates near the surface of the melt in the pulse applying period.     

Effect of high frequency magnetic field on CZ silicon melt convection

Melt flow structure during the silicon single crystal growth process strongly affects the crystal quality. Therefore, melt convection control technique should be developed to obtain the high quality single crystal. For this purpose, we proposed a high frequency magnetic field applied method, and numerically investigated the effect of high frequency magnetic field on Czochralski (CZ) silicon melt convection. The results revealed that the melt convection was strongly affected by the applied electric current and frequency. The temperature distribution just below the crystal became flat if the applied electric current and frequency were selected as optimized value.     

Partly three-dimensional global modeling of a silicon Czochralski furnace. II. Model application: Analysis of a silicon Czochralski furnace in a transverse magnetic field

A three-dimensional (3D) global analysis was carried out numerically for a small silicon Czochralski (CZ) furnace in a transverse magnetic field by a proposed 3D global model. The modeling was conducted with moderate requirements of computer resources and computation time. Most 3D features of the melt flow and thermal field in the furnace could be reproduced in the modeling. The results showed that the melt–crystal interface shape is three-dimensional and temperature difference over the circumference on the crystal and crucible sidewalls is prominent. The non-uniformity of temperature in the azimuthal direction decreases with increase in distance from the melt region. The influence of a transverse magnetic field on the flow pattern of melt and global thermal field in the furnace was analyzed.     

Numerical analysis of LEC growth of GaAs with an axial magnetic field

A set of numerical analyses for momentum and heat transfer for a 3 in. (0.075 m) diameter Liquid Encapsulant Czochralski (LEC) growth of single-crystal GaAs with or without an axial magnetic field was carried out using the finite-element method. The analyses assume a pseudosteady axisymmetric state with laminar flows. Convective and conductive heat transfers, radiative heat transfer between diffuse surfaces and the Navier-Stokes equations for both melt and encapsulant and electric current stream function equations for melt and crystal are considered together and solved simultaneously. The effect of the thickness of encapsulant, the imposed magnetic field strength as well as the rotation rate of crystal and crucible on the flow and heat transfer were investigated.     

Dual‐phase‐lag model on magneto‐thermoelastic rotating medium with voids and diffusion under the effect of initial stress and gravity

In this paper, the propagation of harmonic plane waves is considered in a generalized thermoelastic medium with diffusion and voids in the presence of initial stress, magnetic field, rotation, and gravity in the context of thermoelastic models; classical, Lord Shulman, Green Lindsay as well as dual‐phase‐lag models. We applied the boundary conditions in the physical domain using the normal mode method technique on the surface to obtain the displacements, stresses, temperature, diffusion concentration, and the volume fraction field. Influence of initial stress, magnetic field, rotation, and gravity on temperature, stresses, concentration of diffusion, and the volume fraction is observed through a numerical example. The results obtained will be compared in the presence and absence of the new considered variables, also with the previous results obtained by the others and displayed graphically.