Melt motion in a Czochralski crystal puller with an axial magnetic field: isothermal motion

1986 ◽  
Vol 164 ◽  
pp. 237-273 ◽  
Author(s):  
L. N. Hjellming ◽  
J. S. Walker
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Crystal Growth ◽  
Field Strength ◽  
Axial Magnetic Field ◽  
Molten Silicon ◽  
Crystal Face ◽  
Rotation Rates ◽  
Crucible Rotation ◽  
The Magnetic Field

A magnetic field suppresses turbulence and thermal convection in a Czochralski crystal puller. The amounts and distributions of dopants and oxygen in the crystal are determined by the motion of the molten silicon during crystal growth. This paper presents analytical solutions for the melt motion in a Czochralski puller with a strong, uniform, axial magnetic field. The relatively small electrical conductivity of the crystal plays a key role in determining the flow. Certain combinations of crystal and crucible rotation rates lead to flow patterns with a large volume of almost stagnant fluid under most of the crystal face. The values of these rotation rates depend on the magnetic field strength.

Schwingung eines Plasmazylinders in einem axialen Magnetfeld II

1960 ◽  
Vol 15 (3) ◽  
pp. 220-226 ◽  
Author(s):  
Klaus Körper
Keyword(s):  
Magnetic Field ◽  
Refractive Index ◽  
External Magnetic Field ◽  
Field Strength ◽  
Axial Magnetic Field ◽  
Surface Current ◽  
The Other ◽  
Plasma Cylinder ◽  
Resonance Frequencies ◽  
The Magnetic Field

Radial oscillations are excited in a homogeneous infinite plasma cylinder in a homogeneous axial magnetic field by a surface current which is homogeneous in the axial and azimuthal directions. The modes of oscillations corresponding to the axial and azimuthal components of current are not coupled, and so they may be analysed separately. The magnetic field in the plasma and vacuum is obtained, and the indices of refraction for both types of oscillations are discussed thoroughly. When the currents are parallel to the external magnetic field, the oscillations are characterized by the refractive index of Eccles. On the other hand, when the current is perpendicular to the magnetic field two resonance frequencies exist, which depend on the density of the plasma and the magnetic field strength. — In the latter case the radial characteristic oscillations of the plasma cylinder in an external magnetic field are considered.

Magnetic Control of Transport Phenomena in CZ Crystal Growth Processes

2001 ◽  
Author(s):  
M. Gunzburger ◽  
E. Ozugurlu ◽  
J. Turner ◽  
H. Zhang
Keyword(s):  
Crystal Growth ◽  
Axial Magnetic Field ◽  
Mathematical Formulation ◽  
Computational Techniques ◽  
Control Parameters ◽  
Czochralski Growth ◽  
Design Strategies ◽  
Growth Processes ◽  
Rotation Rates ◽  
Crucible Rotation

Abstract Magnetic fields have been widely used in industry to enhance the performance of crystal growth processes. However, no attempts have been made at applying optimization strategies to effect optimal enhancements. Here, a mathematical formulation and computational techniques are presented to describe optimal control and design strategies for the suppression of turbulent motions in the melt and the minimization of temperature gradients in the crystal in Czochralski crystal growth processes. It is shown that an axial magnetic field can effectively suppress convection in Czochralski growth of silicon. Other control parameters such as crystal and crucible rotation rates are found to be less effective.

Forced Convection During Liquid Encapsulated Crystal Growth With an Axial Magnetic Field

1998 ◽  
Vol 120 (4) ◽  
pp. 844-850 ◽  
Author(s):  
Nancy Ma ◽  
John Walker ◽  
David Bliss ◽  
George Bryant
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Forced Convection ◽  
Magnetic Field Strength ◽  
Axial Magnetic Field ◽  
Vertical Wall ◽  
Czochralski Growth ◽  
Centripetal Acceleration ◽  
Radial Gap ◽  
The Magnetic Field

This paper treats the forced convection, which is produced by the rotation of the crystal about its vertical centerline during the liquid-encapsulated Czochralski or Kyropoulos growth of compound semiconductor crystals, with a uniform vertical magnetic field. The model assumes that the magnetic field strength is sufficiently large that convective heat transfer and all inertial effects except the centripetal acceleration are negligible. With the liquid encapsulant in the radial gap between the outside surface of the crystal and the vertical wall of the crucible, the forced convection is fundamentally different from that with a free surface between the crystal and crucible for the Czochralski growth of silicon crystals. Again unlike the case for silicon growth, the forced convection for the actual nonzero electrical conductivity of an indium-phosphide crystal is virtually identical to that for an electrically insulating crystal. The electromagnetic damping of the forced convection is stronger than that of the buoyant convection. In order to maintain a given balance between the forced and buoyant convections, the angular velocity of the crystal must be increased as the magnetic field strength is increased.

On the Configuration of the Magnetic Field of β CrB

1976 ◽  
Vol 32 ◽  
pp. 613-622
Author(s):  
I.A. Aslanov ◽  
Yu.S. Rustamov
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Radial Velocity ◽  
Magnetic Field Strength ◽  
Complex Shape ◽  
Rotation Period ◽  
Field Variation ◽  
Magnetic Field Variation ◽  
Secular Variations ◽  
The Magnetic Field

SummaryMeasurements of the radial velocities and magnetic field strength of β CrB were carried out. It is shown that there is a variability with the rotation period different for various elements. The curve of the magnetic field variation measured from lines of 5 different elements: FeI, CrI, CrII, TiII, ScII and CaI has a complex shape specific for each element. This may be due to the presence of magnetic spots on the stellar surface. A comparison with the radial velocity curves suggests the presence of a least 4 spots of Ti and Cr coinciding with magnetic spots. A change of the magnetic field with optical depth is shown. The curve of the Heffvariation with the rotation period is given. A possibility of secular variations of the magnetic field is shown.

scholarly journals Effect of Magnetic Field on the Forced Convective Heat Transfer of Water–Ethylene Glycol-Based Fe3O4 and Fe3O4–MWCNT Nanofluids

2021 ◽  
Vol 11 (10) ◽  
pp. 4683
Author(s):  
Areum Lee ◽  
Chinnasamy Veerakumar ◽  
Honghyun Cho
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Field Strength ◽  
Ethylene Glycol ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Hybrid Nanofluid ◽  
Forced Convective Heat Transfer ◽  
The Magnetic Field

This paper discusses the forced convective heat transfer characteristics of water–ethylene glycol (EG)-based Fe3O4 nanofluid and Fe3O4–MWCNT hybrid nanofluid under the effect of a magnetic field. The results indicated that the convective heat transfer coefficient of magnetic nanofluids increased with an increase in the strength of the magnetic field. When the magnetic field strength was varied from 0 to 750 G, the maximum convective heat transfer coefficients were observed for the 0.2 wt% Fe3O4 and 0.1 wt% Fe3O4–MWNCT nanofluids, and the improvements were approximately 2.78% and 3.23%, respectively. The average pressure drops for 0.2 wt% Fe3O4 and 0.2 wt% Fe3O4–MWNCT nanofluids increased by about 4.73% and 5.23%, respectively. Owing to the extensive aggregation of nanoparticles by the external magnetic field, the heat transfer coefficient of the 0.1 wt% Fe3O4–MWNCT hybrid nanofluid was 5% higher than that of the 0.2 wt% Fe3O4 nanofluid. Therefore, the convective heat transfer can be enhanced by the dispersion stability of the nanoparticles and optimization of the magnetic field strength.

Investigating flexible textile-based coils for wireless charging wearable electronics

2019 ◽  
Vol 50 (3) ◽  
pp. 333-345 ◽  
Author(s):  
Danmei Sun ◽  
Meixuan Chen ◽  
Symon Podilchak ◽  
Apostolos Georgiadis ◽  
Qassim S Abdullahi ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Electromagnetic Field ◽  
Electric Field ◽  
Dimensional Stability ◽  
Screen Printing ◽  
Wearable Electronics ◽  
Wireless Charging ◽  
The Magnetic Field ◽  
Screen Printed

Smart and interactive textiles have been attracted great attention in recent years. This research explored three different techniques and processes in developing textile-based conductive coils that are able to embed in a garment layer. Coils made through embroidery and screen printing have good dimensional stability, although the resistance of screen printed coil is too high due to the low conductivity of the print ink. Laser cut coil provided the best electrical conductivity; however, the disadvantage of this method is that it is very difficult to keep the completed coil to the predetermined shape and dimension. The tested results show that an electromagnetic field has been generated between the textile-based conductive coil and an external coil that is directly powered by electricity. The magnetic field and electric field worked simultaneously to complete the wireless charging process.

Nonlinear evolution of a wave packet propagating along a hot magnetoplasma column

1987 ◽  
Vol 37 (1) ◽  
pp. 107-115
Author(s):  
B. Ghosh ◽  
K. P. Das
Keyword(s):  
Magnetic Field ◽  
Multiple Scales ◽  
Nonlinear Evolution ◽  
Axial Magnetic Field ◽  
Modulational Instability ◽  
Wave Train ◽  
Dielectric Medium ◽  
Ion Effects ◽  
The Magnetic Field ◽  
Uniform Plasma

The method of multiple scales is used to derive a nonlinear Schrödinger equation, which describes the nonlinear evolution of electron plasma ‘slow waves’ propagating along a hot cylindrical plasma column, surrounded by a dielectric medium and immersed in an essentially infinite axial magnetic field. The temperature is included as well as mobile ion effects for ail possible modes of propagation along the magnetic field. From this equation the condition for modulational instability for a uniform plasma wave train is determined.

scholarly journals The effects of magnetic field strength on the properties of wind generated from hot accretion flow

2018 ◽  
Vol 615 ◽  
pp. A35 ◽  
Author(s):  
De-Fu Bu ◽  
Amin Mosallanezhad
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Pressure Gradient ◽  
Magnetic Field Strength ◽  
Magnetic Pressure ◽  
Gas Pressure ◽  
Accretion Flow ◽  
Accretion Flows ◽  
Black Hole Accretion ◽  
The Magnetic Field

Context. Observations indicate that wind can be generated in hot accretion flow. Wind generated from weakly magnetized accretion flow has been studied. However, the properties of wind generated from strongly magnetized hot accretion flow have not been studied. Aims. In this paper, we study the properties of wind generated from both weakly and strongly magnetized accretion flow. We focus on how the magnetic field strength affects the wind properties. Methods. We solve steady-state two-dimensional magnetohydrodynamic equations of black hole accretion in the presence of a largescale magnetic field. We assume self-similarity in radial direction. The magnetic field is assumed to be evenly symmetric with the equatorial plane. Results. We find that wind exists in both weakly and strongly magnetized accretion flows. When the magnetic field is weak (magnetic pressure is more than two orders of magnitude smaller than gas pressure), wind is driven by gas pressure gradient and centrifugal forces. When the magnetic field is strong (magnetic pressure is slightly smaller than gas pressure), wind is driven by gas pressure gradient and magnetic pressure gradient forces. The power of wind in the strongly magnetized case is just slightly larger than that in the weakly magnetized case. The power of wind lies in a range PW ~ 10−4–10−3 Ṁinc2, with Ṁin and c being mass inflow rate and speed of light, respectively. The possible role of wind in active galactic nuclei feedback is briefly discussed.

scholarly journals Hydromagnetic dynamos in rotating spherical fluid shells in dependence on the Prandtl number, density stratification and electromagnetic boundary conditions

2014 ◽  
Vol 44 (4) ◽  
pp. 293-312 ◽  
Author(s):  
Tomáš Šoltis ◽  
Ján Šimkanin
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Magnetic Fields ◽  
Prandtl Number ◽  
Inner Core ◽  
Polar Regions ◽  
Number Density ◽  
Magnetic Diffusion ◽  
Spherical Fluid ◽  
The Magnetic Field

Abstract We present an investigation of dynamo in a simultaneous dependence on the non-uniform stratification, electrical conductivity of the inner core and the Prandtl number. Computations are performed using the MAG dynamo code. In all the investigated cases, the generated magnetic fields are dipolar. Our results show that the dynamos, especially magnetic field structures, are independent in our investigated cases on the electrical conductivity of the inner core. This is in agreement with results obtained in previous analyses. The influence of non-uniform stratification is for our parameters weak, which is understandable because most of the shell is unstably stratified, and the stably stratified region is only a thin layer near the CMB. The teleconvection is not observed in our study. However, the influence of the Prandtl number is strong. The generated magnetic fields do not become weak in the polar regions because the magnetic field inside the tangent cylinder is always regenerated due to the weak magnetic diffusion.

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