Melt Height Research Articles

Modeling the Impact of Varying Levels of Inclusion Adhesion on Deposition in a Pilot‐Scale Nozzle

The deposition and accumulation of inclusions is the dominant mechanism in nozzle clogging of the submerged entry nozzle. Previous modeling attempts of inclusion deposition have assumed that any contact between the inclusion and nozzle wall results in adhesion. Herein, an Eulerian–Lagrangian simulation with a stochastic adhesion model is used to study the effects of different inclusion‐wall sticking probability (Swall) on inclusion deposition. The results indicate that inclusion deposition is affected by both melt height and Swall. Lower melt heights result in increased deposition deeper into the nozzle and greater maximum particle area number density. The effect of Swall on the global deposition ratio can be divided into two regimes. When Swall increases from 0–0.05, there is a rapid rise in the global deposition ratio. When Swall > 0.05, the global deposition ratio increases only modestly with Swall. Changes to Swall also affect the location of deposition. When Swall decreases, the high and mid cases show greater relative deposition in the cone and taper sections of the nozzle, while the low melt height case shows greater relative deposition in the straight section of the nozzle.

Дослідження розподілу кисню по довжині монокристалів кремнію, легованих компонентами з різним типом провідності

The purpose of the article is the study of convective flows and their influence on the growth of single crystals of silicon by the Czochralsky method from a large melt, which contributes to the emergence of non-stationary convection. Therefore, simulation of convection for the growth of silicon single crystals is an important step in the development of conditions for the growth of perfect single crystals. Silicon substrates are used to manufacture more than 90% of semiconductor devices and solar cells. A special role in the development of electronics is played by monocrystalline silicon, which is used for the manufacture of semiconductor devices and integrated microcircuits. The main requirements for the development of technology for the production of silicon substrates is an increase in quality at a decrease in cost. Promising technologies of 10-nm size and 3D-transistor structures significantly increase the requirements for uniformity of distribution of components, including layering in silicon single crystals. For the mathematical modeling of convective flows, melt flows were considered for a cylindrical crucible with a radius of 150 mm at a melt height of up to 40 mm. Such parameters ensure stationary convection in molten silicon. Methods of reducing stratification have been studied and developed for more than 50 years, but have not yet found a definitive solution. This method of single crystal growth is the most controlled and allows to influence the convective flows in the silicon melt below the phase interface with ultrasonic waves in the megahertz range. The effectiveness of using ultrasound in the extraction of semiconductor single crystals depends on the creation of special conditions for introducing them into the melt. 
 Reducing the influence of oxygen on the electrophysical properties of silicon single crystals is an intractable problem of silicon technology. One of the ways to solve this problem is alloying with an isomorphic impurity, for example, tin. The development of a method of doping single crystals of silicon with tin requires determination of its concentration in the liquid and solid phases

Studies on the melting dynamics of PCM in a semicircular cavity with straight and wavy heating surfaces

Several kinds of curved confinements for phase changing material storages are found application in natural systems, latent heat storages, metal furnaces, and thermal control devices. Semi-circular enclosures have an inherent advantage of decreasing unmelt volume on top with an increase in melt height when heated from bottom. Hence the melt dynamics differs from conventional rectangular enclosures of similar orientation and realizes faster thermal response during the entire regimes of melting. Experimental and numerical studies on Rayleigh Benard convection in a semi-circular enclosure having straight, corrugated, and wavy bottom surface with constant heat flux conditions are presented. Melt front evolution, thermal convection, and unsteady surface heat transfer characteristics of a phase changing material contained in a semicircular confinement are presented in this study. Enthalpy-porosity method based finite volume solver is used to simulate the unsteady thermal convection of PCM in semi-circular enclosure. Experimental thermal response at various locations inside the confinement and shadowgraph images are used to verify the numerical results quantitatively and qualitatively. Present results and correlations (103 < Ra < 109) are useful in design, analysis, and thermal characterization of PCM enclosures of minimum volume and better thermal response finding application in electronic cooling devices and latent energy storages.

Effect of laser welding and laser wire filling on forming and properties of dissimilar steel welded joints

In order to study the effects of different welding methods and different butt gaps on the microstructure and properties of welded joints of steel with unequal thickness, the medium carbon steel of 2 mm 50CrV and low carbon steel of 6 mm SPHE were used as test materials, and the welding was carried out by single laser and laser wire filling welding. The results show that the laser wire filling welding can reduce the welding cracks, and with the increase of the butt gap, the melt height gradually decreases, and the weld morphology transitions from Y shape to H shape. With the increase of the butt gap, the weld defects form. The hardness of weld center decreases with the increase of butt gap. The average hardness of weld formed by laser welding alone is the highest, and the highest hardness of welded joint is located in the heat affected zone of 50CrV medium carbon steel. The tensile strength of welded joints first increases and then decreases with the increase of butt gaps. When the butt gap is 0.6 mm, the surface morphology is good and the tensile strength is the highest. The fracture position of the welding test is on the side of the 2 mm 50CrV medium carbon steel.

Asymmetric PCM melting and thermal convection in a rectangular enclosure with straight and wavy heat transfer passages

Experimental and numerical investigations of thermal convection in the vicinity of a straight and wavy horizontal heat transfer fluid passage (HTF)s placed in a rectangular enclosure filled with phase change material (PCM) are presented. The enthalpy-porosity-based finite volume solver is used to simulate the spatiotemporal evolution of the thermal convection, which is well-complemented by experimental visualization and thermocouple measurements. Heat transfer from the horizontal HTF exhibits asymmetrical melting. Heat diffusion is the dominating energy transfer mechanism on the bottom part of the HTF passage and is compared with the Stefan problem. The temporal evolution of thermal convection on the top part of HTF passage involves three distinct phases of melting, viz. initial conduction phase, Rayleigh–Bénard (R-B) convection with linear convection, and vortex coalescence effects. The final stage of the melting process is influenced by the topography of a peninsula of unmelt PCM, which is influenced by specific top-boundary conditions. Thermal convection in PCM above the wavy HTF passage exhibits restricted plume development leading to an improved melting rate and a higher average melt height. Augmentation of internal convection characteristics of HTF with the evolution of melting is also explored. A systematic investigation of the convection plume development and heat transfer characteristics in PCM by varying the HTF Reynolds (1700<Re<2750) and Stefan numbers (0.4<Ste<0.6) has been carried out, and analyzed the nature of thermal plumes, melt fraction, and average penetration length with the Fourier number. Additionally, novel correlations are proposed between Nusselt and Rayleigh numbers for straight and wavy tubes in the intermediate melting stage (1.3×104<Ra<4.7×107).

Enhancing molten tin methane pyrolysis performance for hydrogen and carbon production in a hybrid solar/electric bubbling reactor

Methane pyrolysis in liquid metals is a worth-developing process for CO2-free hydrogen production. This study investigates methane pyrolysis in molten tin and highlights the impact of several parameters on methane conversion (XCH4) in a novel hybrid solar/electric bubbling reactor. Temperature (1200–1300 °C), total inlet gas flow rate (Q0 = 0.25–0.5 NL/min), melt height (Him = 60-120-235 mm) and hybridization are addressed. Increasing the temperature from 1200 °C to 1300 °C (Q0 = 0.25 NL/min and Him = 120 mm) improves XCH4 (32% vs. 69%). Increasing Q0 from 0.25 to 0.5 NL/min (T = 1200 °C and Him = 120 mm) reduces XCH4 (19% vs. 9%). Doubling the melt height (Him from 60 to 120 mm) increases the residence time of bubbles, which increases XCH4 (7% vs. 19%). A customized sparger is also tested and shows little effect, probably because the holes are relatively large (1 mm diameter). An immersed bed of steel particles (0.2–0.4 mm diameter) instead shows improved results (XCH4 = 32%) at a relatively low temperature (1100 °C). Continuous reactor operation at 1300 °C without clogging is also confirmed. Analysis of carbon accumulated at melt surface during molten media methane pyrolysis reveals a tin-containing sheet-like structure.

An analytical investigation on characterizing the properties of glass composition for crystalline silicon solar cells based on the digital microsystem measurement technology

As a significant component of silver paste, glass frit has a nonnegligible effect on crystalline silicon solar cells. The purpose of this research is to obtain an analysis method to explore the performance of glass frit for solar cells. The samples were measured by digital microscopic system, and the three-dimensional layered tinting model was established. Moreover, the longitudinal cutting was carried out. The data of cross section was analyzed to obtain the information of melt height, wetting base angle, and melting included angle, to further infer the relationship between thermal stability, fluidity, wettability with mathematical model of glass frit through theoretical derivation. The curve fitting method was introduced in detail and the law was summarized. Based on relationship of them, the melting characteristics of glass frit could be quantitatively tested. The vertical view and surface topography were measured by the digital microscope and found that the glass frit underwent shrinkage, softening, wetting, spreading, and equilibrium during sintering. Combined with the image, abundant information was detected from the macroscopic structure of glass surface. Meanwhile, the mechanism of spreading was explained. Finally, the screen-printing technology combined with the 3D microscopic view of the silver grid line proved that glass frit with satisfactory performance can effectively reduce the contact resistance of solar cells, improve the photovoltaic conversion efficiency, verify the feasibility and accuracy of the simulation method equally. This study not only enriches the understanding of glass frit for crystalline silicon solar cells, but also provides a theoretical guidance for the research and determination of its performance. • Digital microscope system was used to record the shape changes of glass samples and more wetting parameters. • This investigation used a combination of mathematical simulation and physical simulation. • The essence of the technology to characterize glass is to combine the fixed droplet technology with optical measurement.

Physically-based, lumped-parameter models for the prediction of oxygen concentration during Czochralski growth of silicon crystals

Lumped-parameter models are derived from boundary layer and other physical arguments to describe oxygen concentration levels during the Czochralski (CZ) growth of silicon. These models are assessed against predictions from a detailed, high-fidelity 2D-3D numerical simulation of the entire CZ puller, whose solutions are realistic but require intense computational effort. Comparisons of predictions show that the lumped-parameter model captures the correct trends of melt oxygen levels influenced by melt height, crucible rotation, and crystal rotation. A simple fitting of coefficients provides reasonably good quantitative predictions by the lumped-parameter model, and its near-instantaneous computations make it an interesting candidate for real-time growth optimization and control. Possible model improvements and extensions are discussed.

Criteria for the onset of convection in the phase-change Rayleigh–Bénard system with moving melting-boundary

Here, for the first time, we report the criterion for the onset of convection in a low Prandtl number phase-change Rayleigh–Bénard (RB) system with an upward moving melt interface in a two-dimensional square box for a wide range of Rayleigh number Ra and Stefan number Ste (defined as the ratio between the sensible heat to the latent heat). High fidelity simulations were performed to study the phenomenon of the onset of convection. Unlike the classical RB system in the phase-change RB system, it was found that the onset of convection depended on Ste and Fourier number τ, in addition to Ra. The phase-change RB system with upward moving melt interface can be classified into two groups: slow expanding phase-change RB system (Ra ≤ 104) and moderate/fast melting phase-change RB system (Ra &amp;gt; 104). The slow melting phase-change RB system becomes unstable when the effective Rayleigh number based on the melt height is ≈1295.78, consistent with the finding by Vasil and Proctor [“Dynamic bifurcations and pattern formation in melting-boundary convection,” J. Fluid Mech. 686, 77 (2011)]; however, moderate and fast melting phase-change RB systems become unstable when the product of the local Rayleigh number Ra based on the melt-layer height hyt and the Fourier number based on the melt-layer height reaches a threshold value. Interestingly, it is seen that the criteria for the onset of convection for moderate and fast melting phase-change RB systems show a power law kind of form such that Racrτcr = aSteb + c. In addition, during the initial conduction regime before the onset of convection, it is seen that the Nusselt number at the hot wall is Nuh ∼ τ0.5, and during the onset of convection, i.e., during the formation of the initial convection rolls, the Nusselt number at the hot wall is Nuh ∼ τd, where the value of the exponent d is 2 for low Rayleigh numbers and 4 for higher Rayleigh numbers. This study reports some general characteristics of the onset of convection and some organized behavior in the transient melting phase-change RB system, which are not yet explored and reported in the open literature. This work may lead to significant understanding of different applications of fluid-dynamical melting phase-change RB systems in both natural and engineering systems.

Slag eye formation in single and dual bottom purged industrial steelmaking ladles

ABSTRACTArgon gas is often injected from the bottom of the ladle during steel refining operations. The injected gas interacts with the liquid (metal and slag) bath and enhances the momentum, heat, and mass transfer rate in the melt. However, during these gas–liquid interactions, an opening of the slag layer called slag eye is formed, which exposes the molten metal surface to the atmosphere, which is generally undesirable. In the current work, a transient, three-dimensional mathematical model is used to study the turbulent gas–liquid interactions in single as well as dual bottom blown industrial steelmaking ladles. A Coupled Level Set Volume of Fluid (CLSVOF) model is used for tracking the steel-argon, steel-slag, and argon-slag interfaces, from which the slag-eye area has been predicted. It is found that the inlet gas purging rate, melt height, slag layer thickness, angular and radial positions of the gas inlets affect the slag opening area. Non-dimensional empirical correlations are proposed to predict the slag opening area in both single as well as dual purged ladles, using non-linear regression analysis.

Directional solidification of gallium under time-dependent magnetic fields with in situ measurements of the melt flow and the solid-liquid interface

The results of solidification experiments with gallium in a square-based 220 × 220 mm2 container under the influence of alternating and travelling magnetic fields are presented. Such experiments are relevant for the growth of multi-crystalline silicon ingots for solar cells using directional solidification. The time-dependent magnetic fields are generated by a system of two inductors supplied with alternating current. The axial temperature field for solidification is established by thermostat-controlled heat exchangers at the top and the bottom of the container. A new approach for a reproducible directional solidification process using a special seeding technique is presented. The melt flow and interface positions are measured in-situ during solidification by using ultrasound sensor arrays for a 2D flow mapping, and single ultrasound transducers for interface detection. The experiments reveal significant changes of the flow structure and the interface shape with decreasing melt height. The results are compared with numerical simulation and a setup-independent categorization of the observed flow structures is proposed. Conclusions for silicon growth processes are discussed.

Possible causes of electrical resistivity distribution inhomogeneity in Czochralski grown single crystal silicon

Electrical resistivity distribution maps have been constructed for single crystal silicon wafers cut out of different parts of Czochralski grown ingots. The general inhomogeneity of the wafers has proven to be relatively high, the resistivity scatter reaching 1–3 %. Two electrical resistivity distribution inhomogeneity types have been revealed: azimuthal and radial. Experiments have been carried out for crystal growth from transparent simulating fluids with hydrodynamic and thermophysical parameters close to those for Czochralski growth of silicon single crystals. We show that a possible cause of azimuthal electrical resistivity distribution inhomogeneity is the swirl-like structure of the melt under the crystallization front (CF), while a possible cause of radial electrical resistivity distribution inhomogeneity is the CF curvature. In a specific range of the Grashof, Marangoni and Reynolds numbers which depend on the ratio of melt height and growing crystal radius, a system of well-developed radially oriented swirls may emerge under the rotating CF. In the absence of such swirls the melt is displaced from under the crystallization front in a homogeneous manner to form thermal and concentration boundary layers which are homogeneous in azimuthal direction but have clear radial inhomogeneity. Once swirls emerge the melt is displaced from the center to the periphery, and simultaneous fluid motion in azimuthal direction occurs. The overall melt motion becomes helical as a result. The number of swirls (two to ten) agrees with the number of azimuthally directed electrical resistivity distribution inhomogeneities observed in the experiments. Comparison of numerical simulation results in a wide range of Prandtl numbers with the experimental data suggests that the phenomena observed in transparent fluids are universal and can be used for theoretical interpretation of imperfections in silicon single crystals.

Determination of the particle content in laser melt injected tracks

Surfaces of machine parts or tools are subjected to corrosive stresses or wear. To increase the wear resistance of surfaces, metal matrix composite (MMC) can be applied. For higher wear resistance, it is important to achieve a high particle content and a homogenous particle distribution. In this work, aluminium bronze substrate was reinforced by spherical fused tungsten carbides via laser melt injection. The laser power, travel speed and powder mass flow were varied. The influence of these process parameters on the hard particle content was investigated in single tracks. Furthermore, laser melting and laser melt injecting were compared. Laser melt injecting resulted in a significant increase in the track volume. Analytical calculation showed that the volume increase was higher than the volume of the injected particles. Single tracks composed of MMC could be produced without cracks and pores. Depending on the energy input per unit length, undesired melting of the particles was observed. The particle content was investigated via binary pictures from metallographic cross-sections using two different software packages. An approach to calculate the particle content as a function of the width, depth and height of laser melt injected tracks via circle segments is presented.

Three-dimensional experiment of heat transfer for molten oxidic pool

The effectiveness of in-vessel retention (IVR) of core melt during severe accident in light water reactor strongly depends on whether the heat removed from boundaries could exceed the heat generated in the molten pool in lower head of reactor pressure vessel (RPV). Natural convection in the oxidic pool plays a key role in determining the heat transfer behavior inside the molten pool. A Molten pool Oxide-layer heat tRaNsfer experiment (MORN) facility was built to investigate the heat transfer characteristic of the molten oxidic pool with the intention to verify the heat transfer correlation of the pool. The test facility consists of a three dimensional hemisphere test section with an inner radius of 0.4 m. The outer boundary of the test section could be cooled by different methods (radiation or convection), so as to study the influence of external cooling condition on the crust formation of oxidic pool. Three kinds of material have been chosen as the simulants. They are water, NaNO3/KNO3(mole ratio 1:4) and a non-eutectic binary mixture of calcium-boron oxide (30 wt%CaO-70 wt%B2O3) respectively. At first period, several water and salt experiments with the melt height of 340 mm were performed and the data were analyzed. Though the normalized temperature distribution of the pool was nearly the same between water and salt experiments, the heat flux across the side wall differed much. The heat flux distribution of the water experiment rose nearly linearly with polar angle till to the melt surface. The heat flux of salt experiment at the low angle was larger than that of water, decreased slightly with angle increasing and then rose quickly till to the melt surface. This is consistent with the LIVE and COPRA experiments with the same boundary condition. The maximum normalized heat flux of the water experiment was approximate 1.6 and that of the salt experiment was about 2.2. The downward heat transfer of MORN is smaller than the correlation derived by COPO, mini-ACOPO and BALI experiments, but is consistent as LIVE, COPRA experiment.

Dimensionless parameters controlling fluid flow in electromagnetic cold crucible

A 3-D numerical model was established for predicting the flow field in a square electromagnetic cold crucible (EMCC) used for melting and directionally solidifying TiAl alloys. Four dimensionless parameters that characterise the melt flow in the EMCC were derived, those being the Hartman (Ha), magnetic Reynolds (Rω), coils-melt position (h) and the ratio of the melt height to length (H/L) numbers. Parametric simulations and experiments were carried out to understand the effects of processing parameters such as the intensity and frequency of the current, the relative coils-melt position and the melt shape on the flow field. The meridional flow normally consists of two vortices in the half meridian plane, the lower vortex decreases with increasing Ha, Rω and h (hb>hm), as well as decreasing H/L. Higher Ha, H/L and lower h induce intensive fluid flow in the melt due to the stronger EM coupling, which could promote the uniformity of solute in the melt. The turbulence kinetic energy is significantly influenced by the length scale of the turbulent flow and the flow velocity in the melt, it increases with increasing Ha, h and H/L, while reduces and tends to be stable at higher Rω. Relatively higher flow velocity and turbulence kinetic energy can be obtained when Rω is close to 10. The weakened flow in the vicinity of solid/liquid interface under lower Ha and Rω, as well as higher h and H/L is beneficial for continuous growth of columnar crystals during the directional solidification process.

Dominant dimensionless parameters controlling solute transfer during electromagnetic cold crucible melting and directional solidifying TiAl alloys

Electromagnetic cold crucible (EMCC) is widely applied to melt and solidify refractory and reactive materials, the electromagnetically driven flow in the melt leads to intensive transfer behaviors of solute and strongly affects crystal growth. In this paper, a 3-D numerical model for predicting the solute transfer behaviors in a square EMCC used for melting and directional solidifying was established and verified. A two-way coupling method was proposed to calculate the electromagnetically driven flow and its effects on solute transfer. Influences of the dominant dimensionless parameters on solute transfer behaviors in the EMCC were examined, those being the Hartman (Ha), magnetic Reynolds (Rω), coils-melt position (h) and the ratio of the melt height to length (H/L) numbers. Results demonstrate that the solute segregation tends to appear in the vicinity of solid/liquid (S/L) interface, the top of meniscus and the confluence of two eddies near the wall of meniscus. The solute segregation degree (Se=Cmax−CminC0) decreases with increasing Ha, which contributes to the augment of flow intensity in the melt. Moreover, the Se decreases linearly with increasing Rω owing to the intensive oscillation of melt flow. The enhanced EM coupling with increasing H/L results in the decrease of Se in the melt. However, the solute segregation in the corner of the meniscus gradually aggravates with increasing h, which results from the enlarging of lower eddies in the bulk of the melt. The solute segregation in the vicinity of S/L interface is strongly influenced by the scale and the flow intensity of lower eddies, which could change the phase transition path and morphology of crystal during directional solidification process. Larger value of Ha, Rω and H/L, as well as smaller h are beneficial to alleviate the solute segregation in the vicinity of S/L interface.

Fabrication of High-Porosity Lotus-Type Porous Aluminum in Vacuum

Lotus-type porous aluminums with porosities from 10 to 26 pct were fabricated with the Bridgman-type directional solidification method (Gasar). A vacuum atmosphere is critical to obtain high-porosity lotus-type porous aluminum by the Gasar process. The lotus-type porous aluminum was directionally solidified under a pure hydrogen pressure of 0.2 to 16 kPa. The influence of hydrogen pressure on the porosity and pore size in vacuum was investigated. The porosity and pore size increase with decreasing hydrogen pressure, but there exists a maximum porosity at some critical hydrogen pressure. Since a low hydrogen pressure is adopted, the effect of capillary pressure and hydrostatic pressure on the porosity becomes important. With the decreasing of hydrogen pressure, the influence of hydrostatic pressure and capillary pressure on porosity becomes stronger and stronger. The influence of melt height, which is proportional hydrostatic pressure, on porosity and pore size was investigated. The calculated porosities considering capillary pressure and hydrostatic pressure are in good agreement with experimental results.

Levoglucosan on Tibetan glaciers under different atmospheric circulations

Tibetan glaciers are natural documents of the specific biomass burning biomarker levoglucosan from regions around. However, knowledge about the characteristics of levoglucosan distributions on Tibetan glaciers under the different climate systems is poorly understood. In this study, we detected levoglucosan in snow samples from the Zuoqiupu (ZQP) Glacier affected by the Indian summer monsoon and the Muji (MJ) Glacier dominated by the westerlies. Results found that the ZQP Glacier was more heavily affected by fire emissions than the MJ Glacier, caused by stronger emission sources on the windward direction and shorter transport distances. Elevations for the appearance of levoglucosan maxima on glacier surfaces are roughly around the equilibrium line altitudes. However, levoglucosan displays a wider distribution range on the MJ glacier than on the ZQP glacier due to weaker summer melt. Injection height of fire smokes and glacial melt can affect the altitudinal distribution of levoglucosan. Black carbon and levoglucosan show different temporal variations in snow-pit samples on those two glaciers. The post-depositional effects, e.g. the melting and refreezing processes, can modulate the vertical distribution of levoglucosan in snow/ice layers. Our results are helpful for understanding the geochemical behaviors of levoglucosan happened on Tibetan glacier surfaces.

Low Melt Height Solidification of Superalloys

Effect of a reduced melt height in the directional solidification of a superalloy has been investigated by two methods: vertical Bridgman (VB) and vertical Bridgman with a submerged baffle (VBSB). The latter is a relatively new technique and provides a reduced melt height ahead of the solidifying interface. A low melt height leads to a larger primary dendrite arm spacing but a lower mushy length, melt-back transition length, and porosity. The VBSB technique yields up to 38 pct reduction in the porosity. This may improve a component’s mechanical strength especially in a creep-fatigue type dynamic loading.

Growing Single Crystals with a Low Melt Height and an Axial Vibration

Single crystal growth of antimony-doped germanium is investigated by the vertical Bridgman (VB), axial heat processing (AHP), and axial vibrational control (AVC) methods. In the VB method, the existence of a radial temperature gradient in the melt leads to an inhomogeneous solute distribution which affects the quality of the grown crystal. However, in the AHP growth, the melt height above the interface and the radial temperature gradient in the melt can be reduced by immersing a baffle with a high thermal conductivity. Consequently, the radial solute segregation can be reduced. In order to provide even a better solute homogeneity, the immersed baffle can be vibrated axially which forms the AVC growth. Seven Sb-doped Ge crystals are grown with the three mentioned methods in order to investigate the effect of the melt height, the pulling velocity, and amplitude and frequency of the vibration on the homogeneity of the solute distribution, the achieved single crystal length, the morphological stability, and t...