Directional Solidification Process Research Articles

Effects of the hot zone design during the growth of large size multi-crystalline silicon ingots by the seeded directional solidification process

In this study, the installation of insulation blocks in the hot zone is utilized to assist in the growth of multi-crystalline silicon ingots with 800kg of silicon charge using the seeded directional solidification method. A transient global numerical simulation is carried out to investigate the heat and mass transport during growth process. At a higher solidification fraction, lower concavity of the crystal–melt interface near the crucible wall can be obtained as compared to the standard model. The lowest concavity and highest energy saving is achieved when insulation blocks are added to the side of a directional solidification block and to the low part of the side insulation. The simulation results for this design also show a reduction of the melt velocity. The average oxygen concentration is slightly higher along the crystal–melt interface, compared to the standard one.

Influence of Crucible Thermal Conductivity on Crystal Growth in an Industrial Directional Solidification Process for Silicon Ingots

We carried out transient global simulations of heating, melting, growing, annealing, and cooling stages for an industrial directional solidification (DS) process for silicon ingots. The crucible thermal conductivity is varied in a reasonable range to investigate its influence on the global heat transfer and silicon crystal growth. It is found that the crucible plays an important role in heat transfer, and therefore its thermal conductivity can influence the crystal growth significantly in the entire DS process. Increasing the crucible thermal conductivity can shorten the time for melting of silicon feedstock and growing of silicon crystal significantly, and therefore large thermal conductivity is helpful in saving both production time and power energy. However, the high temperature gradient in the silicon ingots and the locally concave melt-crystal interface shape for large crucible thermal conductivity indicate that high thermal stress and dislocation propagation are likely to occur during both growing and annealing stages. Based on the numerical simulations, some discussions on designing and choosing the crucible thermal conductivity are presented.

Simulation of liquid channel of Fe-C alloy directional solidification by phase-field method

In directional solidification, two characteristic parameters determine the dendritic growth: the thermal gradient and the pulling velocity. To achieve the suitable microstructure and improve the performance of casting, they are usually used to resize the pulling velocity or temperature gradient in directional solidification process. The structures obtained under different directional solidification conditions, and their associated properties both have been hot research points. It is difficult to observe the microstructure, which is usually on a micrometer scale, directly in experiment, and the phase-field method becomes a strong tool to understand the dendrite growth pattern. We mainly study the liquid channel formed after Fe-C alloy dendrite tip splitting under the specific condition of directional solidification and analyze the influence on liquid channel of pulling velocity in this paper. We choose the fixed thermal gradient G =20 K/mm which is on the order of the experimental value, and pulling velocity VP no more than 10 mm/s to keep the cooling rate in the range of low speed in dendrite growth, so that the interface kinetic effect can be neglected. Recent experimental results show the different interfacial energies in various compositions of Al-Zn alloy and Fe-C alloy, then we can investigate a series of directional solidification microstructures with fixed alloy Fe-0.5 wt.%C composition at different interfacial energies in our simulations. We find that the liquid channel is formed as a result of anisotropy competition between system and materials, the length and C concentration of liquid channel increase with the pulling velocity increasing, while the diameter of liquid channel is constant. It is interesting to find that there is a minimum of pulling velocity almost equal to 1 mm/s, the tip will not split and no liquid channel forms in the following steps either when the velocity is smaller than the minimum. We also compare the segregation caused by solute enrichment in liquid channel and solute segregation between dendrite arms in a series of simulations: the former is more serious than the latter. Then we point out the way to reduce the segregation caused by liquid phase channel by reducing the pulling velocity properly. It will be more practical to couple the flow field with other external field, such as magnetic field, in the simulation.

A mathematical model for distribution of calcium in silicon by vacuum directional solidification

Calcium is one of the main impurity elements in silicon. The removal of calcium strongly affects the quality of the polycrystalline silicon ingot produced by a vacuum directional solidification method. Based on the considerations of the theory of segregation, mass transfer and evaporation during vacuum directional solidification process, a mathematical model for calcium distribution in silicon was proposed and it can be used to explain the removal mechanism. In order to confirm the mathematical model, an industrial scale experiment on UMG-Si with an initial purity of 99.98 wt. % was performed. Since the reaction temperature strongly influences both the evaporation and segregation of calcium, the dependences of effective segregation coefficient (keff) and the evaporation coefficient (kE) on temperature were carefully investigated. The results showed that the proposed mathematical model was highly consistent with the experimental data and the calcium removal efficiency mainly relied on the evaporation step.

Complex banded structures in directional solidification processes

A combination of theory and numerical simulation is used to investigate impurity superstructures that form in rapid directional solidification (RDS) processes in the presence of a temperature gradient and a pulling velocity with an oscillatory component. Based on a capillary wave model, we show that the RDS processes are associated with a rich morphology of banded structures, including frequency locking and the transition to chaos.

Effect of alternating magnetic field on the removal of metal impurities in silicon ingot by directional solidification

Multicrystalline silicon ingots without and with alternating magnetic field during directional solidification process under industrial system were obtained from metallurgical grade silicon (MG-Si). The concentrations and normalized concentrations of metal impurities in the two silicon ingots were studied. The result shows that the concentrations and normalized concentrations in high-purity area of the silicon with alternating magnetic field are lower than those of the ingot without alternating magnetic field. The transport mechanism for metal atoms in the diffusion layer area has been changed due to the alternating magnetic field. Alternating magnetic field introduces a convection to reduce the thickness of diffusion layer in the molten silicon, which results in a decreased effective segregation coefficients. Enhancing transport driving force of metal atoms in molten silicon is the effective way to improve the removal rate of metal impurities.

The effects of microstructure and growth rate on microhardness, tensile strength, and electrical resistivity for directionally solidified Al–Ni–Fe alloys

Directional solidification of eutectic alloys attracts considerable attention because of microhardness, tensile strength, and electrical resistivity influenced by eutectic structures. In this research, we examined processing of Al–Ni–Fe (Al–6.5wt.%Ni–1.5wt.%Fe) eutectic by directional solidification. The alloy was prepared by vacuum furnace and directionally solidified in Bridgman-type equipment. During the directional solidification process, the growth rates utilized varied from 8.25 μm/s to 164.80 μm/s. The Al–Ni–Fe system showed a eutectic transformation, which resulted in the matrix Al, rod Al3Ni, and plates Al9NiFe phases. The eutectic spacing between (λAl3Ni−λAl3Ni,λAl9NiFe−λAl9NiFe)was measured. Additionally, the microhardness, tensile strength, and electrical resistivity of the alloy were determined using directionally solidified samples. The effects of growth rates on microhardness, tensile strength, and electrical resistivity for directionally solidified Al–Ni–Fe eutectic alloy were investigated, and the relationships between them were experimentally obtained. It was found that the microhardness, tensile strength, and electrical resistivity were affected by both eutectic spacing and the solidification parameter.

The effect of radiative heat transfer characteristics on vacuum directional solidification process of multicrystalline silicon in the vertical Bridgman system

In the vertical Bridgman system for multicrystalline silicon vacuum directional solidification process, the radiation heat transfer characteristics have a significant impact on the quality of crystal growth. In this paper, the effect of heat transfer characteristics under different pulling-down rates on the vacuum directional solidification process was investigated. Simplified radiation view factor dependent on pulling-down rate in pilot-scale vertical Bridgman system was derived. Combined with the transient simulation results, we obtained the heat transfer characteristics inside the furnace, and proposed the optimization scheme by using a rate of slowly first and then faster to pull down the crucible, which can not only satisfy thermal conditions of crystal growth, but also shorten the solidification time and effectively reduce the energy consumption. In addition, according to the characteristics of the radiative heat transfer under vacuum condition and the change of view factor, it was found that an improved design by widening the cold zone of the furnace can narrow the temperature gradient in the silicon ingot, and greatly decrease the thermal stresses, which in turn can aid in the design of future industrial equipment and process improvements.

Investigation of liquid oxide interactions with refractory substrates via sessile drop method

The wetting of refractory substrates by oxide alloys has been investigated using a high-temperature sessile drop bench. The aim of this study was to select the best crucible material for directional solidification processes such as the Bridgman, edge-defined film-fed growth or micro-pulling down methods. Contact angles and surface tension were determined via high-resolution imaging. The O2 partial pressure in the furnace atmosphere was also measured. Alumina and a eutectic ceramic called A/YAG/Z (Al2O3/Y3Al5O12/ZrO2) were studied by investigating the following systems: alumina/molybdenum, alumina/tungsten and alumina/iridium; A/YAG/Z–molybdenum, A/YAG/Z–tungsten and A/YAG/Z–iridium. The results show intermediate wetting for both oxides (30° < θ <50°). This is an original result for A/YAG/Z. Several previous studies reported good wetting (7° < θ <20°) for alumina. Accurate surface tension values could not be obtained by image processing. Therefore, the Wilhelmy method was used, giving γ = 0.63 ± 0.03 N m−1 for alumina, which is comparable to the value of 0.67 ± 0.03 N m−1 reported in the literature. The surface tension obtained for A/YAG/Z was 0.71 N m−1, but this value was influenced by the approximate density used. A metal-like layer was observed on the apex of the drops after solidification. According to an SEM–EDS analysis, most of these layers were composed of molybdenum, tungsten and oxygen. Based on thermodynamic calculations, a mechanism which takes into account the oxidation of Mo parts and the dissolution of oxides in the drop is proposed.

Crystal orientation control in TiAl–Nb alloys through a double directional solidification process

Intermetallic Ti–46Al–5Nb (at.%) alloys were directionally solidified by single directional solidification (SDS) process and double directional solidification (DDS) process using a Bridgman directional solidification furnace. Microstructure and crystal orientation neighboring the initial growth interface as well as the quenched mushy zone before starting directional solidification were investigated in the SDS and DDS processes, respectively. The results show that the dendrite morphology changes from equiaxial to columnar, but the directional dendrite segregation is almost keep the continuity across the initial growth interface after SDS and DDS processes, respectively. Crystal orientations in the regions neighboring the initial growth interface have preferential modifications along the growth direction. Compared with that in the first DS of DDS, the length of the initial mushy zone significantly decreases, but the β dendrite is well-orientated in the mushy zone in the second DS. Crystal orientation can be well-controlled in DDS by modifying the β growth morphology as well as the orientation in initial mushy zone of the two DS processes. The directional dendrite parallel to the growth direction and the preferred β orientation are considered as the main reasons to β seed crystallization. The process of the β seed crystallization is also discussed. Based on the β seeding, the DDS process can align the β dendrite orientation and promote the peritectic transformation undergoing completely, thus control the lamellar colony boundaries as well as the lamellar microstructures inside of the colonies.

Influence of the Size Effect on the Microstructures of the DWDS- and Bridgman-Solidified Single-Crystal CMSX-4 Superalloy

To evaluate the potential benefits of utilizing the downward directional solidification process (DWDS) for controlling the homogeneity of microstructures, single-crystal CMSX-4 superalloy bars having different sizes of cross sections have been directionally solidified at a withdrawal rate of 1 mm/min using the DWDS and Bridgman processes. By varying the sizes of the cross sections, the DWDS process demonstrated higher thermal gradients, with smaller microstructural variations. The higher and more uniform thermal gradients not only refined the microstructures but also improved the microstructural homogeneity. In contrast to this, the Bridgman cast bars exhibited large-sized pores and a high volume of microporosity regardless of the cross-sectional size.

Nitride bonded silicon nitride as a reusable crucible material for directional solidification of silicon

Nitride bonded silicon nitride (NBSN) has the potential of a reusable crucible material for directional solidification of silicon. This is demonstrated in this work by reusing a NBSN crucible six times for the directional solidification of undoped multicrystalline (mc) silicon ingots. The progress of the ingot contamination at subsequent use of the NBSN crucible was studied systematically. Minority carrier lifetime, electrical resistivity as well as impurity content were analyzed after each solidification run. The results were compared to those obtained from ingots which were crystallized by using identical directional solidification process parameters in standard fused silica crucibles with silicon nitride coating. The impurity content of the ingots can be clearly correlated to the impurity content of the NBSN crucible. The main impurity is the acceptor B. Its concentration in the ingots decreases from about 1017 atoms/cm3 to 1016 atoms/cm3 with continued reuse. The contamination mechanism is most likely due to outdiffusion from the crucible wall into the Si melt.

Directional Solidification of Graphene/Paraffin Nanofluids Assisted by Electromagnetic Field

Graphene nanoparticles and sodium dodecyl benzene sulfonate (SDBS) were dispersed in Paraffin by ultrasonic vibration. This nanofluid was then put into a rectangular cavity, and solidified in vertical direction from the bottom to the top. Then, joined electromagnetic field with a electric-field intensity of 110v and a magnetic induction intensity of 0.1T during directional solidification process above, also, a same nanofluid solidification without electromagnetic field for compare Photoes were taken during directional solidification and after solidification to show the interface shape during solidification and the distribution of nanoparticles after solidification. The environmental scanning electron microscope (ESEM) was also used to observe the different distribution of nanoparticles in the vertical direction of solid phase after solidification. It was found that directional solidification without electromagnetic field made graphene nanoparticles distributed to the top area of the solid, particles clustered seriously while they were barely appeared to the bottom area of the solid. The joining of electromagnetic field made them distribute in all area of the solid, dispersed better, particle size also became smaller than that without electromagnetic field. we thought that directional solidification assisted by electromagnetic field broke the force balance of nanoparticles, and particles were more easily to engulfed by solid interface compared to those without electromagnetic field. As a result nanoparticles dispersed better in the solid after solidification.

Comparative study of the segregation behavior and crystallographic orientation in a nickel-based single-crystal superalloy

The segregation behavior and crystallographic orientation of a nickel-based single-crystal CMSX-6 superalloy produced by the downward directional solidification process have been investigated. The results were compared with those in the Bridgman process. In comparison to the Bridgman process, the fluctuations in the concentrations of Al, Ti, Ta, Co, Mo and Cr became smaller along the path from the dendrite lobe through the interdendritic region to the adjacent dendrite lobe. This suggests that the degree of the segregation of these alloying elements was reduced by using the DWDS process. In addition to this, the angle between the dendrites' preferred growth direction and the heat flow direction in the DWDS cast samples, and the splaying region were smaller than those in the Bridgman solidified samples. This indicates that better crystal orientation can be obtained in nickel-based single-crystal superalloy components by using the downward directional solidification process.

A method for flattening the solidification front in directional solidification technology

Nonplanar solidification front causes defects in directional solidification process. The transverse temperature gradient, which can be divided into radial temperature gradient and circumferential temperature gradient, is one of the reasons causing the nonplanar solidification front. This paper presents a method by varying the wall thickness of the mould to decrease the circumferential temperature gradient and hence flatten the solidification front. The equations for calculating the wall thickness were deduced by heat transfer analysis. The optimized mould contour was obtained by solving the equations numerically. It was proved by simulation that the circumferential temperature gradient can be almost reduced by 40%. Furthermore, the starting time difference of solidification at one cross section along the circumferential direction almost reduces by half. Additionally, this paper also researches the influences of parameters of the mould and the furnace etc. on the shape of the mould and the circumferential temperature gradient. The circumferential temperature gradient decreases as the thermal conductivity and the emissivity of the mould increase. And the temperature of the cooling ring impacts little on the circumferential temperature gradient. According to the development trend of the blade manufacturing, this method may be applied widely.

Back diffusion of iron impurity during silicon purification by vacuum directional solidification

A theoretical model for investigating the back diffusion of iron impurity during silicon purification by vacuum directional solidification is proposed in this paper. The back diffusion of iron impurity in directional solidification process can markedly reduce the purifying effect; thus, clarifying the back-diffusion behavior of iron impurity has great significance in silicon purification by directional solidification. Results show that the influence of back diffusion becomes more obvious with increased solidification proportion. At the end of solidification, the degree of back diffusion relative to Scheil equation calculation reaches nearly 200%. Experimental verification reveals that the calculation that considers back diffusion is more consistent with experimental results than when back diffusion is ignored. Thus, the distribution of iron impurity during silicon purification by directional solidification can be more accurately calculated or predicted when back-diffusion is considered in solidification.

Controlling frontal photopolymerization with optical attenuation and mass diffusion.

Frontal photopolymerization (FPP) is a versatile directional solidification process that can be used to rapidly fabricate polymer network materials by selectively exposing a photosensitive monomer bath to light. A characteristic feature of FPP is that the monomer-to-polymer conversion profiles take on the form of traveling waves that propagate into the unpolymerized bulk from the illuminated surface. Practical implementations of FPP require detailed knowledge about the conversion profile and speed of these traveling waves. The purpose of this theoretical study is to (i) determine the conditions under which FPP occurs and (ii) explore how optical attenuation and mass transport can be used to finely tune the conversion profile and propagation kinetics. Our findings quantify the strong optical attenuation and slow mass transport relative to the rate of polymerization required for FPP. The shape of the traveling wave is primarily controlled by the magnitude of the optical attenuation coefficients of the neat and polymerized material. Unexpectedly, we find that mass diffusion can increase the net extent of polymerization and accelerate the growth of the solid network. The theoretical predictions are found to be in excellent agreement with experimental data acquired for representative systems.

Effect Of Natural Convection On Directional Solidification Of Pure Metal

AbstractThe paper is focused on the modeling of the directional solidification process of pure metal. During the process the solidification front is sharp in the shape of the surface separating liquid from solid in three dimensional space or a curve in 2D. The position and shape of the solid-liquid interface change according to time. The local velocity of the interface depends on the values of heat fluxes on the solid and liquid sides. Sharp interface solidification belongs to the phase transition problems which occur due to temperature changes, pressure, etc. Transition from one state to another is discontinuous from the mathematical point of view. Such process can be identified during water freezing, evaporation, melting and solidification of metals and alloys, etc.The influence of natural convection on the temperature distribution and the solid-liquid interface motion during solidification of pure copper is studied. The mathematical model of the process is based on the differential equations of heat transfer with convection, Navier-Stokes equation and the motion of the interface. This system of equations is supplemented by the appropriate initial and boundary conditions. In addition the continuity conditions at the solidification interface must be properly formulated. The solution involves the determination of the temporary temperature and velocity fields and the position of the interface. Typically, it is impossible to obtain the exact solution of such problem. The numerical model of solidification of pure copper in a closed cavity is presented, the influence of the natural convection on the phase change is investigated. Mathematical formulation of the problem is based on the Stefan problem with moving internal boundaries. The equations are spatially discretized with the use of fixed grid by means of the Finite Element Method (FEM). Front advancing technique uses the Level Set Method (LSM). Chorin’s projection method is used to solve Navier-Stokes equation. Such approach makes possible to uncouple velocities and pressure. The Petrov-Galerkin formulation is employed to stabilize numerical solutions of the equations. The results of numerical simulations in the 2D region are discussed and compared to the results obtained from the simulation where movement of the liquid phase was neglected.

Large scale phase-field simulations of directional ternary eutectic solidification

Pattern formation in ternary eutectic microstructures is difficult to predict because of the complex interactions between diffusion and surface energies, as well as the large number of possible configurations which three phases can assume. The silver–aluminum–copper (Ag–Al–Cu) ternary eutectic is of particular interest to researchers, but its study is complicated by an unusually large solubility change. Due to this change, it is difficult to observe the patterns that form during the solid–liquid phase transition experimentally. This causes significant differences between the structure that forms during solidification and what is observed after traditional directional solidification processing. In order to model the solidification behavior and pattern formation in representative volume elements, large scale phase-field simulations are employed. Two different parameter sets are used. The first set uses the phase fractions and compositions of the as-solidified structure. The other used phase fractions found at lower temperatures in order to be comparable to experimental microstructures available in the literature. The second set of simulation results is compared quantitatively to experimental micrographs and found to be in good agreement. The predicted three-dimensional microstructures for the as-solidified structure are presented.

NUMERICAL SIMULATION OF DIRECTIONAL SOLIDIFIED MICROSTRUCTURE OF WIDE-CHORD AERO BLADE BY BRIDGEMAN PROCESS

The aero turbine is spun by high-temperature and high-pressure burning gases. The practice has proven that the directional solidification(DS) turbine blade with perfect column grains has still excellent high-temperature performance in this kind of working environment. This means that the size and orientation of column grains have great influence on the high-temperature property and performance of turbine blades. On the other hand,the high-quality blade is not easy to be produced in DS process due to the difficulty of obtaining the desired temperature field needed to produce the grains with ideal morphology. In addition, the growth of columnar grains in the wide- chord hollow guide blade is obstructed by the complex camber and the platform. How to produce turbine blades with desired microstructures is the key problem in the DS process. Numerical simulation of the DS process is an effective way to investigate the growth and the morphology of the grains and hence to optimize the process.In this work, a mathematical- physical model for simulating the DS process of wide- chord blade is established in which nucleation and grain growth in the blade in the DS process are modeled by the cellular automation(CA)method with multi-scale dynamic bidirectional coupling technology. Some general analytic indicators are proposed to assess the morphology of mushy zone and grains in a blade quantitatively. Based on the simulated results by using the usual starter blocks 1, 2 and 3, a new starter block is designed considering numerically controlled cutting.Temperature fields and grains in DS processes and corresponding indicators at different withdrawal rates for above4 starter blocks are numerically predicted to investigate the influences of varying these technological parameters,and hence to determine the influence mechanism to the DS process. For comparison, the DS validation experiments by using starter blocks 1, 2 and 3 have been carried out. The numerical and experimental results agree well, their morphologies including those faulty grains are similar. It is found that higher withdrawal rate leads to larger concavation of mushy zone, but the effect of chill is stronger than that of withdrawal rate if the contact area between casting and chill plate is large enough. Better grain structure in a blade is achieved by starter block 3 than by starter blocks 1 and 2. By starter block 4, the amount of column grains is larger and the amount of lateral grain boundaries is smaller, compared with that of starter blocks 1, 2 and 3. Therefore higher withdrawal rate could be adoptable without excessive concavation of mushy zone, resulting in parallel column grains, finer dendrites in the blade, and much higher blade productivity. Optimum withdrawal rates are also determined for starter blocks 3 and 4.