Directional Solidification Process Research Articles

Mechanical stirring influence on solute segregation during plane front directional solidification

The present paper focuses on directional solidification processes for photovoltaic silicon purification. The use of a mechanical stirrer in the melt to enhance impurity segregation is investigated through numerical simulations. The 3D forced convection flow is resolved in a transient regime thanks to a sliding mesh approach. The hydrodynamic model is coupled to a solute transport simulation in a quasi-steady approximation (i.e. with constant liquid height). Velocity measurements are performed by Particle Image Velocimetry on a water model in order to validate hydrodynamic simulations. Numerical results show that an efficient segregation can be achieved, even for high solidification rates, thanks to mechanical stirring. The numerical model provides meaningful insights for process optimization as it correlates the impurity repartition on the solidification front to the stirring parameters. Finally, the numerical segregation results are compared to an analytical model of the solute boundary layer. It is found that the analytical model provides a good estimate of the mean segregation regime from an hydrodynamic simulation of the forced convection flow, which makes it a useful tool for process design.

Microstructure control and creep behavior of Ti-47Al-6Nb-0.1C alloy by directional solidification

Newly designed Ti-47Al-6Nb-0.1C at.% alloy was directionally solidified by cold crucible under 45 kW at the growth rate of 5–16.67 μm/s. The macro/microstructure evolution, room-temperature tensile property and creep behavior are investigated. The results show that this alloy was well directionally solidified by cold crucible at the growth rate of 5–11.67 μm/s, and they display primary β solidification at this growth-rate range. It is also found that the lamellar spacing is mainly controlled by growth rate, and the lamellar spacing decreases with the increasing of growth rate according to relationship d=1751V−0.58. Moreover, the extent of microsegregation increases with the increasing of growth rate, and thus the effect of microsegregation on creep behavior is discussed. After controlling directional solidification process at growth rate of 5–8.33 μm/s, this alloy exhibits good creep properties with creep life more than 800 h at 800 °C/200 MPa, and the acceptable room-temperature tensile property with yield strength 436–452 MPa and elongation 1.62–1.68%.

Numerical Simulation of Polysilicon Solid-liquid Interface Transmogrification in Heat Transfer Process

The shape of solid-liquid interface during the directional solidification process, which is difficult to be observed and measured in actual processes, controls the grain orientation and grain size of polysilicon ingot. We carried out numerical calculations of the directional solidification progress of polycrystalline silicon and invested the means to deal with the latent heat of solidification in numerical simulation. The distributions of the temperature field of the melt for the crystallization progress as well as the transformation of the solid-liquid interface were obtained. The simulation results are consistent with the experimental outcomes. The results show that the curvature of solid-liquid interface is small and stability, larger grain sized columnar crystal can be grown in the laboratory-scale furnace at a solidification rate of 10 μm•s-1. It shall provide important theoretical basis for metallurgical process and polysilicon production technology.

Numerical Modelling on Modified Directional Solidification Process of Multi-crystalline Silicon Growth for Photovoltaic Applications

A transient global model was used to investigate the effect of bottom grooved furnace upon the directional solidification (DS) process of multi-crystalline silicon (mc-Si). The numerical simulation assumed geometry is perfect 2D axis-symmetry. The temperature distribution, crystal-melt (c-m) interface, thermal stress and dislocation density have been simulated. The modified heat exchanger block system was used for controlling the temperature gradient at the bottom of the crucible. The obtained result shows convex shape of the c-m interface. The von Mises stress and dislocation density were reduced while using the bottom grooved furnace. This work was carried out in the different grooves of radius 30 and 60 mm of the heat exchanger block of the DS furnace.

Optimization of heat transfer during the directional solidification process of 1600 kg silicon feedstock

In this study, the power ratio between the top and side heaters and the moving velocity of the side insulation are designed to control the shape of the crystal-melt interface during the growth process of a 1600 kg multi-crystalline silicon ingot. The power ratio and insulation gap are adjusted to ensure solidification of the melt. To ensure that the crystal-melt interface is slightly convex in relation to the melt during the entire solidification process, the power ratio should be augmented gradually in the initial stages while being held to a constant value in the middle stages. Initially the gap between the side and the bottom insulation is kept small to reduce thermal stress inside the seed crystals. However, the growth rate will be slow in the early stages of the solidification process. Therefore, the movement of the side insulation is fast in the initial stages but slower in the middle stages. In the later stages, the side insulation gap is fixed. With these modifications, the convexity of the crystal-melt interface in relation to the melt can be maintained during the growth process with an approximately 41% reduction in the thermal stress inside the growing ingot and an 80% reduction in dislocation density along the center line of the ingot compared with the original case.

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.

A cellular automaton simulation of W–Ni alloy solidification in laser solid forming process

An alloy cellular automaton (CA) model is developed for the microstructure simulation in directional solidification and laser solid forming (LSF) process. The CA model's capture rule was modified by a limited neighbor solid fraction (LNSF) method. A multiscale two-dimensional model is presented for simulating laser remelting process, which is the same as LSF without the addition of metallic powders into melt pool. The metallurgy process in melt pool was simulated, including temperature distribution, pool shape and solidification of microstructure. The microstructure evolution of tungsten–nickel alloy (W–Ni) during LSF is also simulated by present CA model.

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.

Effect of temperature gradient on the diffusion layer thickness of impurities during directional solidification process

The diffusion layer thickness of impurity during directional solidification process was evaluated under different temperature gradient conditions. The thickness of Fe, Cu, Ni and Ti in silicon ingot under 9.74K/m were 6.19mm, 4.92mm, 4.61mm and 8.70mm, respectively; The thickness of Fe, Cu, Ni and Ti in silicon ingot under 28.49K/m were reduced to 3.35mm, 1.21mm, 1.85mm and 5.81, respectively. The diffusion layer thickness was reduced by the large temperature gradient to lead a low effective segregation coefficient. As a result, the impurity concentration of silicon ingot under 28.49K/m was reduced to 0.94ppmw. The strong vortex in the solid-liquid boundary interface was enhanced by the large temperature gradient, as the main transport mechanism to accelerate the diffuse of impurity atom in the diffusion layer，which effectively reduced the thickness of diffusion layer.

Insignificant elastic-modulus mismatch and stress partitioning in two-phase Mg–Zn–Y alloys comprised of [formula omitted]-Mg and long-period stacking ordered phases

Elastic-modulus mismatch and the resultant stress partitioning in two-phase Mg–Zn–Y alloys comprised of α-Mg and long-period stacking ordered (LPSO) phases were studied. Two-phase polycrystals containing anisotropically oriented 18R- or 14H-type LPSO phase and single-phase polycrystals consisting of α-Mg or 18R-type LPSO phase were prepared by extrusion and directional solidification processes and their complete sets of anisotropic elastic properties were measured using resonant ultrasound spectroscopy. Elastic properties of the single and two-phase alloys were analyzed using Eshelby's inclusion theory, effective-medium approximation, and inverse Voigt-Reuss-Hill approximation, in which the crystallographic textures and microstructures formed by the preparation processes were taken into account. The analyses revealed that the elastic properties of 18R-LPSO phase were not unique and they depended on the solute Zn and Y atom concentrations. Additionally, the elastic modulus of 18R-LPSO phase embedded in the two-phase alloy was lower than that of the alloy consisting of single-phase 18R-LPSO phase. The analysis using first-principles calculations based on density functional theory indicated that the low elastic modulus was caused by low density and low stability of short-range ordered solute atom clusters embedded in the LPSO phase of the two-phase alloy. Because of low elastic modulus in the LPSO phase, the elastic mismatch and resultant elastic interaction between the α-Mg and LPSO phases were very small. As a result, the formation of LPSO phase had little effect on the stress partitioning to the LPSO phase, which was independent of the LPSO-phase morphology.

Dimensional Control of Nickel-Based Single Crystal Turbine Blade Investment Casting by Process Control Optimization

The main research is aimed at the deformation control of single crystal turbine blade margin plate. The measurement data and numerical results of margin plate are compared. The previous research indicates that the margin plate warpage deformation is related to the directional solidification structure and process parameters. However, the margin plate structure is designed by experience and usually the structure can not be changed. Thus, an optimizing method for the process parameters is put forward to control the deformation of blade margin plate. The characterization model for describing the margin plate warpage deformation is established by using analytic hierarchy process method. The chill plate temperature, shell mould preheating temperature, pouring temperature and withdraw rate are selected as the main process parameters to control the margin plate warpage deformation. Using the process optimization, the margin plate warpage deformation is reduced from 0.232295 to 0.181698 mm, decreasing 21.8%.

Large-scale simulation of dendrite growth in directional solidification castings (Phys. Status Solidi B 10/2017)

The modified shape function dendritic (MSFD) model was built to simulate the growth of a large number of dendrites in directional solidification (DS) in casting scale. The cover figure (cf. article no. 1600860 by Hang Zhang and Qingyan Xu) shows experimental dendritic morphologies in cross and longitudinal sections fitted by the numerical results with different pre-set Euler angles (φ1, ψ, φ2). The results agreed well, which proved that the transform matrix M was suitable for the dendritic morphology description. For the DS process, an MSFD model coupled with macro models was proposed to simulate the growth of thousands of micro dendrites and their distribution. Furthermore, the crystal selection of the spiral selector is clearly represented by the simulation method that employed the MSFD model, and the findings reveal the distribution of dendrites within the thinnest wall of a single-crystal turbine blade and the solidification sequence of the dendrites. Hence, the modified model coupled with macro-simulation models can be used to predict the morphology and distribution of DS dendrites with respect to large-scale castings produced by the DS process.

Experimental study on mechanical properties of silica-based ceramic core for directional solidification of single crystal superalloy

The effects of holding time in Bridgman furnace on mechanical properties of injection molded silica-based ceramic cores for directional solidification of SX superalloy have been investigated. The cylindrical samples (S0) were sintered at 1000℃ for 60min, and some of the sintered samples (S1, S2, S3) were treated by heat treatment at 1500℃ to simulate the directional solidification process. Isothermal uniaxial compression tests of ceramic core samples were conducted on a Gleeble-1500D mechanical simulator. Weibull approach was used to describe the strength distribution of silica-based ceramic cores. As a result, the mean compressive strength of the sample (S0) is 40.43MPa. The mean compressive strengths of the samples (S1, S2, S3) with heat treatment at 1500℃ are 54.34MPa, 53.60MPa and 53.81MPa, respectively, which are significantly larger than that of S0. The mean elastic moduli of the samples (S1, S2, S3) with heat treatment at 1500℃ are 2726.39MPa, 2855.91MPa and 2797.14MPa, respectively, which is significantly higher than that of S0. The refractory particle evolution of the ceramic core during the directional solidification process is analyzed, and the microstructural investigations show that the crack propagation of ceramic core sintered at 1000℃ is mainly through the sintering necks between particles. However, the crack propagation of ceramic core holding at 1500℃ is extended through the entire large particles. The re-sintering process of ceramic core holding at 1500℃ compensates the negative effect of cracks due to the volume contraction during β- to α-phase transformation and the rapid cooling process, and improves the ceramic core uniformity and mechanical properties.

Simulation Studies of Annealing Effect on a mc-Si Ingot for Photovoltaic Application

A multi-crystalline silicon (mc-Si) ingot was grown by the directional solidification (DS) process for photovoltaic (PV) application. We have numerically investigated shear stress and thermal stress for different annealing time and temperature of the directionally solidified mc-Si ingot after the solidification and also we discuss the melt-crystal (m-c) interface during the solidification. Initially the planar m-c interface is observed during the solidification process, after that a slightly convex m-c interface is obtained for the rest of the solidification process. Maximum shear stress has least value at the center region of the mc-Si ingot for 900 K annealing temperature. Maximum shear stress has least value at the peripheral region of the mc-Si ingot for 700 K annealing temperature. The whole mc-Si ingot has lower thermal stress at 700 K annealing temperature. 5 h annealing time is enough to decrease the internal stress of the mc-Si ingot. Increase of the annealing time beyond 5 h does not further decrease the stress significantly.

Large-scale simulation of dendrite growth in directional solidification castings

In this study, the growth and distribution of directional solidification (DS) dendrites in entire cross-sections of DS superalloy castings are simulated based on a modified shape function dendritic (MSFD) model coupled with the cellular automaton-finite difference (CA-FD) method. The macro-thermal transfer and columnar grain growth are calculated using CA-FD with a macro time-step, and then, the original and boundary conditions for the dendrite-growth simulation are determined via the interpolation of the macro temperature and the projection of the 3D preferential grain orientation using a matrix, M. The dendrite growth calculation cyclically proceeds based on the MSFD model. It is used to predict the growth of hundreds of dendrites throughout the cross-section of a DS casting by considering the macro-solidification parameters. The MSFD model is further applied to predict the competitive growth of DS dendrites and their distribution in the cross-sections of a spiral selector and a fake single crystal turbine blade. The results of the simulation correlate with the results of the DS experiment. Hence, the modified model coupled with the macro-simulation models can be used to predict the morphology and distribution of DS dendrites with respect to large-scale castings produced by the DS process.

Numerical Simulation of Directional Solidification Process of Single Crystal Ni- Based Superalloy Casting

Abstract The analysis of influence of mould withdrawal rate on the solidification process of CMSX-4 single crystal castings produced by Bridgman method was presented in this paper. The predicted values of temperature gradient, solidification and cooling rate, were determined at the longitudinal section of casting blade withdrawn at rate from 1 to 6mm/min using ProCAST software. It was found that the increase of withdrawal rate of ceramic mould results in the decrease of temperature gradient and the growth of cooling rate, along blade height. Based on results of solidification parameter G/R (temperature gradient/solidification rate), maximum withdrawal rate of ceramic mould (3.5 mm/min), which ensures lower susceptibility to formation process of new grain defects in single crystal, was established. It was proved that these defects can be formed in the bottom part of casting at withdrawal rate of 4 mm/min. The increase of withdrawal rate to 5 and 6 mm/min results in additional growth of susceptibility of defects formation along the whole height of airfoil.

The Precipitation Behavior of γ′ Phase in Single Crystal Ni-Based DD6 Superalloy for Turbine Blade

The precipitation behavior of γ′ precipitates in typical section dimensions of DD6 single crystal superalloy turbine blade was investigated experimentally during directional solidification process. The phase transformation temperatures in the single crystal Ni-based DD6 superalloy from DSC analysis and JmatPro simulation were basically in consistent with the isothermal solidification experiments. The solidification route of DD6 single crystal superalloy could be described as follows: L1 → γ + L2; L2 → (γ + γ′)eutectic + MC; γ → γ′/γ. With increasing continuous cooling rates, the primary γ′ precipitates tended to be refined, and the size distributions of the primary γ′ precipitates at every temperature measuring position followed the normal distribution. In comparison to the interdendritic regions, nearly a 60% reduction in the average sizes of the primary γ′ precipitates was measured in the dendritic core regions. The result of the primary γ′ size difference was strongly affected by the multi-component segregations between the interdendritic and dendritic regions, where the γ′ forming elements of Al and Ta segregated towards the interdendritic regions. Furthermore, the secondary γ′ precipitation was found to occur within a relatively wide corridor of γ matrix for low cooling rates (12.6, 23.3 and 29.7 °C/min) during the directional solidification process. The occurrence of the secondary γ′ precipitation resulted from the complex interaction of multiple thermodynamic and kinetic factors in the γ′ nucleation and the diffusion rate of γ′ forming elements.

High Temperature Rupture Life of Nickel-Based Superalloy under Directional Solidification with High Temperature Gradient

The stress rupture life of DZ125 nickel-based superalloy that was prepared by directional solidification process under the temperature gradient of 500 K/cm has been studied at 900°C and 235MPa. The results showed that with the increase of directional solidification rate from 50 μm/s to 800 μm/s, the primary dendrite arm spacing reduced from 94 μm to 35.8 μm and γ' precipitates reduced and more uniformed in size. The high temperature stress rupture life of as-cast sample increased firstly and then decreased and reached its maximum at the solidification rate of 500 μm/s. The dislocation configuration of sample with refine dendritic structure after stress rupture was investigated and discovered that the dislocations in different parts of sample had different morphology and density, which indicated that the deformation of as-cast samples were uneven during high temperature stress rupture. A lot of dislocations intertwined around carbides and at the interface of γ/γ', and the dislocation networks were destroyed and the dislocations entered γ' precipitate by the way of cutting.

Directional solidification of Al–Cu–Si–Mg quaternary eutectic alloy

The effects of growth rates on the microstructure, microhardness, tensile strength, and electrical resistivity were studied in directionally solidified Al–Cu–Si–Mg (Al–28 wt%Cu–6wt.%Si–2.2 wt%Mg) quaternary eutectic alloy. The directional solidification process was carried out at five different growth rates (V = 9.63–173.5 μm/s) at a constant temperature gradient (G = 6.88 K/mm). The microstructure of the directionally solidified Al–Cu–Si–Mg quaternary eutectic alloy consists of Al solid solution, irregular Si plates, and intermetallic Al2Cu (θ) and Cu2Mg8Si6Al5 (Q) phases with honeycomb morphology. The dependencies of lamellar spacing, microhardness, tensile strength, and electrical resistivity on growth rates were found to be λCuAl2=19.05V−0.41, λCu2Mg8Si6Al5=51.28V−0.43, λSi=8.74V−0.46, HV=170.7+79.08V0.25,HV=237.68(V)0.043, σ=343.45(V)0.15, andρ=3.42×10−8(V)0.10, respectively, for the Al–Cu–Si–Mg quaternary eutectic alloy. The bulk growth rates were also determined as λSi2V=92.24, λCuAl22V=669.2, and λCu2Mg8Si6Al52V=4205.5μm3/s by using the measured values ofλMg2Si, λCuAl2, λCu2Mg8Si6Al52, and V for the Si plates and intermetallic Al2Cu (θ) and Cu2Mg8Si6Al5 (Q) phases in the Al–Cu–Si–Mg eutectic alloy, respectively.

Towards wall functions for the prediction of solute segregation in plane front directional solidification

The present paper focuses on solute segregation occurring in directional solidification processes with sharp solid/liquid interface, like silicon crystal growth. A major difficulty for the simulation of such processes is their inherently multi-scale nature: the impurity segregation problem is controlled at the solute boundary layer scale (micrometers) while the thermal problem is ruled at the crucible scale (meters). The thickness of the solute boundary layer is controlled by the convection regime and requires a specific refinement of the mesh of numerical models. In order to improve numerical simulations, wall functions describing solute boundary layers for convecto-diffusive regimes are derived from a scaling analysis. The aim of these wall functions is to obtain segregation profiles from purely thermo-hydrodynamic simulations, which do not require solute boundary layer refinement at the solid/liquid interface. Regarding industrial applications, various stirring techniques can be used to enhance segregation, leading to fully turbulent flows in the melt. In this context, the scaling analysis is further improved by taking into account the turbulent solute transport. The solute boundary layers predicted by the analytical model are compared to those obtained by transient segregation simulations in a canonical 2D lid driven cavity configuration for validation purposes. Convective regimes ranging from laminar to fully turbulent are considered. Growth rate and molecular diffusivity influences are also investigated. Then, a procedure to predict concentration fields in the solid phase from a hydrodynamic simulation of the solidification process is proposed. This procedure is based on the analytical wall functions and on solute mass conservation. It only uses wall shear-stress profiles at the solidification front as input data. The 2D analytical concentration fields are directly compared to the results of the complete simulation of segregation in the lid driven cavity configuration. Finally, an additional output from the analytical model is also presented. We put in light the correlation between different species convecto-diffusive behaviour; we use it to propose an estimation method for the segregation parameters of various chemical species knowing segregation parameters of one specific species.