Phase-field lattice-Boltzmann study on fully coupled thermal-solute-convection dendrite growth of Al-Cu alloy

Dendrite growth is a complex liquid-solid phase transition process involving multiple physical factors.A phase-field lattice-Boltzmann method was developed to simulate the two-and three-dimension dendrite growth of Al-Cu alloy.The effect of fully coupled thermal-solute-convection interaction on the dendrite growth was investigated by incorporating a parallel-adaptive mesh refinement algorithm into the numerical model.By accurately reproducing the latent heat release,solute diffusion and convective transport behaviors at the liquidsolid interface,the interaction mechanism among thermal-solute-convection transport as well as their coupling effects on the dendrite growth dynamics were discussed.The simulation results show that the release of latent heat slows down the dendrite growth rate,and both natural and forced convection disrupt the symmetrical growth of dendrites.Their combination makes the growth of dendrites more complex,capturing important physical aspects such as recalescence,dendrite tip splitting,dendrite tilting,dendrite remelting,and solute plume in the simulation case.Based on the robustness and powerful ability of the numerical model,the formation mechanisms of these physical aspects were revealed.

Effect of traveling-wave magnetic field on dendrite growth of high-strength steel slab: Industrial trials and numerical simulation

The dendrite growth behavior of high-strength steel during slab continuous casting with a traveling-wave magnetic field was studied in this paper. The morphology of the solidification structure and composition distribution were analyzed. Results showed that the columnar crystals could deflect and break when the traveling-wave magnetic field had low current intensity. With the increase in current intensity, the secondary dendrite arm spacing and solute permeability decreased, and the columnar crystal transformed into an equiaxed crystal. The electromagnetic force caused by the traveling-wave magnetic field changed the temperature gradient and velocity magnitude and promoted the breaking and fusing of dendrites. Dendrite compactness and composition uniformity were arranged in descending order as follows:columnar-toequiaxed transition (high current intensity), columnar crystal zone (low current intensity), columnar-to-equiaxed transition (low current intensity), and equiaxed crystal zone (high current intensity). Verified numerical simulation results combined with the boundary layer theory of solidification front and dendrite breaking–fusing model revealed the dendrite deflection mechanism and growth process. When thermal stress is not considered, and no narrow segment can be found in the dendrite, the velocity magnitude on the solidification front of liquid steel can reach up to 0.041 m/s before the dendrites break.

Parameter calculation and result storage for phase-field simulation in α-Mg dendrite growth of Mg-5-wt% Zn alloy

Parameter calculation and result storage, as two necessary steps in phase-field simulation play an important role in ensuring the accuracy of simulation results. A strategy of parameter calculation and result storage is presented for phase-field simulation in α-Mg dendrite growth of Mg-5-wt% Zn alloy under isothermal solidification. Based on the phase diagram and empirical formulas, key parameters of the phase-field model, such as equilibrium partition coefficient k, liquidus slope m, solutal diffusion coefficient in liquid Dl, and solutal diffusion coefficient in solid Ds, can be obtained.Both structured grid method and structured point method can be used to store simulation results, but using the latter method will reduce about 60% storage space and 37.5% storage time compared with the former. Finally, convergent simulation results of α-Mg dendrite growth are obtained and they are in good agreement with the experimental results about optical micrograph, which verify the accuracy of parameters and stability of storage method.

Simulation and experimental validation of three-dimensional dendrite growth

A three-dimensional （3-D） modified cellular automaton （MCA） method was developed for simulating the dendrite morphology of cubic system alloys. Two-dimensional （2-D） equations of growth velocities of the dendrite tip, interface curvature and anisotropy of the surface energy were extended to 3-D system in the model. Therefore, the model was able to describe the morphology evolution of 3-D dendrites. Then, the model was applied to simulate the mechanism of spacing adjustment for 3-D columnar dendrite growth, and the competitive growth of columnar dendrites with different preferred growth orientations under constant temperature gradient and pulling velocity. Directional solidification experiments of NH4Cl-H2O transparent alloy were performed. It was found that the simulated results compared well with the experimental results. Therefore, the model was reliable for simulating the 3-D dendrite growth of cubic system alloys.

Numerical simulation of dendrite growth in Ni-based superalloy casting during directional solidification process

An understanding of dendrite growth is required in order to improve the properties of castings. For this reason, cellular automaton-finite difference(CA-FD) method was used to investigate the dendrite growth during directional solidification(DS)process. The solute diffusion model combined with macro temperature field model was established for predicting the dendrite growth behavior. Model validation was performed by the DS experiment, and the cooling curves and grain structures obtained by the experiment presented a reasonable agreement with the simulation results. The competitive growth of dendrites was also simulated by the proposed model, and the competitive behavior of dendrites with different misalignment angles was also discussed in detail.Subsequently, 3D dendrites growth was also investigated by experiment and simulation, and both were in good accordance. The influence on dendrites growth of initial nucleus was investigated by three simulation cases, and the results showed that the initial nuclei just had an effect on the initial growth stage of columnar dendrites, but had little influence on the final dendritic morphology and the primary dendrite arm spacing.

Phase field modeling of multiple dendrite growth of Al-Si binary alloy under isothermal solidification

Phase field method offers the prospect of being able to perform realistic numerical experiments on dendrite growth in metallic systems. In this study, the growth process of multiple dendrites in AI-2-mole-%-Si binary alloy under isothermal solidification was simulated using phase field model. The simulation results showed the impingement of arbitrarily oriented crystals and the competitive growth among the grains during solidification. With the increase of growing time, the grains begin to coalesce and impinge the adjacent grains. When the dendrites start to impinge, the dendrite growth is obviously inhibited.

Phase field modeling of dendrite growth

Single dendrite and multi-dendrite growth for Al-2 mol pct Si alloy during isothermal solidification are simulated by phase field method. In the case of single equiaxed dendrite growth, the secondary and the necking phenomenon can be observed. For multi-dendrite growth, there exists the competitive growth among the dendrites during solidification. As solidification proceeds, growing and coarsening of the primary arms occurs, together with the branching and coarsening of the secondary arms. When the diffusion fields of dendrite tips come into contact with those of the branches growing from the neighboring dendrites, the dendrites stop growing and being to ripen and thicken.

Effects of RE and Sr additions on dendrite growth and phase precipitation in AZ91D magnesium alloy

To develop AZ91D alloys with fine microstructure, effects of the addition of rare earth (RE), Sr and RE + Sr on the dendrite growth and phase precipitation in AZ91D magnesium alloy were studied, respectively. The results show that the microstructure is refined and the morphology of β-Mg17A112 phase is modified with RE or Sr addition, especially with the RE+Sr composite addition which can reduce the average grain size of AZ91D alloy obviously to 141 μm. The needle-like or block-like new phases adhering to β-Mg17A112 phase form at interdendrites during solidification. The enrichment of RE or/and Sr elements in front of the solidification interface, especially at the tips of α-Mg dendrite, which restricts the growth of α-Mg dendrite, changes the preferential growth of α-Mg and finally results in the grain refinement and the blunting of α-Mg dendrite.

Effect of nonlinear liquidus and solidus on dendrite growth in bulk undercooled melts

On the base of nonlinear liquidus and solidus,an extended model for dendrite growth in bulk undercooled melts was developed under local non-equilibrium conditions both at the interface and in the bulk liquid.In terms of thermodynamic calculations of the phase diagram,the model predictions are relatively realistic physically,since few fitting parameters are used in the model predictions.Adopting three characteristic velocities,i.e.the critical velocity of absolute solute stability(VC*),the velocity of maximal tip radius(VRm),and the velocity of bulk liquid diffusion(VD),a quantitative agreement is obtained between the model predictions and the experimental results in undercooled Ni-0.7%B and Ni-1%Zr(molar fraction) alloys,and the overall solidification process can be categorized.

Solute distribution in KNbO 3 melt-solution and its effect on dendrite growth during rapid solidification

This paper reports that the rapid solidification of mixed Li2B4O7 and KNbO3 melted in a Pt loop heater has been performed experimentally by the method of quenching, and various morphologies of KNbO3 crystals have been observed in different regions of the quenched melt-solution. Dendrites were formed in the central region where mass transfer is performed by diffusion, whereas polygonal crystals with smooth surface grew in the marginal region where convection dominates mass transport. Based on measurement of KNbO3 concentration along crystal interface by electronic probe analysis, it finds the variety of crystal morphologies, which is the result of different solute distributions： in the central region the inhomogeneity of solute concentration is much sharper and morphological instability is easier to take place; nevertheless in the marginal region the concentration homogeneity has been greatly enhanced by convection which prevents the occurrence of morphological instability. Additional solute distribution in the melt along the primary dendrite trunk axis as well as that in mushy zones has also been determined. Results show that the solute concentration in the liquid increases linearly with distance from the trunk tip and more solutes were found to be concentrated in mushy zones. The closer the mushy zone is to trunk tip, the lower the solute concentration will be there.

A lattice Boltzmann–cellular automaton study on dendrite growth with melt convection in solidification of ternary alloys

A lattice Boltzmann （LB）-cellular automaton （CA） model is employed to study the dendrite growth of A1-4.0 wt%Cu- 1.0 wt%Mg alloy. The effects of melt convection, solute diffusion, interface curvature, and preferred growth orientation are incorporated into the coupled model by coupling the LB-CA model and the CALPHAD-based phase equilibrium solver, PanEngine. The dendrite growth with single and multiple initial seeds was numerically studied under the conditions of pure diffusion and melt convection. Effects of initial seed number and melt convection strength were characterized by new- defined solidification and concentration entropies, The numerical result shows that the growth behavior of dendJ-ites, the final microstructure, and the micro-segregation are significantly influenced by melt convection during solidification of the ternary alloys. The proposed solidification and concentration entropies are useful characteristics bridging the solidification behavior and the microstructure evolution of alloys.

Numerical Simulations of Equiaxed Dendrite Growth Using Phase Field Method

Phase field method offers the prospect of being able to perform realistic numerical experiments on dendrite growth in a metallic system. In this paper, the equiaxed dendrite evolution during the solidification of a pure material was numerically simulated using the phase field model. The equiaxed dendrite growth in a two-dimensional square domain of undercooled melt (nickel) with four-fold anisotropy was simulated. The phase field model equations was solved using the explicit finite difference method on a uniform mesh. The formation of various equiaxed dendrite patterns was shown by a series of simulations, and the effect of anisotropy on equiaxed dendrite morphology was investigated.

Growth and inhibition of zinc anode dendrites in Zn-air batteries:Model and experiment

Zinc(Zn)-air batteries are widely used in secondary battery research owing to their high theoretical energy density,good electrochemical reversibility,stable discharge performance,and low cost of the anode active material Zn.However,the Zn anode also leads to many challenges,including dendrite growth,deformation,and hydrogen precipitation self-corrosion.In this context,Zn dendrite growth has a greater impact on the cycle lives.In this dissertation,a dendrite growth model for a Zn-air battery was established based on electrochemical phase field theory,and the effects of the charging time,anisotropy strength,and electrolyte temperature on the morphology and growth height of Zn dendrites were studied.A series of experiments was designed with different gradient influencing factors in subsequent experiments to verify the theoretical simulations,including elevated electrolyte temperatures,flowing electrolytes,and pulsed charging.The simulation results show that the growth of Zn dendrites is controlled mainly by diffusion and mass transfer processes,whereas the electrolyte temperature,flow rate,and interfacial energy anisotropy intensity are the main factors.The experimental results show that an optimal electrolyte temperature of 343.15 K,an optimal electrolyte flow rate of 40 ml·min^(-1),and an effective pulse charging mode.

Phase-Field Lattice-Boltzmann Study for α-Mg Dendrite Growth of Mg-5wt%Zn Alloy with Forced Convection

Melt flow can significantly change the transport of heat and solute,dendrite growth.In this work,a phase-field lattice-Boltzmann model was developed to studyα-Mg dendrite growth of Mg-5wt%Zn alloy with forced convection.Results show that the existence of forced convection and overlap of thermal and solute fields makes thermal and solute fields distribution nonuniform.Thus,the symmetry of dendrite morphology is destroyed.The solid temperature and concentration of the downstream dendrite tip front with forced convection are higher than that without forced convection,while the concentration of the upstream dendrite tip front is lower.The solute transport through melt flow will be hindered by developed sidebranching.With flow velocity increase,the upstream temperature gradient and thickness of the downstream solute enrichment layer increase gradually,while the downstream temperature gradient and thickness of the upstream solute enrichment layer decrease gradually.Meanwhile,the upstream dendrite tip velocity will increase gradually,while the downstream dendrite tip velocity will decrease at first and then unchanged.This study is helpful to establish the relationship betweenα-Mg dendrite growth and melt flow,which is beneficial to understand the role of melt flow on dendrite morphologies.

In-situ physical/chemical cross-linked hydrogel electrolyte achieving ultra-stable zinc anode-electrolyte interface towards dendrite-free zinc ion battery

Hydrogen evolution reaction(HER),zinc corrosion,and dendrites growth on zinc metal anode are the major issues limiting the practical applications of zinc-ion batteries.Herein,an in-situ physical/chemical cross-linked hydrogel electrolyte(carrageenan/polyacrylamide/ZnSO_(4),denoted as CPZ)has been developed to stabilize the zinc anode-electrolyte interface,which can eliminate side reactions and prevent dendrites growth.The in-situ CPZ hydrogel electrolyte improves the reversibility of zinc anode due to eliminating side reactions caused by active water molecules.Furthermore,the electrostatic interaction between the SO_(4)^(-)groups in CPZ and Zn^(2+)can encourage the preferential deposition of zinc atoms on(002)crystal plane,which achieve dendrite-free and homogeneous zinc deposition.The in-situ hydrogel electrolyte offers a streamlined approach to battery manufacturing by allowing for direct integration into the battery.Subsequently,the Zn//Zn half battery with CPZ hydrogel electrolyte can enable an ultra-long cycle over 5500 h at a current density of 0.5 mA cm^(-2),and the Zn//Cu half battery reach an average coulombic efficiency of 99.37%.The Zn//V_(2)O_5-GO full battery with CPZ hydrogel electrolyte demonstrates94.5%of capacity retention after 2100 cycles.This study is expected to open new thought for the development of commercial hydrogel electrolytes for low-cost and long-life zinc-ion batteries.

Recently developed strategies to restrain dendrite growth of Li metal anodes for rechargeable batteries

Lithium metal has been regarded as one of the most promising anode materials for high-energy-density batteries due to its extremely high theoretical gravimetric capacity of 3860 mAh·g^-1 along with its low electrochemical potential of-3.04 V.Unfortunately,uncontrollable Li dendrite growth and repetitive destruction/formation of the solid electrolyte interphase layer lead to poor safety and low Coulombic efficiencies(CEs)for long-term utilization,which largely restricts the practical applications of lithium metal anode.In this review,we comprehensively summarized important progresses achieved to date in suppressing Li dendrite growth.Strategies for protection of Li metal anodes include designing porous structured hosts,fabricating artificial solid electrolyte interface(SEI)layers,introducing electrolyte additives,using solid-state electrolytes and applying external fields.The protection of Li metal anodes can be achieved by regulating the stripping and deposition behaviours of Li ions.Finally,the challenges remaining for lithium metal battery systems and future perspectives for Li metal anodes in practical applications are outlined,which are expected to shed light on future research in this field.

Comparison of Cellular Automaton and Phase Field Models to Simulate Dendrite Growth in Hexagonal Crystals

A cellular automaton （CA）-finite element （FE） model and a phase field （PF）-FE model were used to simulate equiaxed dendritic growth during the solidification of hexagonal metals. In the CA-FE model, the conservation equations of mass and energy were solved in order to calculate the temperature field, solute concentration, and the dendritic growth morphology. CA-FE simulation results showed reasonable agreement with the previously reported experimental data on secondary dendrite arm spacing （SDAS） vs cooling rate. In the PF model, a PF variable was used to distinguish solid and liquid phases similar to the conventional PF models for solidification of pure materials. Another PF variable was considered to determine the evolution of solute concentration. Validation of both models was performed by comparing the simulation results with the analytical model developed by Lipton-Glicksman-Kurz （LGK）, showing quantitatively good agreement in the tip growth velocity at a given melt undercooling. Application to magnesium alloy AZ91 （approximated with the binary Mg-8.9 wt% AI） illustrates the difficulty of modeling dendrite growth in hexagonal systems using CA-FE regarding mesh-induced anisotropy and a better performance of PF-FE in modeling multiple arbitrarily-oriented dendrites growth.

Phase field simulation of dendrite growth under convection

The phase-field model coupled with a flow field was used to simulate the solidification of pure materials by the finite difference method. The effects of initial crystal radius, the space step and the interface thickness on the dendrite growth were studied. Results indicate that the grain grows into an equiaxial dendrite during free flow and into a typical branched structure under forced flow. The radius of an initial crystal can affect the growth of side-branches but not the stability of the dendrite＇s tip when an appropriate value is assigned to it. With an increase in space steps, side-branches appear at the upstream of the longitudinal principal branch and they grow rapidly. With an increase in the interface thickness, the trunk of the longitudinal upstream and lateral principal branches grow longer and become more slender while the number of secondary branches increases.

Application of non-equilibrium dendrite growth model considering thermo-kinetic correlation in twin-roll casting

Upon non-equilibrium solidifications, dendrite growth, generally as precursor of as-solidified structures,has severe effects on subsequent phase transformations. Considering synergy of thermodynamics and kinetics controlling interface migration and following conservation of heat flux in solid temperature field, a more flexible modeling for the dendrite growth is herein developed for multi-component alloys,where, two inherent problems, i.e. correlation between thermodynamics and kinetics(i.e. the thermokinetic correlation), and theoretical connection between dendrite growth model and practical processing,have been successfully solved. Accordingly, both the thermodynamic driving force G and the effective kinetic energy barrier Qeffhave been found to control quantitatively the dendrite growth(i.e. especially the growth velocity, V), as reflected by the thermo-kinetic trade-off. Compared with previous models, it is the thermo-kinetic correlation that guarantees quantitative connection between the practical processing parameters and the current theoretical framework, as well as more reasonable description for kinetic behaviors involved. Applied to the vertical twin-roll casting(VTC), the present model, realizes a good prediction for kissing points, which influences significantly alloy design and processing optimization.This work deduces quantitatively the thermo-kinetic correlation controlling the dendrite growth, and by proposing the parameter-triplets(i.e. G-Qeff-V), further opens a new beginning for connecting solidification theories with industrial applications, such as the VTC.

Effects of β-Dendrite Growth Velocity on β→a Transformation of Hypoperitectic Ti–46Al–7Nb Alloy

Solidification characteristics of Ti–46Al–7Nb melts were studied by the electromagnetic levitation technique.A maximum melt undercooling up to 240 K has been achieved. When the undercooling is lower than the critical value DT＊ = 205 K, the alloy possesses typical hypoperitectic solidification characteristic which can be evidenced by a peritectic layer observed in the as-solidified microstructure. However, the Widmansta¨tten structure can be observed at large undercooling regime of DT C DT＊, where peritectic reaction cannot proceed and c lamellar precipitation within a plates is suppressed. Based on the BCT dendrite growth model, the dendrite growth velocities were calculated as a function of undercooling. Theoretical analysis indicates that the growth mechanism of the primary b phase transforms from solutaldiffusion-controlled to thermal-diffusion-controlled in the undercooling range of 188–205 K, which can be attributed to the onset of solute trapping at the critical undercooling. Meanwhile, with increasing undercooling, the solute trapping effect becomes more dominant as a consequence.