Dendrite Growth Kinetics Research Articles

Dendrite growth kinetics and microstructure evolution mechanism of Ni2TiAl intermetallic compound within substantially undercooled liquid Ni64Al19Ti17 alloy

The dendrite growth kinetics and microstructure evolution mechanism of the Ni2TiAl intermetallic compound within substantially undercooled liquid Ni64Al19Ti17 alloy were investigated using electrostatic levitation (ESL) and drop tube (DT) techniques. The growth velocity of primary Ni2TiAl dendrites displayed a power-law relation with liquid undercooling, achieving a maximum of 80 mm/s at the undercooling of 254 K (0.16 TL). The solidification pathway transformed from primary Ni2TiAl growth plus subsequent (Ni3Ti+Ni2TiAl) eutectic growth into the successive growth of Ni2TiAl and Ni3Ti phases as the alloy undercooling increased sufficiently. The high cooling rates of freely falling alloy droplets effectively suppressed the martensitic transformation observed for primary Ni2TiAl intermetallic compound under typical ESL radiative cooling condition. Both nanoindentation and Vickers hardness performances of the Ni2TiAl phase formed under these two conditions exhibited conspicuous enhancement due to grain refinement effects. The microstructures with martensitic transformation under ESL condition showed higher hardness than those under DT condition despite their larger grain size.

Primary dendrite growth within binary Fe71Ge29 eutectic alloy under duplex levitation states

The primary β-Fe3Ge2 dendrite growth kinetics within liquid Fe71Ge29 eutectic alloy was studied by both acoustic levitation and electrostatic levitation techniques, with maximum experimental undercoolings of 130 and 143 K, respectively. At small undercoolings, (α1 + β-Fe3Ge2) eutectic growth proceeded and then transformed to lamellar (ε-Fe3Ge + β-Fe3Ge2) microstructure by peritectoid reaction. Once liquid undercooling reached 56 K, β primary phase started to nucleate preferentially and its maximum growth velocity attained 13.5 mm/s at 143 K undercooling. By acoustic levitation processing, β dendrites were distributed inside the alloy droplet. Under electrostatic levitation state, β dendrites were distributed both at the periphery and within the interior of alloy droplet, and their volume fraction was significantly higher than that under acoustic levitation. Numerical simulation results indicated that a duplex flow was induced by alloy droplet shape oscillation and acoustic streaming. The flow exhibited maximum intensity near the alloy surface, which inhibited the achievement of larger undercoolings during acoustic levitation.

Rapid dendritic growth kinetics of primary phase within supercooled Zr-V alloy at electrostatic levitation state

The liquid Zr100−xVx (x = 8.6, 16.5, 30) alloys were undercooled to the maximum undercooling of 364 K (0.18 TL), 405 K (0.21 TL), and 375 K (0.21 TL), respectively, by using electrostatic levitation technique. The Zr91.4V8.6 and Zr83.5V16.5 alloys present only one recalescence during liquid/solid phase transition, while the Zr70V30 alloy presents a transformation from two recalescence to one recalescence phenomenon with a critical undercooling of approximately 300 K. According to the LKT/BCT model, the calculated results of the primary β-Zr dendrite growth velocity in undercooled liquid Zr91.4V8.6 and Zr83.5V16.5 alloys agree well with the experiments. The velocity inflection points at 119 K of Zr91.4V8.6 alloy and 201 K of Zr83.5V16.5 alloy could be explained by the competition between solutal undercooling control and thermal undercooling control modes. For Zr70V30 alloy solidified in the P1 with twice recalescence, a critical second undercooling of 253 K and corresponding undercooling of 65 and 244 K are obtained. When the undercooling is in the range of 65–244 K, the second undercooling would be greater than 253 K, and the residual liquid phase would solidify into anomalous eutectic microstructure for Zr70V30 alloy. The Vickers hardness of Zr100−xVx (x = 8.6, 16.5, 30) alloys all show a quadratic relationship with undercooling. Under electrostatic levitation condition, the mechanical property of Zr-V alloys could be significantly regulated through solidifying the alloys at different undercoolings.

Recent Developments of Carbon Dots for Advanced Zinc‐Based Batteries: A Review

AbstractRechargeable Zn‐based batteries provide a compelling supplement to subsistent energy storage devices owing to their high energy density, good safety, and low cost. Nevertheless, inherent imperfections such as dendrite growth, side reactions, and andante reaction kinetics, severely impede their commercialization. As new 0D nanomaterials, carbon dots (CDs) with unique characteristics and excellent electrochemical activity, exhibit promising potential exploitation in electrochemistry and electrocatalysis areas. Herein, the adhibition of CDs in resolving the aforementioned drawbacks of Zn‐based batteries is introduced. To begin with, concepts, physicochemical properties, and synthetic methods of CDs are discussed. Next, recent developments and advances exploiting CDs in respectively ameliorating the performance of the Zn anode, the cathode, and electrolytes of Zn ion batteries and bifunctional electrocatalytic activities including oxygen reduction reaction and oxygen evolution reaction for Zn‐air batteries, are roundly reviewed and minutely generalized. Finally, current challenges and prospects are surveyed as well, aiming to offer a reference for the blossom of advanced Zn‐based batteries.

A distinctive kinetics transition from stable hcp to metastable fcc dendrite growth within liquid Re95W5 refractory alloy

ABSTRACT A transition of dendrite growth kinetics from stable hcp to metastable fcc phases was observed for refractory Re95W5 alloy in an electrostatic levitation state, which attained a liquid undercooling up to 872 K (0.26T L). Stable hcp dendrite dominated in the single recalescence for pure Re in the whole of its undercooling regime, but prevailed for Re95W5 alloy only in the specific range of 159–867 K undercooling. The rapid dendrite growth velocity displayed a power-law relationship with the degree of undercooling. Once the refractory alloy melt was undercooled beyond 867 K undercooling, metastable fcc dendrite grew primarily from the liquid phase in the first recalescence, which was followed by a complete ‘fcc to hcp’ solid-state transformation in the second recalescence. An abrupt change of growth kinetics took place to depress the dendrite growth velocity drastically from 41.8 m·s−1 for stable hcp phase at 867 K undercooling to 10.9 m·s−1 for metastable fcc phase at 872 K undercooling.

Scaling law for growth of misoriented equiaxed Al-Cu dendrites: A phase-field study with in situ experiment validation

We consider the effect of a mutual misorientation between two interacting equiaxed dendrites in polycrystalline materials on the scaling law of growth from undercooled melt. This effect is investigated by three-dimensional quantitative phase-field simulations of Al-Cu alloy solidification in thin samples. It has been found that the equiaxed dendritic growth kinetics changes due to the reduced solute interaction when considering mutual grain misorientation, and both the characteristic growth rate and primary dendritic arm length can be approximately correlated linearly to the misorientation of two dendrites. The scaling law, which originally uses the solute composition and the distance between two nuclei as physical parameters to describe the dynamics of primary dendritic arms, is then adapted with consideration of the misorientation. Compared with the previous scaling law that only concerns face-to-face growth of two dendrites, the predictions of the newly proposed scaling law taking the grain orientation in account are in better agreement with the experimental data.

Dual‐Functional Electrode Promoting Dendrite‐Free and CO2 Utilization Enabled High‐Reversible Symmetric Na‐CO2 Batteries

Sodium‐carbon dioxide (Na‐CO2) batteries are regarded as promising energy storage technologies because of their impressive theoretical energy density and CO2 reutilization, but their practical applications are restricted by uncontrollable sodium dendrite growth and poor electrochemical kinetics of CO2 cathode. Constructing suitable multifunctional electrodes for dendrite‐free anodes and kinetics‐enhanced CO2 cathodes is considered one of the most important ways to advance the practical application of Na‐CO2 batteries. Herein, RuO2 nanoparticles encapsulated in carbon paper (RuCP) are rationally designed and employed as both Na anode host and CO2 cathode in Na‐CO2 batteries. The outstanding sodiophilicity and high catalytic activity of RuCP electrodes can simultaneously contribute to homogenous Na+ distribution and dendrite‐free sodium structure at the anode, as well as strengthen discharge and charge kinetics at the cathode. The morphological evolution confirmed the uniform deposition of Na on RuCP anode with dense and flat interfaces, delivering enhanced Coulombic efficiency of 99.5% and cycling stability near 1500 cycles. Meanwhile, Na‐CO2 batteries with RuCP cathode demonstrated excellent cycling stability (>350 cycles). Significantly, implementation of a dendrite‐free RuCP@Na anode and catalytic‐site‐rich RuCP cathode allowed for the construction of a symmetric Na‐CO2 battery with long‐duration cyclability, offering inspiration for extensive practical uses of Na‐CO2 batteries.

A Nature-Inspired Separator with Water-Confined and Kinetics-Boosted Effects for Sustainable and High-Utilization Zn Metal Batteries.

Uncontrollable dendrite growth and sluggish ion-transport kinetics are considered as the main obstacles for the further development of high-performance aqueous zinc ion batteries (AZIBs). Here, a nature-inspired separator (ZnHAP/BC) is developed to tackle these issues via the hybridization of the biomass-derived bacterial cellulose (BC) network and nano-hydroxyapatite particles (HAP). The as-prepared ZnHAP/BC separator not only regulates the desolvation process of the hydrated Zn2+ ions (Zn(H2 O)6 2+ ) by suppressing the water reactivity through the surface functional groups, alleviating the water-induced side-reactions, but also boosts the ion-transport kinetics and homogenize the Zn2+ flux, resulting in a fast and uniform Zn deposition. Remarkably, the Zn|Zn symmetric cell with ZnHAP/BC separator harvests a long-term stability over 1600h at 1mAcm-2 , 1mAhcm-2 and endures stable cycling over 1025 and 611h even at a high depth of discharge (DOD) of 50% and 80%, respectively. The Zn|V2 O5 full cell with a low negative/positive (N/P) capacity ratio of 2.7 achieves a superior capacity retention of 82% after 2500 cycles at 10Ag-1 . Furthermore, the Zn/HAP separator can be totally degraded within 2 weeks. This work develops a novel nature-derived separator and provides insights in constructing functional separators toward sustainable and advanced AZIBs.

Generalized stability criterion for controlling solidification segregation upon twin-roll casting

• Systematical framework integrating dendritic growth model, overall solidification kinetic model and generalized stability was constructed. • Processing parameters of the casting speed and the flow speed of cooling water in twin-roll casting are coupled. • Sub-rapid solidification kinetics, concentration and segregation by different processing parameters couple were established. • New strategy was proposed: high initial driving force suppresses centerline segregation, and high final generalized stability suppresses edge segregation. Macro- and micro-segregation formed upon twin-roll casting (TRC) can be inherited from sub-rapid solidification to solid-state transformation, even to plastic deformation, thus deteriorating drastically mechanical properties of as-produced thin sheets. Although many works focusing mainly on controlling fields of thermal, concentration and convection have been reported, how to control artificially and quantitatively the segregation using a theoretical connection between processing parameters and solidification models, has not been realized, yet. Regarding it, a systematical framework integrating non-equilibrium dendritic growth and overall solidification kinetics with the TRC parameters, was constructed applying a generalized stability (GS) conception deduced from transient thermodynamic driving force Δ G t and transient kinetic energy barrier Q eff t evolving upon solidification. Departing from this framework considering synergy of thermodynamics and kinetics (i.e., thermo-kinetic synergy), a criterion of high Δ G t -high GS guaranteed that the macro (i.e., the centerline) and the micro (i.e., the edge) segregation can be suppressed by increasing Δ G t and GS at the beginning and the ending stage of sub-rapid solidification, respectively. This typical thermo-kinetic combination producing the microstructure can be inherited into the plastic deformation, as reflected by corresponding strength-ductility combinations. This work realized quantitative controlling of TRC by a theoretical connection between processing parameters and solidification models, where, an optimization for sub-rapid solidification segregation using the GS conception including Δ G t and Q eff t has been performed.

Alkali Adatom-amplified Schottky contact and built-in voltage for stable Zn-metal anodes

Development of rechargeable Zn-metal batteries is limited by side reactions, dendrite growth, and low ion-diffusion kinetics on Zn-anodes. Herein, alkali-metal adatom-modified amorphous carbon cluster passivation films (CCF-Ms) were formed on Zn-anodes by radiofrequency plasma thermal evaporation and alkali-metal hydroxide treatment. Plasma energy and alkali-metal hydroxide adatoms develop p-type semiconducting property and chemical durability of the carbon film by inducing dangling bonds and O-containing functional groups, to form Schottky contact between CCF-M and Zn metal with significant Schottky barrier (ΦSB) and built-in voltage (Vbi). CCF-M, ΦSB, and Vbi effectively enhanced the corrosion resistance, dendrite suppression, and Zn2+-transport kinetics of the Zn-anode, respectively. Specifically, Zn2+ was guided to deposit rapidly and uniformly below CCF-M without dendrites and side reactions during over 5000 and 1302 cycles in symmetric cell at 1.0 and 10 mA cm−2, respectively, with a capacity retention of ∼83% after 5000 cycles at 1.0 A g−1V2O5 in Zn|V2O5 full cell.

Rapid dendritic solidification and structure hardening mechanism of substantially undercooled quaternary nickel alloys

The high undercooling and rapid solidification of liquid quaternary Ni-5%Cu-5%Sn-5%Si and Ni-5%Cu-5%Sn-5%Ge alloys were achieved by glass-fluxing technique to explore their dendritic growth kinetics, microstructural evolution and hardening mechanisms. The dendrite growth velocity of α-Ni phase was found to increase with the rise of bulk undercooling, which could be described by power law functions for both alloys. With the increase of liquid alloy undercooling, the morphology of α-Ni phase transformed from developed dendrites into equiaxed grains. Both the fine grain hardening and solute hardening effects resulted in the elevated Vickers hardness for these two alloys. Nano-sized Ni3Si precipitations were detected within the first alloy, which distributed homogeneously in the α-Ni phase matrix and transformed from faceted to nonfaceted morphology at sufficiently large undercoolings. The precipitate hardening effect dominated the Vickers hardness enhancement for this Si containing alloy. Rapid solidification could modulate the formation of ordered precipitate phase and thus improve the hardening effect by changing dislocation motion conditions.

Li6PS5Cl microstructure and influence on dendrite growth in solid-state batteries with lithium metal anode

Enabling lithium metal is key toward maximizing the energy density of solid-state batteries (SSBs) with a solid electrolyte (SE) as the separator. However, the formation of pores at the LiǀSE interface during stripping and short-circuiting during cathodic plating through dendrite growth hinder stable cycling at higher current density. The interface and bulk microstructure of SEs govern the dendrite growth mechanism and hence the maximum or critical current density (CCD) an SE can sustain before shorting. Herein, via the control of the grain size of Li 6 PS 5 Cl (LPSCl), we show that interface and bulk microstructure can be simultaneously tailored to significantly influence the CCD. Based on the microstructure-strength relationship, we discuss mechanical failure mechanisms in SSBs derived from correlations between focused ion beam (FIB)-SEM and electrochemical data analyses. We propose that the microstructural influence on local current density and dendrite growth is well connected to the concept of crack growth resistance, or “R curve behavior,” observed in certain materials. • Interface and bulk microstructure of solid electrolytes govern dendrite growth kinetics • Li 6 PS 5 Cl grain size control gives control over interface and bulk microstructure • Critical current density depends on the grain size of the solid electrolyte • A dendrite growth mechanism is proposed based on the microstructure-strength relationship Dendrite growth in solid-state batteries is strongly correlated with stress initiation at the interface and subsequent stress propagation/shielding in the electrolyte bulk. Through the grain size distribution of the solid electrolyte separator, Singh et al. show that the anode interface and bulk electrolyte microstructure can be tailored, which influences the critical current density.

(Digital Presentation) Monitoring Dendrite Growth in Aqueous Zinc Ion Batteries with Guided Ultrasonic Waves

Dendrites form on the surface of metal electrodes as a battery undergoes repeated charging and discharging. The formation of dendrites not only affects the electrochemical performances of a battery but may also cause internal short-circuiting and thermal runaway events. Hence, there is a clear need to understand the formation mechanisms and growth kinetics of dendrites. Currently available technologies such as (in-situ) X-ray computed tomography and scanning electron microscopy can be used in a laboratory environment to study dendrite formation. However, they are often prohibitively expensive or unsuitable for long-term, large-scale, and in-operando monitoring.In this study we present an ultrasound-based technique which is cheap, with potential to scale up, and suitable in both laboratory and industrial environments. Different from conventional ultrasonic approaches which excite ultrasonic waves that propagating through layers of cathode, anode and electrolyte, the method presented in this study utilises miniature transducers which excite fundamental shear-horizontal (SH0*) guided ultrasonic waves that propagate along the cathode and anode. Hence, the presented method can individually monitor the condition of multiple electrodes which may be undergoing different ion-insertion mechanisms.A proof-of-concept study was performed on a symmetric aqueous zinc ion cell to explore the sensitivity of SH0* mode guided ultrasonic waves to zinc metal plating/stripping and dendrite formation at the electrode-electrolyte interface. We observed that the attenuation and velocity of waves show cyclical variations when the cell was in a chronopotentiometric cycling test. Variations of wave attenuation and velocity on the opposing working and counter electrode are observed to be in the opposite senses and the increasing/decreasing trends depend on the states (i.e., charging/discharging) of the cell. The cyclical variations of the ultrasound properties are only partially reversible and a monotonic drift can be observed which increases with increasing number of cycles.Coupling the ultrasonic measurements with images acquired by an optical microscope, clear correlations can be observed between changes in ultrasonic wave properties and zinc dendrite thickness. The partially reversible cyclical variations can be attributed to zinc plating/stripping that occur at the electrode-electrolyte interface. The irreversible, monotonic drifting can be attributed to the growth of zinc dendrites on the electrode surface. Hence, these findings demonstrate that the SH0* mode guided ultrasonic waves can offer valuable insights on physical changes at the electrode-electrolyte interface. It is therefore possible to quantitatively model and predict dendrite growth based on ultrasonic measurements. In conclusion, we believe the presented method can inspire more quantitative research on dendrite formation and in-operando monitoring of battery health. Figure 1

Rapid crystal growth kinetics of tungsten dendrites under electrostatic levitation state

The rapid crystal growth kinetics of tungsten dendrites within extremely refractory W60Re40 liquid alloy was examined under electrostatic levitation state. Tungsten dendrite growth through two solidification modes was revealed through modulating the active nucleation and spontaneous nucleation within the liquid undercooling range between 145 and 470 K, leading to the displacement of normal peritectic transition by metastable isomorphous solidification. The tungsten dendrites kept the priority growth direction of 〈100〉 and their growth velocity versus undercooling showed a power law function. The liquid alloy would solidify through normal peritectic transition if assisted with active nucleation from bottom Mo electrode.

Designing on solvent composition of dual-salt low concentration electrolyte for inhibiting lithium dendrite growth at −20 ℃

Lithium metal batteries (LMBs) are expected to become a new generation of energy storage technology based on the high theoretical specific capacity and low potential of lithium metal anode. In order to promote the commercial application of LMBs, lithium dendrite has become an urgent issue to be resolved to improve the battery safety. Since temperature is a key factor on dendrite growth kinetics, it is of great significance to design novel electrolytes for LMBs to inhibit lithium dendrite growth at low temperature conditions. In this work, γ-butyrolactone (GBL) with low melting point, ethyl propanoate (EP) with high wettability and low viscosity, and fluoroethylene carbonate (FEC) with excellent film-forming performance are chosen as the electrolyte components (GBL/EP/FEC, 7:3:1 w/w/w). Lithium tetrafluoroborate (LiBF4) and lithium difluorophosphate (LiDFP) are used as dual salts to reformulate a low-concentration electrolyte (LCE) of 0.5 mol L−1 (M), i.e., 0.4 M LiBF4 + 0.1 M LiDFP. The solvent compositions of the LCE electrolyte are optimally designed for Li||LiNi0.8Co0.1Mn0.1O2 (NCM811) cells, resulting in good low-temperature cycling performance without affecting the room-temperature performance. The electrolyte enables the Li||NCM811 cells to maintain both 97% capacity after 100 cycles at room temperature and obviously suppress lithium dendrite growth at −20 °C.

Numerical Analysis Growth Kinetics of Dendrite Tip during Laser Welding Nickel-Based Single-Crystal Superalloy Part I: Supersaturation-Driven Dendrite Growth

When three welding conditions, including welding configuration, welding speed and laser power, are sequentially altered, supersaturation of liquid aluminum is crystallography-dependently determined to limit growth kinetics of dendrite tip with decease of thermo-metallurgical factors for solidification cracking to salvage the weld properties during emerging laser welding repair of multicomponent nickel-based single-crystal superalloy. After comparing growth crystallography between right side and left side of weld, the distribution of supersaturation of liquid aluminum is axis- symmetrically developed by favorite (001)/[100] dendrite growth kinetics, while the distribution is nonaxisymmetrically developed by detrimental (001)/[110] dendrite growth kinetics. High heat input is inappropriately procured by either high laser power or slow welding speed to insidiously boost supersaturation of liquid aluminum, worsen alloying partition and solute copiousness, heterogeneously exacerbate morphology and size of dendrite growth, whereby stray grain formation is strongly produced. In order to ameliorate dendrite growth, low heat input is usefully rendered by either low laser power or high welding speed to attenuate supersaturation of liquid aluminum, narrow solidification temperature range and obviate dendrite tip undercooling alongside columnar interface in order to augment crack-resistant dendrite of epitaxial growth. The overall supersaturation of liquid aluminum is crystallography-dependent. During across whole melt-pool solidification interface, supersaturation of nonsymmetric (001)/[110] welding configuration is not as small as symmetric (001)/[100] welding configuration under well-controlled heat input, thereby fosters the kinetic factors for stray grain development to obstruct columnar dendrite and consequently weaken unidirectional morphology. It is crystallographically favorable for relief of supersaturation with axis- symmetrical dendrite growth. The mechanism of crack-vulnerable dendrite growth elimination through circumspect improvement of supersaturation-controlled growth kinetics is constructively proposed for feasible crackless rejuvenation of laser welding or laser cladding. The theoretical predictions are scrupulously supported by corroborative metallograph observation.

Phase and microstructure selection in peritectic alloys under high G-V ratio

Abstract A new model for the case of a superposition of a phase transformation and a microstructure transition from columnar plane front to equiaxed dendritic growth for peritectic alloys is presented. This model is applied to Fe–Ni alloys where a phase transition from γ to δ takes place when the solute content decreases. The results of the model are compared with predictions of the nucleation constitutional undercooling model. They show that the peritectic two-(solid) phase region is restricted and may completely disappear depending on nucleation undercooling and dendrite growth kinetics.

Effect of Inclusion and Filtration on Grain Refinement Efficiency of Aluminum Alloy

It is well known that the filtration efficiency of ceramic foam filters (CFF) on aluminum melt can be significantly reduced by the addition of grain refiner particles under a high inclusion load. Also, it is usually considered that the filtration process has little impact on grain refinement efficiency. In this work, the influence of inclusions and filtration on the grain refinement effect of AA 6060 alloy has been studied. This was done through TP-1 type solidification experiments where the aluminum melt prior to and after the filter during a pilot-scale filtration test was investigated. In the experiments, 80 PPi CFFs were used to filtrate aluminum melt with an ultra-high inclusion load and two addition levels of Al–3Ti–1B master alloys. It is found that both inclusions and filtration significantly reduce the grain refinement efficiency of the grain refiner master alloys. A detailed characterization of the used filters shows that the reduction of grain refinement efficiency is due to the strong adherence of TiB2 particles to the oxide films, which are blocked by the CFF during filtration. A grain size prediction model based on deterministic nucleation mechanisms and dendritic growth kinetics has been applied to calculate the solidification grain size and estimate the loss of effective grain refiner particles during filtration. It is shown that due to the strong adherence between TiB2 particles and oxide films in the melt, the high addition level of aluminum chips also has an influence on reducing the grain refinement efficiency of aluminum melt without filtration. The results of this study extended our understanding of the behavior and performance of inoculant particles in CFF and their interactions with the inclusions.

Phase-field modeling of dendritic growth of magnesium alloys with a parallel-adaptive mesh refinement algorithm

A two-dimensional phase field (PF) model was developed to simulate the dendritic solidification in magnesium alloy with hcp crystal structure. By applying a parallel-adaptive mesh refinement (Para-AMR) algorithm, the computational efficiency of the numerical model was greatly improved. Based on the PF model, a series of simulation cases were conducted and the results showed that the anisotropy coefficient and coupling coefficient had a great influence on the dendritic morphology of magnesium alloy. The dendritic growth kinetics was determined by the undercooling and equilibrium solute partition coefficient. A significant finding is acquired that with a large undercooling, the maximum solute concentration is located on both sides of the dendrite tip in the liquid, whereas the maximum solute concentration gradient is located right ahead of the dendrite tip in the liquid. The dendrite tip growth velocity decreases with the increase of the equilibrium solute partition coefficient, while the variation trend of the dendrite tip radius is the opposite. Quantitative analysis was carried out relating to the dendritic morphology and growth kinetics, and the simulated results are consistent with the theoretical models proposed in the previously published works.

Field variable diffusion cellular automaton model for dendritic growth with multifold symmetry for the solidification of alloys

The substantial mesh dependency caused by the discrete properties of cells and limitations of the sharp interface model are the inherent disadvantages of the cellular automaton (CA) model, which leads to difficulties in simulating dendritic growth with multifold symmetry and random preferred orientations for the solidification of alloys. A novel field variable diffusion CA (FCA) model is proposed by referring to the concept of the gradient energy term for diffuse interfaces in the phase field method. The diffusion equation for the field variable based on the constructed gradient functional is derived using the gradient descent method and is introduced into the CA model to reduce the mesh dependency. The FCA model deals with the solidification/remelting growth kinetics of the solid–liquid interface according to the lever rule and by considering the constitutional supercooling and Gibbs–Thomson effect. Free dendritic growth from undercooled melts and competitive dendritic growth during the directional solidification of Al–4 wt% Cu and Mg–5.26 wt% Al alloys were calculated to validate the accuracy of the FCA model for four-fold, six-fold symmetric dendritic morphologies and growth kinetics. The FCA model can efficiently reproduce multi-equiaxed and columnar dendrites with multifold symmetry and random preferred orientations as well as graphically reveal essential dendritic growth information, such as coarsening of secondary arms and side branch fusion.