Dendritic Evolution Research Articles

The Impact of Two and Three Dimensional Assumptions on Coupled Structural Mechanics and Microstructure Solidification Modelling

It is usual for computational efficiency to simulate growing alloy dendrites during solidification using a two-dimensional model. However, the fidelity of such simulations is to be questioned, since observations show that three-dimensional models lead to significantly more realistic results in comparison to experiments under many situations. Even in thin sample cases, the properties affecting, for example, mechanical behaviour are intrinsically three-dimensional. However, partly due to the lack of published work on the, topic the impact of 2D assumptions on the evolution and structural mechanical behaviour of dendrites has not been properly explored. In this study, solidification using the Cellular Automata (CA) method was coupled to a Finite Volume Structural Mechanics Solver (FVSMS) capable of both 2D and 3D modelling, applied to a selection of representative problems which clearly demonstrate that structural mechanics is another factor in the modelling of dendrites where two-dimensional assumptions can lead to significantly altered behaviour when compared to three-dimensional reality.

Revealing Morphology Evolution of Lithium Dendrites by Large‐Scale Simulation Based on Machine Learning Force Field

AbstractSolving the dendrite growth problem is critical for the development of lithium metal anode for high‐capacity batteries. In this work, a machine learning force field model in combination with a self‐consistent continuum solvation model is used to simulate the morphology evolution of dendrites in a working electrolyte environment. The dynamic evolution of the dendrite morphology can be described in two stages. In the first stage, the energy reduction of the surface atoms induces localized reorientation of the originally single‐crystal dendrite and the formation of multiple domains. In the second stage, the energy reduction of internal atoms drives the migration of grain boundaries and the slipping of crystal domains. The results indicate that the formation of multiple domains might help to stabilize the dendrite, as a higher temperature trajectory in a single crystal dendrite without domains shows a higher dendrite collapsing rate. Several possible modes of morphological evolutions are also investigated, including surface diffusion of adatoms and configuration twists from [100] exposed surfaces to [110] exposed surfaces. In summary, reducing the surface and grain boundary energy drives the morphology evolution. Based on the analysis of these driving forces, some guidelines are suggested for designing a more stable lithium metal anode.

Modeling of dendritic solidification and numerical analysis of the phase-field approach to model complex morphologies in alloys

Dendrites are one of the most widely observed patterns in nature, and occur across a wide spectrum of physical phenomena—from snow flakes to river basins; from bacterial colonies to lungs and vascular systems; and in solidification and growth patterns in metals and crystals. The ubiquitous occurrence of these “tree-like” structures can be attributed to their excellent space-filling properties, and at times, dendritic structures also spatially manifest fractal-like distributions. As is the case with many fractal-like geometries, the complex multi-level branching structures in dendrites pose a modeling challenge, and a full resolution of dendritic structures is computationally very demanding. In the literature, extensive theoretical models of dendritic formation and evolution, essentially as extensions of the classical moving boundary Stefan problem exist. Much of this understanding is from the analysis of dendrites occurring during the solidification of metallic alloys, as this is critical for understanding microstructure evolution during metal manufacturing processes that involve solidification of a liquid melt. Motivated by the problem of modeling microstructure evolution from liquid melts of pure metals and metallic alloys during metal additive manufacturing, we developed a comprehensive numerical framework for modeling a large variety of dendritic structures that are relevant to metal solidification. In this work, we present a numerical framework encompassing the modeling of Stefan problem formulations relevant to dendritic evolution using a phase-field approach and a finite element method implementation. Using this framework, we model numerous complex dendritic morphologies that are physically relevant to the solidification of pure melts and binary alloys. The distinguishing aspects of this work are—a unified treatment of both pure metals and alloys; novel numerical error estimates of dendritic tip velocity; and the study of error convergence of the primal fields of temperature and the order parameter with respect to numerical discretization. To the best of our knowledge, this is a first of its kind study of numerical convergence of the phase-field equations of dendritic growth in a finite element method setting. Further, using this numerical framework, various types of physically relevant dendritic solidification patterns like single equiaxed, multi-equiaxed, single columnar and multi-columnar dendrites are modeled in two-dimensional and three-dimensional computational domains.

Linearized Tracking of Dendritic Evolution in Rechargeable Batteries

The formation of the dendritic microstructures during the electrodeposition is a complex process depending on several physical/chemical parameters. We establish an analytical framework for tracking the one dimensional dendritic interface based on the asynchronous developments in the concentration C and the electric potential V. Comparing the dynamics of the interface vs the ions, we establish linearized forms of the concentration C and the electric potential V during the quasi-steady-state evolution. Subsequently, we investigate the potentiostatic (V 0) and galvanostatic (i 0) conditions, where we have analytically attained the dependent parameters (i or V) and justified their respective variations in the binary electrolyte. Consequently, we have quantified the role of original concentration C 0, the inter-electrode potential V 0, the electrolyte diffusivity D and the inter-electrode separation l on the value and the growth rate of the dendritic interface. In particular, for the given infinitesimal dendritic growth, we have shown a higher efficacy for the electromigration than the diffusion, especially during the instigation period of the electrodeposition.

Mesoscopic-scale study of convection-induced morphological evolution of solid-air dendrites in liquid hydrogen

The trace amount of air infiltration that may occur during the utilization of liquid hydrogen may be confronted with a severe security risk. Considering the effect of convection, a six-fold symmetric solid-air dendrite growth numerical model is established for the coupling of flow field, temperature field and solute field during solidification process. For regular Cartesian grids, a factor is introduced to reduce the anisotropy of grids, and its validity is verified. The reliability of the model is evaluated by comparing the numerical results of the growth of ice-dendrite with the same face-centered cubic structure with the experimental results, and the subsequent numerical results of solid-air dendrites growth rate match well with the results of analytical theory. On this basis, the growth characteristics of solid-air dendrites under diffusion condition and natural convection and forced convection conditions are studied. The results show that the tip of each dendrite arm has a consistent growth rate under diffusion condition, and the dendrites present a six-fold symmetric morphology. The dendrite growth is promoted in the upstream and inhibited in the downstream under both natural convection and forced convection conditions, and the morphology of the reshaped dendrites lose symmetry. Forced convection promotes upstream more than it inhibits downstream. The mechanism of the two conditions affecting the growth of solid-air dendrites and the differences between them are explained in detail.

Dendrite evolution and quantitative characterization of γ′ precipitates in a powder metallurgy Ni-based superalloy by different cooling rates

The effect of cooling rate after super-solvus heat treatment on the morphological evolution of γ′ precipitates in an advanced powder metallurgy Ni-based superalloy, FGH4113A, was systematically investigated. The quantitative relationship between the cooling rate and γ′ precipitates was elucidated in detail. The results showed that at cooling rates of 200 °C/min and 600 °C/min, the primary branch of dendritic γ′ grew along the< 111 > direction, whereas the secondary branch grew along the< 100 > and {111} directions. In addition to the interfacial and elastic strain energies, the width of the γ′ channel significantly impacted the evolution of the secondary dendritic orientation of γ′. As the cooling rate decreased, the size and volume fraction of the γ′ precipitates increased, whereas the nucleation density of the γ′ precipitates decreased. A strong power-law relationship between the characterization of the γ′ precipitates (such as volume fraction, nucleation density, particle size) and the cooling rate was revealed analytically. Meanwhile, the γ′ morphologies evolved from spheres to cuboids, concave cuboids, octets, and dendrites as the cooling rate decreased. The evolution mechanism and stability of γ′ precipitates were proposed to control their morphology and optimize the properties of superalloys. • The width of γ channel affected the dendrite evolution direction of γ′ secondary branches were demonstrated. • The growth mechanisms of different secondary branches of dendrite γ′ were illustrated. • The different morphology evolution paths of γ′ during cooling rates were revealed. • The power exponential relationship between d s γ ′ , d t γ ′ , f , ρ d grain boundary width and cooling rates were revealed.

Operando Optoelectrochemical Analysis of Single Zinc Dendrites with a Reflective Nanopore Electrode.

Dendrites can severely impair zinc battery performance. An in-depth understanding of the dynamic morphology evolution of dendrites with operando approaches is pivotal when addressing these issues. However, in previous studies, the corresponding electrochemical signals are usually ensemble and averaged. It is very challenging to obtain detailed information about the key morphology-performance relationship. Herein, correlated high-resolution operando optical and electrochemical studies of single dendrites on Pt reflective nanopore electrodes are reported. The zinc deposition and dissolution can be directly imaged by a high NA optical microscope, while corresponding galvanic charging and discharging curves are obtained. The correlated information of morphology changes and dynamic overpotential fluctuations under different circumstances unveils the competition between active growth vs. passivation. The isolated zinc formation at the single dendrite level is also evaluated. The methodology can be further extended to elucidate the direct relationship between dendrite evolution and electrochemical responses in various battery systems.

Lattice Boltzmann Simulation of Non-Steady-State Particulate Matter Filtration Process in Woven Fiber

To enhance the design process of high-performance woven fibers, it is vital to clarify the evolution of particle dendrites, the dynamic pressure drop, and the capture efficiency with respect to dust loading during the non-steady-state filtration process. A general element (orthogonal elliptical fibers) of woven filter cloths is numerically simulated using the 3D lattice Boltzmann-cell automation (LB-CA) method, where gas dynamics is solved by the LB method while the solid particle motion is described by the CA probabilistic approach. The dendrite morphologies are evaluated under various particle diameters, aspect ratios, packing densities, and inlet fluid velocities. For submicron particles in the “Greenfield gap” range, it is revealed that the normalized pressure drop is an exponential function of the mass of deposited particles, and the rate of increase is exactly proportional to the perimeter of the elliptical fibers. Moreover, the normalized capture efficiency is a linear function of the deposited mass. It is not advisable to increase the packing density too much, as this might simply increase the pressure drop rather than enhancing the normalized capture efficiency. It is also worth noting that the fitting slope is more likely to grow linearly once the aspect ratio exceeds 1.6, indicating that orthogonal elliptical woven fibers offer higher capture efficiency than normal orthogonal cylindrical woven fibers. The work is beneficial to gain insights into the angular distribution of particle dendrites, as well as the prediction of dynamic growth of pressure drop and capture efficiency of the elliptical fiber. These efforts could help to deepen the understanding and realize assistant designing for the filtration performance of woven fiber in the future.

Modeling on transient microstructure evolution of solid-air solidification process under continuous cooling in liquid hydrogen

The safety hazard brought by the oxygen-rich solid formed by the solidification of air in liquid hydrogen cannot be ignored. A numerical model describing the evolution of dendrite during solidification of nitrogen-oxygen binary solutions in liquid hydrogen is developed. By introducing the reduction factor, the growth anisotropy of the six-fold symmetric dendrite simulated by the Cartesian grid is effectively reduced. The reliability of the model is verified by comparing the tip growth rate of dendrites with six-fold symmetry with analytical models. On this basis, the microstructure evolution and solute segregation of solid-air dendrites are investigated. The results show that with the increase of the cooling rate, the dendrite growth rate accelerates while aggravating the solute segregation, and the outer edge of the dendrite is more likely to reach the oxygen-rich state. The improvement in solute diffusibility enables dendrites to reach an oxygen-rich state at larger sizes, but also accelerates dendrite growth. The initial composition has little effect on the microstructure evolution and growth rate of the solid-air dendrite. However, in the presence of forced convection, the solid-air dendrite morphology loses its symmetry and makes the upstream dendrite arms reach an oxygen-rich state at a smaller size. This study helps to understand the air solidification process in liquid hydrogen and provides theoretical guidance for the safety research of liquid hydrogen system.

Investigating the Effects of Dendrite Evolution on Microsegregation in Al–Cu Alloys by Coupling Experiments, Micro-modeling, and Phase-Field Simulations

Investigating the Effects of Dendrite Evolution on Microsegregation in Al–Cu Alloys by Coupling Experiments, Micro-modeling, and Phase-Field Simulations

Assessing Microstructure Tensile Properties Relationships in Al-7Si-Mg Alloys via Multiple Regression

The development of Al-based alloys presumes a detailed understanding of the microstructure evolution during solidification since the as-solidified microstructure also has effects on the subsequent thermo-mechanical processing. In the present investigation Al-7wt.%Si-xMg (x = 0.5 and 1 wt.%) alloys are subjected to transient directional solidification with a view to characterizing the microstructure evolution, with special focus on both dendritic evolution and the inherent features of the Mg2Si and π-AlSiFeMg intermetallics. Experimental power-type functions relating the primary, secondary and tertiary interdendritic spacings to the solidification cooling rate and growth rate are developed. It is observed that the Mg content added to the Al-7wt.%Si alloy and the consequent increase in the Mg2Si fraction tends to increase the values of the primary dendritic spacing. However, this same behavior is not verified for the growth evolution of dendritic side branches. A multiple linear regression (MLR) analysis is developed permitting quantitative correlations for the prediction of tensile properties and hardness from microstructural parameters to be established. The increase in the Mg alloy content from 0.5 to 1 was shown to promote an increase in both the ultimate tensile strength (σu) and elongation.

Fullerene-Derivative C60-(OLi)n Modified Separators toward Stable Wide-Temperature Lithium Metal Batteries

Lithium metal anode has been considered as the “holy grail” for realizing the next-generation high-energy rechargeable batteries, yet its practical use has been plagued by hazardous dendrite evolution owing to hostless metal deposition/dissolution at Li-electrolyte interface. To address the above issue, here we show that a Li+-contained fullerene derivative, C60-(OLi)n, has been prepared and used to modify conventional polypropylene separators for suppressing the Li dendrites at the interface. During the electrochemical reaction, the -OLi groups attached to the fullerene easily react with Li, forming a Li2O-enriched, artificial solid electrolyte interphase between the anode and the electrolyte. Owing to high Li+ conductivity of Li2O, the Li2O-enriched interphase serves as ion redistributor to guide homogeneous Li deposition/dissolution at the Li-electrolyte interface. By employing the C60-(OLi)n-modified separator, symmetric Li-Li cells and LiNi0.8Co0.1Mn0.1O2||Li full cells show ultra-long cycle lives and a wider range of operation temperature down to −40 °C. This work provides insights into surface protection and dendrite control of Li-metal anode towards practical realization of high-performance rechargeable Li-metal batteries.

Microstructural evolution and local mechanical properties of dendrites in Al0.6CoCrFeNi high entropy alloy

The microstructural evolution and local mechanical properties of dendrites, including the fcc dendritic core (DC) and bcc/B2 inter-dendritic (ID) regions of Al0.6CoCrFeNi high entropy alloy (HEA) at different annealing temperatures were investigated by electron microscopy and nanoindentation tests. In the fcc DC region, nanoparticles of the ordered L12 phase precipitated at 600 and 700 °C. At 800 °C, the L12 phase was replaced by a fine needle-like ordered B2 phase, and B2 coarsened with increasing temperature. In the bcc/B2 ID region, as the annealing temperature increases, the disordered bcc gradually transforms to the σ phase, and the σ phase stably exists at 700 and 800 °C. The nanoindentation test results showed that the L12, fine B2, and σ phases significantly increased the hardness of the DC and ID regions. In addition, the solidification paths of the as-cast alloy and the phase evolution mechanisms in the DC and ID regions were explored in conjunction with thermodynamic calculations. The investigation of the structural evolution and mechanical behavior of different microscopic regions will facilitate HEA design.

Influence of hexagonal to orthorhombic phase transformation on diffusion-controlled dendrite evolution in directionally solidified Sn–Ni peritectic alloy

The hexagonal to orthorhombic (HO) transformation from β-Ni3Sn2 (hexagonal) phase to α’-Ni3Sn2 (orthorhombic) phase was confirmed in directionally solidified Sn–Ni peritectic alloys. It is shown that the remelting/resolidification process which is caused by both the temperature gradient zone melting (TGZM) and Gibbs−Thomson (G−T) effects can take place on secondary dendrites. Besides, the intersection angle between the primary dendrite stem and secondary branch (θ) is found to increase from π/3 to π/2 as the solidification proceeds. This is the morphological feature of the HO transformation, which can change the diffusion distance of the remelting/ resolidification process. Thus, a diffusion-based analytical model is established to describe this process through the specific surface area (SV) of dendrites. The theoretical prediction demonstrates that the remelting/resolidification process is restricted when the HO transformation occurs during peritectic solidification. In addition, the slope of the prediction curves is changed, indicating the variation of the local remelting/resolidification rates.

Elastomer–Alginate Interface for High‐Power and High‐Energy Zn Metal Anodes

AbstractSpontaneous corrosion and uncontrolled dendrite accumulation of Zn rapidly degrades zinc–metal battery performance. Artificial interfaces have been widely fabricated on Zn metal anodes, yet most interfaces are detrimental to ion transfer and adapt poorly to spatial changes during Zn plating/stripping. Herein, a hybrid interface, consisting of a thermoplastic polyurethane (TPU) fiber matrix and Zn‐alginate (ZA) filler, is designed, which serves as a physical barrier between anode and electrolyte to inhibit side reactions. Encouragingly, ZA regulates Zn2+ transport and endows uniform Zn deposition by inducing plating/stripping underneath the hybrid interface. At the same time, the TPU frame acts as a super‐elastic constraint to further suppress rampant dendrite evolution and accommodate a large amount of deposited Zn. Consequently, the interface‐protected Zn anode delivers high cycling stability (1200 h at 5 mA cm–2/5 mA h cm–2; 500 h at 10 mA cm–2/10 mA h cm–2), realizing an exceptional cumulative capacity of over 6000 mA h cm–2. This enhancement is well maintained in the full cell when coupled with a vanadium‐based cathode. The unique matrix‐filler architecture and mechanistic insights unraveled in this study are expected to provide a general principle in designing functional interfaces for metal anodes.

The effect of cross-section geometry of castings on dendrite evolution in Mg Gd alloys by in situ X-ray radiography

The solidification process of Mg-15Gd(wt.%)alloys with different cross-section geometry is investigated in situ by synchrotron radiation imaging technology. The evolution of dendrites, including the nucleation and growth processes, has been recorded and analyzed for magnesium alloys with different cross-section geometry. It is shown that the cross-section geometry of the samples has significant effect on the number of dendrites, the growth rate of dendrites, and the solute distribution. We find that the cross-sectional change does not conducive to the nucleation of dendrites. The variable cross-section facilitates the growth of dendrites while the T-type section inhibits the growth of dendrites. The solute in the variable cross-section sample (VSS) is enriched at the shoulder while the solute in the T-type section sample (TSS) tends to concentrate at the bottom of the boss. Meanwhile, the fracture and drift of dendrites in VSS and TSS are observed. As a result, the grain fragments tend to form stray crystals

Microstructure of Lithium Dendrites Revealed by Room-Temperature Electron Microscopy

The uncontrolled deposition/dissolution process of lithium dendrites during electrochemical cycling in batteries limits the large-scale application of Li metal anodes. Investigating the microstructure of Li dendrites is a focal point. Currently, the only way to protect and observe sensitive Li dendrites is through low-temperature transmission electron microscopy (LT-TEM), whereas room-temperature characterization is still lacking. In this work, the room-temperature microstructure of Li dendrites was obtained by TEM using both vacuum- and inert-gas-transfer methods. Detailed comparison between LT- and room-temperature (RT-)TEM characterizations was provided to show the pros and cons of each method. Especially, RT-TEM shows the advantage of flexible incorporation with multifunctional characterizations, such as 3D tomography. By using RT-TEM, microstructural evolution of Li dendrites during the electrodeposition/dissolution process, including increase of the quantity of inorganic Li2O compounds in the solid electrolyte interphase, lateral growth behavior, and two types of inactive Li, has been revealed, enriching the understanding of the structure-property relationship of Li dendrites.

Time invariance of three-dimensional morphology of equiaxed dendrite: A phase-field study

Dendrite morphology has a significant effect on solute segregation and fluid flow in bulk metallic materials. Therefore, the detailed morphological evolution of dendrites is important to better understand these processes. Recently, three-dimensional (3D) dendrite morphology has been analyzed using interface shape distribution (ISD) maps that are spanned by the curvedness and shape factor of the local solid−liquid interface in an Al−Cu alloy. Data were collected through in-situ observations using synchrotron radiation imaging techniques [J.W. Gibbs et al.: Sci. Rep., 5 (2015) 11824]. This methodology is quite effective for describing 3D dendrites. In this study, we thoroughly investigated the morphological evolution and the related ISD map of free-growing equiaxed dendrites in an Al−3mass%Cu alloy using a quantitative phase-field model. The ISD was found to differ depending on the degree of undercooling. Importantly, the results indicate the presence of a time-invariant feature after sufficient branching and growth of secondary arms, when the degree of undercooling is substantial enough to produce a bunch of branching. The time invariance is considered a universal feature of equiaxed dendrite growth.

Towards the Stable Evolution of Dendrites in the Case of Intense Convection in the Melt

The solid-phase pattern in the form of a dendrite is one of the frequently met structures produced from undercooled liquids. In the last decades, an analytical approach describing the steady-state crystal growth in the presence of conductive heat and mass transport has been constructed. However, experimental works show that crystal patterns frequently grow in the presence of convection. In this paper, a theoretical description based on convective heat and solute concentration transport near the solid/liquid phase interface is developed. The stable regime of crystallization in the presence of vigorous convection near the steady-state crystal vertex is studied. The stability analysis, determining the stable growth mode, and the undercooling balance law have been applied to deduce the stable values for the growth rate and tip diameter. Our analytical predictions (with convective transport) well describe experimental data for a small melt undercooling. Moreover, we compare both convective and conductive mechanisms in the vicinity of the crystal vertex. Our theory shows that convective fluxes substantially change the steady-state growth of crystals.

Revealing the Two-Dimensional Surface Diffusion Mechanism for Zinc Dendrite Formation on Zinc Anode.

Aqueous zinc-ion battery is regarded as one of the promising devices for large-scale energy storage systems owing to its high safety, cost-effectiveness, and competitive electrochemical properties. However, the dendrite growth on zinc metal anodes dramatically hinders its further practical applications, and the internal mechanism of dendrite evolution is still unclear. The introduction of a protective layer on the anode interface is an effective method to avoid zinc dendrite growth. Herein, a two-dimensional (2D) atomic surface diffusion mechanism is proposed to reveal the evolution of zinc deposition from tiny protrusion to dendrite under uneven electric and ionic fields. Further, the conductive copper nitride (CN) protective layer is constructed on the zinc metal anode by a facile and scalable magnetron sputtering approach. Their protective layer possesses a high zinc affinity and high diffusion barrier for zinc atom migration, leading to spacious nucleation, and uniform zinc deposition, thus significantly boosting the electrochemical stability. For the first time, the role of the restricted 2D atomic surface diffusion mechanism in inhibiting the formation of zinc tiny protrusion that induces uneven electric and ionic fields is revealed. This work can provide a novel insight for future research on dendrite-free zinc metal anodes by interfacial modification.