Dendritic Evolution Research Articles

Operando visualisation of battery chemistry in a sodium-ion battery by 23Na magnetic resonance imaging

Sodium-ion batteries are a promising battery technology for their cost and sustainability. This has led to increasing interest in the development of new sodium-ion batteries and new analytical methods to non-invasively, directly visualise battery chemistry. Here we report operando 1H and 23Na nuclear magnetic resonance spectroscopy and imaging experiments to observe the speciation and distribution of sodium in the electrode and electrolyte during sodiation and desodiation of hard carbon in a sodium metal cell and a sodium-ion full-cell configuration. The evolution of the hard carbon sodiation and subsequent formation and evolution of sodium dendrites, upon over-sodiation of the hard carbon, are observed and mapped by 23Na nuclear magnetic resonance spectroscopy and imaging, and their three-dimensional microstructure visualised by 1H magnetic resonance imaging. We also observe, for the first time, the formation of metallic sodium species on hard carbon upon first charge (formation) in a full-cell configuration.

Simulation of dendritic remelting and fragmentation using coupled cellular automaton and Eulerian multiphase model

Dendritic structures are one of the most complicated forms of crystallization in nature and technology and strongly affect the properties of as-cast metals. The evolution of dendrites during solidification process is important for the optimization of materials structure and performance. Current computational models focus mainly on predicting the growth of dendrites, while neglecting the phenomenon of remelting and fragmentation. In this study, we develop, validate and apply a solute induced dendrite remelting model achieved by fully coupling cellular automaton (CA) and finite volume method (FVM). Our model successfully simulates the evolution of dendrites with both growth and remelting processes included. In comparison with other existing work, the present model is developed on the basis of an Eulerian two-phase model which allows us to treat the solid and liquid as two separate phases and for first time to fully describe the interactions of phase transformation, fluid flow, heat transfer and solute transport between those two phases. Our novel framework is applied on a single Al-4.5 wt% Cu alloy nucleus placed in undercooled melt. The results reveal that four stages of dendrite remelting exist, with the last stage leading to fragmentation. Fragmentation is shown to occur when the connection points between downstream dendrite arms and vertical primary dendrite arms are melted. No fragment is observed on the upstream side.

Microstructural characterization of dendritic evolution using two-point statistics

Characterizing large four-dimensional materials datasets is difficult due to the presence of complex microstructures and time-varying length scales. We showcase the use of two-point statistics as an efficient and un-biased way of extracting materials parameters from an Al-Cu alloy during solidification. The evolution of dendrite primary arm thickness, average secondary arm spacing, and average tip-to-tip spacing were tracked using two-point Pearson auto-correlations of scaled mean curvatures. Insights into competitive side-branching are also reported. We show both visually and quantitatively that most length scales change rapidly during early stages of dendritic growth, but slow as diffusion fields of dendrites overlap.

Dendritic copper microstructured electrodeposits for efficient and selective electrochemical reduction of carbon dioxide into C1 and C2 hydrocarbons

Here, we report synthesis of copper microstructures-based electro-catalyst with controlled morphologies and crystallinity via a rudimentary simple and green electrochemical dissolution method. The variations in the growth pattern of the dendritic shaped Cu microstructures were studied to understand the evolution of Cu dendrites with respect to several electrolysis parameters viz. applied bias voltage, concentration of organic additives, i.e. L-ascorbic acid, and electrolysis time and temperature. We show that these microstructures demonstrate efficient and selective electrochemical conversion of CO2 into CO along with methane and ethane from CO2-saturated moistened di-methyl sulfoxide (DMSO) electrolyte solution. Our results establish that the selectivity for C1 or C2 hydrocarbons (methane or ethane) as a major product can be tuned systematically by altering the extent of branching in dendrite microstructures as well as the extent of exposure of (111) and (200) facets. The production of C1 and C2 hydrocarbons along with CO in the present study can be ascribed to the availability of protons from the residual water (<0.2 % v/v or ca. 1000 ppm) in hygroscopic DMSO. The optimized dendritic shaped electro-catalyst is perceived to have the fine branching and exposed facets that convert CO2 into CO with Faradaic Efficiency (F.E.) of 32 %, ethane with F.E. of 29 % and methane with F.E. of 5%. The production of ethane reaches a maximum of 33 % at -1.5 V (NHE), which to the best of our knowledge is the highest reported so far for electroreduction of CO2 over Cu in organic media.

Competitive dendrite growth during directional solidification of a transparent alloy: Modeling and experiment.

A two-dimensional (2-D) cellular automaton-finite difference method (CA-FDM) model and in situ observation experiments of directional solidification using a transparent alloy of SCN-2wt.% ACE are employed to investigate various microstructural evolution of columnar dendrites during directional solidification. In the present model, the growth of columnar dendrites is simulated using a CA technique. The solute diffusion is solved using the FDM. The model is capable of visualizing the interaction between the formation of dendrite arrays with identical or different growth orientations, and the evolving solute concentration field. Several dendritic competitive growth modes between two converging and diverging dendrite arrays are reproduced. The simulation results agree well with the experimental observations. The simulations are also performed to study the effects of temperature gradient and cooling rate on the growth morphology of diverging dendrites. It is found that with the increase of temperature gradient and cooling rate, the tertiary branches produced from the well-developed side branches of the unfavorably oriented grain at the divergent grain boundaries are more likely to become the new primary dendrite arms.

Observation of side arm splitting studied by high resolution X-ray radiography

Abstract The local dynamics of dendritic side arms during the growth stage were studied by in-situ radiography observations at high spatial resolution of better than 1 μm. A flat sample of a Ga–In alloy was solidified top-down applying a vertical temperature gradient. The evolving dendritic microstructure was visualized using synchrotron X-ray imaging at the beamline ID19 (ESRF, France). The experimental investigations on the dendrite evolution revealed a transition from a four-fold symmetry to a hyperbranched dendritic morphology. Both the side arm-splitting phenomenon – responsible for this morphological transition – as well as the arm growth dynamics were characterized using image processing.

Simulation and synthesis of silver dendritic nanostructures for surface-enhanced Raman scattering

Silver dendritic nanostructures (AgD) is investigated for surface-enhanced Raman scattering (SERS) with simulation and experiments, the simulations showed that there is a significant absorbance over a broad spectrum from the AgD, this indicated that AgD is a good candidate for SERS. The simulations helped to study the parameters of the AgD that affects the SERS and we applied these simulation results for experimental designs, in which our experimental results of synthesis and characterization results of Raman spectrum showed consistence with the simulation results. These simulation results are very helpful in deciding the experimental parameters for efficient and effective synthesizing and reproduction of hierarchical silver dendritic nanostructure. The AgD were produced using displacement redox reaction between AgNO3 solution and Copper foil. We found that the concentration of AgNO3 played major role on the rate of reaction, and the rapid growth of the silver nanostructures was observed as the reaction time increases. The structural and morphological evolution of silver dendrites was examined with Scanning Electron Microscope (SEM). The Raman enhancement of AgDs was evaluated using Elman's reagent (DTNB) and Rhodamine 6G (R6G). The silver dendrites have great potential for diverse sensing applications ranging from food safety control, environmental monitoring and assessment, forensic investigation, and to medical diagnosis.

Numerical simulation of dendritic evolution based on an improved cellular automaton model involving solute field

This paper studied the single crystal growth of Fe-0.64C alloy under a fixed cooling rate, proposed an improved cellular automaton model. The influence of solute field on dendrite growth is especially considered into the model. And a new solute distribution scheme based on Fick's first law and solute conservation was proposed from the microscopic scale. In addition, the present work improved the acquisition algorithm, which takes the growth length of the interface cell to the neighbouring cell as the determination condition of the capture. A solid fraction calculation method based on the solidification area of interface cell to total area is also proposed. The results show that this model can not only dynamically display the formation process of secondary dendrites and high-order dendrites, but also simulate the distribution of solute inside the dendrites and at the interface front.

A New Efficient Quantitative Multi-component Phase Field: Lattice Boltzmann Model for Simulating Ti6Al4V Solidified Dendrite Under Forced Flow

Ti6Al4V is a widely used, multi-component alloy in additive manufacturing, during which the fluid flow in the molten pool significantly affects the solidified dendrites. To predict and further control the microstructure, modeling and simulating the microstructure evolution play a critical role. In this study, a newly developed, efficient, quantitative multi-component phase-field (PF) model is coupled with a lattice Boltzmann (LB) model to simulate Ti6Al4V solidified dendrite evolution under fluid flow. The accuracy and convergence behavior of the model is validated by the Gibbs–Thomson relation at the dendrite tip. Single and multiple two-dimensional (2D) equiaxed dendrite evolution cases under forced flow were simulated. Results show that the dendrite pattern is influenced remarkably by the fluid flow. Underlying mechanisms of the asymmetrical evolution are revealed by discussing the interaction among the flow, composition distribution and dendrite morphology, quantitatively. The dendrite kinetics are also derived, which ascertains the relationship between tip velocity and undercooling and inlet velocity and is the foundation for larger-scale simulation. We believe that the coupled quantitative multi-component PF–LB framework employed in this study helps in investigating the solidified dendrite morphology evolution in a deep and quantitate manner.

The Pyridinic-to-Graphitic Conformational Change of Nitrogen of Graphitic Carbon Nitride on Lithium Coordination during Lithium Plating

The reversibility of lithium plating/stripping should be guaranteed in lithium metal batteries. Seriously polarized lithium growth during plating leads to the dendritic evolution of lithium metal due to the uneven current distribution on the electrically conductive surface. Artificial protective layers covering electrodes (e.g., polymer film on copper foil) have been used to narrow the gap of the current density between positions on the conductive surface. Herein, we incorporated an active ingredient to attract lithium ions into the dendrite-suppressing layer. Pyridinic nitrogen of graphitic carbon nitride (g-C3N4) served as the lithium ion affinity center. Conformation of the nitrogen was changed from pyridinic to graphitic in the presence of lithium ions, which confirms the coordination of lithium ion to the pyridinic nitrogen. Lithium metal was plated between the g-C3N4 layer and the copper current collector (or the lithium metal). The homogeneous lithium nucleation expected from the active role of the pyridinic nitrogen on regulating ionic pathways suppressed the dendritic growth of lithium metal and decreased the overpotential required for the initial metal nucleation. Due to the top-down ion flux regulation on the uppermost surface (or tip) of lithium metal, the reversibility of lithium plating/stripping was dramatically improved.

Phase-field lattice-Boltzmann investigation of dendritic evolution under different flow modes

ABSTRACTNumerical modelling offers an effective method to investigate the effect of convection on dendritic growth; however, the current numerical approach to modelling convection behaviour is simplified, e.g. only simulating a shear flow by setting a constant inlet velocity and a zero-velocity-gradient outlet boundary condition. In this work, based on a phase-field lattice-Boltzmann approach, the effect of various flow modes on dendritic growth is investigated by introducing an external force term to induce flow. Numerical tests (2-D and 3-D) validate that the results according to the force-induced flow agree well with those by the velocity-imposed flow. Intricate convection effects under complex boundary conditions are discussed in detail. Furthermore, this force-induced flow mode allows additional freedom by eliminating the restriction on the initial position of the nuclei, which provides new ways to the microstructure modelling under complex convection.

Dendritic Growth Under Natural and Forced Convection in Al-Cu Alloys: From Equiaxed to Columnar Dendrites and from 2D to 3D Phase-Field Simulations

The interaction between convection and solute transport during solidification has significant influence on the dendritic evolution. By employing the phase-field lattice-Boltzmann approach together with the parallel and adaptive-mesh-refinement algorithm, the dendritic evolution under convection is simulated in both 2D and 3D cases. The flow-induced redistribution of the solute alters both tip velocity and the development of dendritic arms. The effect of both convection and undercooling is quantified and compared using the length ratio of the dendritic arms. The effect of convection behavior (i.e., natural and forced) and domain dimension (i.e., 2D and 3D) on dendritic growth is discussed. Results show that the convection effect is mainly dominated by the convection mode, and the melt flow in 2D can produce biased results comparing with those in 3D.

GPU-accelerated three-dimensional large-scale simulation of dendrite growth for Ti6Al4V alloy based on multi-component phase-field model

Ti6Al4V is one of the most widely used ternary alloys in additive manufacturing. Its mechanical properties are highly determined by the prior β phase. However, simulation of the ternary alloy solidified microstructure is limited for the lack of available methods. In this study, we carried out two-dimensional (2D) and three-dimensional (3D) simulations based on a new multi-component (MC) phase-field (PF) model by extending Karma’s binary PF theory. The correctness and accuracy of the MC model are validated by the Gibbs-Thomson relation at dendrite tip. With the equipment multiple GPUs, the highest speedup ratio more than 150 is obtained compared with serial programming running on one of the top CPUs and simulations with billion nodes can be completed within acceptable time. Using this model as benchmark, previous Ti6Al4V dendrite evolution using pseudo-binary PF model is investigated and found magnifying the driving force and growth artificially. 3D large-scale directional solidification simulations also shed light on dendrite merging which leads coarse primary dendrites. We believe that the GPU-accelerated MC PF framework provides an accurate and efficient insight in understanding the solidifying evolution for Ti6Al4V.

In Situ Observation of Dendrite Behavior of Electrode in Half and Full Cells

Lithium dendrites may cause internal short-circuiting, fires, and even explosions. Unfortunately, the study of dendrites has been hindered by the impossibility of in situ observations. This work proposes a new double-scale in situ experimental setup that records the dendrite evolution of half and full cells during small-current-density electrochemical testing. The experiments confirmed that dendritic growth eventually connects the cathode to the anode, with significant effects on the cell voltage. In the full and half-cells, the attached dendrites decreased and increased the voltage, respectively. During discharge, the bubbles generated by the side reaction affected the dendrite evolution in both cells. A detailed model of lithium dendrite evolution mechanism in the anode is also proposed.

Modeling of microstructure and microsegregation formation during solidification of Al-Si-Mg alloys

A two-dimensional (2-D) cellular automaton (CA) model considering phase equilibria according to the Calphad method is proposed for the simulation of solidification microstructures and microsegregation of Al-Si-Mg alloys. The present model encompasses the essential aspects of thermodynamics and kinetics of phase transformation during solidification of ternary Al-rich alloys, particularly nucleation and growth of primary dendrites, irregular binary and ternary eutectic phases, as well as the time-dependent mass transport of two solutes. The proposed CA model is applied to simulate the evolution of primary dendrites and irregular eutectic microstructures of Al-Si-Mg alloys. The influence of the cooling rate on the solidified microstructures and microsegregation is investigated. The following features are reproduced well by the CA simulations: microstructural length scales correlate with the cooling rate; the homogeneity of the primary α-phase is quantified depending on the cooling rate and deviates considerably from Scheil-type calculations; back diffusion is accompanied by a decrease in the eutectic fraction, considering that some amount of eutectic β-phase is dissolved to maintain solute conservation and adjustment of equilibrium in the eutectic.

Formation of low-angle grain boundaries under different solidification conditions in the rejoined platforms of Ni-based single crystal superalloys

Abstract

Effect of fluid flow on solidified equiaxed dendrite morphology evolution based on phase field - lattice Boltzmann method

Fluid flow can significantly change the evolution of microstructural morphology. However, relatively little is known how the fluid flow, concentration and microstructure affect each other quantitatively, which is essential to optimize processing parameters. A quantitative simulation study of Al-Cu solidified equiaxed dendrite evolution under forced flow based on phase field - lattice Boltzmann method (PF-LBM) is carried out. Results obtained are validated by Gibbs-Thomson relation at the dendrite tip. Compared with the equiaxed dendrite evolution without flow, the upstream dendrite arm is enhanced while the downstream arm is inhibited. Besides, as the inlet flow rate increases, the secondary arms attached onto the upstream primary arm and the upstream side of the primary arm normal to the inflow velocity has been well developed. Results show that sidewise instabilities of the primary dendrite arm and onset of secondary arm is caused by the local concentration perturbation and will be enhanced or inhabited by the flow. It is believed that the coupled PF-LBM method is able to handle dendrite evolution under forced flow quantitatively, which helps in investigating the solidified dendrite morphology evolution.

Phase field simulation of dendrite evolution during powder-based laser metal deposition

An algorithm for simulation of laser metal deposition (LMD) processes is developed, which implements the concept of multi-scale modeling of crystallization. The macro-level model takes into account the coupled dynamics of the free surface (melt-gas) and the energy and mass transfer of the multiphase mixture, which is applied on scales of the order of a few to tens of millimeters. The micro-level model describes the evolution of dendritic structures using the phase-field method (PFM) at scales of the order of a few to tens of micro-meters. Wherein, the resulting macroscopic temperature distribution in the system defines the boundary and initial conditions of the micro-model, which, in turn, control the growth patterns and evolution of the dendrites. In local sub-region, the evolution of the dendrite in an advantageous position was simulated, i.e. having favorable thermodynamic conditions of its growth. Before solving the micro-scale problem with the PFM, the 3D mesh conversion procedure to the new 2D mesh is performed in the sub-region of interest. To do this, we select the plane in which the local temperature gradient vector lies. The test dynamic profiles of the phase field and temperature in different spatial regions of the formed bead are calculated. Simulations used the values of physical quantities for iron. The results of calculations showed that the developed numerical model qualitatively describes the physics of crystallization and the formation of dendrites in the LMD process. The effect on the growth dynamics of dendritic structures of such PFM parameters as thermal noise and the anisotropy amplitude is analyzed. It is shown that thermal fluctuations strongly affect the branching of dendrites. With an increase in the fluctuation amplitude, the phase boundary becomes unstable with the formation of secondary and tertiary branches.

A Phase-Field Lattice-Boltzmann Study on Dendritic Growth of Al-Cu Alloy Under Convection

Effects of convection (forced and natural) on dendritic evolution of the Al-Cu alloy were investigated using a phase-field lattice-Boltzmann approach. The non-linear coupled equations were solved by applying a parallel and adaptive mesh refinement algorithm. Important physical aspects including dendritic fragmentation, splitting, and formation of solute plumes were simulated. Results showed that the dendritic growth patterns under convection exhibited remarkable difference from those without convection. The presence of flow led to variation of solute diffusion and upstream–downstream dendritic growth difference, which further influenced the development of dendritic arms and multi-dendritic competitive growth. When the convection intensity was magnified, the convection-induced anisotropy became dominated, and the growth patterns changed accordingly to accommodate the local thermodynamic variation.

Fundamental Understanding of Solid Electrolyte Interface (SEI) Effects on Li Dendrite Evolution: Multi-Scale Modeling Study

Safety concerns of lithium (Li) metal battery (LMB) originated from Li dendrite formation, and the resulting internal electric short circuit have become the major obstacle for successful practical usage of LMB. Significant research has been conducted to understand the mechanisms of dendritic growth of Li, and develop strategies to prevent the Li dendrite formation1; however, the progress has been limited due to the lack of fundamental understanding of the solid electrolyte interface (SEI) influence on the dendrite formation and growth. In this work, we present the modeling results of Li dendrite formation and growth based upon an extended phase-field model (PFM) for Li electrodeposition, atomisticlly informed by the density functional theory (DFT) calculation. The PFM2 is developed employing MOOSE framework 3, based on the work of Guyer et al.4,5 and Bazant6 on the topic of phase-field modeling of electrodeposition. The SEI model is based upon the grain boundary (GB) model7 considering the Li-ions diffusion across the GB. Utilizing DFT calculation, we could successfully obtain the anisotropic strength of the Li dendrites, the energy of Li nucleation and the Li+ diffusion coefficient across the SEI. Subsequently, the thermodynamically consistent free energy density and the gradient energy coefficient, which is modeled by taking into account the surface energy anisotropy, are used in the PFM to predict the spatiotemporal evolution of Li dendrites in the presence of SEI. We investigate three regimes of Li dendrite growth, such as Li filaments evolution, Li bush-like structure evolution and the transition between Li filaments and bush-like morphologies. The Li filaments nucleation and growth is more straightforward, with clear dependency on Li+ and potential distribution. The Li bush-like structure evolution is more complicated, where the electric potential distribution and Li+ flux profile reveal relatively complex nonlinear influence on the Li electrodeposition. Thus, the present study, in addition to improving the fidelity of the PFM of Li electrodeposition, identifies critical regimes of Li filaments growth and splitting, allowing for a more profound understanding of the SEI influence on Li dendrite evolution. Based upon this work, the development of strategies towards prevention of Li dendrites formation for long-lasting, high-density LMB will be facilitated.