Dendritic Array Research Articles

Three-dimensional dendritic needle network model for alloy solidification

We present a three-dimensional (3D) formulation of the multiscale Dendritic Needle Network (DNN) model for dendritic microstructure growth. This approach is aimed at simulating quantitatively the solidification dynamics of complex hierarchical networks in spatially extended dendritic arrays, hence bridging the scale gap between phase-field simulations at the scale of a few dendrites and coarse-grained simulations on the larger scale of entire polycrystalline structures. In the DNN model, the dendritic network is represented by a network of branches that interact through the solutal diffusion field. The tip velocity V(t) and tip radius ρ(t) of each needle is determined by combining a standard solvability condition that fixes the product ρ2V and a solute flux conservation condition that fixes the product ρV2 in 2D and ρV in 3D as a function of a solutal flux intensity factor F(t). The latter measures the intensity of the solute flux in the dendrite tip region and can be calculated by contour (2D) or surface (3D) integration around the tip of each needle. We first present an extended formulation of the 2D DNN model where needles have a finite thickness and parabolic tips. This formulation remains valid for a larger range of tip Péclet number than the original thin needle formulation and is readily extended to 3D needles with paraboloidal tips. The 3D DNN model based on this thick-needle formulation is developed for both isothermal and directional solidification. Model predictions are validated by comparisons with known analytical solutions that describe the early transient and steady-state growth regimes. We exploit the power of the DNN model to characterize the competitive growth of well-developed secondary branches in 3D on the scale of the diffusion length. The results show that the length of active secondary branches increases as a power law of distance behind the tip with an exponent in good quantitative agreement with experimental measurements. Finally, we apply the model to simulate the three-dimensional directional solidification of an Al-7wt% Si alloy, which we directly compare to observed microstructures from microgravity experiments onboard the International Space Station. The predictions of selected microstructural features, such as dendrite arm spacings, show a good agreement with experiments. The computationally-efficient DNN model opens new avenues for investigating the dynamics of large dendritic arrays at length and time scales relevant to solidification experiments and processes.

Degenerate seaweed to tilted dendrite transition and their growth dynamics in directional solidification of non-axially oriented crystals: a phase-field study.

We report the results of a phase-field study of degenerate seaweed to tilted dendrite transition and their growth dynamics during directional solidification of a binary alloy. Morphological selection maps in the planes of (G, Vp) and (ε4, Vp) show that lower pulling velocity, weaker anisotropic strength and higher thermal gradient can enhance the formation of the degenerate seaweed. The tip undercooling shows oscillations in seaweed growth, but it keeps at a constant value in dendritic growth. The M-S instability on the tips and the surface tension anisotropy of the solid-liquid interface are responsible for the formation of the degenerate seaweed. It is evidenced that the place where the interfacial instability occurs determines the morphological transition. The transient transition from degenerate seaweed to tilted dendrite shows that dendrites are dynamically preferred over seaweed. For the tilted dendritic arrays with a large tilted angle, primary spacing is investigated by comparing predicted results with the classical scaling power law, and the growth direction is found to be less sensitive to the pulling velocity and the primary spacing. Furthermore, the effect of the initial interface wavelength on the morphological transition is investigated to perform the history dependence of morphological selection.

3D NiS dendritic arrays on nickel foam as binder-free electrodes for supercapacitors

In this work, we have successfully fabricated unique three-dimensional (3D) dendritic NiS nanosheet arrays on nickel foam (NiS–Ni) through a simple solution method, oxidizing fresh nickel foam under a heat treatment and following a sulfidation process without the need for any additional nickel sources, surfactant, or templates. The morphology of the NiS–Ni was observed by SEM and TEM, while the crystallinity was revealed by XRD pattern. When tested as the electrode for supercapacitors, the NiS dendritic arrays grown on nickel foam display excellent performance, demonstrating the specific capacity of 465.9 F g−1 at the current density of 1 A g−1. After 7000 cycles, the NiS–Ni electrode can maintain 101.79 % of its highest value, which demonstrates its superior cycle stability performance. Also, the NiS–Ni electrode exhibits high capacity retention when fast charging. These results establish that the NiS–Ni binder-free electrode exhibits greatly improved electrochemical performance with high capacitance and excellent cycling stability.

EBSD study of the morphology and orientation of the primary and eutectic phases in Al–Cu alloys during solidification under a strong magnetic field

The effect of a strong magnetic field on the morphology and orientation of the Al2Cu dendrite and Al–Al2Cu eutectic in Al–Cu alloys was studied using electron backscatter diffraction (EBSD) technology. The experimental results revealed that the applied magnetic field modified the morphology and orientation of both the Al2Cu dendrite and the Al–Al2Cu eutectic significantly. The magnetic field caused a break in the Al2Cu dendrite and the degeneration of Al–Al2Cu eutectic lamellae during directional solidification. It was also found that the magnetic field caused the formation of dislocations in the α-Al and Al2Cu phases during directional solidification. In addition, the primary and eutectic Al2Cu phases were oriented with the 〈001〉 crystal direction along the magnetic field during volume solidification. Both α-Al and Al2Cu phases were oriented with the 〈001〉 crystal direction along the solidification direction during directional solidification under an axial magnetic field. The above phenomena were enhanced as the magnetic field increased; this could be attributed to magnetic crystalline anisotropy of the material and thermoelectric magnetic effects. This study may offer experimental evidence that shows that thermoelectric magnetic effects significantly influence dendrite arrays during directional solidification in a magnetic field.

Hierarchical forest-like photoelectrodes with ZnO nanoleaves on a metal dendrite array

Hierarchical forest-like photoelectrodes were prepared by assembling nano-ZnO on an array of micro-metal dendrites, aiming to artificially construct an efficient photo-electrochemical system similar to plants in a forest, with photons harvested by the crown-like photoanodes in the sunshine, and synthetic reactions driven by the root-like electrode in the shadow.

Fabrication of Metamaterials Based on Gold Dendritic Cells

Abstract We demonstrate a visible light frequencies metamaterials (MMs) composed of disordered dendritic cells, and a novel bottom-up approach to fabricate the MMs using chemical method. When the diameter of the cell is about 500 nm, the as-prepared gold dendritic nanostructural array exhibits passbands at wavelength of 470, 540 and 670 nm, respectively. The MMs also realize slab focusing effect at visible wavelength. It would be significant to accelerate the development of visible frequencies MMs.

Oscillatory cellular patterns in three-dimensional directional solidification.

We present a phase-field study of oscillatory breathing modes observed during the solidification of three-dimensional cellular arrays in microgravity. Directional solidification experiments conducted onboard the International Space Station have allowed us to observe spatially extended homogeneous arrays of cells and dendrites while minimizing the amount of gravity-induced convection in the liquid. In situ observations of transparent alloys have revealed the existence, over a narrow range of control parameters, of oscillations in cellular arrays with a period ranging from about 25 to 125 min. Cellular patterns are spatially disordered, and the oscillations of individual cells are spatiotemporally uncorrelated at long distance. However, in regions displaying short-range spatial ordering, groups of cells can synchronize into oscillatory breathing modes. Quantitative phase-field simulations show that the oscillatory behavior of cells in this regime is linked to a stability limit of the spacing in hexagonal cellular array structures. For relatively high cellular front undercooling (i.e., low growth velocity or high thermal gradient), a gap appears in the otherwise continuous range of stable array spacings. Close to this gap, a sustained oscillatory regime appears with a period that compares quantitatively well with experiment. For control parameters where this gap exists, oscillations typically occur for spacings at the edge of the gap. However, after a change of growth conditions, oscillations can also occur for nearby values of control parameters where this gap just closes and a continuous range of spacings exists. In addition, sustained oscillations at to the opening of this stable gap exhibit a slow periodic modulation of the phase-shift among cells with a slower period of several hours. While long-range coherence of breathing modes can be achieved in simulations for a perfect spatial arrangement of cells as initial condition, global disorder is observed in both three-dimensional experiments and simulations from realistic noisy initial conditions. In the latter case, erratic tip-splitting events promoted by large-amplitude oscillations contribute to maintaining the long-range array disorder, unlike in thin-sample experiments where long-range coherence of oscillations is experimentally observable.

Phase-field simulation of tilted growth of dendritic arrays during directional solidification

The tilted growth of dendritic arrays during directional solidification of non-axially oriented crystals has been simulated in two-dimensional system by using a quantitative phase-field model. A convergence study with respect to the diffuse interface width has been carried out, showing that the results are reasonably independent of the diffuse interface width for W0/d0⩽11.3. A parametric study is performed to investigate the effects of the primary spacing, the misorientation angle and the pulling velocity on the tip undercooling, the upper limit of primary spacing, and the tilted angle. Results show that the tip undercooling decreases when increasing the primary spacing or decreasing the misorientation angle. It has been found that the upper limit, resulting from tertiary branching, depends on both the solidification condition (the pulling velocity and the thermal gradient) and the preferred crystalline orientation (the misorientation angle) for the tilted growth of dendritic arrays. Previous rotation law, describing the relation between the tilted angle and the Péclet number, is evaluated according to phase-field simulation results. Moreover, the effect of the development of sidebranches on the growth direction selection was discussed. Further studies on the microstructure evolution from the onset of planar instability during directional solidification show that the selection of the steady-state primary spacing is sensitive to the misorientation angle.

Microstructural development and mechanical properties of a near-eutectic directionally solidified Sn–Bi solder alloy

Sn–Bi solders may be applied for electronic applications where low-temperature soldering is required, i.e., sensitive components, step soldering and soldering LEDs. In spite of their potential to cover such applications, the mechanical response of soldered joints of Sn–Bi alloys in some cases does not meet the strength requirements due to inappropriate resulting microstructures. Hence, careful examination and control of as-soldered microstructures become necessary with a view to pre-programming reliable final properties. The present study aims to investigate the effects of solidification thermal parameters (growth rate — VL and cooling rate — ṪL) on the microstructure of the Sn–52wt.%Bi solder solidified under unsteady-state conditions. Samples were obtained by upward directional solidification (DS), followed by characterization through metallography and scanning electron microscopy (SEM). The microstructures are shown to be formed by Sn-rich dendrites decorated with Bi precipitates surrounded by a complex regular eutectic mixture, with alternated Bi-rich and Sn-rich phases. Experimental correlations of primary (λ1), secondary (λ2), tertiary (λ3) dendritic and eutectic spacings (λcoarse and λfine) with cooling rate and growth rate are established. Two ranges of lamellar eutectic sizes were determined, described by two experimental equations λ=1.1 VL−1/2 and λ=0.67 VL−1/2. The onset of tertiary branches within the dendritic array along the Sn–52wt.%Bi alloy DS casting is shown to occur for cooling rates lower than 1.5°C/s.

Three-Dimensional Multiscale Modeling of Dendritic Spacing Selection During Al-Si Directional Solidification

We present a three-dimensional extension of the multiscale dendritic needle network (DNN) model. This approach enables quantitative simulations of the unsteady dynamics of complex hierarchical networks in spatially extended dendritic arrays. We apply the model to directional solidification of Al-9.8 wt.%Si alloy and directly compare the model predictions with measurements from experiments with in situ x-ray imaging. We focus on the dynamical selection of primary spacings over a range of growth velocities, and the influence of sample geometry on the selection of spacings. Simulation results show good agreement with experiments. The computationally efficient DNN model opens new avenues for investigating the dynamics of large dendritic arrays at scales relevant to solidification experiments and processes.

Structure, Growth Process, and Growth Mechanism of Perovskite in High-Titanium-Bearing Blast Furnace Slag

The isothermal crystallization of perovskite in TiO2-CaO-SiO2-Al2O3-MgO high-titanium-bearing blast furnace slag was observed in situ at 1698 K (1425 °C) using a confocal scanning laser microscope. The dendrite structure of perovskite (CaTiO3) thus obtained showed vividly the primary dendrite trunks and secondary dendrite arms. Furthermore, the dendritic growth of perovskite in liquid slag was clearly observed on line. The results showed that the dendrite arrays in which the primary dendrite trunks observed on slag surface were parallel with each other grew toward the same direction. The secondary dendrite arms grew in the perpendicular direction with the primary trucks and stopped growing when they encounter. The perovskite dendrites showed a linear growth at two stages. The dendrites grew faster at early stage at about 5 to 7 μm/s and grew with a lower growth rate at about 1 to 2 μm/s in later stage. Finally, the growth mechanism of perovskite in melt was analyzed with the solidification theory. Based on the theoretical calculation of equilibrium phases in slag, the initial slag could be considered as a binary component system. One component was perovskite and the other component was the sum of all the other species that did not attend the crystallization of perovskite (included SiO2, Al2O3, and MgO, as well as CaO and TiO2 that were not involved in the solid formation). The formation of perovskite required the diffusion of CaO and TiO2 to the solid/liquid interface and the rejection of the other species from the interface. The solid/liquid equilibrium schematic diagram was made based on the calculation.

Dynamical microstructure formation in 3D directional solidification of transparent model alloys: in situ characterization in DECLIC Directional Solidification Insert under diffusion transport in microgravity

To clarify and characterize the fundamental physical mechanisms active in the dynamical formation of three-dimensional (3D) arrays of cells and dendrites under diffusive growth conditions, in situ monitoring of series of experiments on transparent model alloy succinonitrile - 0.24 wt% camphor was carried out under low gravity in the DECLIC Directional Solidification Insert on-board the International Space Station. These experiments offered the very unique opportunity to in situ observe and characterize the whole development of the microstructure in extended 3D patterns. The experimental methods will be first briefly described, including in particular the observation modes and the image analysis procedures developed to quantitatively characterize the patterns. Microgravity environment provided the conditions to get quantitative benchmark data: homogeneous patterns corresponding to homogeneous values of control parameters along the whole interface were obtained. The sequence of microstructure formation will be presented as well as the evolution of the primary spacing which is one of the most important pattern characteristic. Time evolution of this primary spacing during the microstructure development will be analysed to identify the mechanisms of spacing selection and adjustment; the importance of the macroscopic interfacial curvature will be pointed out.

Magnetic CoFe2O4 films with controllable dendritic arrays by a combined method of electrodeposition and anode activation

Magnetic CoFe2O4 films with controllable dendritic arrays were successfully prepared by a combined method of electrodeposition and anode activation.

Cellular automaton simulation of the molten pool of laser solid forming process

A two-dimensional multiscale model is presented for simulating laser melting process, which is the same as laser solid forming (LSF) without the addition of metallic powders into the molten pool. The metallurgical process in molten pool is simulated, including the temperature distribution, the pool shape, and the solidification microstructure. The shape of the molten pool and the microstructure in Fe-C single crystal substrate at a laser scanning speed of 15 mm/s is simulated. Results reveal the instability from planar interface to cell\ dendrite morphologies in the molten pool. At the bottom of the molten pool, the growth morphology is planar interface, which is also called bonding zone. Epitaxial dendrite arrays can be seen to grow above the bonding zone.

Initial transient behavior in directional solidification of a bulk transparent model alloy in a cylinder

To characterize the dynamical formation of three-dimensional (3-D) arrays of cells and dendrites under diffusive growth conditions, in situ monitoring of a series of experiments on a transparent succinonitrile–0.24wt.% camphor model alloy was carried out under low gravity in the Device for the Study of Critical Liquids and Crystallization (DECLIC) Directional Solidification Insert on board the International Space Station (ISS). The present paper focuses on the study of the transient solid–liquid interface recoil. Numerical thermal modeling led us to identify two thermal contributions to the interface recoil that increase with the pulling rate and add to the classical recoil associated with the solute boundary layer formation. As a consequence of those additional contributions, the characteristic front recoil is characterized by a fast initial transient followed by stabilization to a plateau whose location depends on pulling rate. The analysis of comparative experiments carried out on the ground shows the absence of stabilization of the interface position, attributed to longitudinal macrosegregation of the solute induced by convection. This behavior is surprisingly also observed in space experiments for low pulling rates. An order of magnitude analysis of the mode of solute transport reveals that for these conditions, the effective level of reduced gravity on board the ISS is not sufficiently low to suppress convection so that the interface recoils with longitudinal macrosegregation in a similar way as in ground experiments.

Stability range of tilted dendritic arrays during directional solidification

The stability range of primary spacing of the tilted dendritic arrays in directional solidification has been studied by quantitative phase-field simulations. Results show that both the real growth direction and morphological shapes of dendritic arrays change with the primary spacing for different misorientation angles (θ0). It has been found that the lower limit of primary spacing is independent of θ0, but the upper limit of primary spacing is strongly influenced by that. The two kinds of tertiary branching instabilities result in different behaviors of the variation of the upper limit with misorientation angle for different pulling velocities.

Evaluation of cooling rate on electrochemical behavior of Sn–0.3Ag–0.9Zn solder alloy in 3.5 wt% NaCl solution

The corrosion resistance of Sn–0.3Ag–0.9Zn alloy solidified under different cooling rates in 3.5 wt% NaCl solution was evaluated based on potentiodynamic polarization, electrochemical impedance spectroscopy and electrochemical noise. It is found that the corrosion resistance of this alloy improves with the increase of the applied cooling rate, which is attributed to the distinct microstructure. The furnace-cooled and air-cooled alloy with active Zn-rich phase and a microstructure formed by a coarser dendritic array associated with larger size of AgZn3 intermetallic compounds exhibit a worse corrosion resistance due to a serious galvanic corrosion. Besides, the Mott–Schottky measurement and the X-ray photoelectron spectroscopy were performed to analyze the semiconductor properties and composition of the passive film formed on the surface of the alloy. It confirms that the stability and protective ability of the passive films formed on furnace-cooled and air-cooled alloy are worse than that of water-cooled alloy due to their higher oxygen vacancy defects and concentration of unstable SnO. Furthermore, the major corrosion product on the surface of the Sn–0.3Ag–0.9Zn alloys is tin oxide chloride hydroxide.

Two-dimensional phase-field simulations of dendrite competitive growth during the directional solidification of a binary alloy bicrystal

We investigated the competitive growth of dendrites at the converging grain boundaries (GBs) of bicrystals during the directional solidification of an Al–Cu alloy by means of two-dimensional phase-field simulations. In particular, the focus was on the recently observed phenomenon of unusual overgrowth during the directional solidification of a Ni-based superalloy, where the favorably oriented (FO) dendrites are overgrown by the unfavorably oriented (UO) ones. The phase-field simulations were accelerated by parallel computations on graphics processing units. The simulation results showed that unusual overgrowth occurs in Al–Cu alloys, indicating that this phenomenon is a common one in metallic materials. It was also concluded that the differences in the diffusion layers in front of the FO and UO dendrites had a dominant effect on the competitive growth of dendrites at the converging GB as well as on the unusual overgrowth. In addition, unusual overgrowth was observed in all the FO dendrites with a spacing that allowed the dendrite array to grow stably without necessitating a change in the number of dendrites. The FO dendrite at the GB is overgrown by the UO dendrite when the spacing between the FO dendrite at the GB and the next FO dendrite is approximately equal to the critical minimum spacing. However, the unusual overgrowth was not observed for UO dendrites with a large inclination angle. In this case, all the UO dendrites are blocked by the FO dendrite at the GB, and the FO dendrites migrate toward the UO dendrites.

Modeling of morphological evolution of columnar dendritic grains in the molten pool of gas tungsten arc welding

A macro–micro coupled model for epitaxial nucleation and the subsequent competitive dendrite growth was developed to study the morphological evolution of both dendrite and grain structures in molten pool of the gas tungsten arc welding (GTAW) for Fe–C alloy. The simulation of heat and mass transfer in molten pool was conducted by the three-dimensional finite element (FE) model to obtain the transient solidification conditions. The process of epitaxial nucleation and the competitive dendrite growth was simulated by a two-dimensional cellular automata (CA) model. The size and random preferential orientations of substrate grains were considered in this model. The transient thermal conditions used in the CA model were obtained from the results of FE model through the interpolation method. In addition, the effects of the substrate grain size and the welding speed on the morphologies of both dendrite and grain structures were investigated. The simulated results indicate that dendrites with the preferential orientations parallel to the direction of the highest temperature gradient are more competitive during the competitive dendrite growth, and the morphology of resulting columnar grains is determined by the competition between different dendritic arrays. Under the same welding conditions, with the increase of substrate grain size, the average width of resulting columnar grains becomes larger, and the characteristics of dendrite structure within the columnar grains do not change obviously. Without considering the new nucleation in the melt, with the increase of welding speed, the dendrite structure in weld seam becomes much finer, and the average columnar grain width within the calculation domain of the CA model does not change obviously. The trend of the simulated results of dendrite arm spacing under various welding conditions are consistent with the analytical and experimental data.

Urease-induced calcification of segmented polymer hydrogels – A step towards artificial biomineralization

Natural organic/inorganic composites, such as nacre, bones and teeth, are perfectly designed materials with exceptional mechanical properties. Numerous approaches have been taken to synthetically prepare such composites. The presented work describes a new way of mineralizing bulk materials on a large scale following the approach of bioinduced mineralization. To this end, a series of polymer conetworks with entrapped urease were prepared. After polymerization, the entrapped urease shows high enzymatic activity. The bioactive polymer conetworks were then treated with an aqueous mixture of urea and CaCl2. The urease-induced calcification indeed allows formation of carbonate crystals exclusively within the hydrogel even at room temperature. The influence of network composition, degree of cross-linking, immobilized urease concentration and temperature of calcification were investigated. By varying these parameters, spherical, monolithic clusters, as well as bar-like nanocrystals with different aspect ratios in spherical or dendritic arrays, are formed. The grown nanocrystals improve the stiffness of the starting material by up to 700-fold, provided that the microstructure shows a dense construction without pores and strong interaction between crystals and network. The process has the potential to generate a new class of hybrid materials that would be available on the macroscopic scale for use in lightweight design and medicine.