Faceted Dendrites Research Articles

Precipitation characteristics and growth mechanism of Fe and Cr from liquid lead-bismuth eutectic by quenching in liquid nitrogen

The compatibility of structural steels with liquid lead-bismuth eutectic (LBE) restricts the development of the lead-cooled fast reactor (LFR) and the accelerator driven sub-critical (ADS) system. During the reactor operation, alloying elements in steel can dissolve into LBE. The dissolved alloying elements could precipitate in cold parts of the reactor due to the decrease in solubility, which can cause pipe clogging and worsen heat transfer. Therefore, it is necessary to study their precipitation characteristics to provide a reference for the filtration process. In this paper, Fe, Cr, and a mixture of Fe and Cr were added to liquid LBE at 1173 K and quenched in liquid nitrogen to study their precipitation characteristics. The scanning electron microscope (SEM) and field-emission scanning electron microscope (FESEM) were used to analyze the morphology, and the phase structure was identified by an X-ray diffractometer. The chemical compositions of precipitates were analyzed by an energy dispersive spectrometer (EDS, Esprit Compact, Bruker) and an electron probe microanalyzer (EPMA, EPMA-8050 G, Shimadzu). The solid-liquid interface structure and growth mechanism of precipitates were also discussed. The difference in growth mechanisms resulted in various morphologies for the precipitates. There were three morphologies of precipitates: faceted dendrite, polyhedron (cube, octahedron, and hopper), and seaweed dendrite. All the precipitates in LBE have a faceted growth character except the seaweed dendrites, irrespective of their morphology. The growth of Fe, Cr, and Cr-Fe faceted dendrites originated from continuous growth followed by lateral growth. On the contrary, the cubic and octahedral precipitates were controlled by the spiral growth mechanism, and the growth mechanism of hopper crystals was two-dimensional nucleation. The formation of seaweed dendrites was caused by a strong local undercooling of nonfaceted dendrites.

Solidification Behavior of Undercooled Fe75B25 Alloy

The paper presents a study of the phase selection and microstructure evolution of Fe75B25 alloy subjected to solidification at various undercoolings. The alloy invariably solidifies into a primary Fe2B phase and α-Fe/Fe2B eutectic at all the experimental undercoolings up to 381 K. A metastable Fe3B phase does not precipitate, although its growth in this alloy is favored without large-scale solute diffusion involved. It is shown that the phase selection is nucleation-controlled. Solid sites existing in the alloy melt seem more favorable for the nucleation of the Fe2B phase. As undercooling increases, primary the Fe2B phase changes its morphology complexly. It solidifies into coarse faceted dendrites at low undercoolings, developed non-faceted dendrites at moderate undercoolings, seaweeds with dense branches at higher undercoolings, and refined granular grains at undercooling above 147 K.

Microstructure evolution during directional solidification of off-eutectic Al-Cu-Mg alloys

Building on previous studies of invariant ternary eutectic Al-Al2Cu-Al2CuMg, this work aims to deepen our understanding of the microstructural possibilities in the Al-rich region of the Al-Cu-Mg phase diagram by considering the solidification behaviour of several off-eutectic compositions. Four Al-Cu-Mg alloys were directionally solidified at a constant growth rate (1.25 μm/s) and thermal gradient (9-14 K/mm) using a Bridgman-type furnace and analysed using a combination of scanning electron microscopy, energy-dispersive X-ray spectroscopy, X-ray diffraction, and differential scanning calorimetry. Qualitative and quantitative analyses showed a preference for faceted Al2Cu dendrites surrounded by a ternary eutectic matrix in the two Mg-poor samples, even though one composition was not in the primary Al2Cu phase region. The two Al-poor samples consisted of large regions of three different intermetallic phases and little eutectic, making these samples very brittle.

Explicit temperature coupling in phase-field crystal models of solidification

We present a phase-field crystal model for solidification that accounts for thermal transport and a temperature-dependent lattice parameter. Elasticity effects are characterized through the continuous elastic field computed from the microscopic density field. We showcase the model capabilities via selected numerical investigations which focus on the prototypical growth of two-dimensional crystals from the melt, resulting in faceted shapes and dendrites. This work sets the grounds for a comprehensive mesoscale model of solidification including thermal expansion.

Revealing growth mechanisms of faceted Al2Cu intermetallic compounds via high-speed Synchrotron X-ray tomography

This study used high-speed synchrotron X-ray tomography to image the growth of Al2Cu intermetallic compounds in 4D (3D plus time) during solidification of Al-45wt%Cu alloy. Two categories of growth patterns (basic units and dendrites) are identified. Basic units are elongated rods whose cross-section are L, U or hollow-rectangular shapes. The transition from L pattern to U and finally to hollow-rectangular shaped morphology is observed. Faceted dendritic patterns include equiaxed prism and columnar dendrites. Self-repeated layer-by-layer stacking of the basic units (such as L shaped particles) is proposed as a governing mechanism for the growth of Al2Cu faceted dendrites. The growth orientation and morphologies of these patterns are strongly influenced by solidification conditions (temperature gradients, cooling rates and external magnetic fields). Another finding is that when rotating Al-45wt%Cu during upwards directional solidification, under a transverse magnetic field of 0.5T, highly refined and well aligned Al2Cu intermetallic compounds are obtained, much finer than those without the imposition of the magnetic field. This is attributed to a rotational stirring flow that modulates and regulates the temperature and solute distribution. The developed experimental findings provide a physical understanding of the formation of faceted intermetallic compounds during solidification.

Interface morphology evolution of azobenzene from the unsteady to steady state under directional solidification

In this work, the melt-crystal interface of azobenzene at the unsteady and the steady state was in-situ investigated via directional solidification. The experimental results show that, at the unstable stage, interface morphology transforms from planar to zigzag facets at low growth rates and then to faceted dendrites at high growth rates, and the corresponding apex angles change from multiple values to one unified. At the steady state, the interface morphology of azobenzene can maintain planar or zigzag facets or faceted dendrites, and 115° is reserved in the zigzag interface or 50° in the faceted dendrites. Besides, the disappearance of fast-growing planes and the retaining of slow-growing planes contribute to the variation of apex angles from 115° to 50°. Our in-situ observation promotes further understanding of the solidification process in faceted materials.

Effect of WC addition on TiC reinforced Fe matrix composites produced by laser deposition

The TiC/Fe ceramic metal composite (MMC) with WC particles addition was successfully produced by laser deposition process. The effect of the WC addition to the Fe-based MMC on microstructure and mechanical properties was investigated. The results indicated that the MMC deposit consisted of primary TiC, (Ti, W)C, M6C(Fe3W3C and Fe4W2C), austenite, and a little martensite besides initial TiC and WC particles. The MMC matrix was refined by the various M6C including blocks, faceted dendrites, coarse eutectics, eutectic groups, and nanoparticles. With the M6C strengthing, the hardness of the mixed matrix was 13% higher than that of the TiC/Fe composite. Moreover, a core-rim structure appeared on the primary TiC bonding with (Ti, W)C solid solution, as well as the initial TiC. The rim of the (Ti, W)C solid solution can not only improve the MMC toughness but also reduce the lattice misfit of the TiC/Fe interface, which was supposed to improve the interface strength.

Induced side-branching in smooth and faceted dendrites: theory and phase-field simulations.

The present work is devoted to the phenomenon of induced side branching stemming from the disruption of free dendrite growth. We postulate that the secondary branching instability can be triggered by the departure of the morphology of the dendrite from its steady state shape. Thence, the instability results from the thermodynamic trade-off between non monotonic variations of interface temperature, surface energy, kinetic anisotropy and interface velocity within the Gibbs-Thomson equation. For the purposes of illustration, the toy model of capillary anisotropy modulation is prospected both analytically and numerically by means of phase-field simulations. It is evidenced that side branching can befall both smooth and faceted dendrites, at a normal angle from the front tip which is specific to the nature of the capillary anisotropy shift applied. This article is part of the theme issue 'Transport phenomena in complex systems (part 2)'.

Design and microstructural development of a new eutectic Fe-Co-Ni-B multi-principal element alloy system

A new eutectic Fe-Co-Ni-B multi-principal element alloy system was designed. Microstructure evolution and mechanical properties of the Fe-Co-Ni-B alloys with varied content of Fe and B were investigated. For the Fex(CoNi)84−xB16 alloys, it is found that the eutectic structure transforms from anomalous to lamellar, further to rod, and then to faceted dendrite, which was attributed to the transition of crystal structure of B-rich intermetallic phase from orthogonal to tetragonal as the Fe content increases. For the Fe7(CoNi)93−yBy alloys, the primary phase changes from (Fe, Co, Ni)-rich FCC solid solution to B-rich intermetallic with the increase of B content. The Fe7(CoNi)75B18 shows fully lamellar structure consisted of (Fe, Co, Ni)-rich phase and boron-rich phase with cubic and orthogonal crystal structures respectively. It is also found that the compressive strength and hardness of Fe7(CoNi)93−yBy alloys increase significantly but the plasticity decreases as B increases. The introduction of non-metallic element B as principal component provides a new idea for the design of eutectic high entropy alloy.

Phase field model of faceted anatase TiO2 dendrites in low pressure chemical vapor deposition

Anatase TiO2 nanorods with a well-defined ⟨110⟩ texture have been studied using a model-based characterization technique based on a previous modeling framework. Intricate secondary side facet characteristics of tilt angles of 26.5° have been indexed, and a ⟨112⟩ growth direction of the well-aligned facets is identified. These results have not been accessed experimentally but crucial in understanding the nature of the most abundant facets and their structural properties. We find agreement between our results and indirect experimental measurements. Highly exposed {116} facets are found to be responsible for excellent electrochemical surface properties in nanostructured anatase TiO2 thin films.

Dendritic Growth in Si1−xGex Melts

We investigated the types of dendrites grown in Si1−xGex (0 < x < 1) melts, and also investigated the initiation of dendrite growth during unidirectional growth of Si1-xGex alloys. Si1−xGex (0 < x < 1) is a semiconductor alloy with a completely miscible-type binary phase diagram. Therefore, Si1−xGex alloys are promising for use as epitaxial substrates for electronic devices owing to the fact that their band gap and lattice constant can be tuned by selecting the proper composition, and also for thermoelectric applications at elevated temperatures. On the other hand, regarding the fundamentals of solidification, some phenomena during the solidification process have not been clarified completely. Dendrite growth is a well-known phenomenon, which appears during the solidification processes of various materials. However, the details of dendrite growth in Si1−xGex (0 < x < 1) melts have not yet been reported. We attempted to observe dendritic growth in Si1−xGex (0 < x < 1) melts over a wide range of composition by an in situ observation technique. It was found that twin-related dendrites appear in Si1−xGex (0 < x < 1) melts. It was also found that faceted dendrites can be grown in directional solidification before instability of the crystal/melt interface occurs, when a growing crystal contains parallel twin boundaries.

Shaping quality, microstructure, and mechanical properties of melt-grown mullite ceramics by directed laser deposition

Directed laser deposition (DLD) has demonstrated the potential for rapid preparing high-performance melt-grown ceramics applied for the aero-engine hot section components. Mullite has excellent potential for applications in harsh environments and extreme conditions. However, there are defects (pores and cracks) in melt-grown mullite ceramics (MGMC), limiting its application, related to unclear processes, microstructure, and properties. In this work, we investigated the impact of z-increment on shaping quality, microstructure, and mechanical properties. The results reveal that oxygen vacancy concentration is responsible for the variety of sample colors. Low z-increment is beneficial to decreasing porosity, while high z-increment is beneficial to crack suppression. The formation and propagation mechanism of internal cracks at low z-increment are discussed in detail. Mullite crystals in the sample center are "tabular cellular", which are 2:1 high-alumina mullite. While mullite crystals at the sample edge are 3:2 mullite, undergo four stages as z-increment increase; "tabular cellular", "facet dendrite", "rod cellular", and mixed crystal. This evolution of crystal morphology is attributed to the decrease in temperature gradient and the increase of supersaturation. Besides, the flexural strength and microhardness increase first and then decrease with the rise of z-increment, which is the function of defects, compactness, and microstructure.

The in situ observation of faceted dendrite growth during the directional solidification of GaSb

In this work, crystal–melt interfaces were directly observed during the directional solidification of molten GaSb having a stoichiometric composition, and the formation of dendrite structures was studied. With increases in growth velocity, the planar crystal–melt interface became unstable and dendrite growth was initiated. Dendrites having {111} facets were found to grow in either the 〈110〉 or 〈112〉 directions, and a pair of twin boundaries was identified at the center of a dendrite. The results show that the growth of dendrites in GaSb is associated with nucleation at twin-related reentrant corners.

Phase field method simulation of faceted dendrite growth with arbitrary symmetries

Abstract A numerical simulation based on a regularized phase field model is developed to describe faceted dendrite growth morphology. The effects of mesh grid, anisotropy, supersaturation and fold symmetry on dendrite growth morphology were investigated, respectively. These results indicate that the nucleus grows into a hexagonal symmetry faceted dendrite. When the mesh grid is above 640×640, the size has no much effect on the shape. With the increase in the anisotropy value, the tip velocities of faceted dendrite increase and reach a balance value, and then decrease gradually. With the increase in the supersaturation value, crystal evolves from circle to the developed faceted dendrite morphology. Based on the Wulff theory and faceted symmetry morphology diagram, the proposed model was proved to be effective, and it can be generalized to arbitrary crystal symmetries.

On the growth orientation of twin-related faceted dendrites

The growth orientation of twin-related faceted silicon dendrites depends on the undercooling ΔT in the melt, which cannot be explained by the existing models. We propose a model to explain the growth behavior showing that the re-entrant corners would lead to the growth of 〈112〉 dendrites, while the 〈110〉 branch is due to continuous growth. Such a selection could be determined by the velocity ratio Vre-entrant/Vridge that is a function of ΔT. An analytical expression for this ratio is derived and compared to the experimental observations.

Phase-field modeling of twin-related faceted dendrite growth of silicon

We investigated the growth of a twin-related silicon dendrite through a novel phase-field model. The correctness of the model for an equilibrium twined crystal was examined first before we modeled the faceted dendrite growth. The simulated morphologies of 〈112〉 and 〈110〉 faceted dendrites were consistent with experimental observations. The growth orientation of the simulated dendrite depended on the growth rates at the ridges and the re-entrant corners. We further extended the Twin-Plane-Reentrant-Edge (TPRE) mechanism and then proposed a new growth model for faceted dendrites based on our simulations. The undercooling and twin spacing could affect the growth rates at the ridges and the re-entrant corners, which were also explained by the proposed model.

Correlation between microstructure and hardness of a Bi-1.5wt%Ag lead-free solder alloy

In the present study a hypoeutectic Bi-1.5wt%Ag alloy was directionally solidified under transient heat flow conditions and the microstructure was analysed. Bi-Ag alloys are considered as potential alternatives to replace Pb-based alloys as solder materials for metallic connections under high temperatures. However, a lack of understanding regarding the effects of solidification thermal parameters (growth rate - VL, the cooling rate - Ṫ) on microstructural aspects is reported in literature. Another challenge is to improve properties and reliability. The results of the present study include the determination of the tip growth rate and the cooling rate by cooling curves recorded by thermocouples positioned along the casting length, metallography, X-ray fluorescence (XRF) and Vickers hardness. The entire directionally solidified Bi-1.5Ag microstructure was arranged by faceted Bi-rich dendrites surrounded by a eutectic mixture (Bi+Ag). The primary and secondary dendrite arm spacing (λ1 and λ2), the interphase spacing (λ) and the diameter of Ag-rich particles were also measured along the casting length; and experimental growth laws. Relating these microstructural features to the experimental thermal parameters are proposed.

Comparison of phosphorus gettering effect in faceted dendrite and small grain of multicrystalline silicon wafers grown by floating cast method

We attempt to clarify the effect of phosphorus diffusion gettering (PDG) on the differences in microstructures of multicrystalline silicon (mc-Si) wafers. From the results of the floating cast method, the obtained microstructure of mc-Si was determined to contain unique microstructures, consisting of large faceted dendrites and small grains with low and high dislocation densities. The PDG efficiency was evaluated through the change in minority carrier lifetime. As a result, a stronger positive PDG effect was found for large faceted dendrites with low dislocation density, attributed to a small number of defects that can act as recombination centers of carriers. Lifetime improvement was also found in dislocation regions possibly owing to the redistribution of interstitial metals. These results suggest the importance of controlling the microstructure of mc-Si, which could strongly affect the PDG efficiency and existence of incorporated impurities.

Simulation of facet dendrite growth with strong interfacial energy anisotropy by phase field method

Numerical simulations based on a new regularized phase-field model were presented, to simulate the solidification of hexagonal close-packed materials with strong interfacial energy anisotropies. Results show that the crystal grows into facet dendrites, displaying six-fold symmetry. The size of initial crystals has an effect on the branching-off of the principal branch tip along the 〈100〉 direction, which is eliminated by setting the b/a (a and b are the semi-major and semi-minor sizes in the initial elliptical crystals, respectively) value to be less than or equal to 1. With an increase in the undercooling value, the equilibrium morphology of the crystal changes from a star-like shape to facet dendrites without side branches. The steady-state tip velocity increases exponentially when the dimensionless undercooling is below the critical value. With a further increase in the undercooling value, the equilibrium morphology of the crystal grows into a developed side-branch structure, and the steady-state tip velocity of the facet dendrites increases linearly. The facet dendrite growth has controlled diffusion and kinetics.

Interfacial Energy Anisotropy Affecting Dendrite Growth of Magnesium Alloy

Numerical simulations based on a new regularized phase field model were presented, simulating the solidification of magnesium alloy. The effects of weak and strong interfacial energy anisotropy on the dendrite growth are studied. The results indicate that with weak interfacial energy anisotropy, the entire dendrite displays six-fold symmetry and no secondary branch appeared. Under strong interfacial energy anisotropy conditions, corners form on both the main stem and the tips of the side branches of the dendrites, the entire facet dendrite displays six-fold symmetry. As the solidification time increases, the tip temperature and velocity of the dendrite and facet dendrite finally tend to stable values. The stable velocity of the facet dendrite is 0.4 at ε6 is 0.05 and this velocity is twice that observed (0.2) at ε6 is 0.005.