Solidification Velocity Research Articles

Towards a theory of steady-state solidification process with a quasi-equilibrium two-phase region

AbstractThe process of directional crystallization in the presence of a quasi-equilibrium two-phase region located between the solid material and the liquid phase is studied theoretically. The mathematical model of the process is based on heat and mass transfer equations in the solid, liquid and two-phase regions, as well as boundary conditions at the phase interfaces “solid phase” – “two-phase region” and “two-phase region” – “liquid phase”, which are moving with a constant velocity. The process of directional crystallization is given by fixed temperature gradients in the solid and liquid phases, which determine a constant velocity of melt solidification. An exact analytical solution of the nonlinear problem with two moving boundaries of phase transformation is obtained, which is based on the transition to a new independent variable, the solid phase fraction, when integrating the nonlinear heat and mass transfer equations in the two-phase region. As a result of solving the problem, the distributions of temperature and concentration of dissolved impurity, the solid phase fraction in a two-phase region, the laws and velocities of motion of its interphase boundaries are determined. It is analytically shown that the impurity concentration and temperature in the two-phase region are only the functions of solid phase fraction, which, in turn, depends on the spatial coordinate. Analysis of the obtained solutions shows that the solid phase fraction in a two-phase region can be both a decreasing and increasing function of the spatial coordinate, which is directed from the solid material to the melt. This determines the internal structure of two-phase region, its permeability, average interdendritic spacing, distribution of dissolved impurity, crystallization velocity and laws of two-phase region boundaries.

From irregular to regular eutectic growth in the Al-Al3Ni system: In situ observations during directional solidification

We investigate the irregular eutectic growth dynamics of the Al-Al3Ni alloy, in which one of the solid phases (Al3Ni) grows faceted from the liquid. Leveraging in situ optical microscopy and synchrotron transmission x-ray microscopy, we address the question of the degree of coupling between Al and Al3Ni at the growth front and that of the shape of the microstructures left behind in the bulk solid during directional solidification. Real-time optical observations bring evidence for a morphological transition from a eutectic-grain dependent, irregular eutectic growth at low solidification velocity V (typically 1μms−1), to a weakly anisotropic, regular growth at higher V (reaching 10μms−1). Unprecedented x-ray nano-imaging of the solid–liquid interface, and 3D characterization of the growth patterns, were made possible by a new DS setup at Brookhaven National Laboratory’s NSLS-II. At low V, the leading tips of partly faceted Al3Ni crystals are observed to grow not far ahead of the Al growth front. Correlating in situ images and postmortem 3D tomographic reconstructions reveals that the presence of faceted and non-faceted regions of Al3Ni crystals in the solid is a direct consequence of coupling and decoupling during DS, respectively. Upon increasing V, the lead distance of Al3Ni vanishes, and the shape of Al3Ni ceases to be governed by faceted growth. These observations cast light onto the basic mechanisms (faceted growth, diffusive coupling, and the dynamics of trijunctions) governing a faceted to rod-like transition upon increasing V in the Al3Ni system, with broad implications to a large class of irregular eutectics.

Microstructure, multi-scale mechanical and tribological performance of HVAF sprayed AlCoCrFeNi high-entropy alloy coating

Thermal spray high-entropy alloy (HEA) coatings have demonstrated potential for improving the wear resistance of conventional materials used in extreme engineering environments. In the present work, an equiatomic AlCoCrFeNi HEA coating was manufactured using the high velocity air fuel (HVAF) process. The phase and microstructural transformations in gas-atomized (GA) powder during HVAF spraying were analyzed using SEM, EDS and EBSD techniques. The tribological properties of this HEA coating sliding against an Al2O3 ball at both room temperature (RT) and 600 °C were also evaluated. The GA powder was composed of Body Centred Cubic (BCC) + ordered BCC (B2) phases, which transformed to BCC + B2 + minor Face Centred Cubic (FCC) phases during the HVAF coating process, validating the thermodynamic phase prediction projected by the Scheil simulation for non-equilibrium processing conditions. The rapid solidification and high velocity impact-assisted deformation of GA powder resulted in significant grain refinement in the HVAF coating, which ultimately improved the mechanical properties at both micro and nanoscale levels. The wear resistance of the HEA coating at RT was severely impacted by the relatively brittle BCC/B2 phase structure, leading to susceptibility to abrasive wear and surface fatigue. The wear resistance at 600 °C was slightly lower at RT due to the formation of a brittle oxide layer on the worn surface, which induced surface fatigue and aggravated mass loss of the coating.

Temperature Control of Concrete Structure in Bridge Construction by Renewable Energy Technology

In this study, the classical display nonlinear dynamic analysis method was used to detect the temperature of concrete structures in bridge construction. Firstly, two different bridge construction test methods, the Winfrith subfunction and CSCM subfunction, were selected to detect the nonlinear temperature of the simulated concrete, and the temperature of the bridge concrete structure and the residual velocity of solidification were detected and analyzed by combining the nonlinear dynamic algorithm for data processing. The results show that the data of the nonlinear dynamic test in this paper agree with the actual requirements, and the accuracy rate is about 90~95%. In addition, the Winfrith subfunction calculates the data of the large strain force of photovoltaic temperature control energy on concrete. It identifies the nonlinear characteristics of high strain rate, especially the effect of photovoltaic heating, battery stable power supply heating, and the effect of wind on water vapor dissipation, which further proves that renewable energy technology can monitor the temperature of concrete structures in bridge construction, and effectively detect and identify concrete problems to support the construction and later use of bridge concrete.

Enhancing the removal of Fe and Ti from metallurgical silicon by slagging-directional solidification

Metallurgical preparation of solar-grade silicon is the most popular method, benefiting from the low costs and environmentally friendly. The paper employed a metallurgical method to purify silicon and investigated the removal of Fe and Ti from silicon by directional solidification synergized with slagging refining (slagging-directional solidification, SDS). The result showed that lower solidification velocity and stronger cooling conditions during directional solidification (DS) contributed to removing Fe and Ti impurities from ingots. The concentrations of Fe and Ti at the beginning of the ingot obtained by DS at optimum conditions were 0.04 wt% and 0.002 wt%. Based on this, the influence of SDS on Fe and Ti was investigated, finding the concentrations of Fe and Ti at the beginning of the ingot were 0.021 wt% and 0.001 wt% with removal rates of 98.55 % and 98.86 %. Compared to ingots obtained by DS, the removal rates of Fe and Ti increased by 1.31 % and 1.13 %, respectively. The results showed that SDS has been proven to enhance the removal of Fe and Ti from ingot. Finally, the removal mechanism of SDS was analyzed. The method of directional solidification synergized with slagging refining was a novel method to purify with a low cost and environmentally friendly.

Influence of ultrasonic excitation on the melt pool and microstructure characteristics of Ti-6Al-4V at powder bed fusion additive manufacturing solidification velocities

Cavitation and acoustic streaming created by in situ high-intensity ultrasound have been exploited for microstructural refinement during directed energy deposition (DED) additive manufacturing (AM) of alloy Ti‐6Al‐4V. Whether the same ultrasound-driven mechanisms are applicable to powder bed fusion (PBF) of Ti‐6Al‐4V remains uncertain. The primary factors that control the microstructure during deposition processing are the solidification velocity and temperature gradient, which are orders of magnitude higher for PBF than DED processes. This work examines the role of high-intensity ultrasound on the melt pool and resulting microstructure of Ti‐6Al‐4V under PBF solidification conditions. The effect of the laser scanning velocity and ultrasonic excitation on the melt pool and grain structure characteristics is interrogated through controlled line scans and area scans without powder. Temperature field simulations are used to estimate the solidification velocities and temperature gradients and to compare the processing conditions with previously characterized columnar-to-equiaxed transition diagrams. The acoustic pressures during processing are estimated using a coupled field acoustic-elastic finite element simulation and used in a Keller-Miksis model to assess the likelihood of cavitation vs. cavity size. The microstructure of the samples with or without ultrasonic excitation was characterized, allowing the equivalent grain diameters and aspect ratios to be compared. All samples, including those exposed to scanning velocities where cavitation did not occur, showed a reduction in grain aspect ratio when subjected to ultrasonic excitation, but the effect on equivalent grain diameter was inconclusive. A key finding is that the primary effects of ultrasonic excitation may be attributed to acoustic streaming, rather than cavitation, during PBF processing. Further development of the ultrasonic excitation technique explored may permit tailoring of the microstructure and texture characteristics in bulk AM parts.

Achieving high strength 316L stainless steel by laser directed energy deposition-ultrasonic rolling hybrid process

Laser directed energy deposition (LDED) has attracted as a progressive additive manufacturing technique in fabricating the stainless steel components. The rapid melting and solidification velocity under LDED process induces the appearance of pores and the columnar dendritic, which degrades the strength of alloys. Here, a self-developed LDED-UR (ultrasonic rolling) synchronous manufacturing equipment is developed to fabricate the 316L stainless steel, and the characterization of microstructure and mechanical properties are studied. Results show that the size and fraction of pores are significantly reduced by LDED-UR processing, and fine equiaxed grains are obtained under the combined effects of ultrasonic vibration and roller pressure. With the severe plastic deformation, the average grain size of LDED-UR sample is decreased from 76.10 μm to 26.23 μm (LDED sample), and high angle grain boundaries transforms to low angle grain boundaries. Meanwhile, the dislocation density in LDED-UR sample is increased compared to the LDED sample. Owing to the grain refinement and dislocation strengthening, the average microhardness, yield strength, ultimate tensile strength and elongation of the LDED-UR sample reach 268.18 ± 13.90 HV0.2, 442 MPa, 771.2 MPa, and 49.8 %, respectively, which are larger than those of LDED sample (214.13 ± 13.76 HV0.2, 396 MPa, 682 MPa, and 45.5 %). This implies that the superior mechanical properties are obtained by employing in-situ ultrasonic rolling under LDED process. The insight of the influence of microstructure on mechanical properties extends a new approach for enhancing the mechanical properties of LDED alloys.

Control of Interface Migration in Nonequilibrium Crystallization of Li2SiO3 from Li2O-SiO2 Melt by Spatiotemporal Temperature and Concentration Fields.

During liquid-solid transformation, bulk mass and thermal diffusion, along with the evolved interfacial latent heat, work in tandem to generate interfacial thermodynamic and kinetic forces, the interplay of which decides the solidification velocity and consequently the solidified phase attributes. Hence, access to interface dynamics information in dependence of bulk transfer processes is pivotal to tailor the desired quantity of solid phases of unique compositions. It finds particular application for engineering concentrated Lithium (Li) phases out of Li-ion battery slags, thus generating a high value-added product from a conventional waste process stream. However, considerable challenge exists to predict the impact of the diverse external cooling rates on the evolving internal transfer processes and thus tuning solidification routes for achieving phases of interest. Hence, in this work, a thermodynamically consistent nonequilibrium model, by considering spatiotemporal temperature and concentration fields, is developed and applied to study solidification of Li2SiO3 from a Li2O-SiO2 melt that constitutes an important subsystem of the Li containing battery-recycling slags. The approach treats the sharp solid/liquid interface as a moving heat source. In the presence of different heat extraction profiles, it evaluates the spatial temperature heterogeneity and its implicit correlation to internal material fluxes resulting from maximization of dissipation and consequently the interrelation to interface velocities. Model calculations revealed that irrespective of the external cooling rate, for an initial short time duration, the magnitude of which increased with decreasing cooling rates, the interface velocities show a reducing trajectory directly relatable to the reducing thermodynamic forces due to localized interfacial temperature rise from the generated latent heat of fusion from the initial solidification. This is followed by a thermodynamically controlled regime, whereby for each cooling rate, the interface velocities increase until a maxima, the magnitude of which decreases with decreasing cooling rates. Finally, the interface propagation speeds decrease as controlled by the kinetic regime.

Solidification behavior and texture of 316L austenitic stainless steel by laser wire directed energy deposition

The solidification behavior and crystallographic texture of 316L austenitic stainless steel builds fabricated via laser-wire directed energy deposition additive manufacturing (AM) were investigated. Shielding gas set-up and build type (single-track vs. multi-track) were varied, which led to changes in the solidification conditions and the final build compositions. Primary δ-ferrite solidification is predicted based on equilibrium thermodynamic predictions of the bulk feedstock composition. However, the increased solidification velocity of the AM process promotes a solidification mode transition from primary δ-ferrite to primary austenite. Skeletal δ-ferrite and lathy δ-ferrite associated with primary δ-ferrite solidification and interdendritic δ-ferrite associated with primary austenite solidification were observed among the laser-wire directed energy deposition walls. Skeletal and interdendritic δ-ferrite exhibited a (001)δ // (001)γ parallel relationship with austenite and a {001} solidification texture aligned with the build direction for both austenite and δ-ferrite. Lathy δ-ferrite exhibited a Kurdjumov-Sachs orientation relationship, (101)δ//(11¯1)γ, with austenite due to austenite nucleation in the solid-state. It is shown that the solidification behavior of AM 316L is accurately represented by as-built composition data and a dendrite growth model, which combined, encompasses the compositional and solidification condition impacts on the solidification pathway.

Unveiling the Intricacies of a Ductile‐Phase Toughened Intermetallic: An In‐Depth Exploration of a Eutectic Mo–Si–Ti Alloy and its Mechanical Behavior

Herein, the development of directional solidification for a novel high‐temperature Mo–20Si–52.8Ti (at%) ternary alloy using a modified Bridgeman type apparatus is presented. The resulting alloy exhibits a microstructure consisting of a body‐centered cubic solid solution (BCCss) and a hexagonal silicide (Ti,Mo)5Si3 with approximate volume fractions of 50% for each phase. The phases exhibit a crystallographic orientation relationship with and . Different solidification velocities are imposed, which reveal an inverse relationship to the lamellar spacing according to a Jackson–Hunt type scaling. Mechanical characterization using Vickers indentation demonstrates that the BCCss accommodates plasticity through dislocation motion, while the silicide phase exhibits high hardness and brittleness, serving as a crack initiation site. Crack propagation is arrested and deflected at the interface to the BCCss. Fracture toughness measurements via indentation yield a fracture toughness of 3.7 MPa√m for the silicide, somewhat higher than previously reported values for Nb‐, Mo‐, and Cr‐based silicides at room temperature. The directionally solidified specimens show an enhanced fracture toughness attributed to a greater BCCss length scale; thus, combining the ductile and hard phases results in a ductile‐phase toughened intermetallic composite. The findings open up new possibilities for the design of advanced intermetallic composites with improved toughness performance.

Quantification of melt pool dynamics and microstructure during simulated additive manufacturing

The dynamics of laser spot melting and metallic alloy solidification are investigated through synchrotron x-ray radiography, 3D electron backscatter diffraction data, and computational fluid dynamics (CFD) simulations on a model NiMoAl alloy. Solidification velocities are measured from in-situ images to validate a CFD model of the spot melt. TriBeam tomography is used to reconstruct the melt pool in 3D, characterize the microstructure, and validate the CFD model melt pool dimensions. 3D geometrically necessary dislocation (GND) density calculations reveal extensive deformation at the sample surface. GND calculations integrated with the CFD model reveal that the halo of small, equiaxed grains adjacent to the fusion line is a result of recrystallization that occurred in the heat affected zone. By combining in-situ and ex-situ data modalities across a variety of temporal and spatial length scales, the microstructure formation mechanisms and their relationship to melt pool solidification are quantified.

Ice templated and ice seed tailored hydrogels for highly efficient solar evaporator

In recent years, freshwater resources have become a global concern, and solar vapor generation (SVG) has garnered significant attention from researchers. Herein, a novel hydrogel solar evaporator was prepared by incorporating lignin and CuS-rGO into a chitosan-gelatin matrix. The anisotropic and isotropic morphologies of the hydrogel were prepared by pathway control on the solidification velocities of ice crystals and ice seeds. It presented that the anisotropic morphology can improve the refraction of light and increase the utilization rate of light by forming a light trap, leading to higher water evaporation rate. Additionally, ice seed was introduced during the freezing process, producing an anisotropic hydrogel with curled layer structure that endowed lower enthalpy of water evaporation and faster water transfer rate, resulting in high evaporate of 3.62 kg m−2 h−1 under one solar irradiation with photothermal conversion efficiency of 97.7 %. Finally, the gel also demonstrated good mechanical properties, long-term working stability and harsh environment tolerance, which make it ideal for outdoor applications. The hydrogel evaporator had potential to generate 25.24 kg m2 water per day that could meet the huge demand for freshwater as sources.

Constructing solidification microstructure selection map for AlSi10Mg alloy processed by laser powder bed fusion

The cellular structures, which consist of cells and eutectic networks at the cell boundaries, determine the mechanical properties of the Al–Si alloys fabricated by laser powder bed fusion (L-PBF). Therefore, it is scientifically interesting and technologically important to establish the relationship between cellular structures and processing parameters, which is applicable to all kinds of processing methods involving rapid directional solidification, such as L-PBF. In this work, a rapid solidification microstructure selection map (SMSM) of the Al–10Si system in temperature gradient (G)–solidification velocity (V) space is constructed by a synergistic calculation with dendritic and eutectic growth models compatible to the L-PBF process. Considering that the divorced eutectic reaction should occur as the width of the liquid film entrapped in the α-Al cell boundaries becomes smaller than the Al–Si eutectic spacing, the G–V domain suitable for acquiring the cellular structures decorated with divorced eutectic Si networks is determined on the SMSM. The microstructure evolution trends predicted by the SMSM are well consistent with those in the L-PBFed AlSi10Mg melt pools with different processing parameters. The length scales of actual microstructures observed by the experiments from this work and the literature are quantitatively compared to those estimated by the SMSM, and the experimental results are basically in accord with the SMSM. It is demonstrated that divorced eutectic Si networks prefer to form at the bottom of the melt pool, where G is large (> 5 × 106 K/m) and V is small (3 × 10−4–6 × 10−3 m/s) in the SMSM. The outcomes of this work may provide fundamental guidance for tailoring the microstructures of the L-PBFed Al–Si alloys for achieving optimal mechanical properties.

Numerical simulation of VAR for large-scale TC4 alloy during the solidification process

ABSTRACT A three-dimensional multi-physics model of the effect of process parameters on the evolution of the solid–liquid interface during solidification of large-scale Ti-6 wt% Al-4 wt% V (TC4) alloy by[Ballantyne, 1977 #483] (VAR) and a macroscopic model of grain nucleation and growth was established. The simulation results qualitatively reveal the evolution of solid–liquid interface and central cross-sectional solidification structure under various melting conditions, indicating that the melting zone depth increased while the mushy zone width and the number of grains decreased with the increase of melting power; the depth of the melting zone and the width of the mushy zone increase sharply with the increase in solidification velocity, the average grain radius increased, while the number of grains decreased; when the ingot diameter increased from 260 mm to 660 mm, the depth of the melting zone increased and gradually remained stable, and the width of the mushy zone gradually decreased.

On the formation of gradient-distributed dendrites in a single crystal nickel-based superalloy directionally solidified under transverse static magnetic field

Directional solidification (DS) of alloys under static magnetic field has attracted extensive attention due to the development of thermoelectric magnetohydrodynamics (TEMHD). Assessing the influence of static magnetic field on solidification microstructures in single crystal (SX) superalloys is of great significance for both the development of SX superalloys and the understanding of external field-assisted solidification. In this contribution, under different transverse static magnetic fields, the evolution of dendritic structure in a SX nickel-based superalloy directionally solidified over a range of solidification velocities is systematically investigated. The results show that applying a transverse static magnetic field (TSMF) during DS does not disrupt the crystal orientation of SX superalloys. The distribution of dendrites or local primary dendrite arm spacings within the cross section of SX superalloys shows a gradient variation in the direction perpendicular to the TSMF. Additionally, the formation of gradient-distributed dendritic structure is closely related to the applied TSMF intensity and solidification velocity. It is easier to form a gradient-distributed dendritic microstructure at low solidification velocities and high magnetic fields. Based on the experiments and simulations, the formation of gradient-distributed dendritic microstructure is supposed to attribute to the variation of interdendritic constitutional undercooling created by the change of solute concentration in interdendritic region, which is induced by the TEMHD. The SX superalloy with a gradient distribution of dendrites may have potential applications due to its gradient properties. Meanwhile, these findings also provide a new method for preparing alloys with gradient microstructures.

An operando synchrotron study on the effect of wire melting state on solidification microstructures of Inconel 718 in wire-laser directed energy deposition

Directed energy deposition (DED) with a coaxial wire-laser configuration has gained significant attention in recent years for the production of large-scale metallic components because of its low directional dependence, fast deposition rate, high feedstock efficiency, and low manufacturing costs. This work studies the coaxial wire-laser DED process of Inconel 718 alloy under a stable deposition condition with a relatively low input volumetric energy density (55.5 J/mm3). Post characterization reveals a cluster of refined grains at the center-bottom region of the as-printed track. Operando high-energy synchrotron X-ray experiments and multi-physics modeling are applied innovatively to study the fundamental mechanism responsible for the formation of this microstructure. The X-ray diffraction experiment provides direct evidence, which is supported by the simulation, that the feeding wire can reach the melt pool bottom and release solid particles (primarily carbides) near the mushy zone owing to insufficient melting. Consequently, these sub-micron sized particles suppress the growth of large columnar grains and cause the formation of unique microstructural heterogeneity. This discovery offers new opportunities for tailoring the solidification microstructure by controlling the melting state of the feedstock wire in DED process, in addition to commonly known factors such as the thermal gradient and solidification velocity.

The Influences of Micro-Alloying Element Sn and Magnetic Field on the Microstructure Evolution of Al–Bi Immiscible Alloys

An investigation was conducted through directional solidification experiments to explore the impact of micro-alloying element Sn and a magnetic field on the solidification behavior of immiscible Al–Bi alloys, as well as the combined effect of Sn and the magnetic field. Experimental results show that the size distribution of the dispersed particles in the low-speed solidified Al–3.4 wt.%Bi alloy presents two peaks, while it only shows one peak when solidified at a relatively high speed. The addition of Sn not only can enhance the nucleation rate and the number density of the Bi-rich droplets in the sample, but also decrease the Marangoni migration velocity and the axial resultant velocity of minority phase droplets in front of the solidification interface. Thereby it promotes the formation of Al–Bi alloys with a well-dispersed microstructure. A static magnetic field with the strength of 0.2 T increases the number density of the dispersed particles and decreases the average size and the size distribution width of the dispersed particles. Under the effect of Sn addition and static magnetic field, the average radius of the dispersed particles R and the solidification velocity V0 satisfy R∝V0−1/3 when the alloy was solidified at a relatively low velocity, R and V0 satisfy R∝V0−1/2 when the alloy is solidified at a high velocity.

Toward understanding the microstructure characteristics, phase selection and magnetic properties of laser additive manufactured Nd-Fe-B permanent magnets

Nd-Fe-B permanent magnets play a crucial role in energy conversion and electronic devices. The essential magnetic properties of Nd-Fe-B magnets, particularly coercivity and remanent magnetization, are significantly influenced by the phase characteristics and microstructure. In this work, Nd-Fe-B magnets were manufactured using vacuum induction melting (VIM), laser directed energy deposition (LDED) and laser powder bed fusion (LPBF) technologies. The microstructure evolution and phase selection of Nd-Fe-B magnets were then clarified in detail. The results indicated that the solidification velocity (V) and cooling rate (R) are key factors in the phase selection. In terms of the VIM-casting Nd-Fe-B magnet, a large volume fraction of the α-Fe soft magnetic phase (39.7 vol.%) and Nd2Fe17B x metastable phase (34.7 vol.%) are formed due to the low R (2.3 × 10−1 °C s−1), whereas only a minor fraction of the Nd2Fe14B hard magnetic phase (5.15 vol.%) is presented. For the LDED-processed Nd-Fe-B deposit, although the Nd2Fe14B hard magnetic phase also had a low value (3.4 vol.%) as the values of V (<10−2 m s−1) and R (5.06 × 103 °C s−1) increased, part of the α-Fe soft magnetic phase (31.7 vol.%) is suppressed, and a higher volume of Nd2Fe17B x metastable phases (47.5 vol.%) are formed. As a result, both the VIM-casting and LDED-processed Nd-Fe-B deposits exhibited poor magnetic properties. In contrast, employing the high values of V (>10−2 m s−1) and R (1.45 × 106 °C s−1) in the LPBF process resulted in the substantial formation of the Nd2Fe14B hard magnetic phase (55.8 vol.%) directly from the liquid, while the α-Fe soft magnetic phase and Nd2Fe17B x metastable phase precipitation are suppressed in the LPBF-processed Nd-Fe-B magnet. Additionally, crystallographic texture analysis reveals that the LPBF-processed Nd-Fe-B magnets exhibit isotropic magnetic characteristics. Consequently, the LPBF-processed Nd-Fe-B deposit, exhibiting a coercivity of 656 kA m−1, remanence of 0.79 T and maximum energy product of 71.5 kJ m−3, achieved an acceptable magnetic performance, comparable to other additive manufacturing processed Nd-Fe-B magnets from MQP (Nd-lean) Nd-Fe-B powder.

Interplay between facetting and confinement in directional solidification of silicon: A direct comparison between experiments and phase-field simulations

We combine the analysis of experiments based on in situ X-ray imaging and phase-field simulations to get insight into the interplay between faceting and confinement effects in thin silicon samples during directional solidification from a monocrystalline seed. The phase-field model is parametrized by available experimental results, especially regarding the anisotropy functions for the surface energy and for the kinetic attachment coefficient. In the present work, a method is proposed to extrapolate 2D fully quantitative simulations results to 3D thin sample geometry. Two simple seed orientations along the 〈110〉 and 〈100〉 crystal directions are considered. For 〈110〉 direction, it is shown that confinement effects are weak so 2D simulations can be readily compared to the experiments. For 〈100〉 direction, much stronger confinement effects are identified and characterized by a confinement factor that is estimated from phase-field simulations of thin 3D systems. For both directions, the length of the side facets is shown to increase with the solidification velocity and an analytical expression including the confinement factor is obtained for the law relating both quantities. A very quantitative experiment-simulation agreement is obtained in each case.

Interface Response Functions for multicomponent alloy solidification—An application to additive manufacturing

The near-rapid solidification conditions during additive manufacturing can lead to selection of non-equilibrium phases. Sharp interface models via interface response functions have been used earlier to explain the microstructure selection under such solidification conditions. However, most of the sharp interface models assume linear superposition of contributions of alloying elements without considering the non-linearity associated with the phase diagram. In this report, both planar and dendritic Calphad coupled sharp interface models have been implemented and used to explain the growth-controlled phase selection observed at high solidification velocities relevant to additive manufacturing. The implemented model predicted the growth-controlled phase selection in multicomponent alloys, which the other models with linear phase diagram could not. These models are calculated for different steels and the results are compared with experimental observations.