The process of rapid solidification of a binary mixture is considered in the framework of local nonequilibrium model (LNM) based on the assumption that there is no local equilibrium in solute diffusion in the bulk liquid and at the solid-liquid interface. According to LNM the transition to complete solute trapping and diffusionless solidification occurs at a finite interface velocity $V=V_D$, where $V_D$ is the diffusion speed in bulk liquid. In the present work, the boundary conditions at the phase interface moving with the velocity $V$ close to $V_D$ ($V \lesssim V_D$) have been derived to find the non-equilibrium solute partition coefficient. In the high-speed region, its comparison with the partition coefficient from the work [Phys. Rev. E 76 (2007) 031606] is given.
The rapid solidification of a binary mixture in the region of the interface velocities $V$ close to the diffusion speed in the bulk of the liquid phase $V_D$ is considered within the framework of the local nonequilibrium approach. In this high-speed region the derivation of the analytical expression for the response function "temperature-velocity" representing kinetic phase diagram is given without using the concept of the equilibrium phase diagram. The modes of movement of the interface both without and with the drag effect are analyzed. It is shown that the drag effect can be accompanied by …
Numerous experimental data on the rapid solidification of binary systems exhibit the formation of metastable solid phases with the initial (nominal) chemical composition. This fact is explained by complete solute trapping leading to diffusionless (chemically partitionless) solidification at a finite growth velocity of crystals. Special attention is paid to developing a model of rapid solidification which describes a transition from chemically partitioned to diffusionless growth of crystals. Analytical treatments lead to the condition for complete solute trapping which directly follows from the…
On the basis of local nonequilibrium approach, the one-dimensional model of the solute diffusion during rapid solidification of the binary alloy in the semi-infinite volume is considered. Within the scope of the model it is supposed that mass transport is described by the telegrapher equation. The basic assumption concerns the behavior of the diffusion flux and the solute concentration at the interface. Under the condition that these quantities are given by the superposition of the exponential functions the solutions of the telegrapher equation determining the flux and the solute distributions…
Solute trapping is an important phenomenon in rapid solidification of alloys, for which the continuous growth model (CGM) is a popular sharp interface theory. Using matched asymptotic analysis, we show how to quantitatively map the sharp interface behavior of a binary alloy phase field model onto the CGM kinetics of Aziz et al. [1], with a controllable partition coefficient k(V ). We demonstrate the parameterizations that allow the phase field model to map onto the corresponding CGM or classical sharp interface models. We also demonstrate that the mapping is convergent for different interface …
The effect of nonequilibrium solute trapping by a growing solid under rapid solidification conditions is studied using a phase-field model. Considering a continuous steady-state concentration profile across the diffuse solid-liquid interface, a new definition of the nonequilibrium partition coefficient in the phase-field context is introduced. This definition leads, in particular for high growth velocities, to a better description of the available experimental data in comparison with other diffuse interface and sharp-interface predictions.
Solidification structures are determined by the interaction between the interfacial processes and transport processes of heat and solute. In this paper, we investigate planar instability in directional solidification. Firstly, the interfacial evolution at the initial growth stage is simulated, indicating the planar instability is represented by the transition from the planar to the cellular. Secondly, to represent the history-dependence of solidification, constant thermal gradient G and varying pulling speed VP are used in the simulations. The results indicate the cooling rate R ( = G*VP) domi…
Element-Specific Solute Trapping and Grain Structure Evolution during Laser Powder Bed Fusion of Multicomponent Alloys
University of Michigan, Dearborn（密歇根大学迪尔伯恩分校）；Texas A&M University（德克萨斯农工大学）；AlphaSTAR Technology Solutions（AlphaSTAR技术解决方案）；University of Michigan, Ann Arbor（密歇根大学安娜堡分校）
The interaction of objects with a moving solidification front is a common feature of many industrial and natural processes such as metal processing, the growth of single-crystals, the cryopreservation of cells, or the formation of sea ice. Solidification fronts interact with objects with different outcomes, from the total rejection to their complete engulfment. We image the freezing of emulsions in 5D (space, time, and solute concentration) with confocal microscopy. We show the solute induces long-range interactions that determine the solidification microstructure. The local increase of solute…
The interface stability against small perturbations of the planar solid-liquid interface is considered analytically in linear approximation. Following the analytical procedure of Trivedi and Kurz (Trivedi R, Kurz W. Acta Metall 1986;34:1663), which is advancing the original treatment of morphological stability by Mullins and Sekerka (Mullins WW, Sekerka RF. J Appl Phys 1964;35:444) to the case of rapid solidification, we extend the model by introducing the local nonequilibrium in the solute diffusion field around the interface. A solution to the heat- and mass-transport problem around the pert…
Planar solidification from an undercooled melt has been considered using the phase-field model. The solute and the phase fields have been found in the limit of small impurity concentration. These solutions in the limit of vanishing velocity of the interface motion give the equilibrium partition coefficient and the liquidus slope. Asymptotic expansions for the solute and for the phase fields, and the relation between the diffusive speed and the parameters of the phase field model have been found at high growth velocity. A comparison with numerical calculations is presented.
A thorough understanding of pattern selection is necessary for the control of solidification structures, which are dissipative structures created by irreversible processes. In this paper, we simulate solidification evolution with different Preferred Crystallographic Orientations (PCOs) through the Phase-Field model. Then we study the effect of solute segregation on the interface energy, as well as the influence of the interface energy on the pattern selection. At the initial stage, the solute segregation influences the interface energy, determining the instability of the planar interface. Duri…
A phase-field formulation is introduced to simulate quantitatively microstructural pattern formation in alloys. The thin-interface limit of this formulation yields a much less stringent restriction on the choice of interface thickness than previous formulations and permits to eliminate non-equilibrium effects at the interface. Dendrite growth simulations with vanishing solid diffusivity show that both the interface evolution and the solute profile in the solid are well resolved.
We present the results of non-equilibrium molecular dynamics simulations for the growth of a solid binary alloy from its liquid phase. The regime of high pulling velocities, $V$, for which there is a progressive transition from solute segregation to solute trapping, is considered. In the segregation regime, we recover the exponential form of the concentration profile within the liquid phase. Solute trapping is shown to settle in progressively as $V$ is increased and our results are in good agreement with the theoretical predictions of Aziz [J. Appl. Phys. {\bf 53}, 1158 (1981)]. In addition, t…
We present a detailed derivation and thin interface analysis of a phase-field model that can accurately simulate microstructural pattern formation for low-speed directional solidification of a dilute binary alloy. This advance with respect to previous phase-field models is achieved by the addition of a phenomenological "antitrapping" solute current in the mass conservation relation [A. Karma, Phys. Rev. Lett 87, 115701 (2001)]. This antitrapping current counterbalances the physical, albeit artificially large, solute trapping effect generated when a mesoscopic interface thickness is used to sim…
Operando study of the evolution of peritectic structures in metal solidification by quasi-simultaneous synchrotron X-ray diffraction and tomography
University of Hull（赫尔大学）；Westlake University（西湖大学）；Diamond Light Source Ltd.（钻石光源有限公司）；Research Complex at Harwell（哈韦尔研究综合体）；Kunming University of Science and Technology（昆明理工大学）
A low artificial anisotropy cellular automaton (CA) model is developed for the simulation of microstructure evolution in directional solidification. The CA model's capture rule was modified by a limited neighbor solid fraction (LNSF) method. Various interface curvature calculation methods have been compared. The simulated equilibrium shapes agree with the theoretical shapes, when the interface energy anisotropy coefficient is ε=0.01, ε=0.03 and ε=0.05, respectively.The low artificial anisotropy CA model is used in the numerical simulation of the cell-to-dendrite transition (CDT) in directional…
Microstructural and Mechanistic Insights into the Tension-Compression Asymmetry of Rapidly Solidified Fe-Cr Alloys: A Phase Field and Strain Gradient Plasticity Study
The superite phase and phase transition inducing multiscale solidification microstructures and segregations in steels
Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences（中国科学院金属研究所）；Department of Materials Science and Engineering, University of Science and Technology Liaoning（辽宁科技大学材料科学与工程学院）；Shanghai Synchrotron Radiation Facility (SSRF), Shanghai Advanced Research Institute, Chinese Academy of Sciences（中国科学院上海高等研究院）
The microsegregation and dendritic growth mode of Al-5wt%Cu alloy was investigated. In the early solidification stage, the crystal growth mode of interrupted growth and periodic boundary trapping will happen, which results in the segregationless dendritic grains. Microsegregation only exists at the final solidification stage with extremely tiny residual melt fraction. In the tiny residual melt zone, the diffusion of solute from the enriched boundary layer to the residual melt and the convergence of enriched boundaries produce the final microsegregation.
We introduce a new phase-field formulation of rapid alloy solidification that quantitatively incorporates nonequilibrium effects at the solid-liquid interface over a very wide range of interface velocities. Simulations identify a new dynamical instability of dendrite tip growth driven by solute trapping at velocities approaching the absolute stability limit. They also reproduce the formation of the widely observed banded microstructures, revealing how this instability triggers transitions between dendritic and microsegregation-free solidification. Predicted band spacings agree quantitatively w…
We minimized the interface diffuseness in the phase-field models by introducing the parabolic double-well potential and localizing the solute redistribution (or latent heat release) into a narrow region within the phase-field interface. In spite of the parabolic potential with cusps, highly localized solute redistribution and discontinuous diffusivity function adopted in this model, it works remarkably well in numerical computations. The computations on dendritic solidification of an one-sided system yield quantitatively the same results with the anti-trapping model [A. Karma, Phys. Rev. Lett.…
Understanding rapid solidification behavior at velocities relevant to additive manufacturing (AM) is critical to controlling microstructure selection. Although in-situ visualization of solidification dynamics is now possible, systematic studies under AM conditions with microstructural outcomes compared to solidification theory remain lacking. Here we measure solid-liquid interface velocities of Ni-Mo-Al alloy single crystals under AM conditions with synchrotron X-ray imaging, characterize the microstructures, and show discrepancies with classical theories regarding the onset velocity for absol…
In this study, an alloy phase-field model is used to simulate solidification microstructures at different locations within a solidified molten pool. The temperature gradient $G$ and the solidification velocity $V$ are obtained from a macroscopic heat transfer finite element simulation and provided as input to the phase-field model. The effects of laser beam speed and the location within the melt pool on the primary arm spacing and on the extent of Nb partitioning at the cell tips are investigated. Simulated steady-state primary spacings are compared with power law and geometrical models. Cell …
Microstructure evolution during rapid solidification of hypoeutectic Al-Ag alloys near absolute stability
Colorado School of Mines（科罗拉多矿业学院）；Northeastern University（东北大学）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
Additive manufacturing (AM), through directed energy deposition, supports planned composition changes between locations within a single component, allowing for functionally graded materials (FGMs) to be developed and fabricated. The formation of deleterious phases along a particular composition path can cause significant cracking during the AM build process that makes the composition path unviable to produce these FGMs, but it is challenging to predict which phases will be present in as-built additively manufactured parts by analyzing only equilibrium phase relations. Solute segregation during…
By adjusting the interface energy, curvature, and velocity, the anisotropy plays an important role in the interaction between interfacial processes and transport processes, determining the solidification structures. In this paper, through the quantitative phase-field model, the influence of anisotropy on the evolution of interfacial morphologies in directional solidification is investigated. To represent different interfacial anisotropies, the solidification processes with different preferred crystallographic orientations are performed. Then the effect of anisotropy on morphological evolution …
The physics of ice crystal growth from the liquid phase, especially in the presence of salt, has received much less attention than the growth of snow crystals from the vapour phase. The growth of so-called frazil ice by solidification of a supercooled aqueous salt solution is consistent with crystal growth in the basal plane being limited by the diffusive removal of the latent heat of solidification from the solid--liquid interface, while being limited by attachment kinetics in the perpendicular direction. This leads to the formation of approximately disk-shaped crystals with a low aspect rati…
We present a new phase-field formulation for the non-equilibrium interface kinetics. The diffuse interface is considered an integral of numerous representative volume elements (RVEs), in which there is a two-phase mixture with two conserved and two non-conserved concentration fields. This particular way of separating concentration fields leads to two distinct dissipative processes besides the phase boundary migration, i.e., trans-sharp-interface diffusion between different phases within a single RVE and trans-diffuse-interface diffusion between different RVEs within a single phase. A two-part …
From a simple model for the driven motion of a planar interface under the influence of a diffusion field we derive a damped nonlinear oscillator equation for the interface position. Inside an unstable regime, where the damping term is negative, we find limit-cycle solutions, describing an oscillatory propagation of the interface. In case of a growing solidification front this offers a transparent scenario for the formation of solute bands in binary alloys, and, taking into account the Mullins-Sekerka instability, of banded structures.
