The interplay between the diffusion-controlled dynamics of a solidification front and the trajectory of a grain boundary groove at the solid-liquid interface is studied by means of thin-sample directional solidification experiments of a transparent alloy, and by numerical simulations with the phase-field method in two dimensions. We find that low-angle grain boundaries (subboundaries) with an anisotropic interfacial free energy grow tilted at an angle $θ_t$ with respect to the temperature gradient axis. $θ_t$ remains essentially equal to its value imposed at equilibrium as long as the solidification velocity $V$ remains low. When $V$ increases and approaches the cellular instability threshold, $θ_t$ decreases, and eventually vanishes when a steady-state cellular morphology forms. The absence of mobility of the subboundary in the solid is key to this transition. These findings are in good agreement with a recent linear-stability analysis of the problem.
Linear morphological stability analysis of the solid-liquid interface in rapid solidification of a binary system
在线性近似下，分析了平面固-液界面在小扰动下的界面稳定性。按照Trivedi和Kurz（Trivedi R，Kurz W. Acta Metall 1986;34：1663），其推进了Mullins和Sekerka（Mullins WW，Sekerka RF. J Appl Phys 1964; 35：444）的情况下，快速凝固，我们扩展了该模型，通过引入局部非平衡的溶质扩散场周围的界面。在局部非平衡溶质扩散的存在下，给出了扰动界面周围的热质输运问题的一个解。利用发展中的局部非平衡凝固模型，线性形态稳定性的自洽分析与归因于边缘（中性）和绝对形态稳定的快速移动的界面。特别考虑的情况下，在负和正的温度梯度凝固的界面稳定性。相对于Hoglund和Aziz（Hoglund DE，Aziz MJ. Mat Res Soc Symp Proc 1992;205：325）对Si-Sn合金快速凝固过程中界面破裂的临界溶质浓度的研究。
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…
This paper investigates by in situ high-resolution X-ray radiography and tomography the behaviour of colloidal suspensions of alumina particles during directional solidification by freezing. The combination of these techniques provided both qualitative and quantitative information about the propagation kinetic of the solid/liquid interface, the particles redistribution between the crystals and a particle enriched phase and the 3D organisation of the ice crystals. In this first part of two companion papers, the precursor phenomena leading to directional crystallisation during the first instants…
Phase-field modeling of microstructural pattern formation during directional solidification of peritectic alloys without morphological instability
在包晶合金定向凝固过程中，两个稳定的固相（母相和包晶相）竞争生长成亚稳液相，其杂质含量大于任何一个固相。当母相或两个固相在形态上不稳定时，即，对于小的温度梯度/生长速率比（$G/v_p$），一个固相通常生长出并覆盖另一个相，导致与在稀二元合金的单相凝固过程中形成的胞状-枝晶阵列结构非常类似的胞状-枝晶阵列结构。相反，当$G/v_p$大到足以使两相形态稳定时，微结构的形成受到两个固相的成核和生长之间的微妙相互作用的控制。在这种情况下观察到的结构（在对流效应被抑制的小样品中）包括垂直于生长方向的母相和周相的交替层（带），其通过一个相交替成核和横向扩散到另一个相上而形成，如最近的模型[R. Trivedi，Metall. Mater. A 26，1（1995）]，以及部分填充的带（岛），其中周晶相不完全覆盖连续生长的母相。我们开发了一个相场模型，结合成核过程，以探索这些结构的形成的周向凝固。该模型的模拟揭示了从岛屿到乐队的形态过渡，在母相上的成核后，这原来是由一个显着的恒定的加速度，和生长形态的类型，人们可能会期望在纯扩散生长条件下观察到的大样品的周边相的传播的动态。
Real-time quantification of fluid flows around bubbles during directional solidification
Université Lyon 1, CNRS Institut Lumière Matière UMR5306（里昂第一大学，CNRS光与物质研究所）；Sciences et Ingénierie de La Matière Molle UMR 7615, ESPCI Paris, PSL Research University, CNRS, Sorbonne Universités（软物质科学与工程UMR 7615，巴黎高等物理化工学院，PSL研究大学，CNRS，索邦大学）
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 …
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 order to control the grain structure of multi-crystalline (mc) silicon during directional solidification, the development process of grain boundaries (GBs) with respect to the temperature gradient should be understood. A phase-field model incorporated with anisotropic interface energy and anisotropic attachment kinetic coefficient has produced the faceted shape of a growing silicon crystal, which is in agreement with experimental observation. The growth of coupled silicon grains under various growth velocities has been simulated to see the morphology of the solid-liquid front and the develo…
This paper investigates the behaviour of colloidal suspensions of alumina particles during directional solidification, by in situ high-resolution observations using X-ray radiography and tomography. This second part is focussed on the evolution of ice crystals during steady state growth (in terms of interface velocity) and on the particles redistribution taking place in this regime. In particular, it is shown that diffusion cannot determine the concentration profile and the particles redistribution in this regime of interface velocities (20-40 microns/s); constitutional supercooling arguments …
The properties of welded components are dominated by the microstructure evolution in the pool, where the solidification conditions are space-time variational. To represent the variational solidification conditions in the pool, the multi-scale simulation is carried out in this paper, combining the microscopic Phase-Field (PF) equations with the macroscopic thermal processes. Firstly, two different models, the GR model and TF model, are employed to simulate the single crystal solidification at a local region of the pool. Results suggest the TF model is more suitable to reflect the variational co…
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…
We study the evolution of prior columnar $β$ phase, interface $L$ phase, and $α$ phase during directional solidification of a Ti-6Al-4V melt pool. Finite element simulations estimate the solidification temperature and velocity fields in the melt pool and analyze the stress field and thermal distortions in the solidified part during the laser powder bed fusion process. A phase-field model uses the temperature and velocity fields to predict the formation of columnar prior-$β$(Ti) phase. During the solidification of $β$ phase from an undercooled liquid, the residual liquid below the solidus tempe…
When a suspension freezes, a compacted particle layer builds up at the solidification front with noticeable implications on the freezing process. In a directional solidification experiment of monodispersed suspensions in thin samples, we evidence a link between the thickness of this layer and the sample depth. We attribute it to an inhomogeneity of particle density induced by the sample plates. A mechanical model enables us to relate it to the layer thickness with a dependency on the sample depth and to select the distribution of particle density that yields the best fit to our data. This dist…
We investigate solidification of an Al-Al2Cu as a model system to understand the emergence of patterns (such as lamellar, rod and maze-like) within eutectic colonies. To uncover the morphological transitions in-situ and in 3D, we introduce here a new synchrotron-based, X-ray imaging procedure. Our method simultaneously maximizes the temporal (200 ms) and spatial resolution ($0.69^2 μm^2/pixel$) over that of traditional imaging approaches. The wealth of information obtained from this procedure enables us to visualize the development of a crystallographically `locked' eutectic microstructure in …
Revealing 3D Strain and Carbide Architectures in Additively Manufactured Ni Superalloys
European Synchrotron Radiation Facility (ESRF)（欧洲同步辐射装置）；Department of Materials Science & Metallurgy, University of Cambridge（剑桥大学材料科学与工程系）；School of Metallurgy and Materials, University of Birmingham（伯明翰大学冶金与材料学院）；Institut für Werkstofftechnik, Universität Kassel（卡塞尔大学材料技术研究所）；Centre for Additive Manufacturing, School of Engineering, RMIT University（皇家墨尔本理工大学工程学院增材制造中心）
In this paper, we investigate three-phase eutectic growth during thin-film directional solidification of a model symmetric ternary eutectic alloy. In contrast to two-phase eutectics that have only a single possibility, $αβαβ$..., as the growth pattern, during three-phase eutectic growth infinite possibilities exist. Here, we explore the possible existence of pattern selection influenced by the change in the solid-solid interfacial energies and the diffusivities. We begin the study by estimating the undercooling vs. spacing variation for the simplest possible configurations of pattern lengths 3…
