Effect of boundary heat flux on solidification in a forced liquid metal flow: a phase-field simulation

A phase-field model coupling with velocity field is employed to study the effect of boundary heat flux on the microstructure formation of a Ni-40.8%Cu alloy with liquid flow during the solidification, and an anti-trapping current is introduced to suppress the solute trapping due to the larger interface width used in simulations than a real solidifying material. The effect of the flow field coupling with boundary heat extractions on the microstructure formation as well as distributions of concentration and temperature fields are analyzed and discussed. The forced liquid flow can significantly affect the heat and solute diffusions, thus influencing morphology formation, concentration and temperature distributions during the solidification. The solute segregation and concentration diffusion are changed by boundary heat extractions, and the morphology, concentration and temperature distributions are significantly influenced by increasing the heat extraction, which relatively makes the effect of liquid flow constrained. By increasing the initial velocity of liquid flow, the lopsided rate of the primary dendrite arm is enlarged and the growth manner of dendrite arms gets changed, and the transition of the microstructure from dendrite to cellular moves to the large heat extraction direction. Therefore, there exists the competition between the heat flux, temperature gradient and forced liquid flow that finally determines the microstructure formation during directional solidification.     

Comparative study of solute trapping and Gibbs free energy changes at the phase interface during alloy solidification under local nonequilibrium conditions

An analytical model has been developed to describe the influence of solute trapping during rapid alloy solidification on the components of the Gibbs free energy change at the phase interface with emphasis on the solute drag energy. For relatively low interface velocity V < V _D , where V _D is the characteristic diffusion velocity, all the components, namely mixing part, local nonequilibrium part, and solute drag, significantly depend on solute diffusion and partitioning. When V ≥ V _D , the local nonequilibrium effects lead to a sharp transition to diffusionless solidification. The transition is accompanied by complete solute trapping and vanishing solute drag energy, i.e. partitionless and “dragless” solidification.     

二元合金高速定向凝固过程的相场法数值模拟

利用相场法对二元合金高速定向凝固过程进行了模拟，为简化计算，采用了温度冻结近似.模拟了定向凝固时平界面失稳、界面形态演化、溶质浓度分布以及高速绝对稳定性条件下胞晶向平面晶的转变等，得到了不同抽拉速度下胞晶间距、胞晶尖端温度以及有效溶质分配系数等参数，显示了高速生长条件下的溶质截留效应. 关键词： 定向凝固 相场法 高速绝对稳定性 溶质截留     

Influence of local nonequilibrium on the rapid solidification of binary alloys

A local-nonequilibrium model of the diffusion of a solute during the rapid solidification of a binary alloy is considered. The model has two characteristic parameters: the diffusion velocity through the interface V _Di and the diffusion velocity in the bulk of the liquid phase V _D. The influence of local nonequilibrium on the separation of an impurity, the stability of the interface, and the dependence of the temperature of the interface on the velocity of the solidification front is investigated. A comparison with experiment is made. Zh. Tekh. Fiz. 68, 45–52 (March 1998)     

单相合金凝固过程时间相关的界面稳定性(I)理论分析

对定向凝固界面前沿非稳态溶质扩散场进行了系统的对比分析，发现无论在纯扩散还是存在对流的情况下，界面前沿的溶质扩散场通常满足指数分布的形式，可以采用一个统一的公式来描述界面前沿的瞬态溶质扩散场.进而在此基础上，对定向凝固界面形态稳定性进行了统一的时间相关的非稳态分析，发现界面临界稳定性条件的数学描述形式与Mullins和Seker ka理论给出的稳态解完全一致, 只是用时间相关的浓度梯度GtC、界面速度Vi、溶质扩散长度l代替了稳态生长中所得到的GC,V，DL/V.     

Atomistic simulations of nonequilibrium crystal-growth kinetics from alloy melts

Nonequilibrium kinetic properties of alloy crystal-melt interfaces are calculated by molecular-dynamics simulations. The relationships between the interface velocity, thermodynamic driving force, and solute partition coefficient are computed and analyzed within the framework of kinetic theories accounting for solute trapping and solute drag. The results show a transition to complete solute trapping at high growth velocities, establish appreciable solute drag at low growth velocities, and provide insights into the nature of crystalline anisotropies and solute effects on interface mobilities.     

Developments in Phase-Field Modeling of Thermoelastic and Two-Component Materials

A discussion is given of recent advances in phase-field modeling of materials which change phase. On one hand, general models incorporating elasticity properties of the material, nonconserved and conserved order parameters, and nonlocal effects are now available. On the other hand, gradient theories for binary alloys have been developed which reflect such effects as the dependence of capillarity on the concentration of impurities, solute trapping in its dependence on velocity of solidification fronts, and other nonequilibrium phenomena.     

二元合金凝固过程微尺度热质传输的影响分析

针对二元合金凝固的微观偏析现象建立一维平面枝晶模型,考虑溶质在固相中有限扩散,液相完全扩散的情况。通过模拟计算,比较分析了Al-Cu和Fe-C合金微观偏析的特点,并讨论了不同凝固速度以及溶质扩散系数随温度变化与否对微观偏析的影响。分析结果表明,温度场的影响是不可忽略的,应该在研究中予以考虑。     

共晶形态层—棒转变的多相场法研究

利用KKSO多相场模型研究了不同抽拉速度及不同液相溶质扩散系数条件下共晶形态层—棒状转变过程. 模拟结果表明：在抽拉速度较低时,层片共晶首先发生合并现象,然后继续以层片形态生长;增大抽拉速度,发生层片合并后共晶形态由层片向棒状转变;进一步增大抽拉速度,层片不发生合并,仅以初始层片间距进行稳态层片生长. 溶质扩散系数条件的改变同样会导致共晶形态发生层—棒状转变,结果还表明层—棒转变仅在一定参数范围内发生. 模拟结果与实验研究定性符合. 关键词： 层—棒转变 多相场 数值模拟     

Numerical simulation of dendrite growth and microsegregation formation of binary alloys during solidification process

The dendrite growth and solute microsegregation of Fe-C binary alloy are simulated during solidification process by using cellular automaton method. In the model the solid fraction is deduced from the relationship among the temperature, solute concentration and curvature of the solid/liquid interface unit, which can be expressed as a quadric equation, instead of assuming the interface position and calculating the solid fraction from the interface velocity. Then by using this model a dendrite with 0 and 45 degree of preferential growth direction are simulated respectively. Furthermore, a solidification microstructure and solute microsegregation are simulated by this method. Finally, different Gibbs-Thomson coefficient and liquid solute diffusing coefficient are adopted to investigate their influences on the morphology of dendrite.     

A stochastic model for solidification

A 3-dimensional (2-space, 1-time) model relating the diffusion of heat and mass to the kinetic processes at the solid-liquid interface, using a stochastic approach is presented in this paper. This paper is divided in two parts. In the first part the basic set of equations describing solidification alongwith their analysis and solution are given. The process of solidification has a stochastic character and depends on the net probability of transfer of atoms from liquid to the solid phase. This has been modeled by a Markov process in which knowledge of the parameters at the initial time only is needed to evaluate the time evolution of the system. Solidification process is expressed in terms of four coupled equations, namely, the diffusion equations for heat and mass, the equations for concentration of the solid phase and for rate of growth of the solid-liquid interface. The position of the solid-liquid interface is represented with the help of a delta function and it is defined as the surface at which latent heat is evolved. A numerical method is used to solve the equations appearing in the model. In the second part the results i.e. the time evolution of the solid-liquid interface shape and its concentration, rate of growth and temperature are given.     

Diffusionless crystal growth in a eutectic system during rapid solidification

Experiments on nonequilibrium rapid eutectic growth are surveyed. The applicability limits of the modern theoretical models describing rapid solidification of binary systems are assessed. A problem of rapid eutectic growth when the local equilibrium is violated in the solute diffusion field (in the bulk liquid and at the solid-liquid interface) is formulated. An analytical solution to the problem of rapid lamellar eutectic growth under local nonequilibrium conditions in the solute diffusion field is found. It is shown that the diffusion-limited growth of a eutectic pattern ceases as soon as a chemically homogeneous crystalline phase begins to grow when the critical point V=V _D is achieved (V is the solid-liquid interface velocity and V _D is the solute diffusion speed in the bulk liquid). At V ≥ V _D, eutectic decomposition is suppressed and the nascent homogeneous crystalline phase has the initial (nominal) chemical composition of the binary system.     

Dendrite growth characteristics within liquid Fe-Sb alloy

Bulk samples and small droplets of liquid Fe-10%Sb alloys are undercooled up to 429 K (0.24TL) and 568 K (0.32TL), respectively, with glass fluxing and free fall techniques. The high undercooling does not change the phase constitution, and only the αFe solid solution is found in the rapidly solidified alloy. The experimental results show that when the undercooling is below 296 K, the growth velocity of αFe dendrite rises exponentially with the increase of undercooling and reaches a maximum value 1.38 m/s. S...     

Diffusionless crystal growth in rapidly solidifying eutectic systems

Using a local nonequilibrium model of solidification, experiments on rapid eutectic growth are analyzed. An analytical solution of a problem of rapid lamellar eutectic growth under local nonequilibrium conditions in the solute diffusion field is found. It is shown that solute diffusion-limited growth of a eutectic pattern is completely finished, and diffusionless growth of the chemically homogeneous crystalline phase begins to proceed at a critical point V = V(D), where V is the solid-liquid interface velocity and V(D) is the solute diffusion speed in bulk liquid. A suppression of eutectic decomposition occurs in the range V > or = V(D) that results in a growth of homogeneous crystal phase with the initial (nominal) chemical composition of the binary system.     

Convective instability of solidification with a phase transition zone

The morphological instability of solidification is analytically studied in the presence of an anisotropic and heterogeneous phase transition zone with allowance for a liquid flow and convective heat-andmass transfer in this two-phase zone. The mechanism of breaking the stability of solidification is considered; it consists in a convective heat and impurity transfer during a liquid flow along channels in the phase transition zone. The morphological instability is subjected to linear analysis with allowance for a liquid flow in the liquid phase of the system, impurity diffusion in the two-phase zone, and the dependence of the transfer coefficients on the phase composition. The perturbation evolution parameter is determined for an anisotropic and heterogeneous two-phase zone, and neutral stability curves of the process are obtained. It is shown that taking into account impurity diffusion and an increase in the heterogeneity of the phase transition zone broaden the instability region and that a decrease in the anisotropy narrows this region. A new criterion of convective morphological instability of solidification with a two-phase zone is found, and it substantially broadens the instability region when the liquid flow velocity increases.     

深过冷条件下Co_7Mo_6金属间化合物的枝晶生长和维氏硬度研究

采用电磁悬浮和自由落体两种实验技术对二元Co-50%Mo过共晶合金中初生Co_7Mo_6金属间化合物的生长机理和维氏硬度进行了系统研究.电磁悬浮实验中,合金熔体获得的最大过冷度为203 K(0.12T_L),初生Co_7Mo_6枝晶生长速度与过冷度之间呈现幂函数关系.随着过冷度的增大,初生枝晶中Co元素含量单调递增,枝晶尺寸明显减小,并且其维氏硬度逐渐升高.在自由落体状态下,随着液滴直径的减小,合金熔体的过冷度和冷却速率均增大.当液滴直径减小到392μm以下时,初生Co_7Mo_6枝晶从小平面向非小平面形态进行转变.实验发现,深过冷条件下Co_7Mo_6化合物发生了显著的溶质截留效应,其维氏硬度与Co元素分布和形貌特征密切相关.     

深过冷三元Ni-Cu-Co合金的快速枝晶生长

研究了深过冷条件下三元Ni₈₀Cu₁₀Co₁₀合金的快速枝晶生长, 采用电磁悬浮无容器处理方法获得了335 K(0.2T_L)的最大过冷度. X射线衍射分析与差示扫描量热分析均表明,凝固组织为α-Ni单相固溶体. 随过冷度增大, 凝固组织显著细化, 并且当过冷度达110 K时，凝固组织的形态由粗大形枝晶转变为等轴晶. 深过冷条件下溶质截留效应增强, 使得微观偏析程度减小. 对不同过冷度下合金枝晶的生长速度进 关键词： 深过冷 枝晶生长 快速凝固 溶质截留     

Particle Transport through Scattering Regions with Clear Layers and Inclusions

This paper introduces generalized diffusion models for the transport of particles in scattering media with nonscattering inclusions. Classical diffusion is known as a good approximation of transport only in scattering media. Based on asymptotic expansions and the coupling of transport and diffusion models, generalized diffusion equations with nonlocal interface conditions are proposed which offer a computationally cheap, yet accurate, alternative to solving the full phase-space transport equations. The paper shows which computational model should be used depending on the size and shape of the nonscattering inclusions in the simplified setting of two space dimensions. An important application is the treatment of clear layers in near-infrared (NIR) spectroscopy, an imaging technique based on the propagation of NIR photons in human tissues.     

对流作用下枝晶形貌演化的数值模拟和实验研究

合金凝固过程中存在于枝晶尖端液相区的强制对流和自然对流均能改变溶质扩散层厚度,从而会对枝晶形貌产生较大影响.在元胞自动机模型基础上,耦合液体流动方程、热传导方程和溶质对流扩散方程,建立了新的计算微观组织演化的数值模型,并利用该模型研究了强制对流和自然对流对枝晶生长的影响.三维数值模拟结果再现了强制对流作用下等轴枝晶的生长过程,揭示了强制对流对枝晶生长速率和尖端半径的影响特点.同时利用该模型模拟了NH₄Cl-H₂O溶液定向凝固过程中自然对流对柱状晶生长的影响,并采用相应的实验进行验证.模拟结果与实验结果符合良好,从而证明该模型是可靠的,可推广到实际合金系中. 关键词： 元胞自动机 对流 4Cl-H₂O溶液')" href="#">NH₄Cl-H₂O溶液 定向凝固     

液态Ti-Al合金的深过冷与快速枝晶生长

采用电磁悬浮和自由落体两种试验技术研究了液态Ti-25 wt.%Al合金的亚稳过冷能力、晶体形核机制和枝晶生长过程. 试验发现, 即使电磁悬浮无容器状态下仍难以消除润湿角θ ≥60°的异质晶核, 合金熔体过冷度可达210 K (0.11T_L). β-Ti相形核的热力学驱动力随过冷度近似以线性方式增大, 其枝晶生长速度高达11.2 m/s, 从而在慢速冷却条件下实现了快速凝固. 理论计算表明, 随着过冷度的逐步增大, β相枝晶生长从溶质扩散控制转变为热扩散控制. 当过冷度超过100 K时, 非平衡溶质截留效应可使合金熔体发生无偏析凝固. 然而, 单靠深过冷状态不足以抑制β相的后续固态相变. 对于落管中快速凝固的直径77-1048 μm合金液滴, 其冷却速率最高达1.05×10⁵ K/s, 深过冷与快速冷却的耦合作用能更有效地调控凝固组织形成过程.