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.     

Asymmetrical contribution of eutectic growth kinetics on the coupled growth behaviour in rapid eutectic solidification

The interface undercooling in classical eutectic growth theories consists of solute and curvature undercooling with different expression formats. However, a significant difference in interface kinetic coefficients arises for a disordered non-facetted solid solution and an ordered facetted intermetallic compound in that different growth kinetics govern the attachment kinetics at the solid–liquid interface, which correspond to a typical eutectic reaction with a solid solution and an intermetallic compound as its terminal eutectic phases. Following the pioneering work of Jackson and Hunt (Trans. Metall. Soc. AIME 236 1129 (1966) ), the kinetic undercooling is supplemented to interface undercooling and two eutectic phases are considered separately so as to diagnose the effect of the asymmetrical contribution of kinetic undercooling on the coupled eutectic growth behaviour. Further analysis indicates that it is the asymmetrical contribution of kinetic undercoolings of the facetted and non-facetted phases that enables the coupled eutectic composition shift to the facetted phase side so as to weaken the solute undercooling of the facetted phase and balance the kinetic contribution in the rapid solidification of coupled eutectics.     

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.     

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)     

Formation mechanism of primary phases and eutectic structures within undercooled Pb-Sb-Sn ternary alloys

The solidification characteristics of three types of Pb-Sb-Sn ternary alloys with different primary phases were studied under substantial undercooling conditions. The experimental results show that primary (Pb) and SbSn phases grow in the dendritic mode, whereas primary (Sb) phase exhibits faceted growth in the form of polygonal blocks and long strips. (Pb) solid solution phase displays strong affinity with SbSn intermetallic compound so that they produce various morphologies of pseudobinary eutectics, but it can only grow in the divorced eutectic mode together with (Sb) phase. Although (Sb) solid solution phase and SbSn intermetallic compound may grow cooperatively within ternary eutectic microstructures, they seldom form pseudobinary eutectics independently. The (Pb)+(Sb)+SbSn ternary eutectic structure usually shows lamellar morphology, but appears as anomalous eutectic when its volume fraction becomes small. EDS analyses reveal that all of the three primary (Pb), (Sb) and SbSn phases exhibit conspicuous solute trapping effect during rapid solidification, which results in the remarkable extension of solute solubility. Supported by the National Natural Science Foundation of China (Grant Nos. 50121101 and 50395105)     

采用元胞自动机法模拟二元规则共晶生长

基于元胞自动机方法,建立了二元规则共晶生长的数值模拟模型.该模型耦合宏观温度场,考虑了溶质扩散、成分过冷以及曲率过冷等重要因素,实现了二元规则共晶的稳态层片生长.以共晶模型合金为对象,研究了定向凝固条件下不同过冷度、初始层片间距、温度梯度及凝固速率对共晶两相生长形貌及层片间距的影响,再现了两相在溶质扩散及界面能的相互作用下通过形核、分岔、湮没及合并等机理实现共晶层片间距的调整.模拟得到的结果与Jackson-Hunt模型及前人实验结果规律一致.将模型扩展到三维系统,验证了二元规则共晶生长三维模拟的可行性. 关键词： 规则共晶 生长形貌 层片间距 CA方法     

深过冷液态Al-Ni合金中枝晶与共晶生长机理

在自由落体条件下实现了液态Al-4 wt.%Ni亚共晶、Al-5.69 wt.%Ni共晶和Al-8 wt.%Ni过共晶合金的深过冷与快速凝固. 计算表明, (Al+Al₃Ni)规则纤维状共晶的共生区是4.8–15 wt.%Ni成分范围内不闭合区域, 且强烈偏向Al₃Ni相一侧. 实验发现, 随液滴直径的减小, 合金熔体冷却速率和过冷度增大, (Al)和Al₃Ni相枝晶与其共晶的竞争生长引发了Al-Ni 共晶型合金微观组织演化. 在快速凝固过程中, Al-4 wt.%Ni亚共晶合金发生完全溶质截留效应, 从而形成亚稳单相固溶体. 当过冷度超过58K时, Al-5.69 wt.%Ni 共晶合金呈现从纤维状共晶向初生(Al) 枝晶为主的亚共晶组织演变. 若过冷度连续增大, Al-8 wt.%Ni过共晶合金可以形成全部纤维状共晶组织, 并且最终演变为粒状共晶.     

Local nonequilibrium effect on rapid dendritic growth in a binary alloy melt

A model for nonisothermal rapid dendritic growth in an undercooled alloy melt is presented. Taking into account the finite speed of solute diffusive propagation the analytical solution for isoconcentrational needle-like dendrites is obtained. A selection criterion for the dendritic tip radius under local nonequilibrium conditions is found. The predictions of the model are in qualitative and quantitative agreement with experiments.     

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     

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.     

层状共晶定向凝固

本文从理论和实验两方面研究层状共晶定向凝固。理论上将层状共晶定向凝固与胞晶列定向凝固及Hele-Shaw胞中粘性指发展进行类比,给出层状共晶稳态凝固条件下溶质扩散、热传输与界面张力效应之间的耦合系,导出λ²ν=consi标度关系。实验上考察了规则Al-Al₂Cu共晶和非规则Al-Si共晶定向凝固,证实耦合关系存在。还讨论了两种共晶凝固界面特征和热传输的影响。 关键词：     

Eutectic alloy microstructure: atomic force microscopy analysis

The exciting microstructures found in several eutectic alloys are a result of a cooperative growth, which is connected to the atomic transfer in the melt ahead the solid/liquid interface. In a eutectic system, the growth of solid phases depends on the simultaneous rejection of constituents to the liquid phase, which causes adjustments of the melt composition and hence, mass transport by diffusion normal to the growth direction. Generally, eutectic microstructures are examined by using optical (OM) and scanning electron microscopy (SEM). While OM may not provide the necessary resolution, the eutectic microstructure may present three-dimensional features, as a result of etching, which is not always possible to be observed by SEM. As an alternative, this paper describes the use of atomic force microscopy (AFM) in understanding micro-scale feature of a eutectic microstructure. For such a purpose, directionally solidified samples of a Ni–Al–V lamellar eutectic, a Ni–Al–Mo fibrous eutectic and a Ni–Al–Nb three-phase eutectic were examined. The results obtained provided a new picture of multi-phase microstructures and allows one to understand their new characteristics.     

FeSi2合金在高压下的凝固

研究了压力对FeSi2合金凝固组织的影响.与常压下凝固的典型共晶组织不同，高压条件下的凝固组织为初生ε相树枝晶加离异共晶.高压下凝固组织的变化主要是与压力对相图的影响和对凝固过程中溶质原子扩散的影响有关.通过引入压力参量，推导了高压凝固过程中的成分过冷判据，并应用该判据分析了高压凝固树枝晶组织的形成机理. 关键词： 高压 凝固 FeSi2     

过冷Ni-P合金的凝固行为

以揭示共晶系合金在不同过冷度下凝固时初生相的选择规律和凝固组织形成机理为目的, 用熔融玻璃净化和循环过热相结合的方法, 将Ni_100-xP_x(x=18, 19, 19.6, 20, 21, 原子百分比)合金过冷至平衡液相线以下不同的温度, 用高速红外测温仪记录了试样的凝固冷却曲线, 详尽分析了试样的凝固组织.结果表明, 过冷Ni-P合金快速凝固过程中析出的初生相为α-Ni/Ni₃P耦合共晶时, 整个凝固过程中仅出现一次再辉, 在所形成的异常共晶组织中α-Ni颗粒大小分布均匀;而当某一共晶相优先析出时, 另外一相需要在残留液相中重新形核, 致使凝固过程中出现两次再辉, 相应形成颗粒相大小截然不同的两类异常共晶组织;据此绘制了Ni-P合金初生相为共生共晶的区域. Ni-P合金中α-Ni的生长动力学明显快于Ni₃P, 使得在大过冷度下过共晶合金也以α-Ni作为初生相进行凝固.     

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.     

Ternary eutectic growth of Ag-Cu-Sb alloy within ultrasonic field

The liquid to solid transformation of ternary Ag42.4Cu21.6Sb36 eutectic alloy was accomplished in an ultrasonic field with a frequency of 35 kHz, and the growth mechanism of this ternary eutectic was examined. Theoretical calculations predict that the sound intensity in the liquid phase at the solidification interface increases gradually as the interface moves up from the sample bottom to its top. The growth mode of (ε θ Sb) ternary eutectic exhibits a transition of "divorced eutectic- mixture of anomalous and regular structures-regular eutectic" along the sample axis due to the inhomogeneity of sound field distribution. In the top zone with the highest sound intensity, the cavitation effect promotes the three eutectic phases to nucleate independently, while the acoustic streaming efficiently suppresses the coupled growth of eutectic phases. In the meantime, the ultrasonic field accelerates the solute transportation at the solid-liquid interface, which reduces the solute solubility of eutectic phases.     

各向异性表面张力对定向凝固中共晶生长形态稳定性的影响

研究各向异性表面张力对定向凝固中共晶生长形态稳定性的影响.应用多重变量展开法导出了共晶界面表达式和扰动振幅的变化率满足的色散关系.结果表明,共晶生长系统有两种整体不稳定性机理:由非震荡导致的"交换稳定性"机理和由震荡导致的"整体波动不稳定性"机理.震荡有四种典型模式,即:反对称-反对称(AA-),对称-反对称(SA-)、反对称-对称(AS-)和对称-对称(SS-)模式.稳定性分析表明:共晶界面形态稳定性取决于Peclet数ε的某一个临界值ε_*,当ε大于临界值ε_*时,共晶界面形态不稳定;当ε小于临界值ε_*时,共晶界面形态稳定.随着各向异性表面张力增大,对应于AA-,SA-和SS-模式的临界值ε_(aa*),ε_(sa*)和ε_(ss*)随之减小,表明各向异性表面张力减小这三种模式的稳定性区域;然而,随着各向异性表面张力增大,对应于AS-模式的临界值ε_(as*)随之增大,表明各向异性表面张力增大AS-模式的稳定性区域.     

偏晶合金液-液相分离的格子玻尔兹曼方法模拟

本文建立了一个模拟在弥散相液滴的扩散长大、碰撞凝并和Ostwald熟化等因素的作用下偏晶合金液-液相分离过程的二维格子玻尔兹曼方法 (lattice Boltzmann method, LBM) 模型.该模型结合了Shan-Chen的两相流模型和Qin的介观粒子相互作用势模型的优点,并在LB演化方程中引入了反映相变的源项.应用该模型模拟研究了偏晶合金液-液相分离过程中单液滴的生长、两液滴的合并和多液滴的生长规律.结果表明在两液相区中第二相单个液滴的生长是一个通过扩散从非平衡态到平衡态过渡的过程.两液滴合并 关键词： 偏晶合金 液-液相分离 格子玻尔兹曼方法     

Diffusion-controlled phase growth on dislocations†

We treat the problem of diffusion of solute atoms around screw dislocations. In particular, we express and solve the diffusion equation in two dimensions with radial symmetry in an elastic field of a screw dislocation subject to conservation of flux at the interface of a new phase. We consider an incoherent second-phase precipitate growing under the action of the stress field of a screw dislocation. The second-phase growth rate as a function of the supersaturation and a strain energy parameter is evaluated in spatial dimensions d = 2. Our calculations show that an increase in the amplitude of the dislocation force, e.g. the magnitude of the Burgers vector, enhances the second-phase growth in an alloy. Moreover, we calculate the reduction in concentration of solute atoms as a function of radius around a second phase which grows cylindrically (in the radial direction) so that its radius varies as the square root of time for various levels of the dislocation force amplitude.     

NMR studies of restricted diffusion in lyotropic systems

Tortuosity, 1/alpha, and surface-to-volume ratio, S/V, were determined in aqueous solutions of decylammonium, dodecylammonium and tetradecylammonium chlorides of various concentrations by measuring the apparent diffusion coefficient of water, D(app)(delta). This was found to be much smaller than in the bulk state. Such restricted diffusion is interpreted in terms of the Mitra model, where D(delta) depends on diffusion time and is controlled primarily by S/V. The samples exhibit lamellar (L), hexagonal (H) and isotropic (I) liquid crystalline phases. We observed changes in S/V upon phase transition. In the lamellar and hexagonal phases, the system is ordered, resulting in relatively small S/V ratios, compared to the micellar-isotropic phase. We did not observe a dependence on the diffusion time, delta, in the isotropic phase, because the duration of the experiment was not sufficiently short to observe the change from D(app)(delta) to D(eff). We observed the effective diffusion coefficient of water, which directly probes the tortuosity of the system. The S/V ratios were obtained by fitting the Mitra model, using known values of the bulk water diffusion coefficients, and the assumption that D(app) --> D0 for delta --> 0. S/V is correlated with the type of structure, increasing on transition to the isotropic phase and decreasing on transition to other phases. The change in tortuosity is small, but slightly larger for the isotropic phase.