Formation mechanism of anomalous eutectics in highly undercooled Ag--39.9 at%Cu alloy

<正>This paper investigates the solidification behaviour of the Ag—Cu eutectic alloy melt undercooled up to 100 K.It is revealed that lamellar eutectics grow in a dendritic form in the Ag-Cu eutectic melt with undercooling equal to or greater than 76 K.As undercooling increases,the remelted fraction of the primary eutectics during recalescence rises. The severe remelting and the subsequent ripening of the primary eutectic dendrites lead to the formation of anomalous eutectics.     

Effect of interface anisotropy on tilted growth of eutectics: A phase field study

Interfacial energy anisotropy plays an important role in tilted growth of eutectics. However, previous studies mainly focused on the solid—solid interface energy anisotropy, and whether the solid—liquid interface energy anisotropy can significantly affect the tilted growth of eutectics still remains unclear. In this study, a multi-phase field model is employed to investigate both the effect of solid—liquid interfacial energy anisotropy and the effect of solid—solid interfacial energy anisotropy on tilted growth of eutectics. The findings reveal that both the solid—liquid interfacial energy anisotropy and the solid—solid interfacial energy anisotropy can induce the tilted growth of eutectics. The results also demonstrate that when the rotation angle is within a range of 30°—60°, the growth of tilted eutectics is governed jointly by the solid—solid interfacial energy anisotropy and the solid—liquid interfacial energy anisotropy; otherwise, it is mainly controlled by the solid—solid interfacial energy anisotropy. Further analysis shows that the unequal pinning angle at triple point caused by the adjustment of the force balance results in different solute-diffusion rates on both sides of triple point. This will further induce an asymmetrical concentration distribution along the pulling direction near the solid—liquid interface and the tilted growth of eutectics. Our findings not only shed light on the formation mechanism of tilted eutectics but also provide theoretical guidance for controlling the microstructure evolution during eutectic solidification.     

Rapid eutectic growth in undercooled Al-Ge alloy under free fall condition

Eutectic growth in Al-51.6%wt Ge alloy has been investigated during free fall in a drop tube. With decreasing undercooling ΔT, the microstructural evolution has shown a transition from lamellar eutectic to anomalous eutectic. A maximum cooling rate of 4.2×10^4K/s and undercooling of up to 240K (0.35T_E) are obtained in the experiment. The eutectic coupled zone is calculated on the basis of current eutectic and dendritic growth theories, which covers a composition range from 48%－59% Ge and leans towards the Ge-rich side. The two critical undercoolings for the eutectic transition are ΔT_1^*=101K and ΔT_2^*=178K. When ΔT≤ΔT^*_1, the microstructure for Al-51.6% Ge eutectic shows lamellar eutectic. If ΔT≥ΔT^*_2, the microstructure shows anomalous eutectic. In the intermediate range of ΔT^*_1<ΔT<ΔT^*_2, the microstructure is the mixture of the above two types of eutectics.     

Orientation relationship and interfaces in Ni and Co-YSZ cermets prepared from directionally solidified eutectics

Textured Ni-YSZ and Co-YSZ (YSZ: cubic yttria stabilized zirconia) cermets prepared by reduction of directionally solidified NiO-YSZ and CoO-YSZ oxide eutectics respectively display a self-organized microstucture formed by ∼400 nm wide alternating lamellae of YSZ and porous metal suitable for electrochemical applications. The electrochemical properties of the cermets depend on their microstructure. We have analyzed the orientation relationships and interfaces both of the oxide composites and cermets using Scanning Electron Microscopy, Transmission Electron Microscopy, X-ray pole figures and Electron Back-Scattering Diffraction. In spite of the similar crystal structure, growth habits and orientation relationships of NiO-YSZ and CoO-YSZ are different. Also the crystallographic behaviour, when cermets are produced, differs. However the metal-YSZ interfaces are about the most stable ones giving good metal-ceramic adhesion. Due to their lamellar microstructure and good metal-ceramic adhesion these composites present long-term stability at working conditions, which makes them good candidates to be used as anodes in solid oxide fuel cells or electrolyzers.      

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)     

The structure of solid salt eutectics — – Why lamellar or conglomerate?

Using KCl/ZnSO₄ eutectic it has been shown that cooling the melt into a room temperature enclosure forms a lamellar structure, whereas cooling into a heated enclosure (225 °C) forms a conglomerate structure, while an enclosure temperature of 125 °C gave a partially conglomerate structure with some lamellae in process of forming conglomerates.Consideration of the thermal gradients imposed on solidification and consequently the relative time available during which the ions are sufficiently mobile to rearrange their positions, can explain the observation that lamellar structures are formed by higher melting point eutectics, whereas eutectics of lower melting point form conglomerate structures.     

Lamellar pattern formation in small-world media

Numerical and analytical techniques are used to investigate the effects of quenched disorder of small-world networks on the phase ordering dynamics of lamellar patterns as modeled by the Swift-Hohenberg equation. Morphologies for small and large values of the network randomness are quite different. It is found that addition of shortcuts to an underlying regular lattice makes the growth of domains evolving from random initial conditions much slower at late times. As the randomness increases, the evolution is eventually frozen.     

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.     

A phase-field model for simulating various spherulite morphologies of semi-crystalline polymers

A modified phase-field model is proposed for simulating the isothermal crystallization of polymer melts. The model consists of a second-order phase-field equation and a heat conduction equation. It obtains its model parameters from the real material parameters and is easy to use with tolerable computational cost. Due to the use of a new free energy functional form, the model can reproduce various single crystal morphologies of polymer melts under quiescent conditions, including dendritic, lamellar branching, ring-banded, breakup of ring-banded, faceted hexagonal, and spherulitic structures. Simulation results of isotactic polystyrene crystals demonstrate that the present phase-field model has the ability to give qualitative predictions of polymer crystallization under isothermal and quiescent conditions.     

Nucleation behaviour and anomalous eutectic formation in highly undercooled Fe2O3-La2O3 eutectic melts

Employing an aero-acoustic levitator, the Fe₂O₃-16.5 mol% La₂O₃ eutectic alloy was levitated, melted, undercooled and then solidified under a containerless condition when a continuous laser beam heating system was incorporated. By revealing the surface and cross-sectional microstructures, copious nucleation is confirmed to take place in the undercooled melts solidified by either an external seeding or spontaneous crystallization. The nucleation behaviour of eutectic alloys is summarized, indicating that copious nucleation may be an intrinsic attribute of a eutectic system with the exact eutectic composition in unconstrained solidification. Considering the complexity level of crystal structures of eutectic oxide phases in the Fe₂O₃-La₂O₃ alloy, the linear kinetic constants are approximately estimated and the growth kinetics are discussed. The sluggish growth kinetics of the perovskite-type phase, that is LaFeO₃ with a higher complexity level in a unit cell leads to a decoupled growth within a single eutectic colony when the melt is undercooled to exceed the critical undercooling ΔT = 125 K. It is the decoupled growth that results in the formation of anomalous eutectics. The present concept based on the kinetic constant of different phases can also be applicable to account for the growth behaviour of other oxide eutectics when considering the stable and metastable eutectic reactions in different solidification conditions. The nucleation behaviour and growth modes in some oxide eutectic systems have been predicted in the free solidification from an undercooled state.     

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     

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.     

Relativity from Light Front and Bethe–Salpeter Equations

We present some results of two independent relativistic approaches to the few-body problem: light-front dynamics and Bethe–Salpeter equation. We show that implementing relativistic invariance leads to new qualitative properties, and that, even driven by the same interaction Lagrangian, both approaches provide different quantitative results, especially in three-body systems. The case of Bethe–Salpeter equation for computing electromagnetic form factors is discussed.     

Simultaneous estimation of the temperature and heat rate distributions within the combustion region by a new inverse radiation analysis

A new inverse radiation analysis is presented for estimating the heat rate and temperature distributions in the combustion region from the information of the temperature and heat flux profiles of wall elements in the system. The Monte Carlo method is employed to solve the radiative heat transfer equation. The inverse radiation problem is posed as a minimization problem of the least squares criterion, which is solved by the conjugate gradient method. The performance of the present technique of inverse analysis is evaluated and the effects of the errors of the absorption coefficient, emissivity and convective heat transfer coefficient on the inverse analysis are investigated. The results show that the present technique is robust and yields accurate estimation even with noisy measurement.     

A comparative approach to predicting effective dielectric, piezoelectric and elastic properties of PZT/PVDF composites

The present study addresses the problem of quantitative prediction of effective relative permittivity, dielectric loss factor, piezoelectric charge coefficient, and Young's modulus of PZT/PVDF diphasic ceramic-polymer composite as a function of volume fraction of PZT in the different compositions. Theoretical results for effective relative permittivity derived from several dielectric mixture equations like those of Knott, Rother-Lichtenecker, Bruggeman, Maxwell-Wagner-Webmann-Skipetrov or Dias-Dasgupta, Furukawa, Lewin, Wiener, Jayasundere-Smith, Modified Cule-Torquato, Taylor, Poon-Shin and Rao et al. were fitted to the experimental data taken from previous works of Yamada et al. Similarly, the results for effective piezoelectric coefficient and Young's modulus, derived from different appropriate equations were fitted to the corresponding experimental data taken from the literature. The study revealed that only a few equations like modified Rother-Lichtenecker equation, Dias-Dasgupta equation and Rao equation for dielectric and piezoelectric properties while the four new equations developed in the present study of elastic property (Young's modulus) well fitted the corresponding experimental results. Further, the acceptable data put to various regression analyses showed that in most of the cases the third order polynomial regression analysis provided more acceptable fits.     

二元层片共晶凝固过程的特征尺度选择

基于Jackson和Hunt二元规则共晶稳态生长理论,在共晶两相的界面溶质守恒条件中引入密度修正项,改进了共晶两相的界面溶质守恒条件.在此基础上,根据二元层片共晶常规凝固过程中层片组织稳态生长时Gibbs自由能的变化,运用极值形态选择原理确定二元层片共晶凝固过程中层片间距特征尺度选择准则.理论分析表明,对于给定二元共晶合金,在常规凝固条件下的层片间距选择通常为一有限区间.此外,理论分析还表明,二元层片共晶稳态生长时其特征尺度的选择可以呈现超稳定性,而且在给定的凝固条件下超稳定性只和给定合金系的物性参数有关.将该形态选择准则分别运用于物性参数精确已知的Al-Al2Cu,Sn-Pb和CBr4-C2Cl6合金系,表明计算结果与实验结果相符合.     

Formation of an eutectic structure in Al-Mo-Zr alloy crystallization

A eutectic structure has been obtained in crystallization of an Al-Mo-Zr alloy. This structure is represented by lamellar eutectic colonies, consisting of Mo₃Al₈ and Al₂Zr solid solution, between which more disperse triple and double eutectics with Mo₃Al and Mo₂Zr are crystallized.     

Quasi-steady-state modeling of dendritic growth

A new method of the moving-boundary problem analysis is developed. After proposed coordinate transformation, the quasi-steady-state differential equation was reduced to equivalent Laplace equation. Transformed boundary conditions of a rescaled field distribution reflect the presence of rate-dependent sources on interface. Taking into account the local rate-dependence of the Neumann's boundary conditions, non-equilibrium pattern formation was considered. The problem of dendrite fractal growth was reduced to one of interaction of conformal to tips charged particles. Conditions of the quasi-steady growth and the recurrence formula for k-order dendrite spacing were derived. Theoretically obtained scaling laws for interface shape, dendrite spacing, critical sidebranch distance are confirmed by available experimental data.     

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.     

Formation of Mg2Ni nanofibres in a Mg-based metal matrix composite

A Mg–Mg₂Ni nano-eutectic and MgO-reinforced Mg-based metal matrix composite (Mg-MMC) was synthesized by in-situ reactions. When a Mg-rich sample containing 20?wt%?NiO is sintered at 420°C, MgO, Ni and Mg₂Ni are formed in the Mg matrix. When a sample molten at 550°C is furnace-cooled to room temperature, a lamellar two-phase Mg–Mg₂Ni eutectic is formed, with the Mg₂Ni lamella about 1.5?µm thick. Proeutectic Mg together with the MgO formed in situ act as heterogeneous nuclei for the growth of the Mg–Mg₂Ni eutectic. Quenching the molten sample to room temperature results in a lamellar two-phase eutectic containing Mg₂Ni nanofibres. In the eutectic grown at the Mg grain, the Mg₂Ni nanofibres with a diameter of about 25?nm are bent, whereas in the eutectic grown at the MgO grain, the Mg₂Ni nanofibres with a diameter of about 30?nm are long and straight, while the Mg phase of this eutectic is oxygen enriched. The differences in morphologies between the two Mg–Mg₂Ni eutectics are ascribed to the growth rates of Mg and Mg₂Ni, which differ in the eutectic grown at the Mg grain, but remain similar when growth takes place at the MgO grain.