Formation of ■ phase in Cu-Ge peritectic alloys

Rapid growth behavior of ■ phase has been investigated in the undercooling experiments of Cu-14%Ge, Cu-15%Ge, Cu-18.5%Ge and Cu-22%Ge alloys. Alloys of the four compositions obtain the maximum undercoolings of 202 K(0.17TL), 245 K(0.20TL), 223 K(0.20TL) and 176 K(0.17TL), respectively. As the content of Ge increases, the microstructural transition of "α (Cu) dendrite ■ peritectic phase →■ peritectic phase →■ dendrite (ε ■ ) eutectic" takes place in the alloy at small undercooling, while the microstructural transition of "fragmented α (Cu) dendrite ■ peritectic phase →■peritectic phase →■ dendrite ε phase" happens in the alloy at large undercooling. EDS analysis of the Ge content in ■ peritectic phase indicates that undercooling enlarges the solid solubility of α dendrite, which leads to a decrease in the Ge content in ■ phase as undercooling increases. In the Cu-18.5%Ge alloy composed of ■ peritectic phase, the Ge content in ■ phase increases when undercooling increases, which is due to the restraint of the Ge enrichment on the grain boundaries by high undercooling effect.     

过冷熔体中枝晶生长的相场模拟

本文利用相场方法对过冷镍熔体中枝晶生长过程进行了模拟,发现在过冷度低于 200 K时,生长速度与过冷度之间近似呈幂函数关系,当过冷度高于 200 K时,生长速度与过冷度之间基本呈线性关系。伴随着速度/过冷度之间关系的变化,枝晶尖端半径/过冷度的关系则呈现先减小后增加的趋势,并在 200 K时达到最小。本文还将模拟结果与实验值和经典LKT理论进行了比较,对上述关系转变的物理机制进行了分析。     

电磁悬浮条件下液态Fe_(50)Cu_(50)合金的对流和凝固规律研究

基于轴对称电磁悬浮模型,理论计算了二元Fe_(50)Cu_(50)合金熔体内部的磁感应强度和感应电流,分析了其时均洛伦兹力分布特征,进一步耦合Navier-Stokes方程组计算求解了合金熔体内部流场分布规律.计算结果表明,电磁悬浮状态下合金内部流场呈现环形管状分布,并且电流强度、电流频率或合金过冷度的增加,均会导致熔体内部流动速率峰值减小,平均流动速率增大,并使流动速率大于100 mm·s~(-1)区域显著增大.通过与静态凝固实验对比发现,电磁悬浮条件下熔体中强制对流使得合金内部富Fe和富Cu区的相界面呈波浪状起伏形貌,并且富Cu相颗粒在熔体上部分出现的概率增加.     

Rapid solidification of undercooled Al-Cu-Si eutectic alloys

Under the conventional solidification condition, a liquid aluminium alloy can be hardly undercooled because of oxidation. In this work, rapid solidification of an undercooled liquid Al_80.4Cu_13.6Si₆ ternary eutectic alloy was realized by the glass fluxing method combined with recycled superheating. The relationship between superheating and undercooling was investigated at a certain cooling rate of the alloy melt. The maximum undercooling is 147 K (0.18T _E). The undercooled ternary eutectic is composed of α(Al) solid solution, (Si) semiconductor and θ(CuAl₂) intermetallic compound. In the (Al+Si+θ) ternary eutectic, (Si) faceted phase grows independently, while (Al) and θ non-faceted phases grow cooperatively in the lamellar mode. When undercooling is small, only (Al) solid solution forms as the leading phase. Once undercooling exceeds 73 K, (Si) phase nucleates firstly and grows as the primary phase. The alloy microstructure consists of primary (Al) dendrite, (Al+θ) pseudobinary eutectic and (Al+Si+θ) ternary eutectic at small undercooling, while at large undercooling primary (Si) block, (Al+θ) pseudobinary eutectic and (Al+Si+θ) ternary eutectic coexist. As undercooling increases, the volume fraction of primary (Al) dendrite decreases and that of primary (Si) block increases. Supported by the National Natural Science Foundation of China (Grant Nos. 50121101, 50395105) and the Doctorate Foundation of Northwestern Polytechnical University (Grant No. CX200419)     

Metastable phase separation and rapid solidification of undercooled Co-Cu alloy under different conditions

The metastable liquid phase separation and rapid solidification behaviours of Co_61.8Cu_38.2 alloy were investigated by using differential thermal analysis (DTA) in combination with glass fluxing, electromagnetic levitation (EML) and drop tube techniques. It is found that the liquid phase separation process and the solidification microstructures intensively depend on the experimental processing parameters, such as undercooling level, cooling rate, gravity level, liquid surface tension and the wetting state of crucible. Large undercooling and surface tension difference of the two liquids tend to facilitate further separation and cause severe macrosegregation. On the other hand, rapid cooling and low gravity effectively suppress the coalescence of the minority phase. Severe macrosegregation patterns are formed in the bulk samples processed by both DTA and EML. In contrast, disperse structures with fine spherical Cu-rich spheres homogeneously distributed in the matrix of Co-rich phase have been obtained in drop tube.     

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)     

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     

Predicting macroscopic thermal expansion of metastable liquid metals with only one thousand atoms

Results of thermal expansion prediction from atomic scale for metastable liquid metals are reported herein. Three pure liquid metals Ni, Fe, and Cu together with ternary Ni₆₀Fe₂₀Cu₂₀ alloy are used as models. The pair distribution functions were employed to monitor the atomic structure. This indicates that the simulated systems are ordered in atomic short range and disordered in long range. The thermal expansion coefficient was computed as functions of temperature and atom cutoff radius, which tends to maintain a constant when the cutoff radius increases to approximately 15 Å. In such a case, slightly more than 1000 atoms are required for liquid Ni, Cu, Fe and Ni₆₀Fe₂₀Cu₂₀ alloy, that is, the macroscopic thermal expansion can be predicted from the volume change of such a tiny cell. Furthermore, the expansion behaviors of the three types of atoms in liquid Ni₆₀Fe₂₀Cu₂₀ alloy are revealed by the calculated partial expansion coefficient. This provides a fundamental method to predict the macroscopic thermal expansion from the atomic scale for liquid alloys, especially in the undercooled regime.     

On travelling-wave solutions for a moving boundary problem of Hele-Shaw type

We discuss a 2D moving boundary problem for the Laplacian withRobin boundary conditions in an exterior domain. It arises asa model for Hele–Shaw flow of a bubble with kinetic undercoolingregularization and is also discussed in the context of modelsfor electrical streamer discharges. The corresponding evolutionequation is given by a degenerate, non-linear transport problemwith non-local lower-order dependence. We identify the localstructure of the set of travelling-wave solutions in the vicinityof trivial (circular) ones. We find that there is a unique non-trivialtravelling wave for each velocity near the trivial one. Therefore,the trivial solutions are unstable in a comoving frame. Thedegeneracy of our problem is reflected in a loss of regularityin the estimates for the linearization. Moreover, there is anupper bound for the regularity of its solutions. To prove ourresults, we use a quasi-linearization by differentiation, indexresults for degenerate ordinary differential operators on thecircle and perturbation arguments for unbounded Fredholm operators.