Axial macrosegregation in Ga‐doped germanium grown by the vertical gradient freeze technique with a rotating magnetic field

The impact of a rotating magnetic field (RMF) on the axial segregation in Vertical Gradient Freeze (VGF) grown, Ga doped germanium is investigated. Growth experiments were performed using the VGF‐RMF as well as the conventional VGF technique. Carrier concentration profiles characterising the Ga segregation were measured by the Spreading Resistance method and calibrated using Hall values of carrier concentration and mobility. The Ga concentration rises more gradually under RMF action, i.e., the dopant segregation is significantly reduced by the rotating field. This effect is attributed to a better mixing of the melt. Numerical results on the flow velocity confirm this explanation. The RMF induced flow is much more intense than the natural buoyant convection due to the radial temperature gradient and leads to a pronounced decrease of the effective partition coefficient k_eff. In the early stages of growth a k_eff value close to k₀ was obtained, i.e., the gallium was almost homogeneously distributed within the melt. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Solute redistribution profiles during rapid solidification of undercooled ternary Co-Cu-Pb alloy

The solute redistribution and phase separation of liquid ternary Co-35%Cu-32.5%Pb immiscible alloy have been investigated using glass fluxing method. A bulk undercooling of 125 K was achieved and the macrosegregation pattern was characterized by a top Co-rich zone and a bottom Cu-rich zone. The average solute contents of the two separated zones decreased with the increase of undercooling, except for the solute Pb in Cu-rich zone. With the enhancement of undercooling, a morphological transition from dendrites into equaxied grains occurred to the primary α(Co) phase in Co-rich zone. The solute redistribution of Cu in primary α(Co) phase was found to depend upon both the undercooling and composition of Co-rich zone. Stokes migration is shown to be the main dynamic mechanism of droplet movement during liquid phase separation.     

Sensitivity of mesh spacing on simulating macrosegregation during directional solidification of a superalloy

The sensitivity of mesh spacing on simulations of macrosegregation, particularly ‘freckles’, during vertical directional solidification of a superalloy in a rectangular mold was systematically analyzed to achieve accurate predictions in finite element calculations. It was observed that a coarser mesh spacing in the x‐direction horizontal tends to minimize the simulated macrosegregation, whereas a coarser mesh spacing in the y‐direction vertical artificially tends to make the system appear to have more macrosegregation. When solidification conditions either lead to a well‐established freckling case or to a well‐established non‐freckling case, the simulated results are not sensitive to the mesh spacing provided the elements are no larger than about 2d₁ by 2 D/V and 3d₁ by 4 D/V respectively, where d₁ is the primary dendrite arm spacing, D is the diffusivity of the alloy solute with the smallest diffusivity in the liquid, and V is the growth rate. However, when solidification conditions are very close to the transition between freckling and no freckling, the simulated results are sensitive to the mesh spacing, especially in the y‐direction. Based on the mesh sensitivity analysis from the two‐dimensional simulations of rectangular castings of René N5, the mesh with element dimensions no larger than 2d₁ in the x‐direction and 1.5 D/V in the y‐direction are recommended as the most stringent element size. Copyright © 2001 John Wiley & Sons, Ltd.     

考虑固相移动的大尺寸钢锭宏观偏析数值模拟

以欧拉方法和体积元平均技术为基础,建立考虑固相移动的大尺寸钢锭宏观偏析数学模型.研究了纯自然对流和包含固相移动两种情况下宏观偏析形成的模式,分析了临界固相分数和固相密度变化对宏观偏析形成的影响.计算结果表明：无论是否考虑固相移动,A型偏析形成机理是侧壁形成的固相与底部形成的固相之间形成狭窄的补缩通道,此通道内溶质富集且流动不顺畅,最后形成了高成分区域.增大临界固相分数会导致A型偏析带和底部负偏析的加剧.固相密度的增加会引起底部负偏析和顶部正偏析的偏析程度增大,但A型偏析带的长度不随固相密度的增加而增长.将模拟结果和实验结果进行对照,验证了模型的准确性. 关键词： 宏观偏析 固相移动 A型偏析形成 数值模拟     

Rapid solidification and dendrite growth of ternary Fe-Sn-Ge and Cu-Pb-Ge monotectic alloys

The phase separation and dendrite growth characteristics of ternary Fe-43.9%Sn- 10%Ge and Cu-35.5%Pb-5%Ge monotectic alloys were studied systematically by the glass fluxing method under substantial undercooling conditions. The maximum undercoolings obtained in this work are 245 and 257 K, respectively, for these two alloys. All of the solidified samples exhibit serious macrosegregation, indicating that the homogenous alloy melt is separated into two liquid phases prior to rapid solidification. The solidification structures consist of four phases including α-Fe, (Sn), FeSn and FeSn2 in Fe-43.9%Sn-10%Ge ternary alloy, whereas only (Cu) and (Pb) solid solution phases in Cu-35.5%Pb-5%Ge alloy under different undercoolings. In the process of rapid monotectic solidification, α-Fe and (Cu) phases grow in a dendritic mode, and the transition "dendrite→monotectic cell" happens when alloy undercoolings become sufficiently large. The dendrite growth velocities of α-Fe and (Cu) phases are found to increase with undercooling according to an exponential relation.     

Solidification of a Liquid Super-Eutectic Binary Alloy in an Enclosure with a Slanted Side Cooling Wall

Abstract

This study considers the effect of a slanted side cooling wall that has varying inclination angles on the development of thermosolutal convection during the solidification of a super-eutectic aqueous ammonium chloride (NH₄Cl-H₂O) solution. The shadowgraph and particle image velocimetry techniques were employed to observe the flow development and measure the flow velocity during solidification. The transient temperature distribution within the test cell was also measured by type-T thermocouples. Experimental results reveal that a more slanted side cooling wall accelerated the “filling-box” process, thus it could cause more serious A-segregates and material defects in the solidified ingot.     

The effect of solutal undercooling on double‐diffusive convection and macrosegregation during binary alloy solidification: a numerical investigation

In this paper, we present a macroscopic numerical model that is capable of capturing the interaction between the double‐diffusive convective field and a localized fluid flow on account of solutal undercooling during non‐equilibrium solidification of binary alloys. The model is essentially based on a fixed‐grid enthalpy based control volume approach. In the present model, microscopic features pertaining to non‐equilibrium effects on account of solutal undercooling are incorporated through the formulation of a modified partition‐coefficient. The effective partition‐coefficient is numerically modelled by means of a number of macroscopically observable parameters related to the solidifying domain. This feature has made the present treatment different from micro‐macro modelling of alloy solidification, which involves certain parameters that may not be macroscopically resolvable. Numerical simulations are performed for the case of two‐dimensional transient solidification of Pb–Sn alloys (both hypoeutectic and hypereutectic) in a rectangular cavity, employing the present model. The simulation results are also compared with the corresponding experimental results quoted in the literature, and the agreement is excellent. From the results, it can be concluded that non‐equilibrium effects on account of solutal undercooling result in a more enhanced macrosegregation. Copyright © 2002 John Wiley & Sons, Ltd.     

合金凝固过程的数学模型

对合金凝固过程的数值研究自80年代以来取得了很大的发展,文中讨论了当前针对宏观过程的主要的数学模型,介绍了它们的基本思想,求解方法,以及优缺点.指出了微观过程对宏观行为的重要影响及在模型构造过程中考虑宏观-微观耦合的必要性,并针对在工程实际中的应用和以后的研究进行了有关的探讨.