轴向磁场对环形浅液池内硅熔体热毛细对流的影响

为了更好地了解轴向磁场对温度梯度作用下Marangoni-热毛细对流的影响,采用有限差分法对环形浅液池内硅熔体制单晶的流动进行了数值模拟.研究了三种不同边界条件下,Ha数分别为0、10、20、30对应下硅熔体内部流动强度和自由表面速度.结果表明,轴向磁场对浅液池内的Marangoni对流、热毛细对流和耦合的Marangoni-热毛细对流都有较好的抑制作用,且随着磁场强度的增强,抑制作用增加,更有利于提高晶体的结晶质量.当磁场强度和底部热流密度一定时,随着水平温度梯度的增加,靠近内壁的流动得到增强,外壁附近流动反而减弱.     

分离结晶垂直Bridgman法生长CdZnTe晶体的全局数值模拟

采用FLUENT软件对分离结晶Bridgman法生长CdZnTe晶体进行了全局数值模拟.模拟对象为:熔体上部边界条件分别为固壁和自由表面时两种晶体生长系统.重点考虑坩埚和晶体之间狭缝宽度e和重力对分离结晶过程的影响.在计算中分别取e=0 mm、0.5 mm和1 mm三种狭缝宽度,得到了在微重力和常重力条件下的温度分布、结晶界面形状以及流函数分布图.结果表明:在微重力条件下,当熔体上部为固壁时,随着狭缝宽度的增大,热毛细力作用增强,流动强度增强;当熔体上部为自由表面时,则与之相反.在常重力条件下,由于浮力-热毛细对流的共同作用,随着狭缝宽度的增加,流动强度逐渐减弱,有助于提高晶体生长质量.     

旋转磁场对空间浮区内流场及浓度场的影响

采用全浮区模型数值研究了旋转磁场作用下熔区内热毛细对流流动特性,分析了磁场强度对流场及浓度场的影响.研究发现,无磁场时,熔体内杂质浓度场和流场呈现三涡胞对称振荡特征;温度场主要由扩散作用决定,呈对称分布.旋转磁场作用下,Ma数基本保持不变.当磁场强度B0≤1 mT时,熔体内杂质浓度场和流场与无磁场时结构类似,但旋转磁场的搅拌作用使得熔体内周期性振荡提前出现,且当旋转磁场产生的洛伦兹力相对较大时,表面张力产生的三维振荡对流得到很好地抑制.B0=5 mT时,周向波动被完全抑制,熔区内流场和浓度场呈二维轴对称分布.旋转磁场对熔体流动产生的轴向抑制作用和周向搅拌作用,都有助于熔体流动的稳定性、浓度分布以及温度分布的均匀性,从而有利于高质量晶体的生长.     

轴向磁场作用下Czochralski浅液池内热对流特性研究

为了有效抑制熔体热对流并提高晶体的生长质量,采用三维数值模拟方法研究了轴向磁场对双向温差作用下Czochralski浅液池内Marangoni-热毛细对流的影响.在一个给定的底部热流密度条件下,探讨了轴向磁场对稳态流动和非稳态流动的影响,确定了不同磁场强度下流动由三维稳态流动向三维非稳态流动转变的临界Macri.结果表明:随着磁场强度的增大,临界Macri不断增大.轴向磁场对液池内稳态和非稳态Marangoni-热毛细对流均具有较好的抑制效果.对于稳态流动,磁场的引入会使自由表面温度波动幅值受到削弱,波数减少;对于非稳态流动,监测点P处的温度振荡随着磁场强度的增加不断逐渐减弱直至消失,流动由三维非稳态过渡为三维稳态,相应地,温度波动结构也会发生转变.     

微重力下静态磁场对浮区法硅单晶生长的影响

考虑晶体生长界面的变形,利用有限体积方法对侧面加热的空间全浮区法硅单晶生长中熔区内的热质传输、流场及晶体生长界面位置和形态特征进行了数值研究.应用不同中等强度的轴向磁场和勾型磁场对硅熔体内的热毛细对流进行抑制.分析了静态磁场不同强度下熔区中的对流模式,研究表明,轴向和勾型磁场均能有效抑制熔体内的对流,并将热毛细对流挤压到自由表面附近.轴向磁场可有效抑制熔体的径向流动,但难以有效抑制轴向对流;勾型磁场则可以达到更好的控制熔体对流的效果.对不同强度下的固液面形态及位置分析发现:轴向磁场下固液面基本和无磁场时的重合,但磁场强度较小时固液面在自由表面边缘处向单晶侧有个凸起;勾型磁场作用下的固液面比较平滑,其中心区域较无磁场时整体向z轴正向偏移.研究结果可对浮区法晶体生长中获得高质量晶体提供帮助.     

勾形磁场对分离结晶法生长CdZnTe晶体过程中液层热毛细-浮力对流的影响

借助数值模拟手段研究了常重力条件下分离结晶法生长CdZnTe晶体过程中液层热毛细-浮力对流,探讨了不同勾形磁场强度和狭缝宽度对流动的影响.计算选取液层的高径比A为1,狭缝宽度S分别为0.05、0.075以及0.1,磁场Hartmann数分别为45、90及135.结果表明:勾形磁场能够对液层内热毛细-浮力对流起到抑制的作用,且随着磁场强度的增加,流动失稳的临界Marangoni数增大;随着狭缝宽度S的增大,液层内部流动减弱.     

不同驱动力对Cz硅生长中熔体对流影响的数值模拟研究

为了确定Cz单晶硅生长各种驱动力对熔体对流及固/液界面形状的影响,利用CGSim软件,对典型的Cz单晶硅生长中的熔体对流进行数值模拟.研究了重力、表面张力、平流力、晶转、埚转和氩气剪切力等各种驱动力的大小对熔体对流涡胞、涡胞强度、界面形状、温度分布的影响.结果表明:各种驱动力对熔体对流的影响大小依次为:浮力＞表面张力＞晶转力＞氩气剪切力＞埚转力＞平流力;浮力和表面张力使熔体产生一沿坩埚壁上升、从固/液界面附近下降的涡胞,晶转力和氩气剪切力使熔体产生与前面反方向的涡胞,而埚转力产生多个不同流向的对流涡胞,使熔体混合更加均匀,熔体凝固引起的平流力对熔体对流影响不大;增大埚转,熔体中涡胞数量更多、对流换热更充分、温度梯度更小、熔体内的最高温度更低,有利于减少石英坩埚氧的熔解,但界面更向下凹;增大晶转,熔体内的最高温度无明显变化;固定埚转Ωc=-10 r/min,晶转存在一临界值Ωs(C)=60～ 80 r/min,当Ωs＜Ωs(C)时,增大晶转,固/液界面更向上凹,当Ωs＞Ωs(C)时,增大晶转,固/液界面更向下凹.     

数值模拟自然对流对直拉单晶硅的影响

在直拉单晶硅生长的过程中,自然对流对晶体界面的形状、温度场及应力分布影响很大。本文采用二维模型对熔体内自然对流对单晶硅的影响作了数值模拟,在低雷诺数时采用层流模型,高雷诺数时采用紊流模型,Gr的变化范围从3×106到3×1010,这样涵盖了从小尺寸到大尺寸的直拉单晶硅生长系统。数值结果表明熔体的流动状态不仅与熔体的Gr有关,还与熔体高度和坩埚半径的比值密切相关。当Gr>108时,熔体内确实存在紊流现象,层流模型不再适合,随着Gr的增大,紊流现象加剧,轴心处的等温线变得更为陡峭,不利于晶体生长。     

感应加热制备太阳能级铸造准单晶硅熔体流动行为研究

用专业晶体生长软件(CG-Sim)对制备太阳能级准单晶硅用真空感应铸锭炉的热场结构以及在熔炼过程中硅熔体的流动行为进行了研究.结果表明,熔体中电磁力是熔体流动的驱动力之一,并且感应线圈与熔体高度的比值(k)对熔体内电磁力的大小和分布具有很大的影响,当k值为1.2时,熔体内形成一个上下贯通的涡流,有利于杂质的挥发.同时,当感应线圈频率在3000～5000 Hz范围时,熔体对流强度较低,可以增加坩埚-熔体边界层的厚度,降低熔体中的氧含量.     

不同高径比下浮区晶体生长熔体内对流不稳定性分析

本文通过数值模拟的方法,研究了零重力条件下半浮区液桥内熔体热毛细对流的演化规律。在液桥的高度L和温差ΔT保持不变的情况下,通过改变液桥的半径R来改变液桥的高径比(Ar=L/R)。随着高径比Ar的变化,液桥内的对流表现出不同的流动特征。在Ar=0.5时,热毛细对流处于三维稳态;在Ar=1时,流场和温度场从稳态模式向非稳态周期多频振荡模式转变,它们之间的频率关系满足倍频关系(f_n=nf₁);在Ar=1.25时,监测点的速度振荡频率增大,表现为较小幅度的振荡模式,且温度振荡消失。     

Influence of solidification of binary eutectic lamellar systems on surface tension driven convection in zero gravity conditions

The effect of solidification of the lamellar binary eutectic system on the onset of surface tension driven convection (so-called Marangoni instability) is studied in a zero gravity environment. Some main general conclusions concerning the possibility for onset of the Marangoni convection within the melt can be drawn from the analysis, viz., the curvature of the free surface has a destabilizing effect on the onset of the flow; the increased perturbed heat transfer rate from the system stabilizes the melt; the onset of the solutal Marangoni convection closely depends on the ratio of the lamellae half-widths and the solutal Marangoni instability is more sensitive against the perturbations than the temperature Marangoni one.     

Marangoni flow in half-zone liquid bridge of molten tin under ramped temperature difference

A long-run numerical simulation was carried out on a realistic half-zone liquid bridge model of molten tin, which is identical to JAXA's (former NASDA) liquid bridge experiment apparatus. Using the time-dependent temperature difference imposed on both ends of supporting iron rods, the simulation numerically reproduces the experiment for a time period of 3100 s and enables the study of the two-step bifurcation behavior of Marangoni flow. The present study also evaluates the effect of heating velocity on the bifurcations of the Marangoni flow and indicates that the case with a higher heating velocity gives larger critical Marangoni numbers. Moreover, in this study, we investigate the cause of the second critical Marangoni number and critical frequency disagreement between the experimental results and numerical results, and indicate that the second critical Marangoni number determined through free surface temperature oscillations in the experiment may not correspond to the exact onset of oscillatory Marangoni flow.     

Large eddy simulation of Marangoni convection in Czochralski crystal growth

Large eddy simulation model is used to simulate the fluid flow and heat transfer in an industrial Czochralski crystal growth system. The influence of Marangoni convection on the growth process is discussed. The simulation results agree well with experiment, which indicates that large eddy simulation is capable of capturing the temperature fluctuations in the melt. As the Marangoni number increases, the radial velocity along the free surface is strengthened, which makes the flow pattern shift from circumferential to spiral. At the same time, the surface tension reinforces the natural convection and forces the isotherms to curve downwards. It can also be seen from the simulation that a secondary vortex and the Ekman layer are generated. All these physical phenomena induced by Marangoni convection have great impacts on the shape of the growth interface and thus the quality of the crystal. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gravitational Effects on Mixing and Growth Morphology of an In0.5Ga0.5 System

A mixing experiment of multicomponents melts was performed using a uniform temperature furnace in the Second International Microgravity Laboratories (IML-2) mission. Growth morphologies and Ga concentration profiles were analyzed for the samples with the compositional ratio of 0.5 In–0.5 Ga–1.0 Sb grown under microgravity and on earth. The sample with free surface grown under microgravity was nearly spherical in shape, except some parts with projections. Ga was dispersed homogeneously in the bulk because the mixing was enhanced by Marangoni convection due to the concentration gradient. On the other hand, the sample grown on earth was a double cylindrical shape with different diameters, and Ga concentration decreased from top to bottom, showing clearly the effect of gravity. Many needle crystals were formed in both space and earth samples due to rapid cooling. The average size of the needle crystals grown in space was larger than that of the earth sample.     

The Observation of Hydrodynamic Instability in a Cholesteric Liquid Crystal Layer Having a Free Surface

It was for the first time that a hydrodynamic instability has been experimentally observed in a layer of a cholesteric liquid crystal (CLC) having a free surface and being locally heated from below. Steady structures of CLC motion have been obtained in the form of rotating (in the place) spirals consisting of distinct rolls with sharp boundaries; motion in every such roll was note also. It is supposed that the convective instability observed is due to Marangoni effect.     

Radial segregation due to weak convection in a floating zone

The influence of weak convection, caused by surface tension forces, on radial dopant segregation occurring in crystals grown under microgravity conditions is studied numerically. The geometry considered corresponds to a floating-zone configuration with partially coated melt surfaces consisting of small evenly distributed spots of free surfaces. In order to distinguish dopant distribution due to weak convection clearly from distribution due to diffusion the spots only cover one quarter of the periphery. Thus, surface tension-driven convection is allowed only over one quarter of the floating-zone configuration resulting in an asymmetric dopant distribution. The percentage of free surfaces present is varied in order to alter the Marangoni flow rates. The maximum dopant concentration due to radial segregation is plotted as a function of a certain convection level. The results of the present numerical study are supposed to be used to design corresponding space experiments launched at the end of the year 2000.     

Effect of oxygen partial pressure on the marangoni flow of molten metals

Measurements of surface tension of molten silver and iron are reviewed. Surface tension of molten silver and iron show boomerang‐shaped behavior; the maximum surface tension appears at a certain temperature, below which temperature coefficient of surface tension is positive. Due to change of temperature coefficient, Marangoni flow direction shows variation in a liquid bridge configuration.     

Mathematical modeling and experimental investigation of the effect of temperature gradients on crystallization processes under terrestrial and space conditions

Mathematical modeling of the processes of heat and mass transfer during directed crystallization under terrestrial and space conditions is performed on the basis of experimental data on the temperature distribution (boundary conditions). Convective processes are described by the system of Oberbeck-Boussinesq equations together with the heat-conduction equation (the Stefan problem). A dependence of the intensity of thermal gravitational convection on the radial and axial temperature gradients is established. It is shown that one of the necessary conditions for the growth of homogeneous semiconductor crystals under both terrestrial and zero-gravity (on board spacecraft) conditions is the absence of the free surface of a melt (the Marangoni convection) and optimization of the temperature gradients (first of all, the radial gradient).     

Numerical study of influences of buoyancy and solutal Marangoni convection on flow structures in a germanium‐silicon floating zone

This paper presents a numerical study of Marangoni flows in a floating zone of germanium‐silicon crystals, which was performed by using a commercial finite element program FIDAD^TM. The numerical results point out that for fluids with a small Pr number the influence of buoyancy forces cannot be ignored in the numerical model. Furthermore, the competition between the thermocapillary (TC) and solutocapillary (SC) flows in the floating zones was qualitatively examined. If the TC flow is as strong as that in the Si‐rich floating zone, the SC flow may be restricted to the bottom area near the free surface. Otherwise, the SC flow may overcome the TC flow and induce a surface transfer of species. The numerical predictions agree well with the previous experiment results. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Marangoni Convective Effect during Crystal Growth in Space

GaSb:Te and GaInSb samples have been solidified under microgravity conditions during the D2 Spacelab mission. Experimental design and parameters are described. Analysis of the thermal data taken during the flight, associated to numerical simulations of heat transfer in the experiment, with the help of FIDAP, gave the experimental conditions (thermal gradients and growth rate). Quantitative chemical analyses of the samples show a chemical segregation characteristic of strong mixing in the melt during crystal growth. Silica crucibles with an internal screw thread groove on the inner wall were used in order to get dewetting of samples from the crucible. It was therefore supposed that Marangoni convection on the free surface associated to the groove might have been the source of convection. This hypothesis has been studied by numerical simulation using FIDAP and the velocity field obtained is in agreement with a strong perturbation of the solutal boundary layer ahead the solid-liquid interface. This can explain the observed chemical segregation.