THE CONVECTIVE EFFECT ON THE MORPHOLOGICAL INSTABILITY OF KNbO3 CRYSTALS

Experimentally, it was observed that there were various morphologies of KNbO3 crystals in different regions of the melt of Li2B4O7 and KNbO3 mixture in Pt loop heater. Dendrites grew in the central area of the melt, the diffusive-advective region,in which the temperature gradient is negligible; whereas crystals with smooth sur face were observed in the marginal area, the diffusive-convective region, with large temperature gradient. Based on the solute concentration over the KNbO3 crystal surface examined by electronic probe analysis, it was proved that the combinative effect of buoyancy and surface tension convection induced by temperature gradient enhanced the homogeneity of the solute concentration around KNbO3 crystals and thus their morphological stability.     

EVALUATION OF MORPHOLOGY-STABLE CRITICAL SIZE OF KNbO3 CRYSTALS

Skeletal form of KNbO3 crystals growing in Li2B4O7 solvent was in-situ observed at 900°C and it was found that shallow depression started to develop on the surface of KNbO3 crystals when the crystal size exceeded several micron, typically 7 micron.Based on the quantitative criterion derived by Chernov, the estimated critical size of KNbO3 crystals was 1 micron, which was consistent with the experimental measure ment. The kinetic coefficients, kcorner and kcr, in the criterion were experimentally obtained in the diffusive-convective and diffusive-advective flow states respectively.     

EFFECTS OF CONVECTIVE FLUID MOTION UPON OXIDE CRYSTAL GROWTH IN HIGH TEMPERATURE SOLUTION

For understanding of the influence of convective flow on crystal growth, space high temperature in situ observation instrument (SHITISOI) is dedicated to visualize and record the whole growth process of oxide crystals in high temperature up to 1000°C. Model experiments using transparent liquids such as KNbO3 and a mix ture of Li2B4O7+KNbO3 were chosen to investigate effects on ground and in space.On the earth, an investigation of growth kinetics of KNbO3 crystal related to two different states of convection: diffusive-advective flow and diffusive-convective flow,has been performed. The per unit length of a step e is calculated from the exper imental data for two different states of convection. Analyses of these data show the effect of buoyancy convection is to enhance the sharpness of the interface. The growth of KNbO3 crystals from solution of KNbO3+Li2B4O7 was investigated in space. The streamlines of the steady thermocapillary convection in Li2B4O7 solvent was observed. Due to thermocapillary convection, KNbO3 crystal grains grew and filled the whole solution homogeneously. Earth-based quenching experiments are de signed in order to study polyhedral instability of KNbO3 crystal, which is controlled by diffusion mechanism limitation. In all cases, when the crystal was nucleated near air/solution surface, it lost its polyhedral stability and varied from polyhedrons to dedrites. The thickness of diffusion mechanism limitation layer is about 60μm.     

NUMERICAL MODELLING OF VELOCITY AND TEMPERATURE DISTRIBUTIONS OF THE BUOYANCY CONVECTION EFFECT IN KNbO3 MELT

Numerical modelling of velocity and temperature fields in high-temperature KNbO3 melt of a loop-shaped Pt wire heater is carried out by using the commercial com putational code ANSYS for the mathematical solution of the governing equations.Based on the experimental boundary conditions and the Boussinesq approximation,the numerical modelling of a steady and two-dimensional model is applied to study the process under consideration of the buoyancy-driven convection condition. The result is compared with the previous experimental and theoretical data obtained in our laboratory, and the former is in agreement with the latter. Thus a theoretical guide for reasonable growth conditions is provided by studying in depth the real fluid flow effects in the crystal growth from the melt.     

INTERFACIAL MASS TRANSPORT IN OXIDE CRYSTAL GROWTH

A space high temperature in situobservation instrument (SHITISOI) is dedicated to visualize and record the whole growth process of oxide crystal in high temperature melts and solutions. Model experiments using transparent liquids such as KNbO3,Li2B4O7+KNbO3 were chosen to investigate effects of interracial mass transport in oxide crystal growth. For the scaling of the coupled velocity, heat and concentration fields in KNbO3 crystal growth, a rotating crystal growth process was performed and the widths of interfacial concentration, heat and momentum transition zones (The "boundary layers") are obtained, which are 7.5×10-a, 8.6×10-2 and 4.4×10-1 cm,respectively. Hence one can expect that interfacial concentration gradient will be confined to a narrow layer and in region of major concentration change at the in terface. In order to study a mechanism based on the interfacial mass transport resulting from hydrodynamics, the growth of KNbO3 grain in high temperature Li2B4O7 and KNbO3 solutin was studied. The result shows that the pivotal feature in the KNbO3 crystal growth is the initiated by KNbO3 solute surface tension gra dient which is caused by the slow diffusion of KNbO3 solutes. Direct comparison of the model predictions and experimental observed phenomena demonstrate the predictive capability of this model.     

VELOCITY FIELD OF THERMOCAPILLARY CONVECTION IN HIGH-TEMPERATURE OXIDE SOLUTION

We have investigated experimentally and theoretically the thermocapillary convec tive flow phenomena in a loop-shaped Pt wire heater of KNbO3 (20wt.%) and Li2B4O7 solutions. Optical evaluations in connection with thermocouple measure ments made it possible to get a new type of thermocapillary convective flow in the considered system. To study the kinematical behaviour of thermocapillary convec tion, we have measured the stream flow velocities. In a theoretical analysis, the flow velocity due to the thermocapillary effect alone was estimated by balancing the sur face tension forces by viscous forces. The velocity distribution in the solution near the margin of the heater was obtained, which is in agreement with the experimental result.     

偏微分方程组的一种化简方法

以李群为工具,给出了一种化简两个自变量,两个未知函数的一阶偏微分方程组的方法,在一定条件下,可将偏微分方程组化简为一个阶偏微分方程,若能求出此一阶偏微分方程的解,则只需再解一个一阶常微分方程,即可得出原偏微分方程线的解,该方法可用于某些一阶偏微分方程组的求解,其中包括非定常完全气体一维均熵方程和波动方程。     

Solidification of GeSi solid solution in near-zero-G conditions

In summary, it should be stated that the existing theories of segregation during directional crystallization which consider mass transport in melt due only to either concentration diffusion or convective stirring (or both) cannot account for solute segregation picture observed in solid solution crystals which have been obtained aboard Apollo-Soyuz orbital complex. To do this, some other, new models are required.     

Dust acoustic dressed solitons in a four component dusty plasma with nonthermal electron

Nonlinear dust acoustic dressed soliton are studied in a four component dusty plasma. Nonthermal distributions for electrons are considered. The Korteweg–de Vries (KdV) equation is derived by using reductive perturbation technique. A higher order inhomogeneous differential equation is obtained for the higher order correction. The expression for dressed soliton is obtained by the renormalization method. The expressions for higher order correction are determined using a series solution technique.     

用泰勒级数求解非线性代数和微分方程组

提出一种求解非线性代数方程和非线性常微分方程的新方法。所论方程组被转换成增量形式，而解被表示成泰勒级数。在代数方程（多项式形式）的情况下，此算法归结为求解一系列线性方程组，而且在每一增量步中系数矩阵是不变的；在常微分方程组的情况下，此算法归结为一组递归算式，并不要求解方程组。此方法固有的自动走步功能，可保证得到收敛的解，从而大大节省计算时间。     

四元数微分方程最小参数解法研究

对一种求解正交矩阵微分方程的三阶最小参数方法进行改造 ,将其用于四元数微分方程求解 ,并对其在捷联惯性导航系统姿态矩阵实时求解中的应用进行了仿真。结果表明 ,其计算精度比经典的三阶Peano Baker数值解法提高 35倍 ,而浮点运算次数则仅为后者的一半 ,对于提高捷联惯性导航系统姿态计算的精度具有重要意义。     

The structural features of the germanium-silicon solid solution crystals obtained under microgravity

Structural features of germanium-silicon solid solution crystals have been investigated and silicon distribution in the crystals has been studied. All the crystals obtained under microgravity had, in spite of good external shape and facetting, a poorer internal structure than those obtained on Earth. The distribution of silicon have been shown to be non-uniform. High dislocation densities were observed.     

Mathematical simulation of impurity distribution in space processing experiments with semiconductors

The effect of natural convection in the melt on impurity distribution is investigated by numerical simulation in the case of uniaxial growth of semiconductor crystals at low gravity conditions.     

THE SPACE EXPERIMENT OF PROTEIN CRYSTALLIZATION ABOARD THE CHINESE SPACECRAFT SZ-3

Using a new flight hardware, a Chinese mission of space protein crystallization has been performed on the Chinese spacecraft SZ-3 for seven days from March 25 to Apr. 1, 2002. The rate of yielding crystals in the 60 samples is 75%, a little higher than the ground control experiment. Preliminary analysis of the experimental results have shown that among the 16 proteins involved in the mission, about 4 kinds of better diffraction-quality protein crystals were produced in space. At least one kind of protein crystals, i.e. crystals of cytochrome b5 mutant could diffract X ray beyond the highest resolution reported so far. In addition, some rules derived from our numerical studies of the liquid/liquid diffusion protein crystallization were proved by the crystallization of lysozyme as model protein in this space experiment,which also clearly showed the advantages and disadvantages of the gelled protein solution used in microgravity growth of protein crystals. In order to exploit this mission, more diffraction work with the grown crystals and detailed analysis of data to be obtained will be done in the next few months.     

Cahn-Hilliard方程的行波解

主要利用奇异摄动方法,得到一维Cahn-Hilliard方程行波解形式的内、外解.两者匹配得到整体行波解.这个结果的特点是,它不仅将高阶偏微分方程的解用内外解匹配好,而且完全满足方程的边界条件和初始条件.当长时间变化时, Cahn-Hilliard方程的解以行波结构为极限状态.此结果很好地解释Cahn-Hilliard方程的现有理论及数值结果,实际模型和方程的性质也完全符合.     

正交各向异性粘弹性薄板的蠕变屈曲研究

研究有初始挠度的单向受压粘弹性板的蠕变屈曲问题，在建立控制方程时利用了经典薄板理论。通过求解控制方程得到挠度随时间变化的解析表达式，又通过分析得出了具有不同长宽比的粘弹性薄板的瞬时临界载荷及持久临界载荷。     

基于B平面的火星探测直接转移轨道设计方法

将轨道设计转化为常微分方程两点边值(TPBVP)问题,采用微分修正法求解该边值问题.将B平面概念同时应用于地球和火星,借助B平面与双曲线轨道的几何关系解析地给出了两点边值问题的边界条件的建立方法,理论上说明了火星探测直接转移轨道存在4组解的原因,同时提出了控制探测器到达相对火星双曲线轨道近火点时刻的准确参数表示方法.最终给出仿真算例,将轨道设计结果代入STK,结果合理.     

Convection in melts and crystal growth

Convection plays a significant role in determining the electronic properties of semiconductor crystals grown from the melt. Inhomogeneities (doping striations) in these crystals can be caused by unsteady natural convection. Therefore, the origins of unsteady natural convection, which means fluctuating temperatures in a fluid, are investigated in this paper. Several effects have been found at increasing Rayleigh numbers Ra which cause fluctuating temperatures. But it was also observed, that unsteady convection became again steady if Ra was increased to higher values. This effect, which is called relaminarization, is very interesting for crystal growth and is discussed in this paper.     

Convection and impurity distribution in crystal growth in low-gravity environments

Investigations conducted earlier by the authors have established that due to the steady-state field of body forces, convection is capable of giving rise to macroinhomogeneity in transverse impurity distribution in crystals. In the case of semiconductor materials the maximal value of this inhomogeneity is due to a weak convection in the melt, typical of low-gravity conditions. However, in addition to steady gravitational convection, other factors ignored previously, may also be employed in conducting experiments in low-g environments. The present paper discusses the results of theoretical studies of some factors influencing impurity distribution in the melt and the crystal.