Calcium phosphate crystallization under terrestrial and microgravity conditions

Calcium phosphate crystalline powders grown under terrestrial and space (EURECA 1992-1993 flight) conditions in the Solution Growth Facility are analyzed and compared by optical and electron microscopy (scanning and transmission), electron and X-ray microdiffraction and microanalyses. On earth, only small, micrometer size scale, spherolites of hydroxyapatite (HAP) grow. In space, the HAP spherolites reach hundreds of micrometer. Also, octacalcium phosphate (OCP) spherolites up to 3 mm have been obtained. Computer modelling of diffusion in a real chamber has been performed. It suggests high spatial supersaturation gradients at zero gravity which may provide much higher local supersaturations on earth, where convection takes place. The analyses suggest that the dramatic difference between the terrestrial and space samples should come from much lower supersaturation in space.     

The effect of gravity modulation on solutal convection during directional solidification

During directional solidification of a binary alloy at constant velocity, thermosolutal convection may occur due to the temperature and solute gradients associated with the solidification process. For vertical growth in an ideal furnace (lacking horizontal gradients) a quiescent state is possible. For a range of processing conditions, the thermal Rayleigh number is sufficiently small that the stabilizing role of the thermal field during growth vertically upwards may be neglected, and only solutal convection need be considered. The effect of a time-periodic vertical gravitational acceleration (or equivalently vibration) on the onset of solutal convection is calculated based on linear stability using Floquet theory. We find that a stable base state can be destabilized due to modulation, while an unstable state can be stabilized. The flow and solute disturbance fields show both synchronous and subharmonic temporal response to the driving sinusoidal modulation.     

Perfection and homogeneity of space-grown GaSb:Te crystals

A Te-doped GaSb crystal grown by the method of directed crystallization under microgravitation has been studied by X-ray topography. It is shown that the structural perfection of the crystal part grown without contact with the ampule walls is substantially higher than the structural perfection of the crystals grown under terrestrial conditions. The distribution of a Te dopant in the crystal is studied by quantitative X-ray topography, and it is shown that, if the gap between the growing crystal and the ampule is small, the Marangoni convection in the melt can be less intense than the convection provided by residual microgravitation. The relation between the formation of a flat face on the crystallization front (faceting) and the formation of twins is also established.     

籽晶台形状对PVT法同质外延生长氮化铝单晶初始生长的影响

借助专业晶体生长模拟软件FEMAG和自主开发的对流、传质、过饱和度及生长速率预测等有限元模块研究了物理气相传输法(PVT)同质外延生长氮化铝(AlN)单晶工艺时的初始传热及传质过程,并分析了不同形状籽晶台对生长室内的温度场、流场、过饱和度及生长速率的影响。温度场模拟结果表明籽晶台侧部角度改变可影响籽晶表面轴向及径向温度梯度,流场及传质模拟表明籽晶台侧部角度变化对籽晶台周边的传质有巨大影响。传质及过饱和度模拟结果表明,当籽晶台侧部角度为130°时,籽晶表面温度梯度较小且可以完全抑制籽晶台侧部多晶沉积,有利于通过同质外延工艺生长出无寄生、无裂纹的高质量氮化铝单晶锭。     

Solutocapillary convection in germanium‐silicon melts

Surface tension gradients in free crystal growth melts give rise to convective flow. If these gradients are due to thermal gradients, the well known thermocapillary (Marangoni) convection ensues. Concentration gradients due to segregation at the interface during growth can lead to additional solutocapillary convection. A system with large solutocapillary convection is Ge‐Si due to the pronounced segregation and the strong difference in surface tension; solutal buoyancy convection is also present due to the large density difference between Ge and Si. Solutocapillary convection will oppose thermocapillary convection in the Ge‐Si system since Si, having the higher surface tension, is preferentially incorporated into the crystal. A set of experiments directly proving and partially quantifying the effect has been conducted under microgravity during a parabolic flight campaign by recrystallizing Ge‐Si mixtures of different compositions, between 3% and 9% Si, in a crucible with tracers to visualize the movement. Solutocapillary flow with initial flow rates in excess of 5.5 cm/s at the onset of crystallization was measured. A slight dependence of the flow velocity on the initial Si content has been found. Experiments on the ground showed the same effect but with overall smaller speeds; this difference can be explained by the additional action of solutal buoyancy convection. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Evolution and structure of low-angle grain boundaries in 6H–SiC single crystals grown by sublimation method

KOH etching and high-resolution X-ray diffractometry (HRXRD) were used to study the evolution and structure of low-angle grain boundaries (LAGBs), which extended along 〈1 -1 0 0〉 in 6H–SiC bulk crystals grown by the sublimation method. It was found that LAGBs formed in the growth process consisted of an array of threading dislocations and took different configurations under different radial temperature gradients (RTGs). HRXRD results proved that the domain at one side of LAGBs formed under a low radial temperature gradient has only tilts around the c-axis with respect to the other domain at another side of LAGBs.     

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.     

ACRT forced convection and its effects on solute segregation and heat and mass transfer during single crystal growth

A numerical simulation study was carried out for CdZnTe vertical Bridgman method crystal growth with the accelerated crucible rotation technique (ACRT). The convection, heat and mass transfer in front of the solid‐liquid interface, and their effects on the solute segregation of the grown crystal can be characterized with the following. ACRT brings about a periodic forced convection in the melt, of which the intensity and the incidence are far above the ones of the natural convection without ACRT. This forced convection is of multiformity due to the changes of the ACRT parameters. It can result in the increases of both the solid‐liquid interface concavity and the temperature gradient of the melt in front of the solid‐liquid interface, of which magnitudes vary from a little to many times as the ACRT wave parameters change. It also enhances the mass transfer in the melt in a great deal, almost results in the complete uniformity of the solute distribution in the melt. With suitable wave parameters, ACRT forced convection decreases the radial solute segregation of the crystal in a great deal, even makes it disappear completely. However, it increases both the axial solute segregation and the radial one notably with bad wave parameters. An excellent single crystal could be gotten, of which the most part is with no segregation, by adjusting both the ACRT wave parameters and the crystal growth control parameters, e.g. the initial temperature of the melt, the temperature gradient, and the crucible withdrawal rate. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The numerical simulation of heat and mass transfer during growth of a binary system by the travelling heater method

The influence of convection and heat and mass transfer on the shape and position of melt/solid interfaces and on radial composition segregation is analysed numerically for the travelling heater method growth of a binary alloy in a vertical transparent ampoule. Results are presented for crystal and melt with thermophysical properties similar to Cd_xHg_1−xTe with the assumption that the pseudobinary CdTe-HgTe phase diagram is true. The two-dimensional axisymmetric heat transfer equation, hydrodynamical equation and convective diffusion equation are included in the mathematical model. The rates of crystal growth and dissolution are supposed to be proportional to the compositional supercooling in the melt near the interfaces. It is shown for the conditions when convection is absent that the interfaces are asymmetrically positioned respectively to the heater centre line. Intensive convection makes their position more symmetrical but the length of the liquid zone greater. The flow pattern in the melt appears to be greatly influenced by solutal gravitational convection. The nonlinear dependence of the melt density on the temperature and composition are used in the model. The cases when speed of the heater is antiparallel (stable density stratification) or parallel (unstable stratification) to the vector of gravitational acceleration are considered.     

Experimental and numerical investigation of buoyancy driven convection during PDAMNA thin film growth

This paper presents results from numerical simulations as well as laboratory experiments of buoyancy driven convection in an ampoule under varying heating and gravitational acceleration loadings. The modeling effort in this work resolves the large scale natural convective motion that occurs in the fluid during photodeposition of polydiacetelene films which is due to energy absorbed by the growth solution from a UV source. Consequently, the growth kinetics of the film are ignored in the model discussed here, and also a much simplified ampoule geometry is considered. The objective of this work is to validate the numerical prediction on the strength and structure of buoyancy driven convection that could occur under terrestrial conditions during nonlinear optical film growth. The validation is used to enable a reliable predictive capability on the nature and strength of the convective motion under low gravity conditions. The ampoule geometry is in the form of a parallelepiped with rectangular faces. The numerical results obtained from the solution to the Boussinesq equations show that natural convection will occur regardless of the orientation of the UV source with respect to the gravity vector. The least strong convective motion occurred with the UV beam directed at the top face of the parallelepiped. The strength of the convective motion was found to be almost linearly proportional to the total power of the UV source. Also, it was found that the strength of the convective motion decreased linearly with the gravity due to acceleration. The pattern of the convection flow on the other hand, depended on the source location.     

Solutal convection in crystal growth: effect of interface curvature on flow structuration in a three-dimensional cylindrical configuration

Due to temperature and concentration gradients in the molten phase, it is well known that convective flows can develop in the bulk under normal conditions of gravity. These motions modify the shape of the growing interface and the concentration distribution along it. This study will only focus on the case of pure solutal convection and the effect of a given interface curvature on the flow. In particular, the transition from a 3D-flow to a 2D one as a function of the interface curvature is examined in order to investigate possible values of the operating parameters and fluid properties. The main aim is to justify the use of 2D-simulation tools for predicting the convective transport in cylindrical crystal growth ampoules.     

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.     

Growth of BiSbTe3 -Mixed Crystals using a Bridgman Configuration of the TITUS Furnace - Numerical Simulation of Convection and Segregation

A standard Bridgman configuration of the TITUS facility was used to grow BiSbTe ₃ -mixed crystals at normal and at reduced gravity. The growth experiments in space, including a dynamical registration of the temperature distribution of the furnace, were performed during the MIR'97 mission. The transient temperature profiles have been analysed to get thermal boundary conditions for numerical simulations of convection and segregation with the FEM package FIDAP. The calculations have been done within the frame of a 3D model close to the real growth conditions. The aim of the paper is to discuss the resulting Buoyancy driven flow configuration in the melt and its influence on the radial and axial segregation depending on the gravity level.     

Analysis and calculation of the formation of grown-in microdefects in dislocation-free silicon single crystals

The physical model of the formation of grown-in microdefects in dislocation-free Si single crystals has been analyzed. The mathematical models used to describe the processes of defect formation in crystals during their growth are proven to be adequate to the physical model. A technique is proposed to determine and calculate the defect structure in dependence of the crystal growth conditions (growth technique, growth rate, temperature gradients, cooling rate). It is shown that the theoretical study of the real crystal structure in the dependence of the thermal growth conditions using an original virtual technique for analyzing and calculating the formation of grown-in microdefects is a new experimental technique.     

VERTICALLY SUSPENDED SMECTIC FILMS WITH IN-PLANE TEMPERATURE GRADIENTS

Abstract

We present a study of vertically suspended smectic films under the influence of temperature gradients in the film plane. It is shown that such gradients lead to the transport of smectic material, even against the action of the gravitation forces, from the hot to the cold film edge. In addition, we observe thermally driven convection in these films, and it is demonstrated that the surrounding air plays an essential role for this instability. We compare this result with convective patterns in soap films reported by Martin and Wu in Phys. Rev. Lett. 80 1892 (98) and give some evidence that their interpretation has to be modified, the contact with surrounding air has to be taken into account.     

Anomalous effects in dopant distribution in Ge single crystals grown by the floating zone technique aboard spacecrafts

Specific features of Ga-dopant distribution in Ge single crystals grown by the floating zone technique from lightly and heavily Ga-doped Ge melts aboard the Photon spacecrafts have been studied. An anomalously strong concentration dependence of the effective coefficient of Ga distribution in Ge crystallized from melts with a well-developed free surface, which has no analogues under the terrestrial conditions, has been established for the first time. This anomaly is interpreted as a consequence of specific concentration-dependent processes of heat and mass transfer in the molten zone, and, first of all, the intensification of the concentration-capillary convection with an increase of the doping level. The quantitative characteristics of the crystallization parameters necessary for the construction and verification of hydrodynamic models are obtained experimentally. The effect of the observed phenomena on the electrophysical homogeneity of the grown single crystals and possible methods for the control of dopant distribution in such crystals are discussed.     

Influence of temperature conditions in horizontal Bridgman furnace on crystal growth of GaAs

The experimental investigation of the boat shape and boat position in the furnace in the case of unseeded horizontal Bridgman growth of GaAs single crystals was carried out. The relation between axial and radial temperature gradients in the furnace was also studied. On the basis of experimental results the optimum conditions for the growth of low dislocation density GaAs single crystals were derived.     

Radiative Heat Transfer in a Resistance Heated Floating Zone Furnace: A Numerical Study with FIDAPTM

This paper presents a numerical study of radiative heat transfer in a floating zone (FZ) furnace which was performed by using the commercial finite element program FIDAP^TM. This resistance furnace should provide a temperature higher than the melting temperature of silicon (i.e. T_max ≈ 1500 °C) and a variable temperature gradient at the liquid/solid interface (≥ 25 K/cm). Due to the high working temperatures, heat radiation plays the dominant role for the heat transfer in the furnace. For this reason, the quality of view factors used in the wall‐to‐wall model was carefully inspected with energy‐balance checks. A numerical model with two control parameters is applied to study the influence of material and geometrical parameters on the temperature field. In addition, this model allows us to estimate the internal thermal conditions which were used as thermal boundary conditions for partial 3D simulations. The influences of an optical lens system on the radial symmetry of the temperature field were examined with these partial 3D simulations. Furthermore, we used the inverse modeling method to achieve maximum possible temperature gradients at the liquid/solid interface according to the limitation of maximum available power and the maximum stable height of a melt zone.     

Influence of gravitation on the processes of heat and mass transfer in solution crystal growth by the travelling heater method (THM) (III)

The effect of the natural and thermocapillary convection on the vortex configuration in solution during growth of PbTe crystal by the travelling heater method is considered. The estimation of the parameters of growth process (i. e. axial temperature gradients, gravitational acceleration, degree of the solution's surface contact with ampoule), when the vortex configuration undergoes qualitative variation, is given. In terms of the one-dimensional thermodiffusive problem solution the effect produced by the convective stirring on the position of growing and dissolving interfaces is described.     

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)