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This paper reports an overview and some important results of microgravity experiments called Dynamic Surf, which have been conducted on board the International Space Station from 2013 to 2016. The present project mainly focuses on the relations between the Marangoni instability in a high-Prandtl-number (Pr= 67 and 112) liquid bridge and the dynamic free surface deformation (DSD) as well as the interfacial heat transfer. The dynamic free surface deformations of large-scale liquid bridges (say, for diameters greater than 10 mm) are measured with good accuracy by an optical imaging technique. It is found that there are two causes of the dynamic free surface deformation in the present study: the first is the time-dependent flow behavior inside the liquid bridge due to the Marangoni instability, and the second is the external disturbance due to the residual acceleration of gravity, i.e., g-jitter. The axial distributions of DSD along the free surface are measured for several conditions. The critical parameters for the onset of oscillatory Marangoni convection are also measured for various aspect ratios (i.e., relative height to the diameter) of the liquid bridge and various thermal boundary conditions. The characteristics of DSD and the onset conditions of instability are discussed in this paper.

In order to understand the effect of pool rotation on stability of thermocapillary convection, the critical conditions for the incipience of oscillatory flow in rotating shallow annular pools of silicon melt (Pr = 0.011) are investigated by means of linear stability analysis (LSA) under different pool rotation rates ranging from Ta = 0 to 1,513.9 and under microgravity condition. The results indicate that with increase of Ta numbers, the critical Marangoni for the incipience of hydrothermal wave (HTW) increases, i.e., pool rotation stabilizes the steady axisymmetric thermocapillary convection of silicon melt. The critical azimuthal wave number mc decreases linearly with increase of Ta number when Ta ≤ 378.5. However, when Ta > 378.5, mc almost keeps constant with mc = 34. When Ta 550.

The thermocapillary convection and buoyant-thermocapillary convection in the annular pool of silicon melt (Pr=0.011) and silicone oil (Pr=6.7) with depth d=10 mm differentially heated at the outer wall and cooled at the inner wall are investigated by 2-D numerical simulation. The numerical results exhibit that the thermocapillary flow is enhanced by buoyancy force for silicon melt while it is weakened for silicone oil. Linear stability analysis indicates that the buoyancy force destabilizes the thermocapillary convection, which is different from that for silicone oil. The detailed reason of different influence of buoyancy force on the thermocapillary flow with different Pr numbers is explained according to present numerical results.

The thermocapillary convection instability in shallow annular pools with Prandtl numbers (Pr) from 0.011 to 57.9, differentially heated at the outer wall and cooled at the inner wall, is investigated numerically. The critical Marangoni numbers (Mac), critical azimuthal wave numbers (mc) and critical phase velocities (ωc) for the incipience of oscillatory flow are determined by linear stability analysis. The results indicate that the Mac increases steeply with increase of Pr number when Pr≤15.9, while it increases slightly with increase of Pr between Pr=23.9 and 57.9. The mc and ωc decrease with increase of Pr number.

The influence of buoyancy force on the thermocapillary convection instability in the annular pools (Ri = 20 mm, Ro = 40 mm, and depth d ranging from 1 to 10 mm) of silicon melt (Pr = 0.011), differentially heated at the outer wall and cooled at the inner wall, is investigated numerically. The critical Marangoni numbers (Mac) for the incipience of oscillatory flow are determined by linear stability analysis (LSA) under both microgravity and normal gravity conditions. The results indicate that the buoyancy force destabilizes the thermocapillary convection under different liquid layer depths from 3 to 10 mm. With increasing the layer depth, the critical Ma number, critical azimuthal wave number and critical phase velocity decrease. Some of 3-D simulation results are compared with those of LSA. 3-D results are found consistent with the LSA results except for a case of D = 0.05 where 3-D simulation gives a stationary 3-D flow under a large Ma.

Numerical simulations were conducted to study thermocapillary flows in short half-zone liquid bridges of molten tin with Prandtl number Pr = 0.009, under ramped temperature difference. The spatio-temporal structures in the thermocapillary flows in short half-zone liquid bridges with aspect ratios As = 0.6, 0.8, and 1.0 were investigated. The first critical Marangoni numbers were compared with those predicted by linear stability analyses (LSA). The second critical Marangoni numbers for As = 0.6 and 0.8 were found to be larger than that for As = 1.0. The time evolutions of the thermocapillary flows exhibited unusual features such as a change in the azimuthal wave number during the three-dimensional stationary (non-oscillating) flow regime, a change in the oscillation mode during the three-dimensional oscillatory flow regime, and the decreasing and then increasing of amplitudes in a single oscillation mode. The effects of the ramping rate of the temperature difference on the flow modes and critical conditions were studied as well. In this paper, the experimental observability of the critical conditions was also discussed. (C) 2008 Elsevier Inc. All rights reserved.

In order to understand the mechanism of the flow pattern transitions on silicon melt in Czochralski furnaces, we conducted a series of unsteady three-dimensional numerical simulations of silicon melt flow in a slowly rotating shallow annular pool in the counter-clockwise direction. The pool was heated from the outer cylinder and cooled at the inner cylinder. The temperature differences between the vertical outer and inner cylinders ranged from 5 K to 28 K and annular pool rotation rate from 0 and 2 rpm. Bottom and top surfaces of the melt pool were adiabatic. The simulation results indicate that two flow transitions occur when increasing the radial temperature difference along the free surface. At first, the steady two-dimensional flow becomes the first hydrothermal wave and then the second hydrothermal wave with less wave number. The critical conditions for the onset of the instability and the transition zone between the first and the second hydrothermal wave are determined at various rotation rates. Characteristics of the steady and the three-dimensional flows are discussed.

Proper orthogonal decomposition (POD) using method of snapshots was performed on three different types of oscillatory Marangoni flows in half-zone liquid bridges of low-Pr fluid (Pr = 0.01). For each oscillation type, a series of characteristic modes (eigenfunctions) have been extracted from the velocity and temperature disturbances, and the POD provided spatial structures of the eigenfunctions, their oscillation frequencies, amplitudes, and phase shifts between them. The present analyses revealed the common features of the characteristic modes for different oscillation modes: four major velocity eigenfunctions captured more than 99% of the velocity fluctuation energy form two pairs, one of which is the most energetic. Different from the velocity disturbance, one of the major temperature eigenfunctions makes the dominant contribution to the temperature fluctuation energy. On the other hand, within the most energetic velocity eigenfuction pair, the two eigenfunctions have similar spatial structures and were tightly coupled to oscillate with the same frequency, and it was determined that the spatial structures and phase shifts of the eigenfunctions produced the different oscillatory disturbances. The interaction of other major modes only enriches the secondary spatio-temporal structures of the oscillatory disturbances. Moreover, the present analyses imply that the oscillatory disturbance, which is hydrodynamic in nature, primarily originates from the interior of the liquid bridge. (C) 2007 Elsevier B.V. All rights reserved.

Lithium niobate films grown epitaxially on sapphire substrate were prepared using a thermal chemical vapor deposition method from the metalorganic compounds Li(C 11 H 19 O 2 ) and Nb(OC 2 H 5 ) 5 . The range of operating conditions for obtaining pure epitaxially grown LiNbO 3 without other oxides is within that for obtaining pure polycrystalline LiNbO 3 grown on silicon substrate. On analyzing the composition of the epitaxially grown LiNbO 3 film, the composition of the film was similar to that of the LiNbO 3 solid solution in the phase diagram of the Li–Nb composite oxide obtained for crystal growth from a molten solution.

In order to understand the characteristics of thermocapillary–buoyancy flow, we conducted a series of unsteady three-dimensional numerical simulations of thermocapillary–buoyancy flow of 0.65cSt silicone oil (Prandtl number Pr = 6.7) in an annular pool with different depth ( d = 1–11 mm) heated from the outer wall (radius r o = 40 mm) and cooled at the inner cylinder ( r i = 20 mm) with an adiabatic solid bottom and adiabatic free surface. Simulation conditions correspond to those in the experiments of Schwabe [D. Schwabe, Buoyant–thermocapillary and pure thermocapillary convective instabilities in Czochralski systems, J. Crystal Growth 237–239 (2002) 1849–1853]. Simulation results with large Marangoni number predict three types three-dimensional flow patterns. In the shallow thin pool ( d = 1 mm), the hydrothermal wave characterized by curved spokes is dominant. In the deep pools ( d ⩾ 5 mm) the three-dimensional stationary flow appears and this flow pattern corresponds to the Rayleigh-Benard instability, which consists of pairs of counter-rotating longitudinal rolls. When 2 mm ⩽ d ⩽ 4 mm, the hydrothermal wave and three-dimensional oscillatory flow coexist in the pool and travel along the same azimuthal direction with the same angular velocity. The critical conditions for the onset of three-dimensional flows were determined and compared with the experimental results. The characteristics of three-dimensional flows were discussed.

Three-dimensional numerical simulations of transient thermal convection in a shallow molten silicon pool with Czochralski configuration (depth d = 3 mm) have been conducted to understand the transition mechanism of the flow patterns on silicon melt in Czochralski furnaces. The crucible side wall is maintained at constant temperature. Bottom and free surfaces are either adiabatic or allow heat transfer in the vertical direction. The simulation results indicate that two flow transitions occur when the radial temperature difference along the free surface increases. First, the steady two-dimensional flow becomes steady three-dimensional flow, and then it evolves to three-dimensional oscillatory flow when the temperature difference is further increased. This oscillatory flow is characterized by spoke patterns traveling in either the clockwise or counterclockwise direction. It is observed that a transition hysteresis exists from oscillatory three-dimensional flow to steady three-dimensional flow when the radial...

In order to understand the nature of surface patterns on silicon melts in industrial Czochralski furnaces, we conducted a series of unsteady three-dimensional numerical simulations of thermocapillary convections in thin silicon melt pools in an annular container. The pool is heated from the outer cylindrical wall and cooled at the inner wall. Bottom and top surfaces are adiabatic. The results show that the flow is steady and axisymmetric at small temperature difference in the radial direction. When the temperature difference exceeds a certain threshold value, hydrothermal waves appear and bifurcation occurs. In this case, the flow is unsteady and there are two possible groups of hydrothermal waves with different number of waves, which are characterized by spoke patterns traveling in the clockwise and counter-clockwise directions. Details of the flow and temperature disturbances are discussed and number of waves and traveling velocity of the hydrothermal wave are determined.

The influence of pool rotation on the thermocapillary flow in a shallow annular pool (Ri=20 mm, R0=40 mm, and depth d=1 mm) of silicone oil (0.65 cSt, Pr=6.7), heated from the outer wall and cooled at the inner wall, is investigated by numerical simulations and linear stability analysis (LSA). The increase in Ta from 0 to 0.322 and 0.806 destabilizes the basic steady axisymmetric flow field against hydrothermal waves (HTW) and the critical Marangoni number Mac decreases from 8.396×103 to 8.096×103 and 7.999×103, while the critical azimuthal wave number mc increases from 27 to 30 and 33. In rotating annular pool, the HTW propagates in the direction opposite to the pool rotation, when observed from a view point in the rotating coordinate. At Ma=1.34×104, the azimuthal wave number m increases up to 54 and branching of spiral arms occurs near the inner wall. This branching phenomenon occurs only at Ma=1.34×104 and disappears at larger values of Ma. However, at Ma=2×104, two groups of HTWs (m=48 and m=5) coexist and the HTW with m=5 propagates in the same azimuthal direction as that of the pool rotation. Both the numerical simulation and LSA results indicate that the pool rotation destabilizes the basic steady axisymmetric thermocapillary flow in the present Ta range (Ta⩽0.806). The influence of the pool rotation on the instability of the thermocapillary flow is distinguishable even for such a small rotating rate of the shallow annular pool. This can be explained by the additional energy supply from the azimuthal flow field induced by the Coriolis force.

In order to understand the effects of the thermophysical properties of the melt on the transport phenomena in the Czochralski (Cz) furnace for the single crystal growth of silicon, a set of global analyses of momentum, heat and mass transfer in small Cz furnace (crucible diameter: 7.2 cm, crystal diameter: 3.5 cm, operated in a 10 Torr argon flow environment) was carried out using the finite-element method. The global analysis assumed a pseudosteady axisymmetric state with laminar flow. The results show that different thermophysical properties will bring different variations of the heater power, the deflection of the melt/crystal interface, the axial temperature gradient in the crystal on the center of the melt/crystal interface and the average oxygen concentration along the melt/crystal interface. The application of the axial magnetic field is insensitive to this effect. This analysis reveals the importance of the determination of the thermophysical property in numerical simulation. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The characteristics of thermocapillary flow and hydrothermal waves (HTWs) in a shallow pool ( r i = 20 mm , r o = 40 mm and depth d = 1.0 mm ) of silicone oil (0.65 cSt, Pr = 6.7 ), heated from the outer wall and cooled at the inner wall, are investigated by numerical simulations. The critical Marangoni number (Mac) for the incipience of HTWs is determined, using a very fine mesh system (202×603×16), to be M a c = 3.36 × 1 0 5 ( Δ T c = 5.03 K ) under a microgravity condition and M a c = 3.94 × 1 0 5 ( Δ T c = 5.895 K ) for normal gravity. These critical values are smaller than those determined by 2D simulations by a factor of 0.926 for 0 G, and 0.912 for 1 G. The wave number and angular velocity of HTWs vary with Ma. Under small Ma’s, a single group of HTWs propagating in the azimuthal direction become dominant after a long calculation time. Numerical simulations with larger values of Ma show the coexistence of several groups of HTWs with different wave numbers and propagation directions. Analysis of motions of fluid elements indicates that the fluid elements exhibit small azimuthal displacements, although the HTW patterns are constantly traveling in the azimuthal direction. However, interference between different HTW groups causes a large displacement in the azimuthal direction. Numerical simulations reveal the mechanism of the large bending of the curved arms of HTW near the hot wall. Large values of Nusselt number appear at the top of the inner wall. Tempospatial variation of the Nusselt number appears on both walls corresponding to the propagation of HTW patterns.

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.

In order to understand the characteristics of surface patterns on silicon melt in Czochralski furnaces, we conducted a series of unsteady three-dimensional numerical simulations of thermocapillary-buoyancy flow of a shallow molten silicon pool with Czochralski configuration (depth d = 3 mm). The crucible sidewall is maintained at constant temperature. Bottom and free surfaces are adiabatic or allow heat transfer in the vertical direction. The simulation results indicate that two flow transitions occur with increasing the radial temperature difference along the free surface. At first, the steady two-dimensional flow becomes steady three-dimensional flow and then oscillatory three-dimensional flow. The critical conditions for the onset of the instability were determined. Characteristics of the steady and the oscillatory three-dimensional flows were discussed.

TiO 2 photocatalyst films were prepared by low-pressure metal-organic (LPMO) CVD, with varying reaction temperatures and deposition times, using titanium tetra-isopropoxide (TTIP). Firstly, the characteristics of the CVD preparation of TiO 2 films, as a function of the CVD reaction temperature and deposition time, were studied experimentally. Secondly, the photocatalytic activities of TiO 2 films were evaluated by the decomposition rate of methylene blue in aqueous solution using a photo-reactor. The results indicated that film thickness was linearly proportional to the deposition time. The structure of the film was strongly dependent on the reaction temperature and deposition time. Of the TiO 2 films grown, anatase and rutile showed the highest photocatalytic activity, whereas the amorphous TiO 2 films showed lower activities. The photocatalytic activity strongly depended on the film deposition time (or film thickness), but this was nonlinear. The optimum thickness of the TiO 2 catalyst film grown by LPMOCVD is located between 3 μm and 5 μm.

TiO2 photocatalyst films having an anatase crystal structure with different thickness were prepared by the low-pressure metal–organic chemical vapor deposition (LPMOCVD) to examine the effect of growth conditions on photocatalytic activity. Film thickness was linearly proportional to the deposition time. Structure of the film was strongly dependent on the deposition time. In early stage of deposition, fine particles deposit on the substrate. As increasing the deposition time, crystal orientation is gradually selected following the Kolmogorov model and c-axis oriented columnar crystals become dominant. The photocatalytic activity strongly depends on the film deposition time (or film thickness) in nonlinear way. The optimum thickness of TiO2 catalyst film grown by LPMOCVD may locate between 3 and 5 μm.

A set of global numerical simulations based on a simple, laminar, axisymmetric and pseudo steady model of a small silicon CZ furnace was conducted to reveal the influences of the thermophysical properties of the melt and crystal on the non-dimensional crystal pulling rate, i.e., the Peclet number Pe, and the deflection of the melt/crystal interface Δz, for the sensitivity analyses of the properties. The properties investigated here are the temperature coefficient of surface tension, viscosity, thermal conductivity, the thermal expansion coefficient and emissivity of the melt, and the thermal conductivity and emissivity of the crystal. The results demonstrated that, concerning the thermophysical properties of the melt, emissivity is relatively sensitive to Pe and Δz. Concerning the crystal properties, thermal conductivity is more sensitive to Pe, while emissivity is more sensitive to Δz.

In order to understand the nature of surface spoke patterns on silicon melt in industrial Czochralski furnaces, a series of unsteady three-dimensional numerical simulations were conducted for thermocapillary-buoyancy flow of silicon melt in annular pool (inner radius ri = 15 mm, outer radius ro = 50 mm, depth d = 3 mm). The pool is heated from the outer cylindrical wall and cooled at the inner wall. Bottom and top surfaces either are adiabatic or allow heat transfer in the vertical direction. Results show that a small temperature difference in the radial direction generates steady roll-cell thermocapillary-buoyancy flow. With large temperature difference, the simulation can predict three-dimensional oscillatory flow, which is characterized by spoke patterns traveling in the azimuthal direction. The small vertical heat flux (3 W/cm2) does not have significant effects on the characteristics of this oscillatory flow. Details of the flow and temperature disturbances are discussed and the critical conditions for the onset of the oscillatory flow are determined. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

In order to understand the basic characteristics of the gas-phase mass-transfer coefficient ( k g ) in a small silicon Czochralski (Cz) furnace, a very crude model was proposed and the results were correlated by the Sherwood number as a function of Reynolds number. It was confirmed that by installing a gas guide in the hot zone, the mass transfer coefficient was significantly enhanced. A set of global analyses of small Cz furnaces was conducted with different values of diffusivity of SiO in the gas phase ( D SiO ) and of oxygen in the melt phase ( D O ) in order to elucidate which rate process controls the average oxygen concentration ([O] ave ) in the grown crystal. These simulations revealed that in these small Cz furnaces, [O] ave is dependent on the gas phase mass transfer rate and melt flow patterns. A decrease in D SiO causes an increase in [O] ave . An increase in D O tends to increase [O] ave slightly in most cases.

In order to understand the nature of thermocapillary convection under microgravity in a differentially heated annular pool with the outer heated container of radius r o =40 mm and the inner cooled cylinder of r i =20 mm, and an adjustable depth d =3–14 mm, we conducted a series of unsteady two-dimensional numerical simulations with the finite volume method. The pool was filled with the 0.65cSt silicone oil (Prandtl number Pr =6.7). With a large enough temperature difference in the radial direction, the simulation can predict oscillatory thermocapillary flows. Hopf bifurcation neutral curve is delineated in the thermocapillary Reynolds number ( Re )-aspect ratio ( A =( r o − r i )/ d ) plane. It is found that time-dependent motion is only possible if A exceeds a critical value A cri which is around 2.29. Streamline and isotherm patterns are presented at different thermocapillary Reynolds number and the aspect ratio corresponding to stationary and oscillatory states.

In order to understand the effects of temperature coefficient of surface tension (γT) on oxygen transport as well as on the heater power and the melt/crystal interface shape in a small silicon Czochralski furnace, a set of global numerical simulations is conducted using the finite-element method for a wide range of γT between 0 and 0.35×10−3 N/m K. The results for cases without rotations of crystal and crucible indicate that the larger Marangoni effect enhances a toroidal roll cell in the crucible and reduces the heater power and oxygen concentration in the crystal but makes the melt/crystal interface more convex toward melt. When the crystal and the crucible are rotating in counter directions, an upwelling flow near the axis from the bottom of the crucible takes important role in determining the radial distributions of oxygen concentration. γT gives significant effects on the flow pattern, oxygen concentration, heater power and interface shape.

In order to understand the characteristics of surface patterns on silicon melt in Czochralski (Cz) furnaces, we conducted a series of unsteady three-dimensional (3-D) numerical simulations of thermocapillary flow of a shallow molten silicon pool with Cz configuration under microgravity. The crucible sidewall is maintained at constant temperature. Bottom and free surfaces are adiabatic or allow heat transfer in the vertical direction. The simulation results indicate that two flow transitions occur when increasing the radial temperature difference along the free surface for 3-mm-deep layer. At first, the steady two-dimensional (2-D) flow becomes steady 3-D flow and then oscillatory 3-D flow. But the steady 2-D flow exhibits direct transition to an oscillatory 3-D flow for 8-mm-deep layer. The critical conditions for the onset of the instability were determined. Characteristics of the steady and the oscillatory 3-D flows were discussed.

In order to evaluate the experimental observations at NASDA, a long-run numerical simulation was conducted on a realistic model of a half-zone liquid bridge of molten tin, including the supporting iron rods. The model is identical to the apparatus of NASDA's experiment with a radius of 1.5 mm and length of 3 mm. Using time-dependent imposed temperatures on both ends of the rods, which are calculated based on the experimental temperature recordings measured through two thermocouples, the numerical results reproduce the experimentally observed oscillations of local melt free surface temperature with different frequencies and explain the experimental results. The present study also reveals that the first and second critical Marangoni numbers are similar to those predicted by our previous studies corresponding to the marginal stability limits, and indicates that very sensitive temperature measuring system must be developed to detect experimentally the temperature oscillations right after the incipience of oscillatory Marangoni flow, i.e., to determine the critical conditions of flow transitions experimentally through temperature measurements.

Two series of three-dimensional (3-D) numerical simulations were conducted in order to understand 3-D Marangoni convection in half-zone liquid bridges of molten tin. In one series, we determined the second critical Marangoni number for liquid bridges of low-Prandtl-number fluid ( Pr =0.009) at different aspect ratios, As, based on the well-known simple bridge geometry which assumes the liquid bridge is supported between two differentially heated isothermal solid discs. A new type of oscillatory flow was first observed in a simulation of a tin liquid bridge of As=2.0 under highly supercritical conditions at Ma=1.4 Ma c 2 , the whole flow and temperature fields with an azimuthal wave number m =1, exhibiting an apparently twisting oscillations back and forth around the axis, rotates very slowly in the azimuthal direction. In the second series, we conducted numerical simulations based on much realistic bridge geometry. Special emphasis was placed on the effects of less conductive supporting rods on the stability limit of the axisymmetric steady flow and the onset of flow oscillations. Present simulations reveal that the 3-D flow causes non-uniform temperature distributions in the supporting rods. We proposed a new definition of effective temperature difference (Δ T e ) acting on the liquid surface to evaluate the Marangoni number. Thus determined first and second critical Marangoni numbers fall close to, but slightly larger than, those predicted by the simple model. However the deviations are less than 3%. On the other hand, present simulations revealed that very small spatial offsets of temperature measuring points cause significant error in Δ T measurement because of the conduction resistance in the rod under large heat flux. This effect is very important for any liquid bridge experiments using low- Pr fluid. A simple conduction dominant model provides reasonable estimate of Δ T e from the temperature difference measured by thermocouples.

In order to understand the nature of surface patterns on silicon melt in industrial Czochralski furnaces, we conducted a series of unsteady three-dimensional numerical simulations of thermocapillary and thermocapillary–buoyancy flows in thin silicon melt pools in annular containers. The pool is heated from the outer cylindrical wall and cooled at the inner wall. Bottom and top surfaces either are adiabatic or allow heat transfer in the vertical direction. With large temperature difference in the radial direction, the simulation can predict two types of oscillatory convections. One is characterized by spoke patterns traveling in the azimuthal direction. The other one is characterized by radially extended roll cells periodically alternating the azimuthal flow directions but are stationary. The small vertical heat flux (3 W/cm 2 ) does not have significant effects on the characteristics of those oscillatory flows. Details of the flow and temperature disturbances are discussed and the critical conditions for the onset of the oscillatory flow are determined.

三塩化シランを原料としたシリコンエピタキシャル膜成長過程における水平型枚葉式反応器内のガス流れ, 温度場および濃度場の挙動と成膜特性の関係について3次元数値解析を用いて詳細な検討を行った. 成膜速度分布の均一化に, 流路高さを小さく保つこと, 反応器内のガス流入速度を上げること, サセプタを回転させること, 三塩化シラン濃度を高く保つこと, が効果的である. 比較的, 低い流入速度, 低い三塩化シラン濃度の場合でも, 入口流路を3分割し, 各流路幅, 各ガス流入速度を調節することで, 成膜基板上の自然対流の発生位置と強度を制御することが可能で成膜速度分布の均一化に有効である. また, サセプタ回転による成膜速度均一化作用は基板中心付近に関しては効果が無いために, 反応器中央流路部で流速を減少させることは避けるべきである.

The effect of internal radiative heat transfer on the spoke pattern observed on an oxide melt surface was investigated by means of a three-dimensional numerical simulation of LiNbO3 melt flow in an open Czochralski crucible. In the mathematical model, the assumptions that the melt was an incompressible Newtonian Boussinesq fluid, the flow was laminar and the melt free surface was flat were adopted. The crucible wall was assumed to be heated by a constant heat flux. The Marangoni effect on the melt free surface was taken into account. When the internal radiative heat transfer was ignored, i.e., the melt was assumed to be opaque, a spoke pattern was generated and the bulk melt flow was oscillatory; otherwise, the internal radiative heat transfer decreased the temperature gradient and hence suppressed the Marangoni instability, and consequently, the spoke pattern disappeared and the melt flow became steady and axisymmetric. The investigation provided one theoretical explanation for the experimental phenomenon observed by Okano et al. (J. Mater. Process. Manuf. Sci. 4 (1995) 41).

A series of unsteady three-dimensional numerical simulations were conducted for thermocapillary flow of 0.65 cSt silicone oil (Prandtl number Pr =6.7) in annular pools with different depths ( d =1–17 mm) heated from the outer wall (radius r o =40 mm) and cooled at the inner cylinder ( r i =20 mm) with an adiabatic solid bottom and adiabatic free surface. Simulation conditions corresponded to those in the microgravity experiments of Schwabe and Benz (Adv. Space Res. 29 (2002) 629). A temperature difference between the outer and inner walls (Δ T ) generates roll-cell thermocapillary flow. Simulations with large Δ T predicted two types of oscillatory thermocapillary flows. One is the hydrothermal wave with curved spokes, which is dominant only in shallow pools ( d =1–3 mm). The second one is dominant in deep pools ( d >3 mm) and is characterized by traveling straight spoke patterns in the azimuthal direction. Critical conditions for the onset of the oscillatory flow in liquid pools of different depths were determined. Details of the flow and temperature fields were discussed. Oscillation frequencies were compared with the experimental results as functions of Δ T and pool depth d . Quantitative agreements were obtained for small Δ T and shallow pools.

Polycrystalline LiNbO3 films were prepared using the metalorganic compounds, Li(DPM) and Nb(OC2H5)5, by thermal chemical vapor deposition at 5 Torr in the temperature range of 873–1023 K. The range of operation conditions for pure LiNbO3 growth using Nb(OC2H5)5 is wider than that using Nb(DPM)2Cl3 as the Nb source. The distribution of growth rate in the reactor and that of step coverage in chemical-vapor-deposited LiNbO3 are governed by the Nb2O5 growth process, and the reactivity of Nb(OEt)5 is considerably higher than that of Nb(DPM)2Cl3.

Control of melt flow in crystal growth process by application of the magnetic field is a practical technique for silicon single crystals. In order to understand the influence of axial magnetic field on the silicon melt flow and oxygen transport in a silicon Czochralski (Cz) furnace, a set of global numerical simulations was conducted using the finite-element method for the magnetic field strength from 0 to 0.3 T, the crystal rotation rates from 0 to 30 rpm and the crucible counter-rotation rates from 0 to −15 rpm. It was assumed that the flow was axisymmetric laminar in both the melt and the gas, the melt was incompressible and a constant temperature was imposed on the outer wall of the Cz furnace. The results indicate significantly different flow patterns, thermal and oxygen concentration fields in the melt pool when a uniform axial magnetic field is applied.

In order to understand the influence of crystal and crucible rotations on the silicon melt flow and oxygen transport in a small Czochralski (Cz) furnace, a set of global numerical simulations, based on the pseudo-steady and axisymmetric laminar flow model, was conducted using the finite-element method. The crystal rotation rates ranged from 0 to 20 rpm and the crucible rotation rates from 0 to −2.5 rpm. The model evaluated the effects of the thermocapillary force on the radial distributions of oxygen concentration and ( V s,n / G n ) at the melt/crystal interface, where V s,n and G n are the crystal pulling rate and temperature gradient in the direction normal to the melt/crystal interface, respectively. Simulation results indicate that the thermocapillary force causes significant changes in the flow pattern and temperature distribution in the melt but gives small effect on the oxygen concentration in the crystal in the case of a small Cz furnace without a gas guide. On the contrary, installation of a gas guide has a significant effect on the flow fields and the oxygen concentration in the grown crystal.

Three-dimensional numerical simulations of LiNbO3 melt flow in a Pt crucible (47 mmΦ×47 mmH×1.5 mmT) in the Czochralski oxide crystal growth configuration have been performed to investigate the effect of RF coil position on spoke patterns observed on the free surface of oxide melt. The crucible temperature field calculation was coupled with the numerical simulations of melt flow to provide a realistic thermal boundary condition for the melt/crucible interface. The melt was assumed to be an incompressible Newtonian Boussinesq fluid, and the flow was laminar. The free surface of melt and the crystal/melt interface were flat. The heat loss from the free surface was due to thermal radiation alone. The heat generation rate of the crucible was obtained by analyzing the electromagnetic field; the outside surfaces of the crucible were adiabatic. The Marangoni effect was taken into account. It was found that the appearance of the spoke pattern is dependent on the RF coil position. When the RF coil was set low relative to the crucible, the spoke pattern appeared easily; otherwise, the spoke pattern was difficult to be generated. The results of the investigation validated the mechanism of spoke pattern formation reported in J. Crystal Growth 200 (1999) 204.

Marangoni convection during the solidification or remelting process was investigated in a small pool of a liquid Fe-O alloy, by experiments and numerical simulations. Most of the studies of such a system, with a low Prandtl number but a high Schmidt number, have taken into account thermocapillary convection but have left the solutocapillary effect out of consideration. However, our experimental and numerical approaches revealed that solutocapillary convection also plays an important role in the generation of peculiar flow patterns with a single roll cell or two roll cells. The Marangoni convection observed was classified into at least four categories based on the thermocapillary and solutocapillary forces.

Yttria-stabilized zirconia (YSZ) thin film was grown by low-pressure metalorganic chemical vapor deposition (LPMOCVD) using β-diketonate complexes of zirconium and yttrium, tetrakis(2,2,6,6-tetramethyl-3,5-heptadionato) zirconium and tris(2,2,6,6-tetramethyl-3,5-heptadionato) yttrium, respectively. Growth rate distribution and film composition in a hot wall tubular reactor were quantitatively reproduced by a transport model including gas-phase and surface reactions, assuming linear additivity of the individual growth rates of zirconia (ZrO2) and yttria (Y2O3). At low temperatures (773, 823 K), the growth rates are controlled by the gas-phase and surface reactions. Since the rate constants of Y2O3 are larger than those of ZrO2 at low temperatures, the film is richer in Y than the feed ratio. However, at high temperatures (>848 K), the growth rates of each oxide system are limited by the mass transfer rates of each intermediate, and the film composition in the reactor tube is nearly equal to the feed ratio. The shapes of YSZ film grown on micro-size trenches can be qualitatively interpreted by a Monte Carlo simulation assuming a linear combination of the growth rates of ZrO2 and Y2O3. The surface reaction of Y2O3 is faster than that of ZrO2 at low temperatures, thus the film near the mouth of the trench is richer in Y than that at the bottom. However, at high temperature, the film composition becomes constant regardless of its position in the trench, because its growth rate is limited by the mass transfer rates of the intermediates.

To understand the characteristics of the Czochralski (Cz) furnace for the single-crystal growth of silicon, a set of global analyses of momentum, heat and mass transfer in small Cz furnaces (crucible diameter: 7.2 cm, crystal diameter: 3.5 cm, operated in a 10 Torr argon flow environment) is carried out using the finite-element method. The global analysis assumes a pseudosteady axisymmetric state with laminar flow, equilibrium relations at the melt/silica interface and vapor–liquid chemical equilibrium at the melt/gas interface, as well as the segregation coefficient of unity at the melt/crystal interface. Convective and conductive heat transfers, radiative heat transfer between diffuse surfaces and the Navier–Stokes equations for gas and melt phases are all combined and solved together. Thus, the velocities and temperatures obtained are used to calculate the oxygen concentrations. The global analysis code is effectively used to discuss the influences of the Marangoni effect and a gas guide (or a heat shield) placed between the crucible and the crystal. The results indicate that the gas guide reduces the heater power and changes the melt flow pattern and oxygen transport. The melt flow pattern is strongly dependent on the Marangoni effect and gas flow near the surface, and changes the oxygen concentration significantly. This analysis reveals the importance and effectiveness of global analysis.

In this paper, the thermal conductivity and thermal diffusivity of four kinds of polymer melts were measured by using the transient short-hot-wire method. This method was developed from the hot-wire technique and is based on two-dimensional numerical solutions of unsteady heat conduction from a wire with the same length-to-diameter ratio and boundary conditions as those in the actual experiments. The present method is particularly suitable for measurements of molten polymers where natural convection effects can be ignored due to their high viscosities. The results have shown that the present method can be used to measure the thermal conductivity and thermal diffusivity of molten polymers within uncertainties of 3 and 6%, respectively. Further, the thermal conductivity and thermal diffusivity of solidified samples were also measured and discussed.

The transition behavior from stationary to oscillatory thermocapillary flow was experimentally studied with a liquid bridge of molten tin (Prandtl number Pr=0.01) of 1.5 mm in radius. The experimental difficulties such as preventing oxidation of the melt surface and detecting a small amplitude of surface temperature fluctuation without any external disturbances on the flow field were successfully solved by employing a high vacuum condition, ion etching to remove the oxide film on the surface and a high resolution radiation thermometer. A temperature fluctuation was first observed at a Marangoni number Ma of 43.3. Frequency and amplitude of the fluctuation were 0.08 Hz and 0.3 K, respectively, which is significantly larger than temperature resolution of the radiation thermometer used. The temperature oscillation developed with increasing temperature difference imposed between the upper and lower ends of the liquid column and then observed a standing wave of 0.42 Hz with very strong amplitude at a Marangoni number of 91. The flow transition was directly proved by a surface flow visualization experiment. Tin-oxide particles, which were pre-mixed with molten tin, were observed to repeat oscillatory movement along the circumferential direction with 0.5 s interval after the onset of the oscillation. Those results are the first and clear experimental evidence for the transition to oscillatory flow in a low Pr fluid by a non-contact diagnostic, which has never been observed yet. Validity of the experimentally determined critical Marangoni number and the frequency of the standing wave were discussed by comparing with a numerical result.

Photocatalytic activities of TiO2 films were experimentally studied. TiO2 films with different crystal structures (amorphous, anatase, rutile) were prepared by a Low Pressure Metal Organic Chemical Vapor Deposition (LPMOCVD) at different reaction temperatures and also by a Sol-Gel method using TTIP (Titanium Tetra Iso-Pro-poxyde). The Effect of CVD preparation method, CVD reaction conditions, crystal structure and wave-length of UV light on the photocatalytic decomposition rate of methylene blue in aqueous solution were studied. First, the characteristics of CVD preparation of TiO2 films, such as the CVD film growth rate, crystal structure and morphology of the grown TiO2 films, were experimentally studied as a function of CVD reaction temperature. Secondly, photocatalytic activities of TiO2 films were evaluated by using two types of photo-reactors. The results indicated that TiO2 films prepared by CVD exhibit higher photocatalytic activity than a catalyst prepared by the Sol-Gel method. Among the CVD grown TiO2 films, anatase and rutile showed high photocatalytic activities. However, amorphous TiO2 films showed lower activities. The activity of the photocatalysts of anatase films was excellent under all types of UV-lamps. The activity of CVD-prepared anatase films was four to seven times higher than that of photocatalyst films prepared by the Sol-Gel method.

A set of numerical simulations was conducted using a finite difference method to understand the general feature of oscillatory Marangoni convection in half-zone liquid bridges of low Prandtl number fluids (Pr=0, 0.01, 0.02) with a cylindrical liquid surface over a wide aspect ratio range (As=0.6 to 2.2). The simulation results indicated that under smaller temperature differences the flow in the liquid bridge was axisymmetric but it became unstable against three-dimensional (3-D) disturbances beyond a certain threshold value of temperature difference, i.e., the flow became steady 3-D flow at and beyond the first critical Reynolds number Rec1. This steady 3-D flow became unstable against time-dependent 3-D disturbances beyond a second critical condition, Rec2. The numerical simulations revealed the critical conditions and flow structures in detail for Pr=0 fluid and rough sketches for fluids of Pr=0.01 and 0.02. The present results of Rec1 and Rec2 showed good agreements with those of linear stability analyses and with available numerical results. A stability map for low Pr fluids (Pr=0, 0.01 and 0.02) was proposed.

The transient process of the thermocapillary convection was obtained for the large Pu floating half zone by using the method of three-dimensional and unsteady numerical simulation. The convection transits directly from steady and axisymmetric state to oscillatory flow for slender liquid bridge, and transits first from steady and axisymmetric convection to the steady and non-axisymmetric convection, then, secondly to the oscillatory convection for the fatter liquid bridge. This result implies that the volume of liquid bridge is not only a sensitive critical parameter for the onset of oscillation, but also relates to the new mechanism for the onset of instability in the floating half zone convection even in case of large Prandtl number fluid.

熱CVDにおける熱拡散の効果を検討するため，部分加熱された水平型矩形流路内の熱拡散分離現象について実験及び数値計算による解析を行った．実験は，He-SF6，またはNe-SF6の2成分混合ガスを用いて実施した．混合ガスを溶融石英キャピラリー（内径75μm，長さ900mm）で四重極質量分析計（QMS）に導入し，流路内各所の局所濃度を測定した．複雑な流れ場内での熱拡散に対する3次元数値解析を，コントロールボリューム法で行った．熱物性値が既知のこれらの系では，数値計算結果は実験結果と良好に一致した．

In the present paper, a theoretical model is studied on the flow in the liquid annular film, which is ejected from a vessel with relatively higher temperature and painted on the moving solid fiber. A temperature gradient, driving a thermocapillary flow, is formed on the free surface because of the heat transfer from the liquid with relatively higher temperature to the environmental gas with relatively lower temperature. The thermocapillary flow may change the radii profile of the liquid film. This process analyzed is based on the approximations of lubrication theory and perturbation theory, and the equation of the liquid layer radii and the process of thermal hydrodynamics in the liquid layer are solved for a temperature distribution on the solid fiber.

On the surface of various oxide melts under a vertical magnetic field, the rotating spoke pattern appears. In order to provide a first basic view of this phenomenon, a series of three-dimensional numerical simulations of LiNbO3 melt flow in a crucible (47 mmφ × 46 mmH) under a uniform vertical magnetic field were performed. In this model, the oxide melt was assumed to be a dielectric fluid with a uniform electric charge density ce0. The Marangoni effect was also taken into account. The simulations indicated that the spoke pattern is caused by the Marangoni instability and the rotating motion is driven by the Lorentz force caused by the interaction between the vertical magnetic field and the radial motion of charged fluid which is driven by the Rayleigh–Marangoni convection in the crucible. A charge density of 0.1 C/m3 is sufficient to express the experimentally observed rotating spoke patterns on the LiNbO3 melt which were reported by Miyazawa et al. (1996).

In order to understand the well-known surface pattern of oxide melt flow in a Czochralski crucible, a set of three-dimensional numerical simulations of LiNbO 3 melt flow in a crucible (47 mm φ ×46 mm h ) with a rotating disc (23.5 φ mm, rotating at Ω ) was conducted using the finite-difference method. The crucible bottom was assumed to be adiabatic and the side wall was heated by a constant heat flux. Several case studies with a constant temperature of the side wall were considered for comparison. The heat loss from the melt surface caused by radiation to the ambient at a constant temperature was taken into account. The disc/melt interface was assumed to be flat and at melting- point temperature. To investigate the role of surface tension in the melt flow, numerical simulations including and neglecting the Marangoni effect were conducted at each disc-rotation rate. When neglecting the Marangoni effect, the interaction between the buoyancy and the disc rotation produces a wavy ring-like pattern on the melt surface only at approximately Ω=40 rpm. However, if the Marangoni effect is taken into account, a spoke pattern appears on the surface over a wide range of disc-rotation rate (0 rpm ⩽ Ω ⩽45 rpm). At higher disc-rotation rates, the spoke pattern disappears. The flow in the bulk can be classified into three different types according to the disc-rotation rate, i.e., (1) thermally driven axisymmetric flow with no reverse flow at low rotation rates (0–20 rpm), (2) thermally driven axisymmetric flow with reverse flow beneath the disc at moderate rotation rates (20–30 rpm) and (3) nonaxisymmetric unsteady flow at higher rotation rates (⩾40 rpm). The investigation of the effect of the thermal boundary condition indicated that these flow patterns are sensitive to the thermal boundary condition of the crucible side wall.

The effects of gravity and crystal orientation on the dissolution of GaSb into InSb melt and the recrystallization of InGaSb were investigated under microgravity condition using a Chinese recoverable satellite and under normal gravity condition on earth. To investigate the effect of gravity on the solid/liquid interface and compositional profiles. a numerical simulation was carried out. The InSb crystal melted at 525 degrees C and then a part of GaSb dissolved into the InSb melt during heating to 706 degrees C and this process led to the formation of InGaSb solution. InGaSb solidified during the cooling process. The experimental and calculation results clearly show that the shape of the solid/liquid interface and compositional profiles in the solution were significantly affected by gravity. Under microgravity, as the Ga compositional profiles were uniform in the radial direction. the interfaces were almost parallel. On the contrary, for normal gravity condition, as large amounts of Ga moved up in the upper region due to buoyancy, the dissolved zone broadened towards gravitational direction. Also. during the cooling process, needle crystals of InGaSb started appearing and the value of x of InxGa1-xSb crystals increased with the decrease of temperature. The GaSb with the (111)B plane dissolved into the InSb melt much more than that of the (111)A plane. (C) 2000 Elsevier Science B.V. All rights reserved.

Nonlinear oscillations of molten silicon dr ops in an electromagnetic levitator under microgravity are numerically investigated. The electromagnetic field and the magnetic pr essure on the drop surface are calculated by the surface integral method assuming that the skin depth is much smaller than the drop radius. The Galerkin finite element method in combination with the Lagrangian technique is used to analyze the moderate-amplitude axisymmetric oscillations of the silicon dr ops on which the magnetic pressure acts. The effect of the electric curr ent ratio of the heating coils to the levitation coils on the frequency of the oscillations is evaluated for molten silicon dr ops released from either an initially prolate spheroid configuration or four-lobed spherical harmonic configuration. The numerical results show that, in the former case, the frequency decreases with the curr ent ratio. Also, for the latter, the dynamics of the second mode becomes dominant as the curr ent ratio increases, because the inward magnetic pr essure from the heating coil incr eases.