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The mechanism for thermosolutal convection and the coupling effects of flow, temperature and solute fields during the vertical Bridgman growth of Hg1−xCdxTe single crystals have been numerically analyzed. The calculations take into account the thermophysical properties and their dependence on temperature and composition. The results show that there are two main thermal convection cells in the melt caused by two temperature gradients during the growth of Hg1−xCdxTe single crystals. The stabilizing axial solute gradient in the melt will significantly damp the thermal convection cells when the absolute value of the solute Rayleigh number is close to the value of the thermal Rayleigh number. When there is a large solute gradient in the melt, the thermosolutal convection will become unstable, and the upper flow cell will evolve into a two-cell flow pattern. During the growth of Hg1−xCdxTe single crystals, the radial solute segregation in the melt develops non-monotonically with two minima values. Thus, the methods that solely aim at either damping or enhancing the thermosolutal convection are not always able to improve the radial solute segregation.

Thermosolutal convection during vertical Bridgman directional solidification of Ga 1-x In x Sb alloys has been studied by numerical simulation. The transient analysis of heat, momentum and species transport has been performed by using the finite element code FIDAP R . In the case of vertical Bridgman configuration, the thermal convection is driven by the radial temperature gradients. The solute (InSb) rejected at the solid-liquid interface, which is heavier than the GaSb component, damps the thermally driven convection. The solutal effect on the melt convection has been analyzed for low (x = 0.01) and high (x = 0.1) doped Ga 1-x In x Sb alloys. It is found that the damping effect is negligible for Ga 0.99 In 0.01 Sb alloy grown at low pulling rates (V = 1 μm/s), but cannot be neglected if the pulling rate is increased. In the case of concentrated alloys, the low level of convection intensity leads to an increase of radial segregation and interface curvature during the whole growth process as also shown by experiments. The effect of solutal buoyancy force on the melt convection is analyzed for the horizontal Bridgman configuration under microgravity conditions. An inverse but lower solutal effect on the melt convection, as compared with vertical Bridgman arrangement, is observed. The results are in good agreement with the experimental data, and show that convective transport can be observed even for low (2 x 10 -6 g 0 ) residual gravity levels.

This article investigates the effect of thermosolutal convection in liquid phase electroepitaxial (LPEE) growth of GaAs through a two-dimensional numerical simulation model. The model accounts for heat transfer and electric current distribution with Peltier and Joule effects, diffusive and convective mass transport including the effect of electromigration, and fluid flow coupled with temperature and concentration fields. Simulations are performed for two growth cell configurations and the results are analyzed to determine growth rates, substrate shape evolution, and relative contributions of Peltier cooling and electromigration. The simulations predict and help explain a number of experimentally observed features which previous diffusion-based models fail to reproduce. In general, electromigration is found to be the dominant growth mechanism, but the contribution of Peltier cooling to the overall growth rate is found to be significantly enhanced by thermosolutal convection in the solution, and Peltier cooling can in fact become the dominant growth mechanism for certain growth conditions and growth cell configurations. The overall growth rate is found to increase with increasing furnace temperature and applied electric current density. The thermosolutal convection model predicts increased non-uniformity of the grown layers compared with the pure-diffusion model. The shape of the grown layers is also shown to be very sensitive to changes in growth cell configurations.

Observations of the macroscopic shape of the solid-liquid interface and radial solute segregation have been carried out on quenched Pb-30 wt%TI alloys which were grown upwards, that is, for the case for which thermosolutal convection may take place. The solidification front exhibits a structure which is composed of solid plateaux separated by liquid channels and whose amplitude presents a maximum when plotted versus growth rate, which suggests a concomitant maximum in the level of thermosolutal convection. The convective flow adjacent to the solidification front has then been deduced.

Experiments were carried out to test the existence of solutal or thermosolutal convection and its effect on the solute distribution in the solid. Dilute Al-Mg binary alloys were solidified unidirectionally upward in the planar growth range and the temperature variations in the melt ahead of the solidification front were measured by differential thermal analysis (DTA). The Solidification interface was revealed by quenching and the solute distribution in the solid was analyzed. The almost flat solidification interface at the macroscopic scale indicated that thermal convection due to a radial temperature gradient was minimal. Temperature fluctuations in the melt were very small. However, the concentration profile along the axis of the crystal showed macroscopic segregation due to convection, which was more pronounced at slower growth rates and at higher concentration. The character of the convection is discussed in terms of solutal and thermosolutal convection, and a convection criterion is proposed which combines the solutal Rayleigh number, Ra s , and the thermal Rayleigh number, Ra T .

A numerical model is developed to simulate the temperature field, the thermosolutal convection, the solute segregation and the growth interface morphology during the growth of ZnTe crystal from Te rich solution by the temperature gradient solution growth (TGSG) technique. Effects of the temperature gradient on the transport phenomena, the growth interface morphology and the growth rate are examined. The influences of the latent heat and the thermal conductivity of ZnTe crystal on the transport phenomena and the growth interface are also discussed. We find that the mass transfer of ZnTe in the solution is very slow because of the low diffusion coefficient and the lack of mixing in the lower part of the solution. During the growth, dilute solution with high density and low growth temperature accumulates in the central region of the growth interface, making the growth interface change into two distinct parts. The inner part is very concave, while the outer part is relatively flat. Growth conditions in front of the two parts of the growth interface are different. The crystalline quality of the inner part of the ingot is predicted to be worse than that of the outer part. High temperature gradient can significantly increase the growth rate, and avoid the diffusion controlled growth to some extent.

Under a NASA (National Aeronautics and Space Agency)-ESA (European Space Agency) collaborative research project, MICAST (Microstructure formation in casting of technical alloys under a diffusive and magnetically controlled convection conditions), three Al-7 wt% Si samples (MICAST-6, MICAST-7 and MICAST2-12) were directionally solidified aboard the International Space Station (ISS) to determine the effect of mitigating convection on the primary dendrite array morphology. MICAST-6 was processed with a step-increase in the growth speed from 5 to 50 µm s−1, MICAST-7 with a step-decrease from 20 to 10 µm s−1, and MICAST2-12 with constant speed of 40 µm s−1. Nearest-neighbor primary dendrite arm spacings and primary dendrite trunk diameters were measured on transverse sections taken at approximately 5 mm intervals along the length of the MICAST samples. In MICAST samples, especially in the steady-state growth regime, the observed primary dendrite nearest-neighbor spacings show a good agreement with predictions from the Hunt-Lu numerical model. The maximum to minimum (highest 10% to lowest 10%) nearest-neighbor spacing ratio in MICAST samples is 2.10 ± 0.27 in agreement with Hunt-Lu model, which assumes pure diffusive transport. Trunk diameters in MICAST samples also agree well with predictions from a coarsening based model. The terrestrial-grown equivalent samples, on the other hand, display smaller nearest-neighbor spacing, and larger primary dendrite trunk diameters than those predicted from the models. Thermosolutal convection appears to increase the dendrite tip radius, causing the trunk diameter to increase, while simultaneously reducing the primary dendrite spacing. This requires verification-experiments involving directional solidification followed by rapid quenching of the liquid-solid interface in metallic alloys in a low gravity environment. The International Space Station currently does not have on-board hardware to conduct such experiments.

Hypoeutectic Al-7 wt .% Si alloys were directionally solidified vertically downward in cylindrical molds that incorporated an abrupt cross-section decrease (9.5 mm to 3.2 mm diameter) which, after 5 cm, reverted back to 9.5 mm diameter in a Bridgman furnace; two constant growth speeds and thermal gradients were investigated. Thermosolutal convection and cross-section-change-induced shrinkage flow effects on macrosegregation were investigated. Dendrite clustering and extensive radial macrosegregation was seen, particularly in the larger cross-sections, before contraction and after expansion, this more evident at the lower growth speed. This alloy shows positive longitudinal macrosegregation near cross-section decrease followed by negative macrosegregation right after it; the extent of macrosegregation, however, decreases with increasing growth speed. Primary dendrite steepling intensified as solidification proceeded into the narrower section and negative longitudinal macrosegregation was seen on the re-entrant shelves at expansion. A two-dimensional model accounting for both shrinkage and thermo-solutal convection was used to simulate solidification and the resulting mushy-zone steepling and macrosegregation. The experimentally observed longitudinal and radial macrosegregation associated with the cross-section changes during directional solidification of an Al–7Si alloy is well captured by the numerical simulations.

The residual accelerations that are typically present in microgravity environments (g-jitters) contain a broad spectrum of frequencies and may be modeled as stochastic processes. Their effects on the quality of the semiconductor crystals are analyzed here quantitatively with direct numerical simulation. In particular we focus on the dopant segregation effects due to thermosolutal convection as a function of the parameters characterizing the statistics of the stochastic force. The numerical simulation is specified for material parameters of two doped semiconductors (Ge:Ga and GaAs:Se) in realistic conditions of actual microgravity environments. As a general result, we show that the segregation response is strongly dominated by the low-frequency part of the g-jitter spectrum. In addition, we develop a simplified model of the problem based on linear response theory that projects the dynamics into very few effective modes. The model captures remarkably well the segregation effects for an arbitrary time-dependent acceleration of small amplitude, while it implies an enormous reduction of computer demands. This model could be helpful to analyze results from real accelerometric signals and also as a predictive tool for experimental design.

Experiments are carried to investigate free dendritic growth of succinonitrile–acetone alloys in an undercooled melt. The measurements include the steady dendrite tip velocity and radius, the non-axisymmetric amplitude coefficient of the fins near the tip, and the envelope width, projection area, and contour length of the sidebranch structure far from the tip. It is found that the measured dendrite tip growth Peclet numbers agree well with the predictions from a stagnant film model that accounts for thermosolutal convection in the melt. The measured tip selection parameter, σ ⁎ , is verified to be independent of the alloy composition, but shows a strong dependence on the imposed undercooling. The universal amplitude coefficient, A 4 , is measured to be equal to 0.004, independent of the undercooling, but the early onset of sidebranching prevents its accurate determination for more concentrated alloys. For the self-similar sidebranch structure far from the tip, scaling laws are obtained for the measured geometrical parameters. While melt convection causes some widening of the sidebranch envelope, and the early onset of sidebranching for alloy dendrites results in a 25% upward shift of the envelope width, the projection area and, hence, the mean width of a sidebranching dendrite, as well as its contour length in the sidebranch plane, obey universal power laws that are independent of the convection intensity and the alloy composition.

Three Ga1−xInxSb samples with compositions x = 0.04 , 0.1 and 0.2 have been solidified by the vertical Bridgman method. The position and shape of the solid–liquid interface has been marked by electrical pulses all along the growth and revealed by subsequent metallography. The axial and radial segregation of the In has been measured by chemical analysis of the solid. The results show that the effect of the chemical segregation, coupled to thermosolutal convection, leads to huge deformations of the solid–liquid interface, with interface curvature even larger than the sample diameter. A sharp increase of the chemical composition is simultaneously observed in the most concentrated samples and interface destabilization occurs quickly. Interpretation of these results involves a strong coupling of the thermal, hydrodynamical and chemical fields.

A numerical simulation of the travelling heater method (THM) process in the growth of HgTe is carried out. The whole system (furnace, ampoule and charge) is taken into account in the frame of a quasi-steady-state model. The mass conservation condition for the solute in the liquid zone permits the determination of the rate of advance of the crystallisation isotherm as a function of the heater position. We claim to study the evolution of different magnitudes along the growth process, searching for the physical reasons which could be at the origin of defects in the form of thin layers observed in some growing experiences. To solve the governing equations of fluid flow, heat transfer and mass transport we have made use of a commercial code which can run in a PC. The simulation is made by using a three-level strategy, which allows the reduction of the computational effort. In the first level, heat transport is assumed to be by conduction, convection and radiation between the furnace and the ampoule, and by conduction through the ampoule wall, coating, solid and liquid zones. The temperature calculated at this level in the air/ampoule boundary is used as boundary condition for the second and third level. In these two levels the ampoule and its content are studied in detail. Convection in the liquid zone is considered at the second level and thermosolutal convection is finally included at the third level. The analysis of the incoming/outcoming heat flux per second through the ampoule for the whole system shows that the lower part of the ampoule exhibits some ineffectiveness for the heat evacuation at certain positions of the growth run, depending on thermal properties of the whole system and the particular material to be grown. As a consequence, the growth rate suffers a significant variation just for these positions of the heater. From these considerations a plausible interpretation has been proposed to understand the apparition of solvent inclusions in the form of thin layers when a material as HgTe is grown by the THM method.

A tridimensional finite-element model was developed to calculate the thermosolutal convection and macrosegregation during the solidification of dendritic alloys. A single set of conservation equations is solved in the mushy zone, all-liquid, and all-solid regions without internal boundary conditions. The model is applied to simulate the directional solidification of a Pb–Sn alloy in cylinders of square and circular cross section. The calculations are started from an all-liquid state and the evolution of convection, solute and energy transport, and the mushy zone growth are followed in time. The results show details of the channels, which result in freckles, that are not observable in existing two-dimensional simulations. Several qualitative features of channels and freckles previously observed in experiments with transparent systems, like chimney convection, preference of channels to be on surfaces, and enhanced solid growth at the channel mouth (“volcanoes”) are successfully reproduced.

A mathematical model of the dendritic solidification of multicomponent alloys, that includes thermosolutal convection and macrosegregation, is presented. The model is an extension of one previously developed for binary alloys. Numerical simulations are given for ternary and quaternary Ni-base alloys, and the evolution of macrosegregation during solidification is studied. The results show that the segregation patterns vary greatly with cooling conditions, adopting several shapes and levels of intensity. Calculations of segregation in rectangular molds and in molds with smooth and abrupt variations of the cross sections exhibit significant differences in the distribution of macrosegregation due to the change in geometry. In addition, the segregation patterns are found to be particularly sensitive to the values of the equilibrium partition coefficients of the alloy components.

A comparative study of thermosolutal convection was carried out by growing lead bromide by silver bromide and studied the transparent Bridgeman furnace. We doped the high purity lead bromide by silver bromide and studied the microsegregation of silver in the matrix of the crystal. Theories based on two extremes: complete diffusive or convective transport did not agree with the experimental data. X-ray rocking curves and contour scans showed that increasing solutal convection deteriorated the crystal quality.

The effect of a forced Couette flow, parallel to a horizontal crystal-melt interface during directional solidification of an alloy of lead containing tin, on the onset of convective and morphological instabilities, is calculated numerically via a linear stability analysis. Such a flow does not affect perturbations with wave vectors perpendicular to the flow. For perturbations with wave vectors parallel to the flow, the onset of morphological instability is somewhat suppressed and thermosolutal convection is greatly suppressed. When instabilities occur, they are oscillatory and correspond to travelling waves. For values of the crystal growth velocity for which mixed morphological and convective modes occur, the presence of a forced flow produces sufficient decoupling to allow otherwise degenerate branches to be identified.

A comparative experimental study of thermal and thermosolutal convection is carried out by solidifying a concentrated Ge-Si binary system and a dilute Ge-Ga system in a new Bridgman furnace where radial thermal gradients have been minimized and well characterized. Very different solutal boundary layer extents (δ GeSi > 3 cm, δ Gega ≦ 2 mm) are found for the two systems solidified under the same thermal conditions. Simple analytical hydrodynamic models are then used to explain these results. It is demonstrated that the larger boundary layer extent observed for Ge-Si and the corresponding pure diffusive transport regime are the result of the stabilizing effect of the longitudinal solutal gradient in this system. It is also shown that Hart's analytical model [J. Fluid Mech, 49 (1971) 279] can be adapted to describe the thermal/solutal coupling of the fluid flow in crystal growth configurations and therefore to predict, in a first approximation, the segregation behaviour in the crystals through a boundary layer model [Favier, Acta Met. 29 (1981) 197, 205].