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At least 1,657 records · Page 92

Crystal Growth of II-VI Semiconducting Alloys by Directional Solidification

This research study is investigating the effects of a microgravity environment during the crystal growth of selected II-VI semiconducting alloys on their compositional, metallurgical, electrical and optical properties. The on-going work includes both Bridgman-Stockbarger and solvent growth methods, as well as growth in a magnetic field. The materials investigated are II-VI, Hg(1-x)Zn(x)Te, and Hg(1-x)Zn(x)Se, where x is between 0 and 1 inclusive, with particular emphasis on x-values appropriate for infrared detection and imaging in the 5 to 30 micron wavelength region. Wide separation between the liquidus and solidus of the phase diagrams with consequent segregation during solidification and problems associated with the high volatility of one of the components (Hg), make the preparation of homogeneous, high-quality, bulk crystals of the alloys an extremely difficult nearly an impossible task in a gravitational environment. The three-fold objectives of the on-going investigation are as follows: (1) To determine the relative contributions of gravitationally-driven fluid flows to the compositional redistribution observed during the unidirectional crystal growth of selected semiconducting solid solution alloys having large separation between the liquidus and solidus of the constitutional phase diagram; (2) To ascertain the potential role of irregular fluid flows and hydrostatic pressure effects in generation of extended crystal defects and second-phase inclusions in the crystals; and, (3) To obtain a limited amount of "high quality" materials needed for bulk crystal property characterizations and for the fabrication of various device structures needed to establish ultimate material performance limits. The flight portion of the study was to be accomplished by performing growth experiments using the Crystal Growth Furnace (CGF) manifested to fly on various Spacelab missions.

Lehoczky, Sandor L.↗

Crystal Growth of ZnSe and Related Ternary Compound Semiconductors by Vapor Transport

Complete and systematic ground-based experimental and theoretical analyses on the Physical Vapor Transport (PVT) of ZnSe and related ternary compound semiconductors have been performed. The analyses included thermodynamics, mass flux, heat treatment of starting material, crystal growth, partial pressure measurements, optical interferometry, chemical analyses, photoluminescence, microscopy, x-ray diffraction and topography as well as theoretical, analytical and numerical analyses. The experimental results showed the influence of gravity orientation on the characteristics of: (1) the morphology of the as-grown crystals as well as the as-grown surface morphology of ZnSe and Cr doped ZnSe crystals; (2) the distribution of impurities and defects in ZnSe grown crystals; and (3) the axial segregation in ZnSeTe grown crystals.

Su, Ching-Hua↗

Melt Convection Effects in the Bridgman Crystal Growth of an Alloy Under Microgravity Conditions

The solidification of a dilute bismuth-tin alloy under Bridgman crystal growth conditions is investigated in support of NASA's MEPHISTO space shuttle flight experiment. Computations are performed in two-dimensions with a uniform grid. The simulation includes the species-concentration, temperature and flow fields, as well as conduction in the ampoule. Fully transient simulations have been performed; no simplifying steady state approximations are used. Results are obtained under microgravity conditions for pure bismuth, and Bismuth-0.1 at.% Sn and Bi-1.0 at.% Sn alloys. The concentration dependence of the melting temperature is neglected; the solid/liquid interface temperature is assumed to be the melting temperature of pure bismuth for all cases studied. For the Bi-1.0 at.% Sn case the results indicate that a secondary convective cell, driven by solutal gradients, forms near the interface. The magnitude of the velocities in this cell increases with time; this causes increasing solute segregation at the liquid/solid interface.

Simpson James E.↗

Repartitioning of NaCl and Protein Impurities in Lysozyme Crystallization

Nonuniform precipitant and impurity incorporation in protein crystals can cause lattice strain and, thus, possibly decrease the X-ray diffraction resolution. To address this issue, a series of crystallization experiments were carried out, in which initial supersaturation, NaCl concentration, protein purity level and crystallized fraction were varied. Lysozyme and protein impurities, as well as sodium and chloride were independently determined in the initial solution, supernatant and crystals. The segregation coefficients for Na(+) and Cl(-) were found to be independent of supersaturation and NaCl concentration, and decreased with crystallized fraction/crystal size. Numerical evaluation of the extensive body of data, based on a nucleation-growth- repartitioning model, suggests a core of approx. 40 microns in which salt is incorporated in much greater concentrations than during later growth. Small crystals containing higher amounts of incorporated NaCl also had higher protein impurity contents. This suggests that the excess salt is associated with the protein impurities in the core. X-ray topography revealed strain fields in the center of the crystals comparable in size to the inferred core. The growth rates of crystals smaller than 30-40 pm in size were consistently 1.5-2 times lower than those of larger crystals, presumably due to higher chemical potentials in the core.

Vekilov, Peter G.↗

Effects of G-Jitter on Directional Solidification of a Binary Alloy

A study of directional solidification of a weak binary alloy (specifically, Bi - 1 at% Sn) based on the fixed grid single domain approach is being undertaken. The enthalpy method is used to solve for the temperature field over the computational domain including both the solid and liquid phases; latent heat evolution is treated with the aid of an effective specific heat coefficient. A source term accounting for the release of solute into the liquid during solidification has been incorporated into the solute transport equation. The vorticity-stream function formulation is used to describe thermo-solutal convection in the liquid region. In this paper we present a numerical simulation of g-jitter. A background gravity of 1 microgram has been assumed, and new results for the effects of periodic disturbances over a range of amplitudes and frequencies on solute field and segregation have been presented.

Benjapiyaporn, C.↗

In-Situ X-Ray Microscopy of Phase and Composition Distributions in Metal Alloys During Solidification

This research applies a state of the art X-ray Transmission Microscope, to image the solidification of metallic or semiconductor alloys in real-time. By employing a hard x-ray source with sub-micron dimensions, resolutions of up to 3 gm can be obtained with magnifications of over 800 X. Specimen growth conditions were optimized and the best imaging technologies applied to maintain x-ray image resolution, contrast and sensitivity. In addition, a special furnace design is required to permit controlled growth conditions and still offer maximum resolution and image contrast. We have successfully imaged in real-time: interfacial morphologies, phase growth, coalescence, incorporation of phases into the growing interface, and the solute boundary layer in the liquid at the solid-liquid inter-face. We have also measured true local growth rates and can evaluate segregation structures in the solid; a form of in-situ metallography. Composition gradients within the specimen cause vafiations in absorption of the flux such that the final image represents a spatial integral of composition (or thickness). During this study, the growth of secondary phase fibers and lameilae from eutectic and monotectic alloys have been imaged during solidification, in real-time, for the first time in bulk metal alloys. Keywords: x-ray, microscope, solidification, microfocus, real-time, microstructure

Kaukler, William F.↗

Real-Time Investigation of Solidification of Metal Matrix Composites

Casting of metal matrix composites can develop imperfections either as non- uniform distributions of the reinforcement phases or as outright defects such as porosity. The solidification process itself initiates these problems. To identify or rectify the problems, one must be able to detect and to study how they form. Until, recently this was only possible by experiments that employed transparent metal model organic materials with glass beads to simulate the reinforcing phases. Recent results obtained from a Space Shuttle experiment (using transparent materials) will be used to illustrate the fundamental physics that dictates the final distribution of agglomerates in a casting. We have further extended this real time investigation to aluminum alloys using X-ray microscopy. A variety of interface-particle interactions will be discussed and how they alter the final properties of the composite. A demonstration of how a solid-liquid interface is distorted by nearby voids or particles, particle pushing or engulfment by the interface, formations of wormholes, Aggregation of particles, and particle-induced segregation of alloying elements will be presented.

Kaukler, William↗

Low Temperature Photoluminescence of PVT Grown ZnSe and ZnSeTe

ZnSe and ZnSeTe single crystals were grown by physical vapor transport (PVT) technique horizontally and vertically. The grown ZnSe and ZnSeTe single crystals were characterized by low temperature photoluminescence at 5 to 10 K using the 3.4 eV emission of an argon laser. The intensity of the sharp near band edge defect lines at 2.799, 2.783 eV and the intrinsic free exciton line at 2.802 eV were mapped on various crystal surfaces with different orientations to the gravitational field. The results show the effects of gravity vector orientation on the defect segregation. Comparison of the photoluminescence spectra of the ZeSe crystal before and after annealing in the Zn vapor shows that the 2.783 eV line of ZnSe crystal is related to the zinc vacancy. The photoluminescence spectra of the ternary ZnSeTe crystal were characterized by a single broad band from 2.2 to 2.4 eV, with a Full Width at Half Maximum (FWHM) of about 100 meV. The temperature dependence of the peak position and intensity were determined from 7 to 150 K.

Wang, Ling Jun↗

The Role of Marangoni Convection for the FZ-Growth of Silicon

Fluctuations of the electrical resistivity due to inhomogeneous dopant distribution are still a serious problem for the industrial processing yield of doped silicon crystals. In the case of silicon floating-zone growth, the main sources of these inhomogeneities are time- dependent flows in the liquid phase during the growth process. Excluding radio frequency (RF) induced convection, buoyancy and thermocapillary (Marangoni) convection are the two natural reasons for fluid flow. Both originate from temperature/concentration gradients in the melt, buoyancy convection through thermal/concentrational volume expansion, and thermocapillary convection through the temperature/concentration dependence of the surface tension. To improve the properties of grown crystals, knowledge of the strength, the characteristic, and the relation of these two flow mechanisms is essential. By the use of microgravity, the effect and the strength of buoyancy (gravity dependent) and thermocapillary (gravity independent) convection can be separated and clarified. Applying magnetic fields, both convective modes can be influenced: fluid flow can either be damped (static magnetic fields) or overlaid by a regular flow regime (rotating magnetic fields). Two complementary approaches have been pursued: Silicon full zones (experiments on the German sounding rockets TEXUS 7, 12, 22, 29, and 36) with the maximum temperature at half of the zone height and silicon half zones (experiments on the Japanese sounding rockets TR-IA4 and 6) with the maximum temperature at the top of the melt. With the full zone arrangement, the intensity and the frequency of the dopant striations could be determined and the critical Marangoni number could be identified. The half zone configuration is suited to classify the flow pattern and to measure the amplitude and the frequency of temperature fluctuations in the melt by inserting thermocouples or temperature sensors into the melt. All experiments have been carried out in monoellipsoid mirror furnaces. Typical zone geometries are approx. 8 to 14 mm in diameter and height. The crystals grown under microgravity are compared to crystals grown in static axial magnetic fields (B<5 tesla) and in transversal rotating magnetic fields (B<7.5 mT / f=50 Hz). Experimental results are completed by 3D numerical simulations: the obtained temperature and concentration distribution in the melt confirm the damping effect of rotating magnetic fields and explain the change in the radial segregation under static magnetic fields.

Dold, P.↗

Double Diffusive Convection in Materials Processing

A great number of crystals grown in space are plagued by convective motions which contribute to structural flaws. The character of these instabilities is not well understood but is associated with density variations in the presence of residual gravity (g-jitter). As a specific example, past HgCdTe crystal growth space experiments by Lehoczky and co-workers indicate radial compositional asymmetry in the grown crystals. In the case of HgCdTe the rejected component into the melt upon solidification is HgTe which is denser than the melt. The space grown crystals indicate the presence of three dimensional flow with the heavier HgTe-rich material clearly aligned with the residual gravity (0.55-1.55 micro g) vector. This flow stems from double-diffusive convection, namely, thermal and solutal buoyancy driven flow in the melt. The study of double-diffusive convection is multi-faceted and rather vast. In our investigation, we seek to focus on one specific aspect of this discipline that is of direct relevance to materials processing especially crystal growth, namely, the side ways heating regime. This problem has been widely studied, both experimentally and numerically, in the context of solar ponds wherein the system is characterized by a linear salt (solutal) gradient with an imposed lateral temperature gradient. The induced flow instabilities arise from the wide disparity between the fluid thermal diffusivity and the solute diffusivity. The extension of the analysis to practical crystal growth applications has however not been rigorously made and understood. One subtle but important difference in crystal growth systems is the fact that die system solute gradient is non-linear (typically exponential). Besides, the crystal growth problem has the added complexities of solidification, both lateral and longitudinal thermal gradients and segregation phenomena in systems where binary and ternary compounds are being grown. This paper treats the side ways heating problem alone in a model fluid system. Results from detailed numerical calculations, mainly two dimensional are provided. The interactions between a non-linear solute gradient and an imposed transverse thermal gradient are investigated. The buoyancy effects are treated in the traditional Boussinesq approximation and also in a more complete density formulation to address recent concerns of the first approach especially in simulations of the system response in a reduced gravity environment. Detailed flow, temperature and solute field plots along with heat and mass transfer results are presented in the paper. Implications to practical crystal growth systems as discerned from the modeling results are also explored and reported.

Ramachandra, Narayanan↗

Directional Solidification and Characterization of Hg(0.89) Mn(0.11)Te

Two boules of Hg(0.89)Mn(0.11)Te(MMT) were solidified using the vertical Bridgman-Stockbarger method. Translation rates of 0.09 and 0. 18 microns/s were used. The influence of growth rate on axial compositional homogeneity in the MMT boules was evaluated experimentally by conducting precision density measurements on radial slices taken from each boule. In addition, Plane Front Solidification theory and segregation coefficient (k) data for the Hg(1-x)Mn(x)Te system were used to fit theoretical composition profiles to the measured MMT axial composition profiles. The strong correlation between the measured and calculated MMT axial composition profiles indicates diffusion dominated axial solute redistribution in the boules under the applied growth conditions. The analysis of the MMT axial composition profiles by Plane Front Solidification theory allowed the calculation of the effective diffusion coefficient (D(eff) = 3.5 x l0(exp -5) sq cm/s). The k-values for the Hg(1-x)Mn(x)Te system and the D(sub eff) - value were then used to verify that both boules were solidified under conditions which did not exceed the Constitutional Supercooling Criteria under ideal conditions. Finally, a preliminary examination of the radial compositional variation in each MMT was made using Fourier Transform Infra-Red Spectroscopy (FTIR). The radial homogeneity in the MMT boules was found to be comparable for both translation rates.

Price, M. W.↗

Control of Meridional Flow in Circular Cylinders by a Travelling Axial Magnetic Field

Convective flow in a Bridgman or float zone configuration significantly affects the interface shape and segregation phenomena. While the primary causative factor for this flow is buoyancy induced convection in an enclosed Bridgman melt, the presence of a free surface gives rise to surface tension driven flows in the floating zone processing of melts. It is of interest to curtail these flows in order to realize near quiescent growth conditions that have shown to result in crystals with good longitudinal and radial homogeneity and thereby of better overall quality. While buoyancy effects can be reduced by careful processing in a low gravity (space) environment, the reduction of Marangoni flows due to surface tension variations is not that straight forward. Attempts have been made with some limited success with the use of external fields to affect the melt thermo-fluid behavior. The use of a static magnetic field that reduces convective contamination through the effects of a non-intrusively induced, dissipative Lorentz force in an electrically conducting melt is one such approach. Experiments have shown that axial fields of the order of 5 Tesla can significantly eliminate convection and yield close to diffusion limited crystal growth conditions. The generation and use of such high magnetic fields require substantial hardware and incur significant costs for its operation. Lately, the use of rotating magnetic fields has been tested in semiconductor crystal growth. The method is fairly well known and commonly used in metal processing but its adaptation to crystal growth of semiconductors is fairly recent. The elegance of the technique rests in its low power requirement (typically 10-20 milli-Tesla at 50-400 Hz) and its efficacy in curtailing deleterious temperature fluctuations in the melt. A rotating magnetic field imposes a rotational force and thereby induces a circulation within the melt that tends to dominate other sporadic convective effects. Thus a known low level of convective flow is introduced into the system. A new novel variation of the Lorentz force mechanism is proposed and investigated in this study. Since one of the desired process conditions in melt crystal growth is the minimization of convective effects, this investigation examines the use of an external field of magnetic origin to counteract existing convective flow within the melt. This is accomplished by utilizing a running or traveling axial magnetic wave in the system. The concept is similar to the use of vibrational means in order to induce streaming flows that oppose buoyant or surface tension driven convection in the system. The rotation direction as well as the magnitude (strength) of this circulation can be easily controlled by external inputs thus affording a direct means of controlling the developing shape of the crystallizing front (interface). The theoretical model of this technique is fully developed and presented in this paper. Results from the solution of the developed governing equations and boundary conditions are also presented. An experimental demonstration of the concept is presented through the suppression of natural convective flow in a mercury column. Implications to crystal growth systems will be fully explored in the final manuscript.

Mazuruk, K.↗

Influence of Applied Thermal Gradients and a Static Magnetic Field on Bridgman-Grown GeSi Alloys

The effect of applied axial and radial thermal gradients and an axial static magnetic field on the macrosegregation profiles of Bridgman-grown GeSi alloy crystals has been assessed. The axial thermal gradients were adjusted by changing the control setpoints of a seven-zone vertical Bridgman furnace. The radial thermal gradients were affected by growing samples in ampoules with different thermal conductivities, namely graphite, hot-pressed boron nitride (BN), and pyrolytic boron nitride (PBN). Those samples grown in a graphite ampoule exhibited radial profiles consistent with a highly concave interface and axial profiles indicative of complete mixing in the melt. The samples grown in BN and PBN ampoules had less radial variation. Axial macrosegregation profiles of these samples fell between the predictions for a completely mixed melt and one where solute transport is dominated by diffusion. All of the samples were grown on Ge seeds. This resulted in a period of free growth until the Si concentration in the solid was in equilibrium with the Si concentration in the liquid. The length of crystal grown during this period was inversely proportional to the applied axial thermal gradient. Several samples were grown in an axial 5 Tesla magnetic field. Measured macroscopic segregation profiles on these samples indicate that the magnetic field did not, in general, reduce the melt flow velocities to below the growth velocities.

Volz, M. P.↗

Airborne Observations of Aerosol Emissions from F-16 Aircraft

We presented results from the SASS Near-Field Interactions Flight (SNIF-III) Experiment which was conducted during May and June 1997 in collaboration with the Vermont and New Jersey Air National Guard Units. The project objectives were to quantify the fraction of fuel sulfur converted to S(VI) species by jet engines and to gain a better understanding of particle formation and growth processes within aircraft wakes. Size and volatility segregated aerosol measurements along with sulfur species measurements were recorded in the exhaust of F-16 aircraft equipped with F-100 engines burning fuels with a range of fuel S concentrations at different altitudes and engine power settings. A total of 10 missions were flown in which F-16 exhaust plumes were sampled by an instrumented T-39 Sabreliner aircraft. On six of the flights, measurements were obtained behind the same two aircraft, one burning standard JP-8 fuel and the other either approximately 28 ppm or 1100 ppm S fuel or an equal mixture of the two (approximately 560 ppm S). A pair of flights was conducted for each fuel mixture, one at 30,000 ft altitude and the other starting at 35,000 ft and climbing to higher altitudes if contrail conditions were not encountered at the initial flight level. In each flight, the F-16s were operated at two power settings, approx. 80% and full military power. Exhaust emissions were sampled behind both aircraft at each flight level, power setting, and fuel S concentration at an initial aircraft separation of 30 m, gradually widening to about 3 km. Analyses of the aerosol data in the cases where fuel S was varied suggest results were consistent with observations from project SUCCESS, i.e., a significant fraction of the fuel S was oxidized to form S(VI) species and volatile particle emission indices (EIs) in comparably aged plumes exhibited a nonlinear dependence upon the fuel S concentration. For the high sulfur fuel, volatile particle EIs in 10-second-old-plumes were 2 to 3 x 10 (exp 17) / kg of fuel burned and exhibited no obvious trend with engine power setting or flight altitude. In contrast, about 8-fold fewer particles were observed in similarly aged plumes from the same aircraft burning fuel with 560 ppm S content and EIs of 1 x 10(exp 15)/ kg of fuel burned were observed in the 28 ppm S fuel case. Moreover, data recorded as a function of plume age indicates that formation and growth of the volatile particles proceeds more slowly as the fuel S level is reduced. For example, ultrafine particle concentrations appear to stabilize within 5 seconds after emission in the 1100 ppm S cases but are still increasing in 20-second old plumes produced from burning the 560 ppm S fuel.

Anderson, B. E.↗

Determination of the Solid/Liquid Interface Shape and Resultant Radial Homogeneity in Directionally Solidified Hg(0.89)Mn(0.11)Te

Directional solidification and interrupted directional solidification experiments were used to determine tile shape of the solid/liquid interface and the resultant radial homogeneity in Hg(0.89)Mg(0.11)Te. For directionally solidified samples solidified at a rate of 0.09 microns/sec in a thermal gradient of 83 C/cm, a maximum of 0.006 molar percent MnTe radial variation across the Hg0.89)Mn(0.11)Te boules at specific locations was determined using an FTIR technique. This FTIR evaluation of the radial homogeneity also indicated an asymmetrical, convex interface shape during solidification. The asymmetrical, convex shape of the growth interface was confirmed by interrupted directional solidification experiments. These were performed under the same growth conditions as the normally completed directional solidification experiments except that the samples were quenched before the final growth transient was reached. In these experiments, etching and scanning X-ray fluorescence were used to reveal the shape of the solid/liquid interface. Microprobe analysis of composition gradients across the interface was used to confirm the authors' previous work in evaluating the segregation coefficient of Hg(0.89)Mn(0.11)Te alloy. Microprobe analysis of the interface region of the interrupted growth sample revealed a dendritic structure containing secondary and tertiary dendritic arms.

Price, M. W.↗

Detached Growth of Germanium and Germaniumsilicon

Up to now, detached growth was observed mainly under microgravity, i.e. under the absence of hydrostatic pressure that hinders the formation of a free melt meniscus. the detached growth of germanium doped with gallium was obtained under 1 g conditions, the growth was performed in quartz-glass ampoule. Part of the crystal grew without wall contact, the detached growth was observed in-situ with a CCD-camera as well as after the growth process in form of growth lines and the formation of <111> facets on the crystal surface. GeSi crystal (oriientation: <111>, maximum silicon content: 4 at%, seed material: Ge) was grown in a pBN crucible (excluding the possibility of in-situ monitoring of the growth process). The grown crystal exhibits three growth facets, indicating also wall free growth. Surface analysis of the crystals (NDIC, SEM) and characterization of crystal segregation (EDAX, resistivity measurement) and defect structure (EPD, x-ray diffraction measurements) will be presented.

Dold, P.↗

Project Description and Publications List for UAH CMMR

This research combines a state of the art X-ray Transmission Microscope, XTM, with a specially designed x-ray transparent horizontal Bridgman furnace to image (with resolutions up to 3 micrometers) the solidification of metal alloys in real-time. The objective is to obtain real-time dynamic data to provide direct measure of the solute profile in the liquid, phase coalescence and growth in the liquid, and the detailed interface morphology (e,g., dendrites and cells) during solidification. We are also enhancing the XTM data with precise solid-liquid interfacial temperature and the thermal gradient measurement techniques, and working on the application of this technology to the study of the fundamentals of solidification in microgravity. Over the last several years we have successfully imaged in real-time: interfacial-morphologies, phase growth, coalescence, incorporation of phases into the growing interface, and the solute boundary layer in the liquid at the solid-liquid interface. We have also measured true local growth rates and can evaluate segregation structures in the solid. Interfacial undercoolings are being measured either with a special Seebeck furnace or with micro-thermocouple arrays we are developing. These later techniques are presently being incorporated with the XTM furnace. This last year emphasized the investigation of the solute layer in the melt during solidification. Methods were developed to quantify the solute concentrations using x-ray absorption and to compare to predictions from simulations. In addition, work is being completed on a brass-board portable XTM that incorporates a vertical Bridgman furnace.

Kaukler, William F.↗

Growth of Compound Semiconductors in a Low Gravity Environment: Microgravity Growth of PbSnTe

The growth of the alloy compound semiconductor lead tin telluride (PbSnTe) was chosen for a microgravity flight experiment in the Advanced Automated Directional Solidification Furnace (AADSF), on the United States Microgravity Payload-3 (USNP-3) in February, 1996 and on USNW- 4 in November, 1997. The objective of these experiments was to determine the effect of the reduction in convection, during the growth process, brought about by the microgravity environment. The properties of devices made from PbSnTe, an alloy of PbTe and SnTe, are dependent on the ratio of the elemental components in the starting crystal. Compositional uniformity in the crystal is only obtained if there is no significant mixing in the liquid during growth. The technological importance of PbSnTe lies in its band gap versus composition diagram which has a zero energy crossing at approximately 40% SnTe. This facilitates the construction of long wavelength (greater than 6 gm) infrared detectors and lasers. The properties and utilization of PbSnTe are the subject of other papers. 1,2 PbSnTe is also interesting from a purely scientific point of view. It is, potentially, both solutally and thermally unstable due to the temperature and density gradients present during growth. Density gradients, through thermal expansion, are imposed in directional solidification because temperature gradients are required to extract heat. Solutal gradients occur in directional solidification of alloys due to segregation at the interface. Usually the gradients vary with both experiment design and inherent materials properties. In a simplified one dimensional analysis with the growth axis parallel to the gravity vector, only one of the two instabilities work at a time. During growth, the temperature in the liquid increases ahead of the interface. Therefore the density, due to thermal expansion, is decreasing in that direction. However, the phase diagram shows that the lighter SnTe is preferentially rejected at the interface. This causes the liquid density to increase with distance away from the interface.

Fripp, A. L.↗