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Here we report the detection of dust depletion in a misaligned inner disk around UX Tau A using JWST MIRI spectra. Mid-infrared (MIR) continuum "seesaw" variability was detected in this disk by Spitzer and attributed to variable shadows cast on the outer disk by the inner disk. The JWST MIRI spectrum of UX Tau A also shows seesaw variability, but with a significant decrease of emission shortwards of 10 micron to nearly photospheric levels. We argue that UX Tau A's MIR continuum variability is due to depletion of dust in a misaligned inner disk. We speculate that this dust depletion occurs because the inner disk is misaligned from the outer disk, which can disrupt the replenishment of the inner disk from the outer disk. Using contemporaneous measurements of the mass accretion rate of UX Tau A and estimating the amount of dust necessary to produce the MIR excess in the Spitzer observations, we estimate a minimum dust depletion timescale of ~0.1 yr. These observations show that we can indirectly detect the signatures of misaligned inner disks through MIR continuum variability and that in some cases the inner disk may be significantly depleted of dust and become optically thin., Comment: accepted to ApJL

We investigate the problem of designing a minimum cost flow network interconnecting n sources and a single sink, each with known locations in a normed space and with associated flow demands. The network may contain any finite number of additional unprescribed nodes from the space; these are known as the Steiner points. For concave increasing cost functions, a minimum cost network of this sort has a tree topology, and hence can be called a Minimum Gilbert Arborescence (MGA). We characterise the local topological structure of Steiner points in MGAs, showing, in particular, that for a wide range of metrics, and for some typical real-world cost-functions, the degree of each Steiner point is 3., Comment: 19 pages, 7 figures. arXiv admin note: text overlap with arXiv:0903.2124

We investigate the problem of designing a minimum cost flow network interconnecting n sources and a single sink, each with known locations and flows. The network may contain other unprescribed nodes, known as Steiner points. For concave increasing cost functions, a minimum cost network of this sort has a tree topology, and hence can be called a Minimum Gilbert Arborescence (MGA). We characterise the local topological structure of Steiner points in MGAs for linear cost functions. This problem has applications to the design of drains, gas pipelines and underground mine access., Comment: 6 pages, 2 columns, 4 figures

The growth angle that is formed between the side of the growing crystal and the melt meniscus is an important parameter in the detached Bridgman crystal growth method, where it determines the extent of the crystal-crucible wall gap, and in the Czochralski and float zone methods, where it influences the size and stability of the crystals. The growth angle is a non-equilibrium parameter, defined for the crystal growth process only. For a melt-crystal interface translating towards the crystal (melting), there is no specific angle defined between the melt and the sidewall of the solid. In this case, the corner at the triple line becomes rounded, and the angle between the sidewall and the incipience of meniscus can take a number of values, depending on the position of the triple line. In this work, a microscopic model is developed in which the fluid interacts with the solid surface through long range van der Waals or Casimir dispersive forces. This growth angle model is applied to Si and Ge and compared with the macroscopic approach of Herring. In the limit of a rounded corner with a large radius of curvature, the wetting of the melt on the crystal is defined by the contact angle. The proposed microscopic approach addresses the interesting issue of the transition from a contact angle to a growth angle as the radius of curvature decreases.

This investigation involves the comparison of results achieved from three types of crystal growth of germanium and germanium-silicon alloys: Float zone growth, Bridgman growth, and Detached Bridgman growth. The fundamental goal of the proposed research is to determine the influence of containment on the processing-induced defects and impurity incorporation in germanium-silicon (GeSi) crystals (silicon concentration in the solid up to 5%) for three different growth configurations in order to quantitatively assess the improvements of crystal quality possible by detached growth.

Indium iodide (InI) is a promising wide energy band gap nuclear detector material. It is ideal for space experiments because it is non-toxic and has a relatively low melting point of only 351 degrees Centigrade. However, it has been established that melt-grown crystals contain a large amount of second phase inclusions/precipitates. The typical size of inclusions are 1 to 27 microns in diameter, while the volume fraction of all sizes is 300 to 600 parts per million. The SEM-EDS (Scanning Electron Microscopy / Energy Dispersive X-Ray Spectroscopy) analysis of the inclusions has revealed that they all contain oxygen and some contain carbon. At present, under sponsorship of NASA and CASIS (Center for the Advancement of Science in Space), we are conducting ground-based experiments with InI in preparation for the flight experiments to be conducted in the SUBSA (Solidification Using a Baffle in Sealed Ampoules) furnace in the Microgravity Science Glovebox at the International Space Station, planned for the summer/fall of 2017. Earth-based experiments include melt and vapor growth conducted in the SUBSA ground unit, measurements of the volumetric expansion coefficient of the melt, and measurements of the wetting angle of molten InI. Finite element modeling has been conducted to optimize the design of the flight ampoules. Alloying with Tl and Ga has given promising results.

Four different Bridgman growth experiments on Ge:Ga and Ge(sub x)Si(sub 1-x) were performed under microgravity during the FOTON M4 flight in fall 2014 as joint German-Russian experiments. The experiments were also part of the RDGS/ICESAGE project(s) of ESA/NASA on detached growth of Ge and Ge-Si. Three experiments on Ge:Ga investigated different heat and mass transport regimes, i.e. mostly diffusive conditions, flows driven by a rotating magnetic field, and flows driven by vibration. The fourth experiment on Ge(sub 0.98)Si(0.02) investigated detached growth. All four experiments were successful and yielded crystals. Both the Ge-Si experiment and two of the Ge:Ga experiments showed stable detachment from the ampoule wall, although this was not planned for the latter two experiments. The influence of the rotating magnetic field as well as of the vibration was pronounced in the case of the microgram experiments, but dominated by buoyancy convection under 1g.

A series of Ge(sub 1-x) Si(sub x) crystal growth experiments are planned to be conducted in the Low Gradient Furnace (LGF) onboard the International Space Station. The primary objective of the research is to determine the influence of containment on the processing-induced defects and impurity incorporation in germanium-silicon alloy crystals. A comparison will be made between crystals grown by the normal and "detached" Bridgman methods and the ground-based float zone technique. Crystals grown without being in contact with a container have superior quality to otherwise similar crystals grown in direct contact with a container, especially with respect to impurity incorporation, formation of dislocations, and residual stress in crystals. "Detached" or "dewetted" Bridgman growth is similar to regular Bridgman growth in that most of the melt is in contact with the crucible wall, but the crystal is separated from the wall by a small gap, typically of the order of 10-100 microns. Long duration reduced gravity is essential to test the proposed theory of detached growth. Detached growth requires the establishment of a meniscus between the crystal and the ampoule wall. The existence of this meniscus depends on the ratio of the strength of gravity to capillary forces. On Earth, this ratio is large and stable detached growth can only be obtained over limited conditions. Crystals grown detached on the ground exhibited superior structural quality as evidenced by measurements of etch pit density, synchrotron white beam X-ray topography and double axis X-ray diffraction.

A series of Ge(1-x)Si(x) crystal growth experiments are planned to be conducted in the Low Gradient Furnace (LGF) onboard the International Space Station. The experiments are part of the investigation "Influence of Containment on the Growth of Silicon-Germanium" (ICESAGE). The primary objective of the research is to determine the influence of containment on the processing-induced defects and impurity incorporation in germanium-silicon alloy crystals. A comparison will be made between crystals grown by the normal and "detached" Bridgman methods and the ground-based float zone technique. Crystals grown without being in contact with a container have superior quality to otherwise similar crystals grown in direct contact with a container, especially with respect to impurity incorporation, formation of dislocations, and residual stress in crystals. "Detached" or "dewetted" Bridgman growth is similar to regular Bridgman growth in that most of the melt is in contact with the crucible wall, but the crystal is separated from the wall by a small gap, typically of the order of 10-100 microns. Long duration reduced gravity is essential to test the proposed theory of detached growth. Detached growth requires the establishment of a meniscus between the crystal and the ampoule wall. This meniscus can exist over a much larger range of processing parameters in microgravity and the meniscus is more stable under microgravity conditions. The plans for the flight experiments will be described.

A theory describing the shape evolution of detached Bridgman crystals in microgravity has been developed. A starting crystal of initial radius r0 will evolve to one of the following states: Stable detached gap; Attachment to the crucible wall; Meniscus collapse. Only crystals where alpha plus omega is great than 180 degrees will achieve stable detached growth in microgravity. Results of the crystal shape evolution theory are consistent with predictions of the dynamic stability of crystallization (Tatarchenko, Shaped Crystal Growth, Kluwer, 1993). Tests of transient crystal evolution are planned for ICESAGE, a series of Ge and GeSi crystal growth experiments planned to be conducted on the International Space Station (ISS).

In several crystal growth processed based on capillarity, a melt comes into contact with a crucible wall at an angle defined as the contact angle. For molten metals and semiconductors, this contact angle is dependent upon both the crucible and melt material and typical values fall in the range 80-170deg. However, on a microscopic scale, there does not exist a precise and sharp contact angle but rather the melt and solid surfaces merge smoothly and continuously over a distance of up to several micrometers. Accurate modeling requires a more advanced treatment of this interaction. The interaction between the melt and solid surfaces can be calculated by considering two forces: a short-range repulsive force and a longer range (up to a few micrometers) Casimir force. The Casimir force between the two bodies of complex geometry is calculated using a retarded temperature Green's function (Matsubara type) for the photon in the medium. The governing equations are cast in the form of a set of boundary integral equations which are then solved numerically for the case of molten Ge on SiO2. The shape of the molten surface approaching the flat solid body is determined, and the contact angle is defined as the angle between the two surfaces at the microscopically asymptotic distance of 1-2 micrometers. The formulation of this model and the results of the numerical calculations will be presented and discussed.

During the past 40 years, dozens of semiconductor crystal growth experiments have been conducted in space laboratories. The subsequent analysis of the space-grown crystals revealed (i) that weak convection existed in virtually all melt-growth experiments, (ii) de-wetting significantly reduced the level of stress-induced defects, and (iii) particularly encouraging results were obtained in vapor-growth experiments. In 2002, following a decade of ground based research in growing doped Ge and GaSb crystals, a series of crystal growth experiments was performed at the ISS, within the SUBSA (Solidification Using a Baffle in Sealed Ampoules) investigation. Te- and Zn-doped InSb crystals were grown from the melt. The specially designed furnace provided a side-view of the melt and precise seeding measurement of the growth rate. At present, under sponsorship of CASIS (Center for the Advancement of Science in Space, www.iss-casis.org), we are conducting ground-based experiments with indium mono-iodide (InI) in preparation for the "SUBSA II" ISS investigation, planned for 2017. The experiments include: i) Horizontal Bridgman (HB) growth and ii) Vapor Transport (VT) growth. Finite element modeling will also be conducted, to optimize the design of the flight ampoules, for vapor and melt growth.

Aluminum-Lithium alloy 2195 exhibits higher mechanical properties and lower density than aluminum alloy 2219, which is the current baseline material for Space Launch System (SLS) cryogenic tank components. Replacement of Al 2219 with Al-Li 2195 would result in substantial weight savings, as was the case when this replacement was made on the shuttle external tank. A key component of cryogenic tanks are the gores, which are welded together to make the rounded ends of the tanks. The required thicknesses of these gores depend on the specific SLS configuration and may exceed the current experience base in the manufacture of such gores by the stretch forming process. Here we describe the steps taken to enhance the formability of Al-Li 2195 by optimizing the heat treatment and stretch forming processes for gore thicknesses up to 0.75", which envelopes the maximum expected gore thicknesses for SLS tanks. An annealing treatment, developed at Marshall Space Flight Center, increased the forming range and strain hardening exponent of Al-Li 2195 plates. Using this annealing treatment, one 0.525" thick and two 0.75" thick gores were manufactured by the stretch forming process. The annealing treatment enabled the stretch forming of the largest ever cross sectional area (thickness x width) of an Al-Li 2195 plate achieved by the manufacturer. Mechanical testing of the gores showed greater than expected ultimate tensile strength, yield strength, modulus, and elongation values. The gores also exhibited acceptable fracture toughness at room and LN2 temperatures. All of the measured data indicate that the stretch formed gores have sufficient material properties to be used in flight domes.

A series of Ge Si crystal growth experiments are planned to be conducted in the Low 1-x x Gradient Furnace (LGF) onboard the International Space Station. The primary objective of the research is to determine the influence of containment on the processing-induced defects and impurity incorporation in germanium-silicon alloy crystals. A comparison will be made between crystals grown by the normal and "detached" Bridgman methods and the ground-based float zone technique. Crystals grown without being in contact with a container have superior quality to otherwise similar crystals grown in direct contact with a container, especially with respect to impurity incorporation, formation of dislocations, and residual stress in crystals. "Detached" or "dewetted" Bridgman growth is similar to regular Bridgman growth in that most of the melt is in contact with the crucible wall, but the crystal is separated from the wall by a small gap, typically of the order of 10-100 microns. Long duration reduced gravity is essential to test the proposed theory of detached growth. Detached growth requires the establishment of a meniscus between the crystal and the ampoule wall. The existence of this meniscus depends on the ratio of the strength of gravity to capillary forces. On Earth, this ratio is large and stable detached growth can only be obtained over limited conditions. Crystals grown detached on the ground exhibited superior structural quality as evidenced by measurements of etch pit density, synchrotron white beam X-ray topography and double axis X-ray diffraction.

A series of Ge(1-x)Si(x) crystal growth experiments are planned to be conducted in the Low Gradient Furnace (LGF) onboard the International Space Station. The primary objective of the research is to determine the influence of containment on the processinginduced defects and impurity incorporation in germanium-silicon alloy crystals. A comparison will be made between crystals grown by the normal and "detached" Bridgman methods and the ground-based float zone technique. Crystals grown without being in contact with a container have superior quality to otherwise similar crystals grown in direct contact with a container, especially with respect to impurity incorporation, formation of dislocations, and residual stress in crystals. "Detached" or "dewetted" Bridgman growth is similar to regular Bridgman growth in that most of the melt is in contact with the crucible wall, but the crystal is separated from the wall by a small gap, typically of the order of 10-100 microns. Long duration reduced gravity is essential to test the proposed theory of detached growth. Detached growth requires the establishment of a meniscus between the crystal and the ampoule wall. The existence of this meniscus depends on the ratio of the strength of gravity to capillary forces. On Earth, this ratio is large and stable detached growth can only be obtained over limited conditions. Crystals grown detached on the ground exhibited superior structural quality as evidenced by measurements of etch pit density, synchrotron white beam X-ray topography and double axis X-ray diffraction. The plans for the flight experiments will be described.

Solar cells made from directionally solidified silicon cover 57% of the photovoltaic industry's market [1]. One major issue during directional solidification of silicon is the precipitation of foreign phase particles. These particles, mainly SiC and Si3N4, are precipitated from the dissolved crucible coating, which is made of silicon nitride, and the dissolution of carbon monoxide from the furnace atmosphere. Due to their hardness and size of several hundred micrometers, those particles can lead to severe problems during the wire sawing process for wafering the ingots. Additionally, SiC particles can act as a shunt, short circuiting the solar cell. Even if the particles are too small to disturb the wafering process, they can lead to a grit structure of silicon micro grains and serve as sources for dislocations. All of this lowers the yield of solar cells and reduces the performance of cells and modules. We studied the behaviour of SiC particle depots during float-zone growth under an oxide skin, and strong static magnetic fields. For high field strengths of 3T and above and an oxide layer on the sample surface, convection is sufficiently suppressed to create a diffusive like regime, with strongly dampened convection [2, 3]. To investigate the difference between atomically rough phase boundaries and facetted growth, samples with [100] and [111] orientation were processed.

In the photovoltaics industry, the largest market share is represented by solar cells made from multicrystalline silicon, which is grown by directional solidification. During the growth process, the silicon melt is in contact with the silicon nitride coated crucible walls and the furnace atmosphere which contains carbon monoxide. The dissolution of the crucible coating, the carbon bearing gas, and the carbon already present in the feedstock, lead to the precipitation of silicon carbide, and silicon nitride, at later stages of the growth process. The precipitation of Si3N4 and SiC particles of up to several hundred micrometers in diameter leads to severe problems during the wire sawing process for wafering the ingots. Furthermore the growth of the silicon grains can be negatively influenced by the presence of particles, which act as nucleation sources and lead to a grit structure of small grains and are sources for dislocations. If doped with Nitrogen from the dissolved crucible coating, SiC is a semi conductive material, and can act as a shunt, short circuiting parts of the solar cell. For these reasons, the incorporation of such particles needs to be avoided. In this contribution we performed model experiments in which the transport of intentionally added SiC particles and their interaction with the solid-liquid interface during float zone growth of silicon in strong steady magnetic fields was investigated. SiC particles of 7μm and 60μm size are placed in single crystal silicon [100] and [111] rods of 8mm diameter. This is achieved by drilling a hole of 2mm diameter, filling in the particles and closing the hole by melting the surface of the rod until a film of silicon covers the hole. The samples are processed under a vacuum of 1x10(exp -5) mbar or better, to prevent gas inclusions. An oxide layer to suppress Marangoni convection is applied by wet oxidation. Experiments without and with static magnetic field are carried out to investigate the influence of melt convection on the distribution of particles and their incorporation into the crystal. The field strengths applied by a superconducting magnet are 1T, 3T, 4.5T, and 5T. The increase in field strength dampens the melt flow, and so this study provides comparative data to the crystal growth experiment to be carried out onboard the sounding rocket mission TEXUS 51, where purely diffusive growth condition will be achieved under microgravity conditions.

A series of GeSi crystal growth experiments are planned to be conducted in the Low Gradient Furnace (LGF) onboard the International Space Station. An objective of these experiments is to understand the mechanisms of detached Bridgman growth, a process in which a gap exists between the growing semiconductor crystal and the crucible wall. Crystals grown without wall contact have superior quality to otherwise similar crystals grown in direct contact with a container, especially with respect to impurity incorporation, formation of dislocations, and residual stress in crystals. Numerical calculations are used to determine the conditions in which a gap can exist. According to crystal shape stability theory, only some of these gap widths will be dynamically stable. Beginning with a crystal diameter that differs from stable conditions, the transient crystal growth process is analyzed. In microgravity, dynamic stability depends only on capillary effects and is decoupled from heat transfer. Depending on the initial conditions and growth parameters, the crystal shape will evolve towards the crucible wall, towards a stable gap width, or towards the center of the crucible, collapsing the meniscus.

Detached growth, also referred to as dewetted growth, is a Bridgman crystal growth process in which the melt is in contact with the crucible wall but the crystal is not. A meniscus bridges the gap between the top of the crystal and the crucible wall. The meniscus shape depends on the contact angle of the melt with the crucible wall, the growth angle of the melt with respect to the solidifying crystal, the gas pressure differential, the Weber number describing the rotation rate of the crucible, and the Bond number. Only some of the meniscus shapes are stable and the stability criterion is the sign of the second variation of the potential energy upon admissible meniscus shape perturbations. The effects of confined gas volumes above and below the melt and crucible rotation are evaluated. The analysis is applicable to the non-stationary case where the crystal radius changes during growth. Static stability maps (crystal radius versus pressure differential) are obtained for a series of Bond numbers, growth angles and Weber numbers. Also, the specific cases of Ge and InSb, in both terrestrial and microgravity conditions, are analyzed. Stability was found to depend significantly on whether the interior surface was considered to be microscopically rough or smooth, corresponding to pinned or unpinned states. It was also found that all meniscus shapes are statically stable in a microgravity environment.

Detached (or dewetted) Bridgman crystal growth defines that process in which a gap exists between a growing crystal and the crucible wall. Existence of the gap provides several advantages, including no sticking of the crystal to the crucible wall, reduced thermal and mechanical stresses, reduced dislocations, and no heterogeneous nucleation by the crucible. Numerical calculations are used to determine the conditions in which a gap can exist. According to crystal shape stability theory, only some of these gap widths will be dynamically stable. Beginning with a crystal diameter that differs from stable conditions, the transient crystal growth process is analyzed. In microgravity, dynamic stability depends only on capillary effects and is decoupled from heat transfer. Depending on the initial conditions and growth parameters, the crystal shape will evolve towards the crucible wall, towards a stable gap width, or towards the center of the crucible, collapsing the meniscus. The effect of a tapered crucible on dynamic stability is also described.

A series of Ge(1-x)Si(x) crystal growth experiments are planned to be conducted in the Low Gradient Furnace (LGF) onboard the International Space Station. The primary objective of the research is to determine the influence of containment on the processing-induced defects and impurity incorporation in germanium-silicon alloy crystals. A comparison will be made between crystals grown by the normal and "detached" Bridgman methods and the ground-based float zone technique. Crystals grown without being in contact with a container have superior quality to otherwise similar crystals grown in direct contact with a container, especially with respect to impurity incorporation, formation of dislocations, and residual stress in crystals. "Detached" or "dewetted" Bridgman growth is similar to regular Bridgman growth in that most of the melt is in contact with the crucible wall, but the crystal is separated from the wall by a small gap, typically of the order of 10-100 microns. Long duration reduced gravity is essential to test the proposed theory of detached growth. Detached growth requires the establishment of a meniscus between the crystal and the ampoule wall. The existence of this meniscus depends on the ratio of the strength of gravity to capillary forces. On Earth, this ratio is large and stable detached growth can only be obtained over limited conditions. Crystals grown detached on the ground exhibited superior structural quality as evidenced by measurements of etch pit density, synchrotron white beam X-ray topography and double axis X-ray diffraction. The plans for the flight experiments will be described.

Crystals grown without being in contact with a container have superior quality to otherwise similar crystals grown in direct contact with a container, especially with respect to impurity incorporation, formation of dislocations, and residual stress in crystals. "Detached" or "dewetted" Bridgman growth is similar to regular Bridgman growth in that most of the melt is in contact with the crucible wall, but the crystal is separated from the wall by a small gap, typically of the order of 10-100 microns. Ge1-xSix crystals have been repeatedly grown detached in pBN crucibles. Detached-grown crystals exhibited superior structural quality as evidenced by measurements of etch pit density, synchrotron white beam X-ray topography and double axis X-ray diffraction. Experiments have also been conducted to assess the effect of pressure differential across the meniscus in sealed crucibles. The experiments were in agreement with calculations which predicted that stable detachment will only occur in crucibles with a high wetting angle and over a relatively narrow range of pressure differential. Calculations also indicate that the conditions for stable detached growth are greatly expanded in a microgravity environment.

Detached growth, also referred to as dewetted growth, is a Bridgman crystal growth process in which the melt is in contact with the crucible wall but the crystal is not. A meniscus bridges the gap between the top of the crystal and the crucible wall. The Young-Laplace capillary equation was used to calculate the crystal radii of detached states as a function of the pressure differential across the meniscus. The detached states depend on the contact angle of the melt with the crucible wall, the growth angle of the melt with respect to the solidifying crystal, and the Bond number. A static stability analysis was performed on the calculated detached states. The stability criterion was the sign of the second variation of the potential energy upon admissible meniscus shape perturbations. The conditions considered corresponded to the growth of Ge and InSb, in both terrestrial and microgravity conditions. Stability was found to depend significantly on whether the interior surface was considered to be microscopically rough or smooth, corresponding to pinned or unpinned states. It was also found that all meniscus shapes which are single-valued functions of the radius are statically stable in a microgravity environment.

In detached Bridgman growth, a gap exists between the growing crystal and the crucible wall. According to crystal shape stability theory, only specific gap widths will be dynamically stable. Beginning with a crystal diameter that differs from stable conditions, the transient crystal growth process is analyzed. The transient shapes are calculated assuming that the growth angle is constant. Anisotropy and dynamic contact angle effects are considered. In microgravity, dynamic stability depends only on capillary effects and is decoupled from heat transfer. However, heat transfer will influence the crystal-melt interface shape. The local angles and the crystal-melt-vapor triple junction are analyzed and the applicability of the Herring formula is discussed. A potential microgravity experiment is proposed which would enhance our understanding of the detached growth dynamic stability problem.

The Solar Probe Plus mission will launch a spacecraft to the Sun to study it's outer atmosphere. One of the instruments on board will be a Faraday Cup (FC) sensor. The FC will determine solar wind properties by measuring the current produced by ions striking a metal collector plate. It will be directly exposed to the Sun and will be subject to the temperature and radiation environment that exist within 10 solar radii. Conducting grids within the FC are biased up to 10 kV and are used to selectively transmit particles based on their energy to charge ratio. We report on the development of SiC grids. Tests were done on nitrogen-doped SiC starting disks obtained from several vendors, including annealing under vacuum at 1400 C and measurement of their electrical properties. SiC grids were manufactured using a photolithographic and plasma-etching process. The grids were incorporated into a prototype FC and tested in a simulated solar wind chamber. The energy cutoffs were measured for both proton and electron fluxes and met the anticipated sensor requirements.

In detached Bridgman crystal growth, most of the melt is in contact with the ampoule wall, but the crystal is separated from the wall by a small gap, typically 1-100 micrometers. A liquid free surface, or meniscus, bridges across this gap at the position of the melt-crystal interface. Meniscus shapes have been calculated for the case of detached Bridgman growth in cylindrical ampoules by solving the Young-Laplace equation. Key parameters affecting meniscus shapes are the growth angle, contact angle of the meniscus to the ampoule wall, the pressure differential across the meniscus, and the Bond number, a measure of the ratio of gravitational to capillary forces. In general, for specified values of growth and contact angles, solutions exist only over a finite range of pressure differentials. For intermediate values of the Bond number, there are multiple solutions to the Young-Laplace equations. There are also cases where, as a function of pressure differential, existence intervals alternate with intervals where no solutions exist. The implications of the meniscus shape calculations on meniscus stability are discussed.

An extension of the Mullins and Sekerka (MS) linear stability analysis to the unsteady growth rate case is considered for dilute binary alloys. In particular, the stability of the planar interface during the initial solidification transient is studied in detail numerically. The rapid solidification case, when the system is traversing through the unstable region defined by the MS criterion, has also been treated. It has been observed that the onset of instability is quite accurately defined by the "quasi-stationary MS criterion", when the growth rate and other process parameters are taken as constants at a particular time of the growth process. A singular behavior of the governing equations for the perturbed quantities at the constitutional supercooling demarcation line has been observed. However, when the solidification process, during its transient, crosses this demarcation line, a planar interface is stable according to the linear analysis performed.