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NASA NTRS1990

Effect of thermosolutal convection on the solid-liquid interface in Pb-Au alloy

Liquid-solid interface distortion in the region of primary dendrite tips has been investigated in directionally solidified Pb-8 wt pct Au alloy. The distortions are caused by thermosolutal convection despite choice of growth conditions which should have been thermally and solutally stabilizing. The convection produces clustering of primary dendrites on a plane perpendicular to the growth direction. It produces a mushy zone, where the primary dendrites do not protrude with a uniform length, across the specimen cross section, resulting in large macrosegregation in the transverse direction. However, little macrosegregation is observed along the growth direction. The mushy zone, with uneven dendrite lengths, forms in the beginning of directional solidification. Its shape and dendrite distribution do not show much change during subsequent solidification. Tip morphologies of primary dendrites, within the dendrite clusters, appear to follow the morphological stability relationship.

Tewari, S. N.↗

NASA NTRS1989

Ginzburg-Landau theory for the solid-liquid interface of bcc elements. II - Application to the classical one-component plasma, the Wigner crystal, and He-4

The previously developed Ginzburg-Landau theory for calculating the crystal-melt interfacial tension of bcc elements to treat the classical one-component plasma (OCP), the charged fermion system, and the Bose crystal. For the OCP, a direct application of the theory of Shih et al. (1987) yields for the surface tension 0.0012(Z-squared e-squared/a-cubed), where Ze is the ionic charge and a is the radius of the ionic sphere. Bose crystal-melt interface is treated by a quantum extension of the classical density-functional theory, using the Feynman formalism to estimate the relevant correlation functions. The theory is applied to the metastable He-4 solid-superfluid interface at T = 0, with a resulting surface tension of 0.085 erg/sq cm, in reasonable agreement with the value extrapolated from the measured surface tension of the bcc solid in the range 1.46-1.76 K. These results suggest that the density-functional approach is a satisfactory mean-field theory for estimating the equilibrium properties of liquid-solid interfaces, given knowledge of the uniform phases.

Zeng, X. C.↗

NASA NTRS1984

Convection-induced distortion of a solid-liquid interface

Measurements of convective flow fields and solid-liquid interface shapes during the solidification of a pure and a slightly alloyed transparent material reveal that the convective transport of solute can cause a macroscopic depression to develop in the solid-liquid interface. This effect occurs under conditions close to those which are predicted to produce morphological instability of a planar interface. A cellular or dendritic microstructure later develops within the interface depression. The convection is attributed to the effect of radial temperature gradients in the crystal growth apparatus.

Schaefer, R. J.↗

NASA NTRS2003

Advanced Technology Development: Solid-Liquid Interface Characterization Hardware

Characterizing the solid-liquid interface during directional solidification is key to understanding and improving material properties. The goal of this Advanced Technology Development (ATD) has been to develop hardware, which will enable real-time characterization of practical materials, such as aluminum (Al) alloys, to unprecedented levels. Required measurements include furnace and sample temperature gradients, undercooling at the growing interface, interface shape, or morphology, and furnace translation and sample growth rates (related). These and other parameters are correlated with each other and time. A major challenge was to design and develop all of the necessary hardware to measure the characteristics, nearly simultaneously, in a smaller integral furnace compatible with existing X-ray Transmission Microscopes, XTMs. Most of the desired goals have been accomplished through three generations of Seebeck furnace brassboards, several varieties of film thermocouple arrays, heaters, thermal modeling of the furnaces, and data acquisition and control (DAC) software. Presentations and publications have resulted from these activities, and proposals to use this hardware for further materials studies have been submitted as sequels to this last year of the ATD.

Source record↗

NASA NTRS1982

Finite element analysis of the effect of a non-planar solid-liquid interface on the lateral solute segregation during unidirectional solidification

The effect of solid-liquid interface shape on lateral solute segregation during steady-state unidirectional solidification of a binary mixture is calculated under the assumption of no convection in the liquid. A finite element technique is employed to compute the concentration field in the liquid and the lateral segregation in the solid with a curved boundary between the liquid and solid phases. The computational model is constructed assuming knowledge of the solid-liquid interface shape; no attempt is made to relate this shape to the thermal field. The influence of interface curvature on the lateral compositional variation is investigated over a range of system parameters including diffusivity, growth speed, distribution coefficient, and geometric factors of the system. In the limiting case of a slightly nonplanar interface, numerical results from the finite element technique are in good agreement with the analytical solutions of Coriell and Sekerka obtained by using linear theory. For the general case of highly non-planar interface shapes, the linear theory fails and the concentration field in the liquid as well as the lateral solute segregation in the solid can be calculated by using the finite element method.

Carlson, F. M.↗

NASA NTRS1991

Effect of thermal convection on the shape of a solid-liquid interface

The effect of thermal convection on the shape of solid-liquid interface was investigated in experiments conducted in a transparent Bridgman-type directional solidification furnace. The relationship was numerically modeled using a standard 2D finite-difference approach, with the solid-liquid deformable interface approximated by a blocking-off technique. The directional solidification furnace was used with pure succinonitrile (which is also transparent) contained in a long square ampoule made of borosilicate glass. With the furnace in the vertical configuration, a flat interface was observed, in agreement with the model. On the other hand, a highly distorted interface was obtained in the horizontal configuration; the numerical results showed a strong recirculating cell in front of the interface due to natural thermal convection. The results indicate that thermal convection is responsible for the interface distortion.

Mennetrier, C.↗

NASA NTRS1985

Convective influence on the stability of a cylindrical solid-liquid interface

Experiments in which a long vertical, heated wire is surrounded by concentric annuli of a melt and its crystalline solid show that the convection state changes from a stable unicell surrounded by a stationary cylindrical solid-liquid interface, to a complex time-dependent flow surrounded by a rotating, helical solid-liquid interface. This transition occurs at a Grashof number of approximately 150, which is an order of magnitude less than the critical Grashof number calculated for a liquid annulus surrounded by rigid walls. A linear stability analysis has been carried out for an infinitely tall vertical annulus. When the deformable nature of the crystal-melt interface is taken into account in the boundary conditions, two new modes of instability arise. The most dangerous mode is asymmetrical and corresponds to helical waves travelling vertically upwards. The critical Grashof number and the scaling properties of the eigenstate agree with experiments. The results clearly demonstrate the coupling of convection with crystal-melt interfacial instabilities.

Fang, Q. T.↗

NASA NTRS1994

Numerical formulation of composition segregation at curved solid-liquid interface during steady state solidification process

The lateral solute segregation that results from a curved solid-liquid interface shape during steady state unidirectional solidification of a binary alloy system has been studied both analytically and numerically by Coriell, Bosivert, Rehm, and Sekerka. The system under their study is a two dimensional rectangular system. However, most real growth systems are cylindrical systems. Thus, in a previous study, we have followed Coriell etc. formalism and obtained analytical results for lateral solute segregation for an azimuthal symmetric cylindrical binary melt system during steady state solidification process. The solid-liquid interface shape is expressed as a series combination of Bessel functions. In this study a computer program has been developed to simulate the lateral solute segregation.

Wang, Jai-Ching↗

NASA NTRS1985

Influence of Melt Convection on Solid-Liquid Interface Under Terrestrial and Reduced Gravity Environments

Solidification and crystal growth processes involve thermal and solutal gradients within a molten phase. In the presence of gravity, such gradients result in convective flows which interact with diffusion fields at the solid-liquid interface. Dendritic growth kinetics was studied in transparent model systems which freeze similarily to most metals. Succinonitrile shows a strong influence of convection at supercoolings below about 1K. Fluid flows adjacent to solid-liquid interfaces and the behavior of shear flows in vertical annular geometries are studied. Novel low-frequency eigenstates were discovered and classified as coupled modes, for their involvement with interfacial deformation coupled to the fluid flow, and are unknown in systems without deformable interfaces. The dependence of coupled convection modes on interfacial geometry, gravity, fluid properties, and transformation characteristics studied for several annual flow arrangements with nominally pure solid-liquid systems.

Glicksman, M. E.↗

NASA NTRS2000

Solid-Liquid Interface Characterization Hardware

The objective is to develop enabling technology to characterize the solid-liquid interface during directional solidification to unprecedented levels with real-time measurement hardware. Existing x-ray imaging hardware is combined with compact Seebeck furnaces and thermal profiling hardware, under development, to accomplish the measurements. Furnace thermal profiles are continuously measured in addition to the sample characteristics.

Peters, Palmer N.↗

NASA NTRS1990

Analysis of stability of a planar solid-liquid interface in a dilute binary alloy

This paper reconsiders the question of stability of a planar solid-liquid interface in an undercooled alloy melt without making the restrictive assumption of no heat flow in the solid (i.e., Gs = 0). The results of this analysis indicate that, provided the thermal gradient on the solid side of the interface, Gs, is positive, stability can be achieved in an undercooled alloy melt for growth rates R greater than Ra (where Ra is the absolute stability limit of Mullins and Sekerka, 1964). Thus, the absolute stability criterion for steady-state planar growth in an undercooled alloy melt is the same as derived earlier by Mullins and Sekerka for directional solidification. Relaxing the restrictive assumption of Gs = 0 also reveals that there is a regime of stability for low growth rates and low supercoolings.

Laxmanan, V.↗

NASA NTRS1992

Break-down of a planar liquid-solid interface during directional solidification - Influence of convection

The influence of convection on the development of morphological instability at the liquid-solid interface during directional solidification in a positive thermal gradient has been examined in Pb-10 wt pct Sn and succinonitrile-1.9 wt pct acetone. The onset of interfacial breakdown occurs at higher growth speeds in the presence of convection. The linear stability analysis due to Favier and Rouzaud which uses the 'deformable' mass flow boundary layer concept shows a good agreement with the experimentally observed behavior.

Tewari, S. N.↗

NASA NTRS2000

Solid-Liquid Interface Characterization Hardware: Advanced Technology Development (ATD)

This ATD has the goal of enabling the integration of three separate measurement techniques to characterize the solid-liquid interface of directionally solidified materials in real-time. Arrays of film-based metal thermocouple elements are under development along with compact Seebeck furnaces suitable for interfacing with separately developed X-ray Transmission Microscopes. Results of applying film arrays to furnace profiling are shown, demonstrating their ability to identify a previously undetected hardware flaw in the development of a second-generation compact furnace. Results of real-time furnace profiling also confirmed that the compact furnace design effectively isolates the temperature profiles in two halves of the furnace, a necessary feature. This isolation had only been inferred previously from the characteristics of Seebeck data reported. Results from a 24-thermocouple array successfully monitoring heating and isothermal cooling of a tin sample are shown. The importance of non-intrusion by the arrays, as well as furnace design, on the profiling of temperature gradients is illustrated with example measurements. Further developments underway for effectively combining all three measurements are assessed in terms of improved x-ray transmission, increased magnification, integral arrays with minimum intrusion, integral scales for velocity measurements and other features being incorporated into the third generation Seebeck furnace under construction.

Peters, Palmer N.↗

NASA NTRS2013

Bubble Induced Disruption of a Planar Solid-Liquid Interface During Controlled Directional Solidification in a Microgravity Environment

Pore Formation and Mobility Investigation (PFMI) experiments were conducted in the microgravity environment aboard the International Space Station with the intent of better understanding the role entrained porosity/bubbles play during controlled directional solidification. The planar interface in a slowing growing succinonitrile - 0.24 wt% water alloy was being observed when a nitrogen bubble traversed the mushy zone and remained at the solid-liquid interface. Breakdown of the interface to shallow cells subsequently occurred, and was later evaluated using down-linked data from a nearby thermocouple. These results and other detrimental effects due to the presence of bubbles during solidification processing in a microgravity environment are presented and discussed.

Grugel, Richard N.↗

NASA NTRS1989

Determination of the mean solid-liquid interface energy of pivalic acid

A high-confidence solid-liquid interfacial energy is determined for an anisotropic material. A coaxial composite having a cylindrical specimen chamber geometry provides a thermal gradient with an axial heating wire. The surface energy is derived from measurements of grain boundary groove shapes. Applying this method to pivalic acid, a surface energy of 2.84 erg/sq cm was determined with a total systematic and random error less than 10 percent. The value of interfacial energy corresponds to 24 percent of the latent heat of fusion per molecule.

Singh, N. B.↗

NASA NTRS1984

The movement of particles in liquid metals under gravity forces and the interaction of particles with advancing solid-liquid interface

The problems of shrinkage and gas porosity are discussed. Gravity forces enhance the removal of gas bubbles from a metal melt and contribute to the feeding of shrinkage porosity in castings. Experiments are reviewed which determine how large a density difference is required for metal particles to float or sink in a metal melt and to what extent do factors not considered in Stokes Law influence particle movement in a real system. As to the interaction of particles with an advancing solid-liquid interface, the results indicate that the metal particles are not rejected in a metal melt, and that concentrations of particles in a metal following solidification are due to other factors.

Weinberg, F.↗

NASA NTRS1987

Ginzburg-Landau theory for the solid-liquid interface of bcc elements

Consideration is given to a simple order-parameter theory for the interfacial tension of body-centered-cubic solids in which the principal order parameter is the amplitude of the density wave at the smallest nonzero reciprocal-lattice vector of the solid. The parameters included in the theory are fitted to the measured heat of fusion, melting temperature, and solid-liquid density difference, and to the liquid structure factor and its temperature derivative at freezing. Good agreement is found with experiment for Na and Fe and the calculated anisotropy of the surface tension among different crystal faces is of the order of 2 percent. On the basis of various assumptions about the universal behavior of bcc crystals at melting, the formalism predicts that the surface tension is proportional to the heat of fusion per surface atom.

Shih, W. H.↗

NASA NTRS1983

Convection effects at solid-liquid interfaces: Influence of gravity

The stability of the flow between two vertical, infinite, rigid, coaxial cylinders held at different temperatures is analyzed by linear stability theory. For a Prandtl number of 22.8 and a radius ratio of 0.02, the flow is unstable to an axisymmetric perturbation at a critical Grashof number of 2150; the wave speed of the instability is comparable to the maximum velocity of the unperturbed flow. When the rigid outer cylinder-fluid interface is replaced by a crystal-melt interface which can change shape, two new modes of instability occur at lower Grashof numbers.

Glicksman, M. E.↗