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All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Thermosolutal convection during directional solidification. II - Flow transitions

The influence of thermosolutal convection on solute segregation in crystals grown by vertical directional solidification of binary metallic alloys or semiconductors is studied. Finite differences are used in a two-dimensional time-dependent model which assumes a planar crystal-melt interface to obtain numerical results. It is assumed that the configuration is periodic in the horizontal direction. Consideration is given to the possibility of multiple flow states sharing the same period. The results are represented in bifurcation diagrams of the nonlinear states associated with the critical points of linear theory. Variations of the solutal Rayleigh number can lead to the occurrence of multiple steady states, time-periodic states, and quasi-periodic states. This case is compared to that of thermosolutal convection with linear vertical gradients and stress-free boundaries.

Mcfadden, G. B.↗
NASA NTRS1987

Directional solidification in an imperfect furnace

The upward directional solidification of a binary alloy in which the rejected solute is more dense than the solvent is considered. The system is stably stratified both thermally and solutally. If heat is lost through the sidewalls, horizontal thermal gradients drive a steady double-diffusive convection. Solidification cells with small aspect ratios (width/length) A are considered, and asymptotic solutions to the steady double-diffusive system are obtained as A tends to 0 under the assumption heat losses are also small. When the thermal Grashof number is large, buoyancy boundary layers are at the sidewalls. The shape of the crystal-melt interface is determined by the coupled effects of local thermodynamic equilibrium, diffusion and convection.

Brattkus, K.↗
NASA NTRS1984

Effect of a forced Couette flow on coupled convective and morphological instabilities during unidirectional solidification

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.

Coriell, S. R.↗
NASA NTRS1988

Growth of needle-shaped crystals in the presence of convection

The motion of the freezing front between a needle-shaped crystal and a supercooled liquid is analyzed for situations where there is forced convection aligned with the crystal axis. It is shown that in the absence of capillary effects the shape of the crystal-melt interface is a paraboloid of revolution, similar to that found in situations where diffusion is the sole heat-transfer mechanism. A relation between the supercooling, the product of tip velocity and tip radius, and the strength of the flow is derived which reduces to the well-known Ivantsov theory in the absence of convection.

Saville, D. A.↗
NASA NTRS1987

Experimental studies of crystal-melt differentiation in planetary basalt compositions

An important process that controls the evolution of magmas on and within planetary bodies is crystal-melt differentiation. Experimental studies of silicate melt solidification were performed on several planetary and terrestrial melt compositions, and experiments on one of these compositions in the microgravity environment of the space station would provide an opportunity to understand the factors that control crystal growth and crystal-melt exchange processes at crystal-melt interfaces during solidification. Experimental requirements are presented.

Grove, T. L.↗
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 NTRS1989

An ion microprobe study of the intra-crystalline behavior of REE and selected trace elements in pyroxene from mare basalts with different cooling and crystallization histories

The effects of crystallization interaction on the trace element zoning characteristics of pyroxenes are analyzed using electron and ion microprobe techniques. Four pigeonite basalts with similar isochemical composition, but different cooling rates and crystallization histories are studied. Pyroxene quadrilaterals displaying crystallization trends are presented. The crystal chemical rationalization of REE zoning, pattern shapes, and abundances are examined. The data reveal that the trace element zoning characteristics in pyroxene and the partitioning of trace elements between pyroxene and the melt are related to the interaction between the efficiency of the crystallization process, the kinetics at the crystal-melt interface, the kinetics of plagioclase nucleation and the characteristics of the crystal chemical substitutions in the pyroxene and the associated crystallizing phase.

Shearer, C. K.↗
NASA NTRS1991

Disordering and H-embrittlement of Pb(110) surface using embedded atom method and molecular dynamics

The dynamics and structure of the crystal melt interface are of great importance in crystal growth, melting, and other properties of the solid-liquid interface. The Embedded Atom Method (EAM), a semiempirical method developed by Daw and Baskes for determining the energetics of atoms in a bulk environment, is a useful method in the computer simulation. The EAM functions of PB in conjunction with the MD code are employed to study melting and disordering of the Pb(100) surface. The EAM functions are fitted to the bulk experimental data at zero temperature, and it is not clear if it will behave correctly at higher temperatures. In fact, it is shown that use of a similar type of potential at higher temperatures might result in a negative coefficient of thermal expansion. The primary purpose here is to perform MD simulation combined with the EAM functions of PB to study melting of the Pb(100) surface. This provides an accurate test of the EAM functions at higher temperatures. In particular, we calculate the two dimensional structure factor, the two dimensional distribution function, and density profile as a function of temperature up to the melting point of lead.

Karimi, Majid↗
NASA NTRS1990

Instability during directional solidification - Gravitational effects

After an elementary introduction to solidification, recent research that attempts to understand the interaction of fluid flow with a crystal-melt interface under gravitational influence using linear stability analysis is reviewed. Recent numerical calculations of fluid flow and interface morphology during alloy solidification are briefly discussed.

Coriell, S. R.↗
NASA NTRS1991

Measurement and analysis of grain boundary grooving by volume diffusion

Experimental measurements of isothermal grain boundary grooving by volume diffusion are carried out for Sn bicrystals in the Sn-Pb system near the eutectic temperature. The dimensions of the groove increase with a temporal exponent of 1/3, and measurement of the associated rate constant allows the determination of the product of the liquid diffusion coefficient D and the capillarity length Gamma associated with the interfacial free energy of the crystal-melt interface. The small-slope theory of Mullins is generalized to the entire range of dihedral angles by using a boundary integral formulation of the associated free boundary problem, and excellent agreement with experimental groove shapes is obtained. By using the diffusivity measured by Jordon and Hunt, the present measured values of Gamma are found to agree to within 5 percent with the values obtained from experiments by Gunduz and Hunt on grain boundary grooving in a temperature gradient.

Hardy, S. C.↗
NASA NTRS1998

Numerical Modeling of Solidification in Space With MEPHISTO-4

A pre-flight analysis of the directional solidification of BiSn with MEPHISTO-4 is presented. Simplified Bridgman growth under microgravity conditions is simulated using a two dimensional finite element model. This numerical model is a single domain, pseudo-steady state model, and includes the effects of both thermal and solutal convection. The results show that for all orientations of the applied steady state gravity vector, of magnitude 1 micro-g, the directional solidification process remains diffusion controlled. The maximum convective velocity was found to be 4.424 x 10(exp -5) cm/s for the horizontal Bridgman growth configuration. This value is an order of magnitude lower than the growth velocity. The maximum and minimum values or solute concentration in the liquid at the crystal-melt interface were 13.867 at.% and 13.722 at.%, respectively. This gives a radial segregation value of xi = 1.046% at the interface. A secondary objective of this work was to compare the results obtained to those that consider thermal convection only (no solutal convection). It was found that the convective flow patterns in simulations which included solutal convection were significantly different from those which ignored solutal convection. The level of radial segregation predicted by the current simulations is an order of magnitude lower than that found in simulations which ignore solutal convection. The final aim was to investigate the effect of g-jitter on the crystal growth process. A simulation was performed to calculate the system response to a 1 second, 100 micro-g gravity impulse acting normal to the direction of growth. This pulse is consistent with that induced by Orbiter thruster firings. The results obtained indicate that such a gravity pulse causes an increase in the level of radial solute segregation at the interface from the steady state values. The maximum value of solute concentration in the liquid was found to be 13.888 at.%, the minimum value calculated was 13.706 at.%, yielding a radial segregation value of xi = 1.31% at the interface. These values occurred 126 seconds after the pulse terminated. Thus it is anticipated that the process will remain diffusion controlled even when subjected to such g-jitter.

Simpson, James E.↗
NASA NTRS1999

Analysis of X-Ray Microradiographs of Al-Au Interface Quench Profile using Modeling of Solidification Including Double-Diffusion and Convection in the Melt

Experimental data on Al-0.8Au horizontal solidification of a 1 mm thick specimen in a BN crucible shows the effect of growth rate on the solidification interface shape. For translation rates below 0.5 micron/s the interface maintains a plain and flat shape. When the translation rate is 3 to 5 micron/s or more, the interface appearance changes to two planar zones, with the zone closer to the bottom having higher inclination. The interface shapes were measured by first quenching in place during growth. X-ray microscopy shows the interface shape within the quenched sample by viewing through the side of the specimen. In order to provide theoretical explanation of the phenomena, numerical modeling was undertaken using finite element code FIDAP. Double diffusion convection in Al-0.8Au melt and crystal-melt interface curvature during directional solidification was analyzed numerically. Actual thermophysical properties of Al-0.8Au including the binary Al-Au phase diagram were used. Although convection in the sample is weak, for the slower translation rate convection and diffusion is sufficient for the redistribution of initial compositional stratification caused by gravity. When translation rate is raised, neither convection nor diffusion can provide proper mixing so that solidification temperatures differ significantly near the bottom within the bulk of the sample. As a result, the solid-liquid interface appears to have two planar zones with different inclination.

Bune, Andris V.↗
NASA NTRS2004

Detached Growth of Germanium by Directional Solidification

Detached crystal growth technique (dewetting) offers improvement in the quality of the grown crystals by preventing sticking to the walls of the crucible and thus reducing the possibility of parasitic nucleation and formation of lattice defects upon cooling. One of the factors relevant for the phenomena is the pressure differential across the meniscus at the crystal-melt interface. We investigated this effect experimentally. The growth took place in closed ampoules under the pressure of an inert gas (forming gas: 96% Ar + 4% H2). The pressure above the melt was adjustable and allowed for a control of the pressure difference between the top and bottom menisci. The crystals were characterized, particularly by taking profilometer measurements along the grown crystals surface. The effects of the experimental conditions on the detachment were compared with those predicted based on the theory of Duffar et al.

Palosz, W.↗
NASA NTRS2017

Growth Angle - a Microscopic View

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.

Mazurak, K.↗
NASA NTRS1984

The effect of anisotropic crystal-melt surface tension on grain boundary groove morphology

The shape of a stationary solid-liquid interface in a temperature gradient near a grain boundary in a pure material is calculated for anisotropic crystal-melt surface tension and equal thermal conductivities of crystal and melt. Results are compared with those for the well-known problem of the two-dimensional equilibrium shape of a crystal. For small anisotropy, the resulting interface shapes have continuously turning tangents but differ in detail from the grain boundary groove shapes that have been calculated for isotropic surface tension. For larger anisotropy, the interface shapes have discontinuities in slope as a result of missing orientations.

Voorhees, P. W.↗
DOE OSTI2022

Interlayer fusion bonding of semi-crystalline polymer composites in extrusion deposition additive manufacturing

This work focuses on the evolution of interlayer fracture toughness properties of fiber-reinforced, semi-crystalline polymers in the extrusion deposition additive manufacturing (EDAM) process. Further, this work bridges the gap between the additive process conditions (time-temperature history) and the effective layer-to-layer fracture properties developed within a printed component. This is the first step to predict delamination that can occur during printing, during cooling to room temperature after printing, and during service performance of an additively manufactured geometry. A phenomenological model is developed for fusion bonding of semi-crystalline polymer matrix composites by coupling the interdiffusion of polymer chains with the evolution of polymer crystallinity. While the interdiffusion is captured by reptation theory of polymer dynamics, the evolution of crystallinity is modeled by phenomenological crystallization kinetics and crystal melting dynamics. Further, a methodology is developed to determine the critical strain energy release rate, G IC of the interlayer interface and experiments are conducted utilizing the double cantilever beam fracture test geometry. In conclusion, predictions of GIC as a function of thermal history are compared with experiments.

36 MATERIALS SCIENCE↗
NASA NTRS1985

Crystal Melts Under Reduced Gravity

To date, fluid motion due to thermocapillary convection and centrifugal buoyancy has been studied theoretically and numerically, by adapting specialized programs for rotating viscous fluids. It has been shown that by rotating the crystal melt, thermocapillary flow can be confined to a thin layer at the melt-gas interface even when the interfacial velocity is large enough for non-linear effects to be important. Theoretical analysis of the basic processes proceeds, but a much larger effort is now being devoted to the numerical simulation of the actual motion in a rotating crystal melt. A numerical program is under development for the study of the fully nonlinear problem. Although the flow is viewed, to start, as one of rapid rotation (in order that certain boundary layer simplifications can be invoked), a more general approach will allow consideration of the situations and conditions of real practical interest.

Greenspan, H. P.↗
NASA NTRS1988

The surface morphology of crystals melting under solutions of different densities

Examples of solids melting beneath liquids are described for cases where the bulk liquid volume is stabilized against convection by a positive vertical temperature gradient, either with, or without local density inversion at the melting interface. The examples include ice melting beneath brine or methanol solutions and tin or lead melting under molten Sn-20 wt pct Pb or Pb-20 wt pct Sn, respectively. Without density inversion the melting is slow, purely diffusion controlled and the interfaces are smooth; with convection assisted melting the rate increases by some two orders of magnitude and the interfaces develop a rough profile - in the case of ice both irregular and quasi-steady state features are observed. The observations are discussed in terms of prevailing temperature and concentration gradients.

Fang, Dacheng↗