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NASA NTRS1978

Numerical analyses for treating diffusion in single-, two- and three-phase binary alloy systems

Numerical solutions were applicable for planar, cylindrical, or spherical geometries with any diffusion-zone size and any continuous variation of the diffusion coefficient with concentration. Special techniques were included in the analyses to account for differences in molal volumes, initiation and growth of an intermediate phase, disappearance of a phase, and the presence of an initial composition profile in the specimen. A major improvement in solution accuracy was achieved in the two phase analysis by employing a mass conservation criterion to establish the location of the interface rather than the conventional interface-flux-balance criterion. In the three phase analysis, computation time was minimized without sacrificing solution accuracy by treating the three phase problem as a two phase problem when the thickness of the intermediate phase was less than a preset small value. Three computer codes were developed to perform these analyses.

Tenney, D. R.↗

NASA NTRS1981

Diffusion in single-phase binary alloys

DBAS 1 computer program provides analyst with simple algorithms for exact rapid solutions of systems with planar, cylindrical, or spherical interfaces. Conventional solutions are complex and present convergence problems. Two algorithm types are figured for each geometry; one converges rapidly for short and the other for long diffusion times. DBAS 1 is written in FORTRAN IV for batch execution.

Tenney, D. R.↗

NASA NTRS1985

Electrical conductivity and phase diagram of binary alloys. 21: The system palladium-chromium

Pd-Cr alloys were investigated by thermal analysis, hardness measurements, X-ray analysis, microscopic examination of etched pieces, and temperature-resistance curves of the solid alloys. Only one compound, Pd2Cr3, m, 1389 deg, is formed. It possesses a cubic face centered lattice and forms with excess Pd a series of solid solutions with a minimum m.p. at 45 atoms% Pd. Hardness maximum appears at the Pd2Cr3 point. Pd2Cr3 forms no solid solutions with Cr but eutectic point appears at 25 atoms% Pd, m. 1320 deg. The sp. resistance of pure Cr in an atom of H, indicates no allotropic forms. Cr2O3 is solid in molten Cr. Pure Cr melts at 1890 plus or minus 10 deg but Cr contg. Cr2O3 starts to melt at 1770 to 1790 deg.

Grube, G.↗

NASA NTRS1985

Dynamics of Bridgman-Stockbarger growth of non-dilute binary alloys

The coupling between heat and mass transfer in the Bridgman-Stockbarger growth of nondilute crystals induces growth rate transients that are longer than those caused by heat transfer alone. The dynamics of the diffusion-controlled growth for thermophysical properties representative of Pb(1-x)Sn(x)Te and Hg(1-x)Cd(x)Te are computed from a one-dimensional solidification model which includes melt-crystal phase behavior. Results show that the growth rate response to a step change in pull rate for both systems differs from the exponential decay observed for dilute alloys and that growth rates cannot be inferred from axial segregation data in nondilute systems due to the dependence of the segregation coefficient on composition.

Bourret, E. D.↗

NASA NTRS1986

Fault structures in rapidly quenched Ni-Mo binary alloys

Fault structures in two Ni-Mo alloy ribbons (Ni-28 at. pct Mo and Ni-35 at. pct Mo) cast by a free jet chill block melt spinning process were studied. Thin foils for TEM studies were made by electrochemical thinning using an alcohol/butyl cellosolve/perchloric acid mixture in a twin jet electropolishing device. The samples displayed typical grains containing linear faulted regions on the wheelside of the two alloy ribbons. However, an anomalous diffraction behavior was observed upon continuous tilting of the sample: the network of diffraction spots from a single grain appeared to expand or contract and rotate. This anomalous diffraction behavior was explained by assuming extended spike formation at reciprocal lattice points, resulting in a network of continuous rel rods. The validity of the model was confirmed by observations of a cross section of the reciprocal lattice parallel to the rel rods.

Jayaraman, N.↗

NASA NTRS1987

Nonplanar interface morphologies during unidirectional solidification of a binary alloy. II - Three-dimensional computations

A finite difference method is used to obtain three-dimensional steady-state solutions for nonplanar interface morphologies in order to study the situation of equal thermal properties in the crystal and melt with negligible latent heat release. Stable steady-state solutions corresponding to two-dimensional bands and three-dimensional hexagonal nodes, as well as to rectangular interface planiforms, are found using a model of an aluminum-chromium alloy with a distribution coefficient of greater than one. Hexagonal nodes are predicted near the onset of instability, in agreement with weakly nonlinear theory.

Mcfadden, G. B.↗

NASA NTRS1988

Dendritic solidification in binary alloys

Alloys generally solidify dendritically, and associated with that is the microsegregation of impurities. Pure metals also solidify in dendritic form as 'thermal' dendrites, which actually segregate the system's enthalpy. In this investigation, small additions of solute to succinonitrile have been studied and dendritic growth observed in a supercooled melt. This free dendritic growth-mode is similar to that experienced by equiaxed dendrites found in alloy castings. Observations of these free dendrites include measurement of velocity and tip radius of the dendrites at different supercoolings and solute concentrations.

Chopra, M. A.↗

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 NTRS1991

Heats of formation of bcc binary alloys

The method of Bozzolo, Ferrante and Smith is applied for the calculation of alloy energies for bcc elements. The heat of formation of several alloys is computed with the help of the Connolly-Williams method within the tetrahedron approximation. The dependence of the results on the choice of different sets of ordered structures is discussed.

Bozzolo, Guillermo↗

NASA NTRS1990

Numerical Formulation for the Prediction of Solid/Liquid Change of a Binary Alloy

A computational model is presented for the prediction of solid/liquid phase change energy transport including the influence of free convection fluid flow in the liquid phase region. The computational model considers the velocity components of all non-liquid phase change material control volumes to be zero but fully solves the coupled mass-momentum problem within the liquid region. The thermal energy model includes the entire domain and uses an enthalpy like model and a recently developed method for handling the phase change interface nonlinearity. Convergence studies are performed and comparisons made with experimental data for two different problem specifications. The convergence studies indicate that grid independence was achieved and the comparison with experimental data indicates excellent quantitative prediction of the melt fraction evolution. Qualitative data is also provided in the form of velocity vector diagrams and isotherm plots for selected times in the evolution of both problems. The computational costs incurred are quite low by comparison with previous efforts on solving these problems.

Schneider, G. E.↗

NASA NTRS1991

Vertical solidification of dendritic binary alloys

Three numerical techniques are employed to analyze the influence of thermosolutal convection on defect formation in directionally solidified (DS) alloys. The finite-element models are based on the Boussinesq approximation and include the plane-front model and two plane-front models incorporating special dendritic regions. In the second model the dendritic region has a time-independent volume fraction of liquid, and in the last model the dendritic region evolves as local conditions dictate. The finite-element models permit the description of nonlinear thermosolutal convection by treating the dendritic regions as porous media with variable porosities. The models are applied to lead-tin alloys including DS alloys, and severe segregation phenomena such as freckles and channels are found to develop in the DS alloys. The present calculations and the permeability functions selected are shown to predict behavior in the dendritic regions that qualitatively matches that observed experimentally.

Heinrich, J. C.↗

NASA NTRS1992

Spatiotemporal chaos near the onset of cellular growth during thin-film solidification of a binary alloy

Thin-film solidification experiments with a succinonitrile-acetone alloy are used to observe the long time-scale dynamics of cellular crystal growth at growth rates only slightly above the critical value VC = Vc(lambda sub c) for the onset of morphological instability. Under these conditions only very small amplitude cells are observed with wavelengths near the value predicted by linear stability theory lambda = lambda sub c. At long times, microstructures with wavelengths significantly finer than lambda suc c form by nucleation at defects across the interface. These interfaces do not have a unique microstructure, but seem to exhibit spatiotemporal chaos on a long time scale caused by the continual birth and death of cells by tip splitting and cell annihilation in grooves.

Lee, J. T. C.↗

NASA NTRS1992

Heats of formation of bcc binary alloys

Bozzolo, Guillermo↗

NASA NTRS1992

Thermosolutal convection during dendritic solidification of a binary alloy

The FEM model of Heinrich (1988) is presently extended to the case of dendritic vertical solidification under steady-state conditions. An analysis is conducted of the nonlinear governing equations for linear stability, and FEM calculations are performed in cases where instability has been predicted for Pb-Sn melt systems; the results obtained show that the model is more stable than the plane front liquid-solid model, and shows similar, finger-like covection when unstable. It is found that convection in the 'mush' zone is confined to the top of that region; convective motion is driven by convection in the bulk fluid, in the absence of natural convection.

Heinrich, Juan C.↗

NASA NTRS1996

Convective Influence on Radial Segregation During Unidirectional Solidification of the Binary Alloy HgCdTe

In order to simulate the space environment for basic research into the crystal growth mechanism, Hg(0.8)Cd(0.2)Te crystals were grown by the vertical Bridgman-Stockbarger method in the presence of an applied axial magnetic field. The influence of convection, by magneto hydrodynamic damping, on mass transfer in the melt and segregation at the solid-liquid interface was investigated by measuring the axial and radial compositional variations in the grown samples. The reduction of convective mixing in the melt through the application of the magnetic field is found to have a large effect on radial segregation and interface morphology in the grown crystals. Direct comparisons are made with a Hg(0.8)Cd(0.2)Te crystal grown without field and also in the microgravity environment of space during the second United States Microgravity Payload Mission (USMP-2).

Watring, D. A.↗

NASA NTRS1999

Effect of a Nonplanar Melt-Solid Interface On Lateral Compositional Distribution During Unidirectional Solidification of a Binary Alloy with a Constant Growth Velocity V: Theory - Pt. 1

Infrared detected materials, such as Hg(1-x)Cd(x)Te, Hg(1-x)Zn(x)Te have energy gaps almost linearly proportional to their composition. Due to the wide separation of liquidus and solidus curves of their phase diagram, there are compositional segregation in both of the axial and radial directions of these crystals grown in the Bridgman system unidirectionally with constant growth rate. It is important to understand the mechanisms, which affect lateral segregation such that large radially uniform composition crystal can be produced. Following Coriel, etc's treatment, we have developed a theory to study the effect of a curved melt-solid interface shape on lateral composition distribution. The model is considered to be a cylindrical system with azimuthal symmetry and a curved melt-solid interface shape which can be expressed as a linear combination of a series of Bessell's functions. The results show that melt-solid interface shape has a dominant effect on the lateral composition distribution of these systems. For small values of beta, the solute concentration at the melt-solid interface scales linearly with interface shape with a proportional constant of the produce of beta and (1 -k), where beta = VR/D, with V as growth velocity, R as the sample radius, D as the diffusion constant and k as the distribution constant. A detailed theory will be presented. A computer code has been developed and simulations have been performed and compared with experimental results. These will be published in another paper.

Wang, Jai-Ching↗

NASA NTRS1999

Effect of a Nonplanar Melt-Solid Interface on Lateral Compositional Distribution during Unidirectional Solidification of a Binary Alloy with a Constant Growth Velocity V: Theory - Part 1

Infrared detector materials, such as Hg(1-x)Cd(x)Te, Hg(1-x)Zn(x)Te have energy gaps almost linearly proportional to its composition. Due to the wide separation of liquidus and solidus curves of their phase diagram, there are compositional segregations in both of axial and radial directions of these crystals grown in the Bridgman system unidirectionally with constant growth rate. It is important to understand the mechanisms which affect lateral segregation such that large uniform radial composition crystal is possible. Following Coriell, etc's treatment, we have developed a theory to study the effect of a curved melt-solid interface shape on the lateral composition distribution. The system is considered to be cylindrical system with azimuthal symmetric with a curved melt-solid interface shape which can be expressed as a linear combination of a series of Bessell's functions. The results show that melt-solid interface shape has a dominate effect on lateral composition distribution of these systems. For small values of b, the solute concentration at the melt-solid interface scales linearly with interface shape with a proportional constant of the product of b and (1 - k), where b = VR/D, with V as growth velocity, R as sample radius, D as diffusion constant and k as distribution constant. A detailed theory will be presented. A computer code has been developed and simulations have been performed and compared with experimental results. These will be published in another paper.

Wang, Jai-Ching↗

NASA NTRS2001

Cellular Spacing Selection During the Directional Solidification of Binary Alloys. A Numerical Approach

The evolution of cellular solid/liquid interfaces from an initially unstable planar front was studied by means of a two-dimensional computer simulation. The developed numerical model makes use of an interface tracking procedure and has the capability to describe the dynamics of the interface morphology based on local changes of the thermodynamic conditions. The fundamental physics of this formulation was validated against experimental microgravity results and the predictions of the analytical linear stability theory. The performed simulations revealed that in certain conditions, based on a competitive growth mechanism, an interface could become unstable to random perturbations of infinitesimal amplitude even at wavelengths smaller than the neutral wavelength, lambda(sub c), predicted by the linear stability theory. Furthermore, two main stages of spacing selection have been identified. In the first stage, at low perturbations amplitude, the selection mechanism is driven by the maximum growth rate of instabilities while in the second stage the selection is influenced by nonlinear phenomena caused by the interactions between the neighboring cells. Comparison of these predictions with other existing theories of pattern formation and experimental results will be discussed.

Catalina, Adrian V.↗