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All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Kinetic Monte Carlo Simulations of Rod Eutectics and the Surface Roughening Transition in Binary Alloys

In this paper we report on two related topics: Kinetic Monte Carlo simulations of the steady state growth of rod eutectics from the melt, and a study of the surface roughness of binary alloys. We have implemented a three dimensional kinetic Monte Carlo (kMC) simulation with diffusion by pair exchange only in the liquid phase. Entropies of fusion are first chosen to fit the surface roughness of the pure materials, and the bond energies are derived from the equilibrium phase diagram, by treating the solid and liquid as regular and ideal solutions respectively. A simple cubic lattice oriented in the {100} direction is used. Growth of the rods is initiated from columns of pure B material embedded in an A matrix, arranged in a close packed array with semi-periodic boundary conditions. The simulation cells typically have dimensions of 50 by 87 by 200 unit cells. Steady state growth is compliant with the Jackson-Hunt model. In the kMC simulations, using the spin-one Ising model, growth of each phase is faceted or nonfaceted phases depending on the entropy of fusion. There have been many studies of the surface roughening transition in single component systems, but none for binary alloy systems. The location of the surface roughening transition for the phases of a eutectic alloy determines whether the eutectic morphology will be regular or irregular. We have conducted a study of surface roughness on the spin-one Ising Model with diffusion using kMC. The surface roughness was found to scale with the melting temperature of the alloy as given by the liquidus line on the equilibrium phase diagram. The density of missing lateral bonds at the surface was used as a measure of surface roughness.

Bentz, Daniel N.↗
NASA NTRS1993

Numerical model for dendritic solidification of binary alloys

A finite element model capable of simulating solidification of binary alloys and the formation of freckles is presented. It uses a single system of equations to deal with the all-liquid region, the dendritic region, and the all-solid region. The dendritic region is treated as an anisotropic porous medium. The algorithm uses the bilinear isoparametric element, with a penalty function approximation and a Petrov-Galerkin formulation. Numerical simulations are shown in which an NH4Cl-H2O mixture and a Pb-Sn alloy melt are cooled. The solidification process is followed in time. Instabilities in the process can be clearly observed and the final compositions obtained.

Felicelli, S. D.↗
NASA NTRS1989

Morphological instabilities in directional solidification of a binary alloy - End effects

This paper considers the unidirectional solidification of a binary alloy for which the liquid and solid phases are bounded by endwalls. In order to account for the transport of latent heat and solute, thermal and solutal boundary layers must be placed at the solidifying interface. Further, under the assumption of fixed temperature gradients, the presence of the endwalls leads to a velocity of solidification that decreases with time, and hence to an unsteady basic state having a planar interface. From a stability analysis of this state, a nonlinear long-wave evolution equation of Sivashinsky type is derived, with modified coefficients, that shows how the onset of cellular structure is delayed by the presence of endwalls.

Young, Gerald W.↗
NASA NTRS1951

Relations between the modulus of elasticity of binary alloys and their structure

A comprehensive survey of the elastic modulus of binary alloys as a function of the concentration is presented. Alloys that form continuous solid solutions, limited solid solutions, eutectic alloys, and alloys with intermetallic phases are investigated. Systems having the most important structures have been examined to obtain criteria for the relation between lattice structure, type of binding, and elastic behavior.

METALS - STRUCTURES↗
NASA NTRS1987

Dendritic solidification in a binary alloy melt - Comparison of theory and experiment

A simple model for 'constrained' growth of an 'array' of cells or dendrites in a binary alloy melt, in the presence of a positive temperature gradient in the liquid ahead of the tips, is presented. The cell or dendrite tip radius is calculated by adopting both the 'ad hoc' assumption of minimum undercooling at the tips as well as the more recently proposed hypothesis of dendritic growth under conditions of 'marginal stability'. Theoretical predictions of the model have been compared with experimental data in binary succinonitrile-acetone alloys. It has been shown that, according to the present model, the 'marginally stable' state may be virtually indistinguishable from the 'minimum undercooled' state, under the usual conditions of dendritic growth.

Laxmanan, V.↗
NASA NTRS1991

A computational model for the analysis of diffusive binary alloy solid/liquid phase change energy transport

A model is presented for the prediction of solid/liquid, binary alloy, phase change energy transport. The model incorporates only one-dimensional, diffusive transport of both energy and species but is not inherently limited in any way to such a restriction. The model incorporates a previously developed algorithm for single constituent phase change energy transport and is applied to the energy transport as well as the species transport aspects of the problem. The model is applied to four example cooling problems and is shown to perform exceedingly well from an algorithmic point of view.

Schneider, G. E.↗
NASA NTRS1992

Phase-field model for isothermal phase transitions in binary alloys

A new phase field model is described which models isothermal phase transitions between ideal binary alloy solution phases. Equations are developed for the temporal and spatial variation of the phase field, which describes the identity of the phase, and of the composition. An asymptotic analysis, as the gradient energy coefficient of the phase field becomes small, was conducted. From the analysis, it is shown that the model recovers classical sharp interface models of this situation when the interfacial layers are thin, and they show how to relate the parameters appearing in the phase field model to material and growth parameters in real systems. Further, three stages of temporal evolution are identified: the first corresponding to interfacial genesis which occurs very rapidly; the second to interfacial motion controlled by the local energy difference across the interface and diffusion; the last taking place on a long time scale in which curvature effects are important and which correspond to Ostwald ripening. The results of the numerical calculations are presented.

Wheeler, A. A.↗
NASA NTRS1984

Dendritic solidification in a binary alloy melt: Steady-state versus morphological stability theories

A model for dendritic growth in a binary alloy melt, in the presence of a positive temperature gradient in the liquid, is presented. The model describes satisfactorily the transition from a dendritic interface to a planar interface at very low and very large growth rates. A dendrite tip stability parameter is derived, strictly from steady state considerations, without resorting to a perturbation analysis. The estimates of the parameter agree with those obtained by models based on perturbation analyses.

Laymanan, V.↗
NASA NTRS1990

Effect of anisotropic thermal conductivity on the morphological stability of a binary alloy

A linear morphological stability analysis is presented for a planar interface during unidirectional solidification of a binary alloy, in the case of a crystal having an anisotropic thermal conductivity. A dispersion relation shows that the onset of instability depends on the orientation of the growth direction with respect to principal crystallographic axes and on the orientation of the wavevector of the perturbation. The onset of instability can be either oscillatory (traveling waves) or nonoscillatory in time. For growth along a principal axis of the crystal there is an exchange of stabilities, and the onset of instability is nonoscillatory.

Coriell, S. R.↗
NASA NTRS1978

Geometric relationships for homogenization in single-phase binary alloy systems

A semiempirical relationship is presented which describes the extent of interaction between constituents in single-phase binary alloy systems having planar, cylindrical, or spherical interfaces. This relationship makes possible a quick estimate of the extent of interaction without lengthy numerical calculations. It includes two parameters which are functions of mean concentration and interface geometry. Experimental data for the copper-nickel system are included to demonstrate the usefulness of this relationship.

Unnam, J.↗
NASA NTRS1979

An empirical relationship for homogenization in single-phase binary alloy systems

A semiempirical formula is developed for describing the extent of interaction between constituents in single-phase binary alloy systems with planar, cylindrical, or spherical interfaces. The formula contains two parameters that are functions of mean concentration and interface geometry of the couple. The empirical solution is simple, easy to use, and does not involve sequential calculations, thereby allowing quick estimation of the extent of interactions without lengthy calculations. Results obtained with this formula are in good agreement with those from a finite-difference analysis.

Unnam, J.↗
NASA NTRS1972

Temperature dependence of the electron density of states and dc electrical resistivity of disordered binary alloys.

A model calculation of the temperature dependence of the electronic density of states and the electrical conductivity of disordered binary alloys, based on the coherent-potential approximation is made by introducing thermal disorder in the single-band model (Velicky and others). Thermal disorder is found to broaden and smear the static-alloy density of states. The electrical resistivity in weak-scattering alloys always increases with temperature. However, in the strong-scattering case, the temperature coefficient of resistivity can be positive, zero, or negative, depending on the location of the Fermi energy.-

Chen, A.-B.↗
NASA NTRS1999

Directional Solidification of a Binary Alloy into a Cellular Convective Flow: Localized Morphologies

A steady, two dimensional cellular convection modifies the morphological instability of a binary alloy that undergoes directional solidification. When the convection wavelength is far longer than that of the morphological cells, the behavior of the moving front is described by a slow, spatial-temporal dynamics obtained through a multiple-scale analysis. The resulting system has a "parametric-excitation" structure in space, with complex parameters characterizing the interactions between flow, solute diffusion, and rejection. The convection stabilizes two dimensional disturbances oriented with the flow, but destabilizes three dimensional disturbances in general. When the flow is weak, the morphological instability behaves incommensurably to the flow wavelength, but becomes quantized and forced to fit into the flow-box as the flow gets stronger. At large flow magnitudes the instability is localized, confined in narrow envelopes with cells traveling with the flow. In this case the solutions are discrete eigenstates in an unbounded space. Their stability boundary and asymptotics are obtained by the WKB analysis.

Chen, Y.- J.↗
NASA NTRS1988

The effect of an electric field on the morphological stability of the crystal-melt interface of a binary alloy

A fully time-dependent linear stability analysis of the morphological stability of a planar interface during directional solidification of a binary alloy at constant velocity in the presence of an electric field, is performed. The electromigration of solute and the differing electrical conductivities of solid and liquid for a model in which the temperature gradient is constant are taken into account. The present results are compared with the constitutional supercooling criterion, and it is shown there may be substantial differences. A modified constitutional supercooling criterion which is valid over a large range of conditions is derived. It is also found under certain conditions that the onset of instability may be time dependent.

Wheeler, A. A.↗