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Results for “binary alloys”

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At least 343 records · Page 19

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NASA NTRS1986

Fluid mechanics and mass transfer in melt crystal growth: Analysis of the floating zone and vertical Bridgman processes

This research program focuses on analysis of the transport mechanisms in solidification processes, especially one of interest to the Microgravity Sciences and Applications Program of NASA. Research during the last year has focused on analysis of the dynamics of the floating zone process for growth of small-scale crystals, on studies of the effect of applied magnetic fields on convection and solute segregation in directional solidification, and on the dynamics of microscopic cell formation in two-dimensional solidification of binary alloys. Significant findings are given.

Brown, R. A.↗

NASA NTRS1988

Heat of mixing and morphological stability

A mathematical model, which incorporates heat of mixing in the energy balance, has been developed to analyze the morphological stability of a planar solid-liquid interface during the directional solidification of a binary alloy. It is observed that the stability behavior is almost that predicted by the analysis of Mullins and Sekerka (1963) at low growth velocities, while deviations in the critical concentration of about 20-25 percent are observed under rapid solidification conditions for certain systems. The calculations indicate that a positive heat of mixing makes the planar interface more unstable, whereas a negative heat of mixing makes it more stable, in terms of the critical concentration.

Nandapurkar, P.↗

NASA NTRS1988

Directional solidification with heat losses

The upward directional solidification of a dilute binary alloy in a tall, thin, two-dimensional slot is considered. Heat losses from the sidewalls produce curved isotherms, interface deformations, and melt convection. An asymptotic approach is used which relates the small heat loss to the thinness of the solidification cell, and solutions are obtained for the resulting melt convection, interface deflection, and the distribution of heat and solute. The model is compared to the numerical results of Chang and Brown (1983) which exclude the effects of solute buoyancy and thermodynamic equilibrium at the interface. The radial segregation at the interface (consistent with both interface shapes and temperature fields) is computed, and it is found that the radial segregation is independent of interfacial shapes; the radial segregation cannot be calculated from only a knowledge of the interface shape.

Brattkus, K.↗

NASA NTRS1989

Thermosolutal convection during dendritic solidification

This paper presents a mathematical model for directional solidification of a binary alloy including a dendritic region underlying an all-liquid region. It is assumed initially that there exists a nonconvecting state with planar isotherms and isoconcentrates solidifying at a constant velocity. The stability of this system has been analyzed and nonlinear calculations are performed that show the effect of convection in the solidification process when the system is unstable. Results of calculations for various cases defined by the initial temperature gradient at the dendrite tips and varying strength of the gravitational field are presented for systems involving lead-tin alloys. The results show that the systems are stable for a gravitational constant of 0.0001 g(0) and that convection can be suppressed by appropriate choice of the container's size for higher values of the gravitational constant. It is also concluded that for the lead-tin systems considered, convection in the mushy zone is not significant below the upper 20 percent of the dendritic zone, if al all.

Heinrich, J. C.↗

NASA NTRS1989

Buoyancy effects on morphological instability during directional solidification

The onset of morphological instability during the directional solidification of a single-phase binary alloy at constant velocity vertically upwards is treated by a linear stability analysis. The case in which a heavier solute is rejected at the solidifying interface is considered, and the effect of natural convection on the critical concentration for the onset of instability is studied. For tin containing lead, a small destabilization of the system at low growth velocities, and a large increase in the wavelength of the instability at the onset are found. Calculations show that the destabilization is enhanced as the variation of density with solute concentration is reduced, and in the limit of neutrally-dense solute, there is a long wavelength instability for which the critical solute concentration is several orders of magnitude lower than that predicted by the Mullins and Sekerka (1964) analysis in the absence of convection. For the neutrally-dense solute, a simplified analysis indicates the roles played by the interface deformation and thermal convection in promoting the instability. In particular, the destabilization is very sensitive to the ratio of crystal and melt thermal conductivities.

Coriell, S. R.↗

NASA NTRS1989

Electrical properties of materials for high temperature strain gage applications

A study was done on the electrical resistance of materials that are potentially useful as resistance strain gages at high temperatures under static strain conditions. Initially a number of binary alloys were investigated. Later, third elements were added to these alloys, all of which were prepared by arc melting. Several transition metals were selected for experimentation, most prepared as thin films. Difficulties with electrical contacts thwarted efforts to extend measurements to the targeted 1000 C, but results obtained did suggest ways of improving the electrical resistance characteristics of certain materials.

Brittain, John O.↗

NASA NTRS1990

Secondary arm coarsening and microsegregation in superalloy PWA-1480 single crystals: Effect of low gravity

Single crystal specimens of nickel base superalloy PWA-1480 were directionally solidified on ground and during low gravity (20 sec) and high gravity (90 sec) parabolic maneuver of KC-135 aircraft. Thermal profiles were measured during solidification by two in-situ thermocouples positioned along the sample length. The samples were quenched during either high or low gravity cycles so as to freeze the structures of the mushy zone developing under different gravity levels. Microsegregation was measured by examining the solutal profiles on several transverse cross-sections across primary dendrites along their length in the quenched mushy zone. Effect of gravity level on secondary arm coarsening kinetics and microsegregation have been investigated. The results indicate that there is no appreciable difference in the microsegregation and coarsening kinetics behavior in the specimens grown under high or low gravity. This suggests that short duration changes in gravity/levels (0.02 to 1.7 g) do not influence convection in the interdendritic region. Examination of the role of natural convection, in the melt near the primary dendrite tips, on secondary arm spacings requires low gravity periods longer than presently available on KC-135. Secondary arm coarsening kinetics show a reasonable fit with the predictions from a simple analytical model proposed by Kirkwood for a binary alloy.

Vijayakumar, M.↗

NASA NTRS1990

Salt-finger convection under reduced gravity

Salt-finger convection in a double-diffusive system is a motion driven by the release of gravitational potential due to differential diffusion rates. Because of the fact that the destabilizing effect of the concentration gradient is amplified by the Lewis number (the ratio of thermal diffusivity to solute diffusivity) salt-finger convection can be generated at very much reduced gravity levels. This effect may be of importance in the directional solidification of binary alloys carried out in space. The transport of solute and heat by salt-finger convection at microgravity conditions is considered; instability arising from surface tension gradients, the Marangoni instability, is discussed, and the possible consequences of combined salt-finger and Marangoni instability are considered.

Chen, C. F.↗

NASA NTRS1992

Boundary-conforming mapping applied to computations of highly deformed solidification interfaces

A new boundary-conforming mapping is developed for the calculation of highly deformed cellular solidification interfaces in a model of directional solidification of a binary alloy. The mapping is derived through a variational formulation that is designed so that the grid penetrates the grooves between cells along the interface without causing a loss of ellipticity of the mapping equations. A finite element/Newton method is presented for simultaneous solution of the free boundary problem described by the solutal model of directional solidification and the mapping equations. Results are compared to previous calculations and demonstrate the importance of accurate representation of the interface shape for understanding the solution structure.

Tsiveriotis, K.↗

NASA NTRS1992

The effect of compositionally-generated elastic stresses on morphological instability during directional solidification

The effect of compositionally-generated elastic stresses on the conditions for morphological instability during directional solidification of a dilute, ideal binary alloy is investigated using the Gibbs-Thomson equations for an elastically-stressed solid with zero surface stress in equilibrium with a liquid. It is found that these stresses lead to a small stabilization of the Mullins and Sekerka cellular mode of instability. The steady mode is stabilized by a stress-induced modification to the interfacial concentration of the solid, which in turn alters the amount of solute rejected to inhibit the growth of perturbations. The presence of elastic stresses could generate a new oscillatory instability which is most likely to be found in experiments near absolute stability for materials with segregation coefficients near unity and large solute expansion coefficients.

Spencer, B. J.↗

NASA NTRS1992

Cellular instability in rapid directional solidification - Bifurcation theory

Merchant and Davis performed a linear stability analysis on a model for the directional solidification of a dilute binary alloy valid for all speeds. The analysis revealed that nonequilibrium segregation effects modify the Mullins and Sekerka cellular mode, whereas attachment kinetics has no effect on these cells. In this paper, the nonlinear stability of the steady cellular mode is analyzed. A Landau equation is obtained that determines the amplitude of the cells. The Landau coefficient here depends on both nonequilibrium segregation effects and attachment kinetics. This equation gives the ranges of parameters for subcritical bifurcation (jump transition) or supercritical bifurcation (smooth transition) to cells.

Braun, R. J.↗

NASA NTRS1992

Pulsatile instability in rapid directional solidification - Strongly-nonlinear analysis

In the rapid directional solidification of a dilute binary alloy, analysis reveals that, in addition to the cellular mode of Mullins and Sekerka (1964), there is an oscillatory instability. For the model analyzed by Merchant and Davis (1990), the preferred wavenumber is zero; the mode is one of pulsation. Two strongly nonlinear analyses are performed that describe this pulsatile mode. In the first case, nonequilibrium effects that alter solute rejection at the interface are taken asymptotically small. A nonlinear oscillator equation governs the position of the solid-liquid interface at leading order, and amplitude and phase evolution equations are derived for the uniformly pulsating interface. The analysis provides a uniform description of both subcritical and supercritical bifurcation and the transition between the two. In the second case, nonequilibrium effects that alter solute rejection are taken asymptotically large, and a different nonlinear oscillator equation governs the location of the interface to leading order. A similar analysis allows for the derivation of an amplitude evolution equation for the uniformly pulsating interface. In this case, the bifurcation is always supercritical. The results are used to make predictions about the characteristics of solute bands that would be frozen into the solid.

Merchant, G. J.↗

NASA NTRS1993

Solution of free-boundary problems using finite-element/Newton methods and locally refined grids - Application to analysis of solidification microstructure

A new method is presented for the solution of free-boundary problems using Lagrangian finite element approximations defined on locally refined grids. The formulation allows for direct transition from coarse to fine grids without introducing non-conforming basis functions. The calculation of elemental stiffness matrices and residual vectors are unaffected by changes in the refinement level, which are accounted for in the loading of elemental data to the global stiffness matrix and residual vector. This technique for local mesh refinement is combined with recently developed mapping methods and Newton's method to form an efficient algorithm for the solution of free-boundary problems, as demonstrated here by sample calculations of cellular interfacial microstructure during directional solidification of a binary alloy.

Tsiveriotis, K.↗

NASA NTRS1993

The effect of gravitational modulation on convection in vertical Bridgman growth

During vertical directional solidification of a binary alloy at constant velocity, buoyancy-driven solutal convection may occur due to the solute gradient associated with the solidification process. This problem is further complicated if time-periodic forcing is considered, which is relevant to materials processing in a microgravity environment or as a means of dynamic control of flow instabilities. The effect of time-periodic modulation is studied by introducing a gravitational acceleration which is a sinusoidal function of time. The onset of solutal convection is treated by a stability analysis of the linearized governing equations and boundary conditions. Solutions are obtained numerically employing two distinct computational implementations of Floquet theory. Results are presented for materials with large Schmidt number, and an analysis for large frequency and large Schmidt number yields a more complete description of the behavior in this relevant limit.

Murray, B. T.↗

NASA NTRS1992

The effect of gravity modulation on thermosolutal convection

In a gravitational field, the opposing effects of components of different diffusivities, for example, temperature and solute, in the density profile in a fluid may produce convective instabilities that exhibit a broad range of dynamical behavior. The effect of time periodic vertical gravity modulation on the onset of these instabilities in an infinite horizontal layer with stress free boundaries is examined. This work is viewed as a first step in expanding previous results in solidification to the full problem of characterizing the effects of gravity modulation in thermosolutal convection during the directional solidification of binary alloys. Calculations carried out both with and without steady background acceleration are presented, the latter results being relevant to microgravity conditions.

Saunders, Bonita V.↗

NASA NTRS1992

The effect of gravitational modulation on convection in vertical Bridgman growth

During vertical directional solidification of a binary alloy at constant velocity, buoyancy driven solutal convection may occur due to the solute gradient associated with the solidification process. This problem is further complicated if time periodic forcing is considered, which is relevant to materials processing in a microgravity environment or as a means of dynamic control of flow instabilities. The effect of time periodic modulation is studied by introducing a gravitational acceleration which is a sinusoidal function of time. The onset of solutal convection is treated by a stability analysis of the linearized governing equations and boundary conditions. Solutions are obtained numerically by employing two distinct computational implementations of Floquet theory. Results for materials with large Schmidt number are presented, and an analysis for large frequency and large Schmidt number yields a more complete description of the behavior in this relevant limit.

Murray, Bruce T.↗

NASA NTRS1994

Convection and morphological stability during directional solidification

For growth of a vicinal face at constant velocity, the effect of anisotropic interface kinetics on morphological stability is calculated for a binary alloy. The dependence of the interface kinetic coefficient on crystallographic orientation is based on the motion and density of steps. Anisotropic kinetics give rise to traveling waves along the crystal-melt interface, and can lead to a significant enhancement of morphological stability. The stability enhancement increases as the orientation approaches a singular orientation and as the solidification velocity increases. Shear flows interact with the traveling waves and, depending on the direction of the flow, may either stabilize or destabilize the interface. Specific calculations are carried out for germanium-silicon alloys.

Coriell, Sam R.↗

NASA NTRS1994

Shear stabilization of solidification fronts

A linear-stability analysis is performed on the interface formed during the directional solidification of a dilute binary alloy in the presence of a time-periodic flow. In general, the flow is generated by the elliptical motion of the crystal parallel to the interface. The presence of the flow can either stabilize or destabilize the system relative to the case without flow with the result depending on the frequency and amplitude of the oscillations as well as the properties of the material. In the particular, we find that the morphological instability present in the absence of flow can be entirely suppressed with respect to disturbances of the same frequency as the oscillation.

Davis, Stephen H.↗