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At least 19 records

Coarsening in Solid-Liquid Mixtures Studied on the Space Shuttle

Ostwald ripening, or coarsening, is a process in which large particles in a two-phase mixture grow at the expense of small particles. It is a ubiquitous natural phenomena occurring in the late stages of virtually all phase separation processes. In addition, a large number of commercially important alloys undergo coarsening because they are composed of particles embedded in a matrix. Many of them, such as high-temperature superalloys used for turbine blade materials and low-temperature aluminum alloys, coarsen in the solid state. In addition, many alloys, such as the tungsten-heavy metal systems, coarsen in the solid-liquid state during liquid phase sintering. Numerous theories have been proposed that predict the rate at which the coarsening process occurs and the shape of the particle size distribution. Unfortunately, these theories have never been tested using a system that satisfies all the assumptions of the theory. In an effort to test these theories, NASA studied the coarsening process in a solid-liquid mixture composed of solid tin particles in a liquid lead-tin matrix. On Earth, the solid tin particles float to the surface of the sample, like ice in water. In contrast, in a microgravity environment this does not occur. The microstructures in the ground- and space-processed samples (see the photos) show clearly the effects of gravity on the coarsening process. The STS-83-processed sample (right image) shows nearly spherical uniformly dispersed solid tin particles. In contrast, the identically processed, ground-based sample (left image) shows significant density-driven, nonspherical particles, and because of the higher effective solid volume fraction, a larger particle size after the same coarsening time. The "Coarsening in Solid-Liquid Mixtures" (CSLM) experiment was conducted in the Middeck Glovebox facility (MGBX) flown aboard the shuttle in the Microgravity Science Laboratory (MSL-1/1R) on STS-83/94. The primary objective of CSLM is to measure the temporal evolution of the solid particles during coarsening.

Caruso, John J.↗

The Evolution of Dendrite Morphology during Isothermal Coarsening

Dendrite coarsening is a common phenomenon in casting processes. From the time dendrites are formed until the inter-dendritic liquid is completely solidified dendrites are changing shape driven by variations in interfacial curvature along the dendrite and resulting in a reduction of total interfacial area. During this process the typical length-scale of the dendrite can change by orders of magnitude and the final microstructure is in large part determined by the coarsening parameters. Dendrite coarsening is thus crucial in setting the materials parameters of ingots and of great commercial interest. This coarsening process is being studied in the Pb-Sn system with Sn-dendrites undergoing isothermal coarsening in a Pb-Sn liquid. Results are presented for samples of approximately 60% dendritic phase, which have been coarsened for different lengths of times. Presented are three-dimensional microstructures obtained by serial-sectioning and an analysis of these microstructures with regard to interface orientation and interfacial curvatures. These graphs reflect the evolution of not only the microstructure itself, but also of the underlying driving forces of the coarsening process. As a visualization of the link between the microstructure and the driving forces a three-dimensional microstructure with the interfaces colored according to the local interfacial mean curvature is shown.

Alkemper, Jens↗

Structure and grain coarsening during the processing of engineering ceramics

Studies have been made of three ceramic systems (Al2O3, Y2O3/MgO, and SiC/C/B), both to explore a surface area/density diagram approach to examining the coarsening processes during sintering and to explore an alternative coarsening parameter, i.e., the grain boundary surface area (raising it at a given value of the density) and not the pore surface area; therefore, pinning of the grain boundaries by solid-solution drag is the only function evidenced by these results. The importance of such pinning even at densities as low as 75% of theoretical is linked to the existence of microstructural inhomogeneities. The early stages of sintering of Y2O3 powder have been examined using two techniques, BET surface area analysis and transmission electron microscopy. Each has given some insight into the process occurring and, used together, have provided some indication of the effect of MgO on coarsening during sintering. Attempts to further elucidate effects of MgO on the coarsening behavior of Y2O3 by the surface area/density diagram approach were unsuccessful due to masking effects of contaminating reactions during sintering and/or thermal etching. The behavior of the undoped SiC which only coarsens can be clearly distinguished by the surface area/density diagram from that of SiC/C/B which also concurrently densifies. Little additional information was obtainable by this method due to unfavorable sample etching characteristics. The advantages, disadvantages, and difficulties of application of these techniques to the study of coarsening during sintering are discussed.

Shaw, Nancy J.↗

Coarsening in high volume fraction nickel-base alloys

The coarsening behavior of the gamma-prime precipitate has been examined in high volume fraction nickel-base alloys aged at elevated temperatures for times of up to 5000 h. Although the cube rate law was observed during coarsening, none of the presently available coarsening theories showed complete agreement with the experimental particle size distributions (PSDs). These discrepancies were thought to be due to elastic coherency strains which were not considered by the available models. Increasing the Mo content significantly influenced the PSDs and decreased the coarsening rate of the gamma-prime cubes, as a result of increasing the magnitude of the lattice mismatch. After extended aging times, the gamma-prime cubes underwent massive coalescence into plates at a rate which was much faster than the cuboidal coarsening rate. Once the gamma-prime plates were formed, further coarsening was not observed, and this stabilization of the microstructure was attributed to the development of dislocation networks at the gamma-gamma-prime interfaces.

Mackay, R. A.↗

Evolution of Local Microstructures: Spatial Instabilities in Coarsening Clusters

Diffusion-limited capillarity-driven coarsening of precipitates is an important and intensively studied phenomenon. The classic coarsening theory developed by Lifshitz and Syozov and Wagner (LSW theory) is limited to infinitesimally small volume fractions, V(sub nu), therefore neglects all direct interparticle interactions. This work uses modeling and holographic imaging to compare coarsening rates in "high" volume fraction versus low volume fraction microstructures by observing mixed-dimensional droplets (spherical caps on a surface coarsening by two-dimensional diffusion) during ground-based investigations. The method involves filling a cell with selected homogeneous parent phase, and cooling below the consolute temperature to the isopycnic temperature in the two-phase region of a monotectic system. A microgravity holographic experiment is required for three-dimensional observations to minimize sedimentation during long-term coarsening. Determination of sizes and positions of the many droplets in the holographic images requires automation. We have developed software for automated data analysis, and demonstrated good agreement between regenerated maps and scaled photographs of the original holograms for mixed dimensional coarsening. The results of these experiments were presented in a formal microgravity Science Concept Review (SCR) on December 18, 2000.

Source record↗

A Robust Locally Preconditioned Semi-Coarsening Multigrid Algorithm for the 2-D Navier-Stokes Equations

The goal of this thesis is to develop an efficient and robust locally preconditioned semi-coarsening multigrid algorithm for the two-dimensional Navier-Stokes equations. This thesis examines the performance of the multigrid algorithm with local preconditioning for an upwind-discretization of the Navier-Stokes equations. A block Jacobi iterative scheme is used because of its high frequency error mode damping ability. At low Mach numbers, the performance of a flux preconditioner is investigated. The flux preconditioner utilizes a new limiting technique based on local information that was developed by Siu. Full-coarsening and-semi-coarsening are examined as well as the multigrid V-cycle and full multigrid. The numerical tests were performed on a NACA 0012 airfoil at a range of Mach numbers. The tests show that semi-coarsening with flux preconditioning is the most efficient and robust combination of coarsening strategy, and iterative scheme - especially at low Mach numbers.

Cain, Michael D.↗

Software for Refining or Coarsening Computational Grids

A computer program performs calculations for refinement or coarsening of computational grids of the type called 'structured' (signifying that they are geometrically regular and/or are specified by relatively simple algebraic expressions). This program is designed to facilitate analysis of the numerical effects of changing structured grids utilized in computational fluid dynamics (CFD) software. Unlike prior grid-refinement and -coarsening programs, this program is not limited to doubling or halving: the user can specify any refinement or coarsening ratio, which can have a noninteger value. In addition to this ratio, the program accepts, as input, a grid file and the associated restart file, which is basically a file containing the most recent iteration of flow-field variables computed on the grid. The program then refines or coarsens the grid as specified, while maintaining the geometry and the stretching characteristics of the original grid. The program can interpolate from the input restart file to create a restart file for the refined or coarsened grid. The program provides a graphical user interface that facilitates the entry of input data for the grid-generation and restart-interpolation routines.

Daines, Russell↗

Software for Refining or Coarsening Computational Grids

A computer program performs calculations for refinement or coarsening of computational grids of the type called "structured" (signifying that they are geometrically regular and/or are specified by relatively simple algebraic expressions). This program is designed to facilitate analysis of the numerical effects of changing structured grids utilized in computational fluid dynamics (CFD) software. Unlike prior grid-refinement and -coarsening programs, this program is not limited to doubling or halving: the user can specify any refinement or coarsening ratio, which can have a noninteger value. In addition to this ratio, the program accepts, as input, a grid file and the associated restart file, which is basically a file containing the most recent iteration of flow-field variables computed on the grid. The program then refines or coarsens the grid as specified, while maintaining the geometry and the stretching characteristics of the original grid. The program can interpolate from the input restart file to create a restart file for the refined or coarsened grid. The program provides a graphical user interface that facilitates the entry of input data for the grid-generation and restart-interpolation routines.

Daines, Russell↗

Software for Refining or Coarsening Computational Grids

A computer program performs calculations for refinement or coarsening of computational grids of the type called structured (signifying that they are geometrically regular and/or are specified by relatively simple algebraic expressions). This program is designed to facilitate analysis of the numerical effects of changing structured grids utilized in computational fluid dynamics (CFD) software. Unlike prior grid-refinement and -coarsening programs, this program is not limited to doubling or halving: the user can specify any refinement or coarsening ratio, which can have a noninteger value. In addition to this ratio, the program accepts, as input, a grid file and the associated restart file, which is basically a file containing the most recent iteration of flow-field variables computed on the grid. The program then refines or coarsens the grid as specified, while maintaining the geometry and the stretching characteristics of the original grid. The program can interpolate from the input restart file to create a restart file for the refined or coarsened grid. The program provides a graphical user interface that facilitates the entry of input data for the grid-generation and restart-interpolation routines.

Daines, Russell↗

High temperature coarsening of Cr2Nb precipitates in Cu-8 Cr-4 Nb alloy

A new high-temperature-strength, high-conductivity Cu-Cr-Nb alloy with a CrNb ratio of 2:1 was developed to achieve improved performance and durability. The Cu-8 Cr4 Nb alloy studied has demonstrated remarkable thermal and microstructural stability after long exposures at temperatures up to 0.98 T(sub m). This stability was mainly attributed to the slow coarsening kinetics of the Cr2Nb precipitates present in the alloy. At all temperatures, the microstructure consists of a bimodal and sometimes trimodal distribution of strengthening Cr2Nb precipitates, depending on precipitation condition, i.e. from liquid or solid solution, and cooling rates. These precipitates remain in the same size range, i.e. large precipitates of approximately I pm, and small precipitates less dm 300 nm, and effectively pin the grain boundaries thus retaining a fine grain size of 2.7 micro-m after 100 h at 1323 K. (A relatively small number of Cr-rich and Nb-rich particles were also present.) This grain boundary pinning and sluggish coarsening of Cr2Nb particles explain the retention of good mechanical properties after prolonged holding at very high temperatures, e.g., 75% of the original hardness after aging for 100 h at 1273 K. Application of LSW-based coarsening models indicated that the coarsening kinetics of the large precipitates are most likely governed by grain boundary diffsion and, to a lesser extent, volume diffusion mechanisms.

Anderson, Kenneth Reed↗

Evolution of Local Microstructures: Spatial Instabilities of Coarsening Clusters

This work examines the diffusional growth of discrete phase particles dispersed within a matrix. Engineering materials are microstructurally heterogeneous, and the details of the microstructure determine how well that material performs in a given application. Critical to the development of designing multiphase microstructures with long-term stability is the process of Ostwald ripening. Ripening, or phase coarsening, is a diffusion-limited process which arises in polydisperse multiphase materials. Growth and dissolution occur because fluxes of solute, driven by chemical potential gradients at the interfaces of the dispersed phase material, depend on particle size. The kinetics of these processes are "competitive," dictating that larger particles grow at the expense of smaller ones, overall leading to an increase of the average particle size. The classical treatment of phase coarsening was done by Todes, Lifshitz, and Slyozov, (TLS) in the limit of zero volume fraction, V(sub v), of the dispersed phase. Since the publication of TLS theory there have been numerous investigations, many of which sought to describe the kinetic scaling behavior over a 0 range of volume fractions. Some studies in the literature report that the relative increase in coarsening rate at low (but not zero) volume fractions compared to that predicted by TLS is proportional to v(sub v)(exp 1/2), whereas others suggcest V(sub v)(exp 1/3). This issue has been resolved recently by simulation studies at low volume fractions in three dimensions by members of the Rensselaer/MSFC team. Our studies of ripening behavior using large-scale numerical simulations suggest that although there are different circumstances which can lead to either scaling law, the most important length scale at low volume fractions is the diffusional analog of the Debye screening length. The numerical simulations we employed exploit the use of a recently developed "snapshot" technique, and identifies the nature of the coarsening dynamics at various volume fractions. Preliminary results of numerical and experimental investigations, focused on the growth of finite particle clusters, provide important insight into the nature of the transition between the two scaling regimes. The companion microgravity experiment centers on the growth within finite particle clusters, and follows the temporal dynamics driving microstructural evolution, using holography.

Frazier, Donald O.↗

Coarsening in Solid-Liquid Mixtures-2: A Materials Science Experiment for the ISS

A materials science experiment has been developed and readied for operation aboard the International Space Station (ISS). Components of this experiment are onboard ISS and area awaiting the flight of science samples. The goal of the experiment is to understand the dynamics of Ostwald ripening, also known as coarsening, a process that occurs in nearly any two-phase mixture found in nature. Attempts to obtain experimental data in ground-based laboratories are hindered due to the presence of gravity, which introduces material transport modes other than that of the coarsening phenomenon. This introduces adjustable parameters in the formulation of theory. The original Coarsening in Solid-Liquid Mixtures (CSLM) mission, which flew on the Space Shuttle in 1997, produced data from a coarsened eutectic alloy. Unfortunately, both the science matrix and the hardware, while nominally functional, did not account adequately for operations in microgravity. A significantly redesigned follow-on experiment, CSLM-2 has been developed to redress the inadequacies of the original experiment. This paper reviews the CSLM-2 project: its history, science goals, flight hardware implementation, and planned operations and analysis

Hickman, J. Mark↗

Coarsening Experiment Being Prepared for Flight

The Coarsening in Solid-Liquid Mixtures-2 (CSLM-2) experiment is a materials science space flight experiment whose purpose is to investigate the kinetics of competitive particle growth within a liquid matrix. During coarsening, small particles shrink by losing atoms to larger particles, causing the larger particles to grow. In this experiment, solid particles of tin will grow (coarsen) within a liquid lead-tin eutectic matrix. The preceding figures show the coarsening of tin particles in a lead-tin eutectic as a function of time. By conducting this experiment in a microgravity environment, we can study a greater range of solid volume fractions, and the effects of sedimentation present in terrestrial experiments will be negligible. The CSLM-2 experiment is slated to fly onboard the International Space Station. The experiment will be run in the Microgravity Science Glovebox installed in the U.S. Laboratory module.

Hickman, J. Mark↗

Coarsening Experiment Prepared for Flight

The Coarsening in Solid-Liquid Mixtures-2 (CSLM-2) experiment is a materials science spaceflight experiment whose purpose is to investigate the kinetics of competitive particle growth within a liquid matrix. During coarsening, small particles shrink by losing atoms to larger particles, causing the larger particles to grow. In this experiment, solid particles of tin will grow (coarsen) within a liquid lead-tin eutectic matrix. The following figures show the coarsening of tin particles in a lead-tin (Pb-Sn) eutectic as a function of time. By conducting this experiment in a microgravity environment, we can study a greater range of solid volume fractions, and the effects of sedimentation present in terrestrial experiments will be negligible. The CSLM-2 experiment flew November 2002 on space shuttle flight STS-113 for operation on the International Space Station, but it could not be run because of problems with the Microgravity Science Glovebox in the U.S. Laboratory module. Additional samples will be sent to ISS on subsequent shuttle flights.

Hickman, J. Mark↗

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.↗

Densification and coarsening during solid state sintering of ceramics: A review of the models. II - Grain growth

Two processes occur simultaneously during the sintering of a ceramic powder compact: densification and coarsening (or grain growth). Both processes have as their driving force the reduction of the excess free surface energy of the powder particles. Several different mechanisms of atom transport, operating concurrently or consecutively, may be responsible for the two processes. Algebraic, geometric and topological models have been proposed and refined in attempts to determine the mechanism, or mechanisms, responsible for densification under defined processing conditions. These efforts have met with varying degrees of success. Recently, it has become apparent that more attention must be paid to the coarsening processes during sintering. The models for both densification and coarsening during solid state sintering are reviewed with particular emphasis on their applicability to engineering ceramics.

Shaw, Nancy J.↗

Coarsening following a morphological instability in the one-sided model

We study the coarsening of the interfacial pattern separating two coexisting phases after the pattern becomes morphologically unstable. Shortly after the instability, the scale of the structure is given by the most unstable wave number in the linear regime. At later times, nonlinear interactions cause the structure to coarsen. Coarsening is studied by monitoring the time dependence of the two-dimensional power spectrum of the pattern, especially for wave vectors transverse to the direction of growth. Characteristic length scales of the pattern obtained from moments of the power spectrum are asymptotically linear in time. Furthermore, the power spectrum is seen to satisfy a scaling relation, in agreement with previous studies. A normal-velocity autocorrelation function is calculated and found to decay substantially over length scales that are of the order of the scale of the pattern. The issue of spatial anisotropy in the correlation functions is also discussed.

Vinals, Jorge↗

Evolution of Local Microstructures (ELMS): Spatial Instabilities of Coarsening

This work examines the diffusional growth of discrete phase particles dispersed within a matrix. Engineering materials are microstructurally heterogeneous, and the details of the microstructure determine how well that material performs in a given application. Critical to the development of designing multiphase microstructures with long-term stability is the process of Ostwald ripening. Ripening, or phase coarsening, is a diffusion-limited process which arises in polydisperse multiphase materials. Growth and dissolution occur because fluxes of solute, driven by chemical potential gradients at the interfaces of the dispersed phase material, depend on particle size. The kinetics of these processes are "competitive," dictating that larger particles grow at the expense of smaller ones, overall leading to an increase of the average particle size. The classical treatment of phase coarsening was done by Todes, Lifshitz, and Slyozov, (TLS) in the limit of zero volume fraction, V(sub v), of the dispersed phase. Since the publication of TLS theory there have been numerous investigations, many of which sought to describe the kinetic scaling behavior over a range of volume fractions. Some studies in the literature report that the relative increase in coarsening rate at low (but not zero) volume fractions compared to that / 2 1/ 3 predicted by TLS is proportional to V(sub v)(exp 1/2), whereas others suggest V(sub v)(exp 1/3). This issue has been resolved recently by simulation studies at low volume fractions in three dimensions by members of the Rensselaer/MSFC team.

Glicksman, Martin E.↗