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NASA NTRS1986

Ostwald ripening theory

The Ostwald-ripening theory is deduced and discussed starting from the fundamental principles such as Ising model concept, Mayer cluster expansion, Langer condensation point theory, Ginzburg-Landau free energy, Stillinger cutoff-pair potential, LSW-theory and MLSW-theory. Mathematical intricacies are reduced to an understanding version. Comparison of selected works, from 1949 to 1984, on solution of diffusion equation with and without sink/sources term(s) is presented. Kahlweit's 1980 work and Marqusee-Ross' 1954 work are more emphasized. Odijk and Lekkerkerker's 1985 work on rodlike macromolecules is introduced in order to simulate interested investigators.

Baird, J. K.↗

NASA NTRS1988

Numerical simulation of morphological development during Ostwald ripening

The morphological evolution of a small number of particles undergoing Ostwald ripening in two dimensions was investigated using a boundary integral technique. The numerical calculations show that, in many cases, interparticle diffusional interactions do not induce large distortions in particle morphology from a circle, due to the strong local interaction between regions of different curvature on the same particle. Particle migration due to interparticle diffusional interactions was observed, with the migration distance larger than the initial radius of a particle, which is linked to the particle spatial arrangement. As diffusion is the mechanism for the migration, it is expected that particle movement is a generic aspect of the coarsening process at high volume fractions of coarsening phase and, possibly, at low volume fractions. The calculations support unambiguously the Ostwald ripening mechanism for flat formation during liquid-phase sintering. As such, the appearance or regions of low interfacial curvature is a dynamic phenomenon dependent on interparticle diffusion.

Voorhees, P. W.↗

NASA NTRS1990

Structure function calculations for Ostwald Ripening processes

A program for computing the structure function for configurations involved in Ostwald Ripening was written. The basic algorithms are derived from a mathematical analysis of a two-dimensional model system developed by Bortz, et. al. (1974). While it is expected that the values form the computer simulations will reflect Ostwald Ripening, at this point the program is still being tested. Some preliminary runs seem to justify the expectations.

Hassan, Razi A.↗

NASA NTRS1986

Theory of Ostwald ripening in a two-component system

When a two-component system is cooled below the minimum temperature for its stability, it separates into two or more immiscible phases. The initial nucleation produces grains (if solid) or droplets (if liquid) of one of the phases dispersed in the other. The dynamics by which these nuclei proceed toward equilibrium is called Ostwald ripening. The dynamics of growth of the droplets depends upon the following factors: (1) The solubility of the droplet depends upon its radius and the interfacial energy between it and the surrounding (continuous) phase. There is a critical radius determined by the supersaturation in the continuous phase. Droplets with radii smaller than critical dissolve, while droplets with radii larger grow. (2) The droplets concentrate one component and reject the other. The rate at which this occurs is assumed to be determined by the interdiffusion of the two components in the continuous phase. (3) The Ostwald ripening is constrained by conservation of mass; e.g., the amount of materials in the droplet phase plus the remaining supersaturation in the continuous phase must equal the supersaturation available at the start. (4) There is a distribution of droplet sizes associated with a mean droplet radius, which grows continuously with time. This distribution function satisfies a continuity equation, which is solved asymptotically by a similarity transformation method.

Baird, J. K.↗

NASA NTRS1985

Extension of Ostwald Ripening Theory

The objective is to develop models based on the mean field approximation of Ostwald ripening to describe the growth of second phase droplets or crystallites. The models will include time variations in nucleation rate, control of saturation through addition of solute, precipitating agents, changes in temperature, and various surface kinetic effects. Numerical integration schemes have been developed and tested against the asymptotic solution of Liftshitz, Slyozov and Wagner (LSW). A second attractor (in addition to the LSW distribution) has been found and, contrary to the LSW theory, the final distribution is dependent on the initial distribution. A series of microgravity experiments is being planned to test this and other results from this work.

Baird, J.↗

NASA NTRS1985

Growth of Organic Crystals by Ostwald Ripening

The objective of this investigation is to evaluate the growth of various organic crystals by chemical precipitation and Ostwald ripening. Six precipitation reactors were flown on STS-51A. Five of the reactors contained proprietary materials. The sixth contained urea dissolved in ethanol with toluene as the precipitating agent. The size distribution will be analyzed and compared with a similar model being developed.

Egbert, W.↗

NASA NTRS1987

Correlations and Ostwald ripening

A previously developed model (Weins and Cahn, 1973) describing the growth of spheres of a second phase in metal alloys (Ostwald coarsening) is slightly modified to make it possible to study the complete time evolution of the system rather than simply the late-stage scaling behavior. Closed equations are obtained which describe the time evolution of two-particle correlations in the system. The development of the correlations is analyzed, and simpler expressions are found and solved numerically. The results are compared with experimental data for different systems (e.g., Ni-Al, Ni-Cr-Al, Co-Ni-Cr-Ti, Cu-Co, and MgO-Fe), alternate methods, and existing theories.

Marder, M.↗

NASA NTRS1985

Ostwald ripening theory

An approximate analytical technique for extracting the concentration dependence of the interdiffusion coefficient was derived from diffusion measurements carried out with the diaphragm cell. The systematic error incurred in using the technique was estimated and found to be no greater than the random error ordinarily encountered in these experiments.

Baird, J. K.↗

NASA NTRS1988

Ostwald ripening in a system with a high volume fraction of coarsening phase

The coarsening of Sn-rich and Pb-rich solid phases in contact with eutectic liquid in the volume fraction solid range above approximately 0.6, where the development of a solid skeletal structure inhibits sedimentation, is investigated. Particle intercept distributions are shown to be time independent when scaled by the average intercept. It is noted that the coarsening rate constants obtained exceed the values calculated from theory by factors ranging from about 2 to 5.

Hardy, S. C.↗

NASA NTRS1976

Direct observation of small cluster mobility and ripening

Direct evidence is reported for the simultaneous occurrence of Ostwald ripening and short-distance cluster mobility during annealing of discontinuous metal films on clean amorphous substrates. The annealing characteristics of very thin particulate deposits of silver on amorphized clean surfaces of single-crystalline thin graphite substrates have been studied by in situ transmission electron microscopy (TEM) under controlled environmental conditions in the temperature range from 25 to 450 C. It was possible to monitor all stages of the experiments by TEM observation of the same specimen area. Slow Ostwald ripening was found to occur over the entire temperature range, but the overriding surface transport mechanism was short-distance cluster mobility. This was concluded from in situ observations of individual particles during annealing and from measurements of cluster size distributions, cluster number densities, area coverages, and mean cluster diameters.

Heinemann, K.↗

NASA NTRS1975

Direct observation of small cluster mobility and ripening

Direct evidence is reported for the simultaneous occurrence of Ostwald ripening and short-distance cluster mobility during annealing of discontinuous metal films on clean amorphous substrates. The annealing characteristics of very thin particulate deposits of silver on amorphized clean surfaces of single crystalline thin graphite substrates were studied by in-situ transmission electron microscopy (TEM) under controlled environmental conditions (residual gas pressure of 10 to the minus 9th power torr) in the temperature range from 25 to 450 C. Sputter cleaning of the substrate surface, metal deposition, and annealing were monitored by TEM observation. Pseudostereographic presentation of micrographs in different annealing stages, the observation of the annealing behavior at cast shadow edges, and measurements with an electronic image analyzing system were employed to aid the visual perception and the analysis of changes in deposit structure recorded during annealing. Slow Ostwald ripening was found to occur in the entire temperature range, but the overriding surface transport mechanism was short-distance cluster mobility.

Heinemann, K.↗

NASA NTRS2013

Coarsening in Solid-liquid Mixtures: Overview of Experiments on Shuttle and ISS

The microgravity environment on the Shuttle and the International Space Station (ISS) provides the ideal condition to perform experiments on Coarsening in Solid-Liquid Mixtures (CSLM) as deleterious effects such as particle sedimentation and buoyancy-induced convection are suppressed. For an ideal system such as Lead-Tin in which all the thermophysical properties are known, the initial condition in microgravity of randomly dispersed particles with local clustering of solid Tin in eutectic liquid Lead-Tin matrix, permitted kinetic studies of competitive particle growth for a range of volume fractions. Verification that the quenching phase of the experiment had negligible effect of the spatial distribution of particles is shown through the computational solution of the dynamical equations of motion, thus insuring quench-free effects from the coarsened microstructure measurements. The low volume fraction experiments conducted on the Shuttle showed agreement with transient Ostwald ripening theory, and the steady-state requirement of LSW theory was not achieved. More recent experiments conducted on ISS with higher volume fractions have achieved steady-state condition and show that the kinetics follows the classical diffusion limited particle coarsening prediction and the measured 3D particle size distribution becomes broader as predicted from theory.

Ostwald ripening↗

NASA NTRS1983

Gamma prime shape changes during creep of a nickel-base superalloy

Changes in the shape of the gamma-prime phase in the single-crystal nickel base alloy NASAIR 100 during tensile and compressive creep have been investigated experimentally by Laue X-ray diffractometry. It is found that under tensile loading, gamma-prime changes from the initial cubic shape to plates perpendicular to the applied stress. This change occurs during primary creep at 1000 C, 148 MPa. Prolonged creep exposures result in a thickening of the gamma-prime plates that is similar to Ostwald ripening often observed in other superalloys during creep. Under compressive loading, two sets of gamma-prime plates parallel to the applied stress are formed.

Nathal, M. V.↗

NASA NTRS1985

Elevated temperature creep-rupture behavior of the single crystal nickel-base superalloy NASAIR 100

The creep and rupture behavior of 001-line-oriented single crystals of the nickel-base superalloy NASAIR 100 was investigated at temperatures of 925 and 1000 C. In the stress and temperature ranges studied, the steady state creep rate, time to failure, time to the onset of secondary creep, and the time to the onset of tertiary creep all exhibited power law dependencies on the applied stress. The creep rate exponents for this alloy were between seven and eight, and the modulus-corrected activation energy for creep was approximately 350 kjoule/mole, which was comparable to the measured activation energy for Ostwald ripening of the gamma-prime precipitates. Oriented gamma-prime coarsening to form lamellae perpendicular to the applied stress was very prominent during creep. At 1000 C, the formation of a continuous gamma-gamma-prime lamellar structure was completed during the primary creep stage. Shear through the gamma-gamma-prime interface is considerd to be the rate limiting step in the deformation process. Gradual thickening of the lamellae appeared to be the cause of the onset of tertiary creep. At 925 C, the fully developed lamellar structure was not achieved until the secondary or tertiary creep stages. At this temperature, the gamma-gamma-prime lamellar structure did not appear to be as beneficial for creep resistance as at the higher temperature.

Nathal, M. V.↗

NASA NTRS1985

Studies of Model Immiscible Systems

The objectives are to use model transparent monotectics to obtain fundamental information applicable to two-phase systems in general, to apply this understanding to materials of interest in the Microgravity Science and Applications program, and to interpret results of flight experimental involving monotectic alloys. A number of model immiscible systems are in use to study various aspects of two-phase behavior within the miscibility gap and during solidification. Particle growth, coalescence and particle motions are under investigation using a holographic microscopy system. The system is capable of working with particle densities up to 10 to the 7th power particles/cubic centimeters through a 100 micron depth and can resolve particles of the order of 2 to 3 micron in diameter throughout the entire cell volume. Particle size, distribution changes with respect to time and temperature are observable from sequential holograms. Initial experiments using diethylene glycol/ethyl salicylate (DEG/ES) have demonstrated the usefulness of the technique. The thermal system controls temperature to at least plus or minus 0.001 K over the course of an experiment. A time-lapse film, made from holograms, of a succinonitrile/water solution shows particle size and number distribution changes with time under isothermal conditions. The observations are consistent with Ostwald ripening theory.

Frazier, D. O.↗

NASA NTRS1984

Separation of aqueous two-phase polymer systems in microgravity

Phase separation of polymer systems in microgravity is studied in aircraft flights to prepare shuttle experiments. Short duration (20 sec) experiments demonstrate that phase separation proceeds rapidly in low gravity despite appreciable phase viscosities and low liquid interfacial tensions (i.e., 50 cP, 10 micro N/m). Ostwald ripening does not appear to be a satisfactory model for the phase separation mechanism. Polymer coated surfaces are evaluated as a means to localize phases separated in low gravity. Contact angle measurements demonstrate that covalently coupling dextran or PEG to glass drastically alters the 1-g wall wetting behavior of the phases in dextran-PEG two phase systems.

Vanalstine, J. M.↗

NASA NTRS1985

Correlations and droplet growth

Consideration is given to the time development of a system in which small spheres of a stable phase grow out of a supersaturated melt. The spheres then grow and shrink in a manner similar to Ostwald ripening. The growth process of pairs of particles in an effective background accounts for can be used to explain the long time correlations which develop in the system. The correlations broaden the distribution of particles sizes, even for relatively dilute systems.

Marder, M.↗

NASA NTRS1986

Numerical simulation of diffusion-controlled droplet growth Dynamical correlation effects

Diffusion-controlled coarsening (Ostwald ripening) of precipitated solutions is studied by numerical simulation. An algorithm is devised which exploits the screening of solute concentration fields, thereby removing the restriction to small systems of previous work. Simulation of the coarsening of 5000 droplets at 10-percent volume fraction reveals long-ranged dynamical correlations which broaden the droplet size-distribution function and increase the coarsening-rate coefficient.

Beenakker, C. W. J.↗