The growth of dispersed precipitates in solutions

Greenwood, G. W.

doi:10.1016/0001-6160(56)90060-8

Cited by 549 publications

(160 citation statements)

References 4 publications

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“…The relationship between particle surface temperature and particle volume and the thermal resistance between thermally contacting particles cannot be uniquely related to the particle sizes because of variations in particle shape and arrangements. Greenwood ( 1956) has considered the growth rates of dispersed particle precipitates in solutions. This process is called Ostwald ripening.…”

Section: + Explanation Of Linear Increase Of Mean Volumementioning

confidence: 99%

“…This kind of process has been examined theoretically for the case when the particles are dispersed and exchange mass only indirectly by interaction with the solution (Greenwood, 1956 ;Lifshits and Slyozov, 196[ ) and has various applications, examples of which are the growth of dispersed water droplets in the a tmosphere, second phase particles in metals, and crys tals in hydrothermal or high-tem p erature metamorphism of some rocks (Chai, 1973). Of possible glaciological importance is the behavior of p ossible solid inclusions of slightly soluble impurities expected in cold polar ice below eutec tic temperatures (Paren and W alker,[971 ) .…”

Section: Introductionmentioning

confidence: 99%

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Grain Coarsening of Water-Saturated Snow

Raymond

Tusima

1979

J. Glaciol.

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A BSTRACT. Experimental measurements were m ade of changes in grain-size dist ribution with time in snow saturated with solutions of various impurity con te nts. Qualita tively, the changes in grain-size distribution occur by shrinkage a nd eventual d isappearance of the relatively small particles a nd growth of the relatively large pa rticles by a solid mass-exchange process which conserves the total solid mass. The distribution of r elative grain size is fo und to be essen ti a lly time independ ent except for transient effects lasting only several to several tens of hours after the tim e of initial saturation. M ean grain volume in creases at a consta nt rate, which for solutio ns of impurity concentration less than a b out 0.01 mol I-I is (5 to 6) X 10-3 mm 3 h -I • In pure solutions the smallest particles shrink at a characte risti c rate of about 1 X 10-2 mm3 h-I . Once the steady relative-size distribution is esta blish ed , the rate of volume change of ty pical grains varies linearly with grain volume fro m the cha racteristi c negative rate for the smallest particles through zero for particles of m ean volume to positive values for particles of larger volume. The basic feat ures of the changes that ta ke place are explained in terms of heat-flow controlled melting and freezing determined by temperature differences associated with the effect of pa rticle surface curvature o n melting temperature. The constant ra te of inc rease of mean grain volume is a conseque n ce of conservation of total ice volume. The expecta tion that particles of intermedia te size would be neither shrinking or growing leads to the conclusion that the actual rate of increase in mean grain volume is about o ne-half the ch a racteristic melting rate of the smallest particles, which fits the observations. The process of grain growth is slowed by impurities in a way which ca n be predicted from the melting-tempera ture depression caused by the impurity and its diffusion coeffi cient. The transport of heat between grain surfaces is la rgely through t he liquid-filled gaps betwee n them, but about 19 % is conducted through the solid. RESUME . Le grossissemellt des graills de la Ileige saturee ell eau. On a mesure experimenta lement la variation avec le temps d e la repartition d es dimensions des grains dans la neige saturee avec des solutions d e diffhentes teneurs e n impuretes. Qua litativement les cha ngements dans la repartition des dimensions d es grains se produisent par reduction et eventuellement pa r disparition des particules relativement petites et grossissement d es particules " elativement grandes au cours d'un processus d'echange d e matiere qui conserve la masse totale. La distribution de la dimension relative des grains apparait corn me essentiellement independante du temps a l'exception des effets tra nsitoires qui retard e nt de seulement quelques dizaines d'heures le moment de l'equilibre apres le moment d e la saturation initia le. Le volume moye n du grain a ugme nte a un rythme constant qui , pour des solutio ns ...

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Section: + Explanation Of Linear Increase Of Mean Volumementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Grain Coarsening of Water-Saturated Snow

Raymond

Tusima

1979

J. Glaciol.

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“…LS also derived an equation for the depletion of the small concentration of excess solute, X a À X ae , that must accompany the growth of the average precipitate; X a is the solute concentration in the matrix at time t and X ae is its thermodynamic equilibrium value. The kinetics of the processes of growth and solute depletion were shown to obey the equations hri 3 & kt and X a À X ae % ðjtÞ À1=3 , where k and j are rate constants that depend on the thermo-physical parameters of the alloy system, including the chemical diffusion coefficient,D, in the parent phase and the interfacial free energy, r, between the precipitate and matrix phases. A remarkable ingredient of the LSW theory was an analytical equation describing the distribution of particle sizes (PSD).…”

Section: Introductionmentioning

confidence: 99%

A1-L12 interfacial free energies from data on coarsening in five binary Ni alloys, informed by thermodynamic phase diagram assessments

Ardell

2011

J Mater Sci

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The data on coarsening of c 0 -type precipitates (Ni 3 X, with the L1 2 crystal structure) in Ni-Al, Ni-Ga, Ni-Ge, Ni-Si, and Ni-Ti alloys are re-evaluated in the context of recent (TIDC) and classical (LSW) theories of coarsening, with the objective of ascertaining the best values possible of interfacial free energies, r, of the c/c 0 interfaces in these five alloy systems. The re-evaluations include fitting of the particle size distributions, reanalyzing all the available data on the kinetics of particle growth and kinetics of solute depletion, and using thermodynamic assessments of the binary alloy phase diagrams to calculate curvatures of the Gibbs free energies of mixing. The product of the work is two sets of interfacial free energies, one set for the analysis using the recent TIDC theory and the other for the analysis using the classical LSW theory. The TIDC-based analysis yields lower values of r by about a factor of 2/3. All the interfacial energies are considerably larger, by factors ranging from *4 to 10, than those previously reported, which were for the most part calculated from data on coarsening assuming idealsolution thermodynamics. In the TIDC theory the width of the interface, d, is allowed to increase with particle size, r. A simple equation relating r to the ratio of the gradient energy and d is used to show that r can remain constant even though d increases with r. Published work supporting this contention is presented and discussed.

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“…The classical theory for particle coarsening was developed by Greenwood, [13] Lifshitz and Slyozov, [14] and Wagner, [15] and is often referred to as the LSW theory. The classical treatment relies on a diffusion analysis in which the rate of change of the diameter of each particle is independent of the position of other particles.…”

Section: A Austenite Particle Coarseningmentioning

confidence: 99%

Model Fe-Al Steel with Exceptional Resistance to High Temperature Coarsening. Part I: Coarsening Mechanism and Particle Pinning Effects

Zhou

Zurob

O’Malley

et al. 2014

Metall Mater Trans A

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The mechanism by which austenite particles coarsen in a delta-ferrite matrix was investigated in a model Al-containing steel. Special emphasis was placed on the effect of volume fraction on the coarsening kinetics as well as the ability of the particles to pin the growth of delta-ferrite grains. The specimens were heated to temperatures in the range of 1123 K to 1583 K (850°C to 1305°C) in the austenite plus delta-ferrite two-phase region and held for times between 5 minutes and 288 hours, followed by water quenching. When the reheating temperature was higher than 1473 K (1200°C), the coarsening of austenite particles was found to evolve as t 1/3 , which is typical of volume diffusion-controlled behavior. For lower temperatures, the particle coarsening behavior followed t 1/4 kinetics which is consistent with a grain boundary diffusioncontrolled process. The observations were interpreted in terms of the modified LifshitzSlyozov-Wanger theory by considering multi-component diffusion, particle volume fraction, and the fact that this two-phase material is a non-ideal solid solution. Three types of interaction between particle coarsening and grain growth were observed. Grain growth was completely pinned when the particle pinning force was much larger than the driving force for grain growth. When the particle pinning force was comparable to the driving force for grain growth, the deltaferrite grains were observed to grow at a rate which is controlled by the kinetics of coarsening of the austenite particles. Finally, when the particle pinning force was smaller than the driving force for grain growth, significant grain growth occurred but its rate was lower than that expected in the absence of particle pinning. The results point to an effective approach for controlling grain growth at high temperatures.

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The growth of dispersed precipitates in solutions

Cited by 549 publications

References 4 publications

Grain Coarsening of Water-Saturated Snow

Grain Coarsening of Water-Saturated Snow

A1-L12 interfacial free energies from data on coarsening in five binary Ni alloys, informed by thermodynamic phase diagram assessments

Model Fe-Al Steel with Exceptional Resistance to High Temperature Coarsening. Part I: Coarsening Mechanism and Particle Pinning Effects

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