The effect of volume fraction of precipitate on ostwald ripening

Davies, C. K. L.; Nash, Philip; Stevens, R. N.

doi:10.1016/0001-6160(80)90067-x

Cited by 356 publications

(118 citation statements)

References 10 publications

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“…Ardell [162] added a diffusion geometry assumption that predicted a broad grain size distribution, but showed a greater sensitivity to volume fraction than seen experimentally. Davies et al [163] included coalescence events, resulting in a broad grain size distribution. Other treatments have assumed separated spheres and ignored coalescence, leading to an abundance of models not relevant to LPS.…”

Section: Grain Growthmentioning

confidence: 99%

Review: liquid phase sintering

2009

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Liquid phase sintering (LPS) is a process for forming high performance, multiple-phase components from powders. It involves sintering under conditions where solid grains coexist with a wetting liquid. Many variants of LPS are applied to a wide range of engineering materials. Example applications for this technology are found in automobile engine connecting rods and high-speed metal cutting inserts. Scientific advances in understanding LPS began in the 1950s. The resulting quantitative process models are now embedded in computer simulations to enable predictions of the sintered component dimensions, microstructure, and properties. However, there are remaining areas in need of research attention. This LPS review, based on over 2,500 publications, outlines what happens when mixed powders are heated to the LPS temperature, with a focus on the densification and microstructure evolution events.

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Section: Grain Growthmentioning

confidence: 99%

Review: liquid phase sintering

2009

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“…Analysis of previously published experimental data on the c 0 PSDs Ni-Al, Ni-Ga, Ni-Ge, Ni-Si, and NiTi alloys [37] confirms the efficacy of the TIDC Figure 1 a The dependencies of the rate constant for particle growth during coarsening, k(f e ), normalized by the rate constant of the LSW theory, k(0), predicted by 5 theories: MLSW [6], DNS [7], MR [8], BW [9], and VG [10]. b The experimentally measured values of k(f e ) for the coarsening of c 0 Ni 3 Si precipitates in different Ni-Si alloys aged at 650°C.…”

Section: Introductionmentioning

confidence: 52%

“…1a. More recent theories of the effect of f e on coarsening behavior [11][12][13], published after the review by Baldan, predict dependencies of k(f e )/k(0) on f e that lie between the DNS [7] and BW [9] predictions.…”

Section: Introductionmentioning

confidence: 94%

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Non-integer temporal exponents in trans-interface diffusion-controlled coarsening

Ardell

2016

J Mater Sci

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The kinetics of c 0 -type (Ni 3 X) precipitate growth and solute depletion in Ni-Al, Ni-Ga, Ni-Ge, Ni-Si, Ni-Ti and Ni-Al-Cr alloys is successfully predicted by the trans-interface diffusion-controlled theory of coarsening using non-integer temporal exponents, n, satisfying 2 B n B 3, which are obtained from analyses of particle size distributions (PSDs). The origin of non-integer n is concentrationdependent diffusion through the c/c 0 interface. The literature on diffusion of Al and Ni in Ni 3 Al is specifically examined. It is shown unequivocally that the concentration-dependent diffusion of Al can account semi-quantitatively for the value of n that successfully describes the PSDs and kinetics of coarsening of the c 0 precipitates. There is no need to invoke a particle size-dependent c/c 0 interface width, as was done in prior work. It is argued that existing theory and computational modeling of coarsening in systems with highly disparate diffusion mobilities in both phases do not correctly represent the mobilities in the matrix, precipitate, and interface in Ni-Al alloys. These theories predict temporal exponents satisfying 3 B n B 4, for which there is no experimental support.

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“…Asimow [16] modified the coarsening theory by modifying the diffusion geometry, but failed to perform the statistical averaging of the diffusion interactions between particles that is necessary for a satisfactory solution to this problem. Other models were later developed including models by Brailsford and Wynblatt, [18] Voorhees and Glicksman, [19] Marqusee and Ross [20] and Davies et al [21] While the quantitative predictions of the models differ significantly, they all demonstrate that the coarsening rate should be larger than that predicted by the classical LSW model when the volume fraction of particles is large. In order to quantify our observations, the following expression is used, as suggested by Martin et al [22 23] :…”

Section: Bulk Diffusion Controlmentioning

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 effect of volume fraction of precipitate on ostwald ripening

Cited by 356 publications

References 10 publications

Review: liquid phase sintering

Review: liquid phase sintering

Non-integer temporal exponents in trans-interface diffusion-controlled coarsening

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

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