Coarsening models incorporating both diffusion geometry and volume fraction of particles

Tsumuraya, Kazuo; Miyata, Yusuke

doi:10.1016/0001-6160(83)90221-3

Cited by 198 publications

(54 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Alternatively, when the precipitates are too close to each other, the overlapping of the diffusion fields surrounding the precipitates allows the direct transfer of atoms from one precipitate to a neighboring precipitate, a phenomenon which dramatically increases the growth rate of the whole population. 23,24 This increase of the growth rate has not been observed in our experiments.…”

Section: -3contrasting

confidence: 60%

“…6͒, two values significantly larger than those predicted in Ref. 24 for the supersaturations considered here.…”

Section: -3contrasting

confidence: 58%

“…Owing to the small distances involved, the direct interaction between neighboring precipitates appears probable. [22][23][24] Following the LSW theory, much of the theoretical work on the ripening phenomenon was aimed at relaxing its central approximation, introducing some interactions between the particles ͑see Ref. 23 for a review, for example͒.…”

Section: -3mentioning

confidence: 99%

See 2 more Smart Citations

Influence of the initial supersaturation of solute atoms on the size of nanoparticles grown by an Ostwald ripening mechanism

Cherkashin¹,

Claverie²,

Bonafos

et al. 2007

Journal of Applied Physics

View full text Add to dashboard Cite

To cite this version:NikolayWe have designed a GaAs based structure in which the influence of the initial supersaturation of solute atoms, here As, on the nucleation and conservative growth of a precipitate phase during annealing can be studied. Size distributions and densities were extracted from transmission electron microscopy images under well defined and appropriate conditions, and the volume fraction that the precipitate phase occupies was deduced from these measurements for a variety of experimental conditions. We show that in the 0.06%-0.5% supersaturation range, the mean size of the precipitates obtained after annealing does not depend on the initial supersaturation of As atoms. On the other hand, the density of precipitates is proportional to this supersaturation. However, we observe that the increase of the precipitate volume fraction leads to a considerable broadening of the precipitate size distributions. The size invariance revealed here suggests that, for a volume fraction of less than 1%, the populations are in quasiequilibrium with the supersaturated matrix and that the growth is driven by the interchange of As atoms ͑and vacancies͒ between the precipitates and the matrix and not directly from one precipitate to the next. It can be inferred that the diffusion fields surrounding the precipitates do not overlap much during the growth although some deviation from the expected shape of the size distribution may reveal the limitations of the nonlocal mean-field approximation suggested here.

show abstract

Section: -3contrasting

confidence: 60%

“…6͒, two values significantly larger than those predicted in Ref. 24 for the supersaturations considered here.…”

Section: -3contrasting

confidence: 58%

See 1 more Smart Citation

Influence of the initial supersaturation of solute atoms on the size of nanoparticles grown by an Ostwald ripening mechanism

Cherkashin¹,

Claverie²,

Bonafos

et al. 2007

Journal of Applied Physics

View full text Add to dashboard Cite

show abstract

“…Plotnikov et al [29] published data showing that d for the Ni-Al/Ni 3 Al interface decreases rapidly at small particle sizes, the order of the interface width, and continues to decrease slightly during the coarsening Figure 2 Data on the rate constants for coarsening, k(f e ), of c (Ni-Al or Ni-Ge) precipitates in ''inverse'' a Ni 3 Al [40] and b Ni 3 Ge [41] alloys. The curves in both the figures are predictions of the MSLW theory [6] modified by the calculations of Tsumuraya and Miyata [42].…”

Section: Introductionmentioning

confidence: 98%

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

Ardell

2016

J Mater Sci

View full text Add to dashboard Cite

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.

show abstract

“…The kinetics of the growth and coarsening of precipitates have been widely examined and reviewed in the literature. [1][2][3][4][5][6][7][8][9][10][11] Because precipitation of Cu particles in steels improves the high-temperature and fatigue strength, [12][13][14][15] many studies on the precipitation of Cu in stainless steels have been conducted. [16][17][18][19][20][21] Bajguirani et al [17][18][19] reported that precipitation of Cu particles in a 15-5 PH stainless steel occurs first by formation of coherent bcc solute clusters.…”

Section: Introductionmentioning

confidence: 99%

Effect of Nb Addition on the Growth and Coarsening of Cu-particles in Ferritic Stainless Steel

Kobayashi

Takeda

et al. 2014

ISIJ Int.

View full text Add to dashboard Cite

The growth and coarsening of Cu-particles in 18%Cr-1.5%Cu ferritic stainless steels as a function of Nb content was investigated quantitatively. The samples were solution-treated at 1 250°C and then isothermally aged at 700°C for up to 86 400 s. Fine, spherical Cu-particles nucleated and grew during aging. The radius of the Cu particles increased in proportion to the one-third power of the aging time in all the stainless steels. The radius of the Cu particles in the Nb-added stainless steels was always smaller than that in the Nb-free stainless steel. The normalized standard deviation of the size distribution of the Cu particles increased and reached saturation at a certain value during aging. The increase in the standard deviation during aging was delayed by the addition of Nb. The volume fraction of Cu particles increased and reached saturation at a certain value during aging. The addition of niobium delayed the saturation of the volume fraction of the Cu particles. The slow growth of Cu particles in Nb-added stainless steels is thought to be owing to the slow diffusion of Nb atoms from the Cu particles.

show abstract

Coarsening models incorporating both diffusion geometry and volume fraction of particles

Cited by 198 publications

References 23 publications

Influence of the initial supersaturation of solute atoms on the size of nanoparticles grown by an Ostwald ripening mechanism

Influence of the initial supersaturation of solute atoms on the size of nanoparticles grown by an Ostwald ripening mechanism

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

Effect of Nb Addition on the Growth and Coarsening of Cu-particles in Ferritic Stainless Steel

Contact Info

Product

Resources

About