The Precipitate-Nucleation in the Vicinity of Solubility Limit

2005 ◽  
Vol 502 ◽  
pp. 139-144 ◽  
Author(s):  
Toru Miyazaki ◽  
Takao Kozakai ◽  
Claudio G. Schoen
Keyword(s):  
Critical Nucleus ◽  
Critical Size ◽  
Solubility Limit ◽  
Minimum Size ◽  
Miscibility Gap ◽  
Composition Gradient ◽  
Nucleus Size ◽  
Precipitate Particle ◽  
Composition Region ◽  
Precipitate Nucleation

The critical minimum size of stable precipitate in the vicinity of edge of miscibility gap is experimentally determined for the Ni3Si precipitate particle in Ni-Si, Ni3Al in Ni-Al, Cu4Ti in Cu-Ti and Co in Cu-Co binary alloy systems by utilizing the macroscopic composition gradient method recently proposed. The results obtained are as follows: The critical nucleus size shows a rapid increase to several tens of nm in a very narrow composition region less than 0.3at% from the phase boundary. Such a big critical size of nucleus is statistically rationalized by the conventional nucleation theories.

The Development of “Macroscopic Composition Gradient Method” and its Application to the Precipitate-Nucleation Near the Edge of Miscibility Gap

2008 ◽  
Vol 138 ◽  
pp. 43-56
Author(s):  
Toru Miyazaki
Keyword(s):  
Phase Boundary ◽  
Critical Phenomena ◽  
Composition Range ◽  
Solubility Limit ◽  
Nucleation Theory ◽  
Minimum Size ◽  
Miscibility Gap ◽  
Composition Gradient ◽  
Phase Decomposition ◽  
Nucleus Size

A new characterization method, "Macroscopic Composition Gradient (MCG) Method" is proposed to investigate the phase transformations near the phase boundaries, such as the solubility limit, order/disorder line and so on. Since the macroscopic composition gradient in the alloy is prepared so as to step over the phase boundary, the morphological transition of critical phenomena at the phase boundary can be observed by means of analytical transmission electron microscopy. By utilizing this method, the critical minimum size of stable precipitate in the vicinity of edge of miscibility gap is experimentally determined for the Ni3Si in Ni-Si, Ni3Al in Ni-Al, Cu4Ti in Cu-Ti and Co in Cu-Co binary alloy systems. The results are as follows: The critical nucleus size shows a steep increase up to several tens of nm in a very narrow composition range less than 0.3at% from the phase boundary. The Gibbs-Thomson relation and the conventional nucleation theory statistically rationalize such the composition dependence of nucleus size change. However, the nucleus formation is kinetically never rationalized by the conventional nucleation theories. The phase decomposition of supersaturated solid solution progresses by a mechanism of spinodal phase decomposition, even in the composition range near the solubility limit, i.e. a so-called Nucleation- Growth region. Such the phase decomposition behavior is never rationalized by the Boltzmann- Gibbs free energy, which is based on the extensive entropy. The experimental facts obtained here are explained by Tsallis's non-extensive entropy. It should be noted that the present experiments can systematically be conducted in the composition range very near the solubility limit where they has hardly been examined in the past. The MCG method proposed here is considered to open a new way to investigate the microstructure evaluation, particularly for the critical phenomena near the phase boundary.

Homogeneous nucleation in a Poiseuille flow

2021 ◽  
Vol 23 (6) ◽  
pp. 3974-3982
Author(s):  
Fuqian Yang
Keyword(s):  
Poiseuille Flow ◽  
Homogeneous Nucleation ◽  
Critical Nucleus ◽  
Flow Speed ◽  
Nucleus Size ◽  
Average Flow ◽  
Critical Nucleus Size

Variation of the critical nucleus size and the corresponding work of formation with average flow speed at axisymmetric axis.

Trapping Effect on the Kinetic Critical Radius in Nucleation and Growth Processes

2014 ◽  
Vol 790-791 ◽  
pp. 97-102
Author(s):  
Zoltán Erdélyi ◽  
Zoltán Balogh ◽  
Gabor L. Katona ◽  
Dezső L. Beke
Keyword(s):  
Critical Nucleus ◽  
Solid Phase ◽  
Kinetic Monte Carlo ◽  
Mean Field ◽  
Transformation Process ◽  
Nucleus Size ◽  
Critical Nucleus Size ◽  
Acta Mater ◽  
Order Of Magnitude ◽  
The Difference

The critical nucleus size—above which nuclei grow, below dissolve—during diffusion controlled nucleation in binary solid-solid phase transformation process is calculated using kinetic Monte Carlo (KMC). If atomic jumps are slower in an A-rich nucleus than in the embedding B-rich matrix, the nucleus traps the A atoms approaching its surface. It doesn’t have enough time to eject A atoms before new ones arrive, even if it would be favourable thermodynamically. In this case the critical nucleus size can be even by an order of magnitude smaller than expected from equilibrium thermodynamics or without trapping. These results were published in [Z. Erdélyi et al., Acta Mater. 58 (2010) 5639]. In a recent paper M. Leitner [M. Leitner, Acta Mater. 60 (2012) 6709] has questioned our results based on the arguments that his simulations led to different results, but he could not point out the reason for the difference. In this paper we summarize our original results and on the basis of recent KMC and kinetic mean field (KMF) simulations we show that Leitner’s conclusions are not valid and we confirm again our original results.

Incomplete Solubility in Nitride Alloys

1996 ◽  
Vol 449 ◽  
Author(s):  
I. H. Ho ◽  
G.B. Stringfellow
Keyword(s):  
Experimental Data ◽  
Nearest Neighbor ◽  
Solubility Limit ◽  
Lattice Parameter ◽  
Miscibility Gap ◽  
Recent Experimental Data ◽  
Virtual Crystal Approximation ◽  
Group V ◽  
Group Iii ◽  
Nitride Alloys

ABSTRACTA model based on the valence-force-field (VFF) model has been developed specifically for the calculation of the irascibility gaps in III-V nitride alloys. In the dilute limit, this model allows the relaxation of the atoms on both sublattices. It was found that the energy due to bond stretching and bond bending was lowered and the solubility limit was increased substantially when both sublattices were allowed to relax to distances as large as the sixth nearest neighbor positions. Using this model, the equilibrium mole fraction of N in GaP was calculated to be 6×l0−7 at 700°C. This is slightly higher than the calculated results from the semi-empirical delta lattice parameter (DLP) model. Both the temperature dependence and the absolute values of the calculated solubility agree closely with the experimental data. The solubility is more than three orders of magnitude larger than the result obtained using the VFF model with the group V atom positions given by the virtual crystal approximation, i.e., with relaxation of only the first neighbor bonds. Other nitride systems, such as GaAsN, AlPN, AlAsN, InPN, and InAsN were investigated as well. The equilibrium mole fractions of nitrogen in InP and InAs are the highest, which agrees well with recent experimental data where high N concentrations have been produced in InAsN alloys. Calculations were also performed for the alloy systems with mixing on the group III sublattice that are so important for device applications. Allowing relaxation to the 3rd nearest neighbor gives an In solubility in GaN at 800°C of less than 6%. Again, this is in agreement with the results of the DLP model calculation. This result may partially explain the difficulties experienced with the growth of these alloys. Indeed, evidence of solid immiscibility has recently been reported. A significant miscibility gap was also calculated for the AlInN system, but the AlGaN system is completely miscible.

scholarly journals Nucleation rate analysis of methane hydrate from molecular dynamics simulations

2015 ◽  
Vol 179 ◽  
pp. 463-474 ◽  
Author(s):  
Daisuke Yuhara ◽  
Brian C. Barnes ◽  
Donguk Suh ◽  
Brandon C. Knott ◽  
Gregg T. Beckham ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Nucleation Rate ◽  
Methane Hydrate ◽  
Critical Nucleus ◽  
Md Simulations ◽  
Clathrate Hydrate ◽  
Clathrate Hydrates ◽  
Growth Effect ◽  
Nucleus Size ◽  
Critical Nucleus Size

Clathrate hydrates are solid crystalline structures most commonly formed from solutions that have nucleated to form a mixed solid composed of water and gas. Understanding the mechanism of clathrate hydrate nucleation is essential to grasp the fundamental chemistry of these complex structures and their applications. Molecular dynamics (MD) simulation is an ideal method to study nucleation at the molecular level because the size of the critical nucleus and formation rate occur on the nano scale. Various analysis methods for nucleation have been developed through MD to analyze nucleation. In particular, the mean first-passage time (MFPT) and survival probability (SP) methods have proven to be effective in procuring the nucleation rate and critical nucleus size for monatomic systems. This study assesses the MFPT and SP methods, previously used for monatomic systems, when applied to analyzing clathrate hydrate nucleation. Because clathrate hydrate nucleation is relatively difficult to observe in MD simulations (due to its high free energy barrier), these methods have yet to be applied to clathrate hydrate systems. In this study, we have analyzed the nucleation rate and critical nucleus size of methane hydrate using MFPT and SP methods from data generated by MD simulations at 255 K and 50 MPa. MFPT was modified for clathrate hydrate from the original version by adding the maximum likelihood estimate and growth effect term. The nucleation rates calculated by MFPT and SP methods are within 5%, and the critical nucleus size estimated by the MFPT method was 50% higher, than values obtained through other more rigorous but computationally expensive estimates. These methods can also be extended to the analysis of other clathrate hydrates.

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