Diffusion‐Controlled Solid State Reactions

Гусак, А. М.; Lyashenko, Yu. O.; Kornienko, S. V.; Pasichnyy, Mykola; Shirinyan, A.S.; Zaporozhets, Tetiana

doi:10.1002/9783527631025

Cited by 72 publications

(7 citation statements)

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“…Lastly, Coffey et al provided experimental evidence and a theoretical explanation that the nucleation and growth of the first intermetallic phase can occur in two distinct exotherms under slow heating conditions. 31 Other researchers, such as Desre and Yavari 32 and Gusak, 33 have taken a more fundamental approach to predict nucleation by accounting for the sharp concentration gradients that exist in multilayer films. Using thermodynamic parameters, they calculate phase-specific critical concentration gradients, and they argue that nucleation is enabled once the concentration gradient present at a given phase composition is less than the critical value for that phase.…”

Section: Resultsmentioning

confidence: 99%

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Studying exothermic reactions in the Ni-Al system at rapid heating rates using a nanocalorimeter

Swaminathan

Grapes

Woll

et al. 2013

Journal of Applied Physics

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Heats of reaction and heat capacity changes were measured using scanning nanocalorimetry for a nickel and aluminum bilayer where initial heating rates of 104 K/s were achieved. Multiple exotherms were observed on the initial heating, but the number of intermediate exotherms decreased with increasing heating rate. The final phase was the B2 NiAl intermetallic. Results from the nanocalorimeter were compared with a conventional differential scanning calorimeter (operating at 0.7 K/s) to understand the effect of significant (10 000×) increases in heating rate on the phase transformation sequence. The high heating rate in the nanocalorimeter delays reaction initiation, causes the exothermic peaks to shift to higher temperatures, and appears to suppress the formation of intermediate, metastable phases. Potential explanations for this apparent suppression are discussed.

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Section: Resultsmentioning

confidence: 99%

“…35 The model assumes a cubic nucleus of width 2Ár in a concentration gradient, rc, and it assumes the gradient is constant within the nucleus volume. The change in the free energy DG due to nucleation is calculated by [32][33][34] …”

Section: Resultsmentioning

confidence: 99%

Studying exothermic reactions in the Ni-Al system at rapid heating rates using a nanocalorimeter

Swaminathan

Grapes

Woll

et al. 2013

Journal of Applied Physics

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“…Therefore, it looks reasonable to use SKMF for modelling of nucleation behaviour, keeping in mind the interrelation (8). It might be a good tool to check and distinguish the alternative theories of nucleation [22][23][24], especially in the sharp concentration gradients [25,26].…”

Section: Discussionmentioning

confidence: 99%

Martin’s Kinetic Mean-Field Model Revisited—Frequency Noise Approach versus Monte Carlo

Гусак¹,

Zaporozhets²

2018

Metallofiz. Noveishie Tekhnol.

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Development of the non-linear kinetic mean-field model suggested by GeorgeMartin in 1990 is discussed. Its steady-state limit is shown to coincide with Khachaturyan's model. It is proved rigorously that Martin's model and its 3D version always provide decrease of free energy and are unable to model any overcoming of free-energy barrier, including nucleation. To enable nucleation processes within the mean-field models, the introduction of noise is necessary. Contrary to common way of noise introduction (noise of concentration), we introduce the noise of jump frequencies as a basic reason of fluctuations. The new method is called as Stochastic Kinetic Mean Field (SKMF). In this paper, we investigate and compare the dispersion and spatial correlations of concentration fluctuations by three methods-direct Monte Carlo simulation, numeric simulation by SKMF method, and analytic approximation within the scope of SKMF. Comparison confirms the correspondence of frequency noise to the averaging over finite number of Monte Carlo runs (over finite number of copies of the canonical ensemble).

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“…Such behavior reveals the curvature effect on the distribution or wetting of Ag on the surface of the TiO 2 nanotubes. According to the Gibbs–Thomson relation [35–36], the equilibrium concentration of solute atoms on a curved surface is determined by the surface energy and the mean curvature. Thus, the equilibrium concentration of Ag atoms on the inner surface of a TiO 2 nanotube is lower than that on the planar surface of TiO 2 of the same structure, and on the outer surface it is higher than that on the planar surface.…”

Section: Discussionmentioning

confidence: 99%

Fast diffusion of silver in TiO₂ nanotube arrays

Zhang¹,

Liu²,

Zhou³

et al. 2016

Beilstein J. Nanotechnol.

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SummaryUsing magnetron sputtering and heat treatment, Ag@TiO2 nanotubes are prepared. The effects of heat-treatment temperature and heating time on the evolution of Ag nanofilms on the surface of TiO2 nanotubes and microstructure of Ag nanofilms are investigated by X-ray diffraction, field emission scanning electron microscopy, and transmission electron microscopy. Ag atoms migrate mainly on the outmost surface of the TiO2 nanotubes, and fast diffusion of Ag atoms is observed. The diffusivity for the diffusion of Ag atoms on the outmost surface of the TiO2 nanotubes at 400 °C is 6.87 × 10−18 m2/s, which is three orders of magnitude larger than the diffusivities for the diffusion of Ag through amorphous TiO2 films. The activation energy for the diffusion of Ag atoms on the outmost surface of the TiO2 nanotubes in the temperature range of 300 to 500 °C is 157 kJ/mol, which is less than that for the lattice diffusion of Ag and larger than that for the grain boundary diffusion. The diffusion of Ag atoms leads to the formation of Ag nanocrystals on the outmost surface of TiO2 nanotubes. Probably there are hardly any Ag nanocrystals formed inside the TiO2 nanotubes through the migration of Ag.

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Diffusion‐Controlled Solid State Reactions

Cited by 72 publications

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Studying exothermic reactions in the Ni-Al system at rapid heating rates using a nanocalorimeter

Studying exothermic reactions in the Ni-Al system at rapid heating rates using a nanocalorimeter

Martin’s Kinetic Mean-Field Model Revisited—Frequency Noise Approach versus Monte Carlo

Fast diffusion of silver in TiO₂ nanotube arrays

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Diffusion‐Controlled Solid State Reactions

Cited by 72 publications

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Studying exothermic reactions in the Ni-Al system at rapid heating rates using a nanocalorimeter

Studying exothermic reactions in the Ni-Al system at rapid heating rates using a nanocalorimeter

Martin’s Kinetic Mean-Field Model Revisited—Frequency Noise Approach versus Monte Carlo

Fast diffusion of silver in TiO2 nanotube arrays

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Fast diffusion of silver in TiO₂ nanotube arrays