Analytically Solvable Differential Diffusion Equations Describing the Intermediate Phase Growth

Yarmolenko, M. V.; Design, Nemirovich-Danchenko Str.

doi:10.15407/mfint.40.09.1201

Cited by 8 publications

(6 citation statements)

References 8 publications

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“…It agrees with in situ TEM observation of Si precipitate dissolution through the dislocation in the aluminium grain at 623K [17]. So, the diffusion law R=(αt) 1/3 from a point source (practically, through dislocation end point) obtained mathematically in [16] was proved experimentally in [17].…”

supporting

confidence: 84%

“…) ( It was found that dislocations can accelerate diffusion of Si from precipitate P1 (small, R10≈36 nm) to precipitate P2 (large, R2≈50 nm) in an Al grain at 623 K (Tm/T≈1.5, Tm=660.3 o C=660.3+273.15=933.45 K is the melting point of aluminium, ∆l≈100 nm is the dislocation length) by three orders of magnitude as compared with bulk diffusion (Dd=8.2x10 -13 m 2 /s). Moreover, precipitate P1 volume decreasing is linear as a function of time from t0=0 s to t1=900 s (R11≈32 nm) and up to t2=2640 s (R12≈17 nm, at t3=2880 s the precipitate P1 has completely dissolved by diffusion through dislocation end point) [17]…”

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confidence: 95%

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Diffusion Laws and Modified Pascal’s Triangles

Yarmolenko

2022

DDF

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Four main diffusion laws: 1D diffusion in a planar bulk sample or random walks along a straight line x=α1t1/2; 3D diffusion or random walks from a point source and forming small spherical particle: x=α2t1/3; 1D+1D diffusion or random walks along a straight plane with simultaneous outflow into balk: x=α3t1/4; 1D+2D diffusion or random walks along a straight line with simultaneous outflow into balk: x=α4t1/6 are analysed theoretically using mathematical modelling and appropriate physical models. Convex shape of the diffusion profile near the top along a dislocation pipe with simultaneous outflow into balk is predicted. It is shown that the cone angle near the top is increasing with time. Literature experimental data are used for analysis.

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confidence: 84%

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confidence: 95%

Diffusion Laws and Modified Pascal’s Triangles

Yarmolenko

2022

DDF

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“…A method of dislocation pipe diffusion parameter determination during the type B diffusion kinetics was suggested by the model of dislocation pipe diffusion involving outflow [6,20]. The method involves diffusion dislocation pipe kinetics for two different annealing times at the same temperature during the type B kinetics and dislocation pipe kinetics for one annealing time at other lower temperature during the type C kinetics.…”

Section: Diffusion Activation Energy Calculation In Pure Ironmentioning

confidence: 99%

Copper, Iron, and Aluminium Electrochemical Corrosion Rate Dependence on Temperature

Yarmolenko¹

2022

Corrosion - Fundamentals and Protection Mechanisms

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Our investigations show that electrochemical corrosion of copper is faster than electrochemical corrosion of aluminium at temperatures below 100°C. Literature data analysis shows that the Al atoms diffuse faster than the Cu atoms at temperatures higher than 475°C, Al-rich intermetallic compounds (IMCs) are formed faster in the Cu-Al system, and the Kirkendall plane shifts towards the Al side. Electrochemical corrosion occurs due to electric current and diffusion. An electronic device working time, for example, depends on the initial copper cover thickness on the aluminium wire, connected to the electronic device, temperature, and volume and dislocation pipe diffusion coefficients, so copper, iron, and aluminium electrochemical corrosion rates are investigated experimentally at room temperature and at temperature 100°C. Intrinsic diffusivities ratios of copper and aluminium at different temperatures and diffusion activation energies in the Cu-Al system are calculated by the proposed methods here using literature experimental data. Dislocation pipe and volume diffusion activation energies of pure iron are calculated separately by earlier proposed methods using literature experimental data. Aluminium dissolved into NaCl solution as the Al3+ ions at room temperature and at temperature 100°C, iron dissolved into NaCl solution as the Fe2+ (not Fe3+) ions at room temperature and at temperature 100°C, copper dissolved into NaCl solution as the Cu+ ions at room temperature, and as the Cu+ and the Cu2+ ions at temperature 100°C. It is found experimentally that copper corrosion is higher than aluminium corrosion, and the ratio of electrochemical corrosion rates, kCu/kAl > 1, decreases with temperature increasing, although iron electrochemical corrosion rate does not depend on temperature below 100°C. It is obvious because the melting point of iron is higher than the melting point of copper or aluminium. It is calculated that copper electrochemical corrosion rate is approximately equal to aluminium electrochemical corrosion at a temperature of about 300°C, so the copper can dissolve into NaCl solution mostly as the Cu2+ ions at a temperature of about 300°C. The ratio of intrinsic diffusivities, DCu/DAl < 1, increases with temperature increasing, and intrinsic diffusivity of aluminium could be approximately equal to intrinsic diffusivity of copper at a temperature of about 460°C.

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“…Authors [16] didn't calculate diffusion activation energies and the pre-exponential factors, so we can do it using calculated data by k. p. gurov's and a. m. gusak's method or "constant flux method" [3,4,[18][19][20][21][22][23] (Table 2) and eqs. 27:…”

Section: Diffusion Activation Energy Calculation In the Cu-al Systemmentioning

confidence: 99%

Intrinsic Diffusivities Ratio Analysis in the Al-Cu System

Yarmolenko

2020

Phys. Chem. Solid St.

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Copper and aluminium electric corrosion rates are investigated experimentally at room temperature and at temperature 100oC. It is founded that copper corrosion is higher than aluminium corrosion, and ratio of electric corrosion rates, kCu/kAl , decreases with temperature increasing. It is calculated that copper corrosion rate is approximately equal to aluminium corrosion at temperature about 300oC due to Cu2+ ions are less mobile than Cu+ ions. It is obvious physically: the higher temperature is, the grater atoms’ displacements in crystal lattice, Cu atoms can diffuse without two electrons, and Cu2+ ions more strongly interact with crystal lattice than Cu+ ions. A theoretical method to calculate intrinsic diffusivities ratio in double multiphase systems is proposed. The method involves the Kirkendall plane displacement and the general phases thickness only. Intrinsic diffusivities ratios in the Al-Cu system are calculated using literature experimental data. Diffusion activation energies and pre-exponential coefficients for the Cu-Al system are calculated combining literature experimental results. Analysis of literature data shows that the Kirkendall shift changes sign at temperature about 460oC in the Cu-Al system because of intrinsic diffusivities ratio, DCu*/DAl*, dependence from temperature. Such result agrees with copper and aluminium electric corrosion rates investigation.

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Analytically Solvable Differential Diffusion Equations Describing the Intermediate Phase Growth

Cited by 8 publications

References 8 publications

Diffusion Laws and Modified Pascal’s Triangles

Diffusion Laws and Modified Pascal’s Triangles

Copper, Iron, and Aluminium Electrochemical Corrosion Rate Dependence on Temperature

Intrinsic Diffusivities Ratio Analysis in the Al-Cu System

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