Modeling of vacancy flux due to stress-induced migration

Minoru Aoyagi

doi:10.1116/1.1587142

Simulation of Intrinsic Diffusion in Multicomponent Multiphase Systems

MRS Proceedings ◽

10.1557/proc-527-93 ◽

1998 ◽

Vol 527 ◽

Author(s):

M. Hunkel ◽

D. Bergner

Keyword(s):

Single Phase ◽

Diffusion Flux ◽

Wind Effect ◽

Concentration Profiles ◽

Intrinsic Diffusion ◽

Cross Terms ◽

Multiphase Systems ◽

Random Alloy ◽

Simulation Results ◽

Vacancy Flux

ABSTRACTA simulation model for intrinsic diffusion of multicomponent multiphase systems is presented. The model is not restricted onto a certain number of components or phases. For simplicity, Manning's random alloy model with vanishing vacancy wind effect is used. Then the cross terms of the diffusion flux can be neglected. The simulation routine uses equations for the fluxes, the equation of continuity and an equation for the change of the thickness of volume elements due to the vacancy flux. With this model diffusions paths, concentration profiles, fluxes of the components as well as marker positions can be calculated. The shift of interfaces and the growth of new phases can also be determined. The simulation results were compared with experimental data of the Cu-Fe-Ni system. Diffusion was studied in single-phase areas and across interfaces.

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Test of the Manning Vacancy‐Flux Correction in α Cu‐Zn

Journal of Applied Physics ◽

10.1063/1.1708594 ◽

1966 ◽

Vol 37 (4) ◽

pp. 1741-1743 ◽

Cited By ~ 19

Author(s):

D. J. Schmatz ◽

H. A. Domian ◽

H. I. Aaronson

Keyword(s):

Flux Correction ◽

Vacancy Flux

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The Nature of the Vacancy-Wind Effect Occurring in Diffusion via Six-Jump-Cycles in B2 Intermetallics

Defect and Diffusion Forum ◽

10.4028/www.scientific.net/ddf.297-301.1218 ◽

2010 ◽

Vol 297-301 ◽

pp. 1218-1225

Author(s):

Irina V. Belova ◽

Graeme E. Murch

Keyword(s):

Monte Carlo ◽

Monte Carlo Method ◽

Wind Effect ◽

Vacancy Diffusion ◽

Thermodynamic Factor ◽

Perfect Order ◽

Ionic Compounds ◽

Ionic Solid ◽

Vacancy Flux ◽

B2 Structure

First discovered by the late Dr John Manning, the vacancy-wind effect is a subtle phenomenon that occurs when two or more atomic species compete for vacancies in a net vacancy flux. The vacancy-wind effect is incorporated in (for example) the vacancy-wind or Manning factor that appears in the Darken-Manning Equation relating the interdiffusivity, the tracer diffusivities and the thermodynamic factor. The mechanism of the vacancy-wind phenomenon has long been very poorly understood. Recently, a moving reference frame Monte Carlo method was used to illustrate graphically how the vacancy-wind effect operates in both ionic conductivity in an ionic solid with a dilute solute and chemical interdiffusion in concentrated alloys and ionic compounds. That strategy is extended in this paper to show graphically how the vacancy-wind effect operates in interdiffusion in a stoichiometric intermetallic taking the B2 structure. A simple 4-frequency vacancy diffusion model is used. In previous work, it was shown that depending on composition and temperature, this model can exhibit the six-jump-cycle mechanism. It is shown that in the limit of perfect order that there is no vacancy-wind effect associated with this mechanism when both types of cycle operate equally (zero net vacancy flux). The non-unity value of the vacancy-wind factor found for this mechanism under zero vacancy flux conditions is purely a consequence of a particular geometric mix of tracer and collective atom displacements. The concept that a non-zero off-diagonal phenomenological coefficient provides the vacancy-wind effect is verified.

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Reply to comment on “Phenomenological analysis of diffusion coefficients, correlation and vacancy flux effects in binary substitutional alloys”

Scripta Metallurgica ◽

10.1016/0036-9748(81)90181-2 ◽

1981 ◽

Vol 15 (10) ◽

pp. 1165-1166

Author(s):

M.A. Dayananda

Keyword(s):

Diffusion Coefficients ◽

Phenomenological Analysis ◽

Vacancy Flux ◽

Substitutional Alloys

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Activity coefficient and vacancy flux effects on tracer diffusion in silver–gold alloys

phys stat sol (a) ◽

10.1002/pssa.2210050210 ◽

1971 ◽

Vol 5 (2) ◽

pp. 365-373 ◽

Cited By ~ 5

Author(s):

M. H. Greene ◽

A. P. Batra ◽

R. C. Lowell ◽

R. O. Meyer ◽

L. M. Sliekin

Keyword(s):

Activity Coefficient ◽

Tracer Diffusion ◽

Gold Alloys ◽

Vacancy Flux

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Simulation of TiN/HfO2/Pt memristor I–V curve for different conductive filament thickness

Modern Electronic Materials ◽

10.3897/j.moem.7.2.73289 ◽

2021 ◽

Vol 7 (2) ◽

pp. 45-51

Author(s):

Andrey N. Aleshin ◽

Nikolay V. Zenchenko ◽

Oleg A. Ruban

Keyword(s):

Steady State ◽

Oxygen Vacancy ◽

Energy Output ◽

Cylindrical Shape ◽

State Equations ◽

Conductive Filament ◽

Mathematical Basis ◽

Bipolar Mode ◽

Vacancy Flux ◽

Quantitative Calculations

The operation of the TiN/HfO2/Pt bipolar memristor has been simulated by the finite elements method using the Maxwell steady state equations as a mathematical basis. The simulation provided knowledge of the effect of conductive filament thickness on the shape of the I–V curve. The conductive filament has been considered as the highly conductive Hf ion enriched HfOx phase (x < 2) whose structure is similar to a Magneli phase. In this work a mechanism has been developed describing the formation, growth and dissolution of the HfOx phase in bipolar mode of memristor operation which provides for oxygen vacancy flux control. The conductive filament has a cylindrical shape with the radius varying within 5–10 nm. An increase in the thickness of the conductive filament leads to an increase in the area of the hysteresis loop of the I–V curve due to an increase in the energy output during memristor operation. A model has been developed which allows quantitative calculations and hence can be used for the design of bipolar memristors and assessment of memristor heat loss during operation.

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Cavity nucleation on special boundaries

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100112890 ◽

1984 ◽

Vol 42 ◽

pp. 592-593

Author(s):

L. D. Romeu ◽

J. Reyes

Keyword(s):

Diffusional Creep ◽

Cavity Formation ◽

Triple Junctions ◽

Strain Fields ◽

Cavity Nucleation ◽

Burgers Vector ◽

Special Boundaries ◽

Vacancy Flux ◽

Pure Metals ◽

Present Experimental Evidence

All present theories of cavity formation assume cavities are nucleated during creep on geometrical irregularities at grain boundaries and triple junctions. The resulting (required) tensile stress concentration enhances diffusional creep in the vicinity of the boundary producing a high vacancy flux which ends up nucleating a cavity. No mention is done of the role played by the structure of the boundary. In this paper we present experimental evidence indicating that cavity nucleation is dependent on the structure of the boundary and that cavities in pure metals are nucleated at special boundaries.According to Bollman, a lattice dislocation impinging on a boundary can dissociate into grain boundary dislocations with non crystalline Burgers vectors (GBDs). Also, Pond has shown that further dissociation into partials can occur in certain boundaries. When the degree of good fit decreases, the Burgers vector of any possible GBDs decrease and dislocations tend to be largely spread out becoming “dissolved” into the boundary. Boundaries capable of sustaining dislocations with relatively large Burgers vectors (long range strain fields) are called special boundaries.

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