Generalized Frenkel-Kontorova model for point lattice defects

Kovalev, A. S.; Kondratyuk, A. D.; Am, Kosevich; Landau, A. I.

doi:10.1103/physrevb.48.4122

Cited by 12 publications

(6 citation statements)

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“…An unusual feature of the crowdion configuration is that the displacements of atoms in it are effectively one dimensional and that the strain field in the string containing a selfinterstitial atom can be accurately described by an analytically tractable Frenkel-Kontorova model. 32 This model also applies to the treatment of the elastic field of the crowdion defect, 33 making it possible to derive equations of motion for crowdions in the lattice. 34 The multi-string Frenkel-Kontorova model, describing clusters of interstitial atoms, shows that there is a link between the soliton solutions for a crowdion and for an edge dislocation.…”

Section: Introductionmentioning

confidence: 99%

Multiscale modeling of crowdion and vacancy defects in body-centered-cubic transition metals

2007

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We investigate the structure and mobility of single self-interstitial atom and vacancy defects in bodycentered-cubic transition metals forming groups 5B ͑vanadium, niobium, and tantalum͒ and 6B ͑chromium, molybdenum, and tungsten͒ of the Periodic Table. Density-functional calculations show that in all these metals the axially symmetric ͗111͘ self-interstitial atom configuration has the lowest formation energy. In chromium, the difference between the energies of the ͗111͘ and the ͗110͘ self-interstitial configurations is very small, making the two structures almost degenerate. Local densities of states for the atoms forming the core of crowdion configurations exhibit systematic widening of the "local" d band and an upward shift of the antibonding peak. Using the information provided by electronic structure calculations, we derive a family of Finnis-Sinclair-type interatomic potentials for vanadium, niobium, tantalum, molybdenum, and tungsten. Using these potentials, we investigate the thermally activated migration of self-interstitial atom defects in tungsten. We rationalize the results of simulations using analytical solutions of the multistring Frenkel-Kontorova model describing nonlinear elastic interactions between a defect and phonon excitations. We find that the discreteness of the crystal lattice plays a dominant part in the picture of mobility of defects. We are also able to explain the origin of the non-Arrhenius diffusion of crowdions and to show that at elevated temperatures the diffusion coefficient varies linearly as a function of absolute temperature.

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Section: Introductionmentioning

confidence: 99%

Multiscale modeling of crowdion and vacancy defects in body-centered-cubic transition metals

2007

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“…We choose n = 0 to correspond to the particle just before the defect center and use the standard boundary conditions: u n =−∞ = a d , u n =+∞ = 0 for the interstitial and u n =−∞ = 0, u n =+∞ = a d for the vacancy. 37 …”

Section: Resultsmentioning

confidence: 99%

“…We choose n = 0 to correspond to the particle just before the defect center and use the standard boundary conditions: u n=ÀN = a d , u n=+N = 0 for the interstitial and u n=ÀN = 0, u n=+N = a d for the vacancy. 37 Fig. 8 shows the average displacement along the h111i direction for an interstitial in the BCC crystal and along the z-direction for a vacancy in the H crystal for different densities and temperatures.…”

Section: Hertzian Spheresmentioning

confidence: 99%

Defects in crystals of soft colloidal particles

2021

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“…Here x n is the position of particle n along the defect and a d is the crystal lattice spacing in this direction. We choose n = 0 to correspond to the particle just before the defect center and use the standard boundary conditions: u n=−∞ = a d , u n=+∞ = 0 for the interstitial and u n=−∞ = 0, u n=+∞ = a d for the vacancy 37 .…”

Section: A Hertzian Spheresmentioning

confidence: 99%