Microscopic and macroscopic estimates of friction: application to surface diffusion of copper

Gershinsky, Gidon; Georgievskii, Yuri; Pollak, Eli; Betz, G.

doi:10.1016/0039-6028(96)00681-4

Cited by 8 publications

(11 citation statements)

References 36 publications

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“…[28][29][30] One can therefore assume that the diffusing adatom thermalizes basically via interaction with the surface phonons. It should be kept in mind that there are no straight line diffusion channels on the Cu͑111͒ surface, and therefore an adatom performing a long jump must follow a zigzag path alternating fcc and hcp threefold hollow sites.…”

Section: B Long Jumpsmentioning

confidence: 99%

Atomic jumps during surface diffusion

2009

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The characteristics of atomic displacements during surface diffusion of Cu on Cu͑111͒ are studied by means of molecular dynamics simulations. It is found that even at very low substrate temperatures, the majority of the jumps are correlated, i.e., the displacement directions are not randomly chosen but rather keep some sort of memory from the previous moves and are influenced by them. Long jumps, spanning several surface unit cells, are observed at all temperatures. From an analysis of their length probability distribution information can be obtained about the mechanisms of friction and energy transfer between the diffusing adatom and the substrate. Both long jumps and recrossings ͑displacements in which the adatom moves back and forth between two adjacent adsorption sites͒ appear with a higher activation energy than normal diffusion. Finally, the influence of the instantaneous atomic configuration of the substrate on the adatom's trajectory is also highlighted.

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Section: B Long Jumpsmentioning

confidence: 99%

Atomic jumps during surface diffusion

2009

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“…In that case, γ(t) has an algebraically decaying envelope [12][13][14] associated with a hard frequency cutoff in the Fourier transform g w ( ). However, the results of molecular dynamics simulations do not conform to the simple one-dimensional harmonic chain result [11] and there are potential contributions to the friction kernel from additional effects such as inter-adsorbate interactions within an interacting single adsorbate framework [15], that would likely smooth out a hard frequency cutoff. In liquid-phase many-body simulations [16,17] the effective friction kernel is typically not a perfect exponential, but the non-exponential behaviour is not due to a hard cutoff frequency.…”

Section: Introductionmentioning

confidence: 93%

“…In real systems the noise spectrum is generally not white, but is suppressed at high frequencies and can be described using a cutoff frequency ω c , above which the power density is zero or falls rapidly to zero. For example in microcanonical molecular dynamics simulations of an adsorbate on a harmonic solid substrate, the numerically derived cutoff frequency is finite [11]. Any coloured noise spectrum defines a Generalized Langevin equation (GLE).…”

Section: Introductionmentioning

confidence: 99%

The intermediate scattering function for quasi-elastic scattering in the presence of memory friction

Townsend

Ward

2018

J. Phys. Commun.

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We derive an analytical expression for the intermediate scattering function of a particle on a flat surface obeying the Generalised Langevin equation, with exponential memory friction. Numerical simulations based on an extended phase space method confirm the analytical results. The simulated trajectories provide qualitative insight into the effect that introducing a finite memory timescale has on the analytical line shapes. The relative amplitude of the long-time exponential tail of the line shape is suppressed, but its decay rate is unchanged, reflecting the fact that the cutoff frequency of the exponential kernel affects short-time correlations but not the diffusion coefficient which is defined in terms of a long-time limit. The exponential sensitivity of the relative amplitudes to the decay time of the chosen memory kernel is a very strong indicator for the prospect of inferring a friction kernel and the physical insights from experimentally measured intermediate scattering functions. t

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“…In that case, γ(t) has an algebraically decaying envelope [12,13,14] associated with a hard frequency cutoff in the Fourier transform γ(ω). However, the results of molecular dynamics simulations do not conform to the simple one-dimensional harmonic chain result [11] and there are potential contributions to the friction kernel from additional effects such as inter-adsorbate interactions within an interacting single adsorbate framework [15], that would likely smooth out a hard frequency cutoff. In liquid-phase many-body simulations [16,17] the effective friction kernel is typically not a perfect exponential, but the non-exponential behaviour is not due to a hard cutoff frequency.…”

Section: Introductionmentioning

confidence: 93%

The intermediate scattering function for quasi-elastic scattering in the presence of memory friction

Townsend¹,

Ward²

2018

Preprint

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We derive an analytical expression for the intermediate scattering function of a particle on a flat surface obeying the Generalised Langevin Equation, with exponential memory friction. Numerical simulations based on an extended phase space method confirm the analytical results. The simulated trajectories provide qualitative insight into the effect that introducing a finite memory timescale has on the analytical line shapes. The relative amplitude of the long-time exponential tail of the line shape is suppressed, but its decay rate is unchanged, reflecting the fact that the cutoff frequency of the exponential kernel affects short-time correlations but not the diffusion coefficient which is defined in terms of a long-time limit. The exponential sensitivity of the relative amplitudes to the decay time of the chosen memory kernel is a very strong indicator for the prospect of inferring a friction kernel and the physical insights from experimentally measured intermediate scattering functions.

show abstract

Microscopic and macroscopic estimates of friction: application to surface diffusion of copper

Cited by 8 publications

References 36 publications

Atomic jumps during surface diffusion

Atomic jumps during surface diffusion

The intermediate scattering function for quasi-elastic scattering in the presence of memory friction

The intermediate scattering function for quasi-elastic scattering in the presence of memory friction

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