Microstructure and velocity of field-driven solid-on-solid interfaces: Analytic approximations and numerical results

Rikvold, Per Arne; Kolesík, M.

doi:10.1103/physreve.66.066116

Cited by 22 publications

(50 citation statements)

References 35 publications

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“…(18) of Ref. 8. The spin-class populations listed in Table II can now be calculated explicitly for each of the dynamics by replacing X with its corresponding value.…”

Section: Nonlinear Responsementioning

confidence: 99%

Microstructure and velocity of field-driven solid-on-solid interfaces moving under stochastic dynamics with local energy barriers

2006

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We study the microscopic structure and the stationary propagation velocity of (1+1)-dimensional solid-on-solid interfaces in an Ising lattice-gas model, which are driven far from equilibrium by an applied force, such as a magnetic field or a difference in (electro)chemical potential. We use an analytic nonlinear-response approximation [P. A. Rikvold and M. Kolesik, J. Stat. Phys. 100, 377 (2000)] together with kinetic Monte Carlo simulations. Here we consider interfaces that move under Arrhenius dynamics, which include a microscopic energy barrier between the allowed Ising/latticegas states. Two different dynamics are studied: the standard one-step dynamics (OSD) [H. C. Kang and W. Weinberg, J. Chem. Phys. 90, 2824Phys. 90, (1992] and the two-step transition-dynamics approximation (TDA) [T. Ala-Nissila, J. Kjoll, and S. C. Ying, Phys. Rev. B 46, 846 (1992)]. In the OSD the effects of the applied force and the interaction energies in the model factorize in the transition rates (soft dynamics), while in the TDA such factorization is not possible (hard dynamics). In full agreement with previous general theoretical results we find that the local interface width under the TDA increases dramatically with the applied force. In contrast, the interface structure with the OSD is only weakly influenced by the force, in qualitative agreement with the theoretical expectations. Results are also obtained for the force-dependence and anisotropy of the interface velocity, which also show differences in good agreement with the theoretical expectations for the differences between soft and hard dynamics. Our results confirm that different stochastic interface dynamics that all obey detailed balance and the same conservation laws nevertheless can lead to radically different interface responses to an applied force.

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“…(18) of Ref. 8. The spin-class populations listed in Table II can now be calculated explicitly for each of the dynamics by replacing X with its corresponding value.…”

Section: Nonlinear Responsementioning

confidence: 99%

Microstructure and velocity of field-driven solid-on-solid interfaces moving under stochastic dynamics with local energy barriers

2006

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“…Recent studies indicate that different stochastic dynamics, even when they have the same conserved quantities and satisfy detailed balance, lead to important differences in the nanostructure of field-driven interfaces. [5][6][7][8][9] Surfaces driven by hard dynamics ͑in which the single-site transition rates cannot be factorized into one term that depends only on the interaction energies and a second term that depends only on the field energies, in contrast with soft dynamics for which this factorization is possible 10 ͒, such as Glauber, Metropolis, and the two-step transition dynamics approximation ͑TDA͒, 11,12 have a strong dependence on the applied field. For all hard dynamics studied so far, the average step height increases dramatically with increasing field.…”

Section: Introductionmentioning

confidence: 99%

Nanostructure and velocity of field-driven solid-on-solid interfaces moving under a phonon-assisted dynamic

Buendı́a

Rikvold²,

Kolesík

et al. 2007

Phys. Rev. B

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The nanoscopic structure and the stationary propagation velocity of ͑1+1͒-dimensional solid-on-solid interfaces in an Ising lattice-gas model, which are driven far from equilibrium by an applied force, such as a magnetic field or a difference in ͑electro͒chemical potential, are studied by an analytic nonlinear-response approximation ͓P. A. Rikvold and M. Kolesik, J. Stat. Phys. 100, 377 ͑2000͔͒ together with kinetic Monte Carlo simulations. Here, we consider the case that the system is coupled to a two-dimensional phonon bath. In the resulting dynamic ͓K. Saito et al., Phys. Rev. E 61, 2397 ͑2000͒; K. Park and M. A. Novotny, Comput. Phys. Commun. 147, 737 ͑2002͔͒, transitions that conserve the system energy are forbidden, and the effects of the applied force and the interaction energies do not factorize ͑a so-called hard dynamic͒. In full agreement with previous general theoretical results, we find that the local interface width changes dramatically with the applied force. However, in contrast with other hard dynamics, this change is nonmonotonic in the driving force. Results are also obtained for the force dependence and anisotropy of the interface velocity, which also show differences in good agreement with the theoretical expectations for the differences between soft and hard dynamics. However, significant differences between theory and simulation are found near two special values of the driving force, where certain transitions allowed by the solid-on-solid model become forbidden by the phonon-assisted dynamic. Our results show that different stochastic interface dynamics that all obey detailed balance and the same conservation laws nevertheless can lead to radically different interface responses to an applied force. Thus, they represent a significant step toward providing a solid physical foundation for kinetic Monte Carlo simulations.

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“…A non-linear response approximation based on a dynamic mean-field approximation for the equation of motion of the single-step pdf, together with a detailed-balance argument for the stationary state, gives the following expression for the field-dependent X(T, H) [3,4],…”

Section: The Modelmentioning

confidence: 99%

“…Until recently it was commonly believed that dynamics that respect the same conservation laws and all obey detailed balance, give essentially the same qualitative behavior. However, recent results clearly show that there are nonconservative dynamics that, although they all obey detailed balance and the same conservation laws, lead to very different interface microstructures [3,4,5,6,7]. Since many interface properties, such as mobility and chemical activity, are determined by the microstructure, great care must therefore be taken in selecting the appropriate dynamic for the physical or chemical system of interest.…”

Section: Introductionmentioning

confidence: 99%

Field-driven solid-on-solid interfaces moving under a stochastic Arrhenius dynamics: Effects of the barrier height

Buendı́a

Rikvold

Kolesík

2006

Journal of Molecular Structure: THEOCHEM

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We present analytical results and kinetic Monte Carlo simulations for the mobility and microscopic structure of solid-on-solid (SOS) interfaces driven far from equilibrium by an external force, such as an applied field or (electro)chemical potential difference. The interfaces evolve under a specific stochastic dynamic with a local energy barrier (an Arrhenius dynamic), known as the transition dynamics approximation (TDA). We calculate the average height of steps on the interface, the average interface velocity, and the skewness of the interface as functions of the driving force and the height of the energy barrier. We find that the microscopic interface structure depends quite strongly on the barrier height. As the barrier becomes higher, the local interface width decreases and the skewness increases, suggesting increasing short-range correlations between the step heights.

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Microstructure and velocity of field-driven solid-on-solid interfaces: Analytic approximations and numerical results

Cited by 22 publications

References 35 publications

Microstructure and velocity of field-driven solid-on-solid interfaces moving under stochastic dynamics with local energy barriers

Microstructure and velocity of field-driven solid-on-solid interfaces moving under stochastic dynamics with local energy barriers

Nanostructure and velocity of field-driven solid-on-solid interfaces moving under a phonon-assisted dynamic

Field-driven solid-on-solid interfaces moving under a stochastic Arrhenius dynamics: Effects of the barrier height

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