# Capillary fluctuations of surface steps: An atomistic simulation study for the model Cu(111) system

## TL;DR

This study uses molecular dynamics simulations to analyze capillary fluctuations of surface steps on copper, revealing isotropic step stiffness and diffusion-governed fluctuation lifetimes, with results compared to thermodynamic-integration data.

## Contribution

First atomistic simulation study of capillary fluctuations on Cu(111) steps, providing detailed fluctuation spectra and stiffness measurements near melting temperature.

## Key findings

- Step stiffness is isotropic within statistical error.
- Fluctuation lifetimes vary over four orders of magnitude with wave number.
- Simulation results differ significantly from thermodynamic-integration calculations.

## Abstract

Molecular dynamics (MD) simulations are employed to investigate the capillary fluctuations of steps on the surface of a model metal system. The fluctuation spectrum, characterized by the wave number ($k$) dependence of the mean squared capillary-wave amplitudes and associated relaxation times, is calculated for $\left<110\right>$ and $\left<112\right>$ steps on the $\{111\}$ surface of elemental copper near the melting temperature of the classical potential model considered. Step stiffnesses are derived from the MD results, yielding values from the largest system sizes of $(37\pm1) \, \mathrm{meV}/\mathring{\mathrm{A}}$ for the different line orientations, implying that the stiffness is isotropic within the statistical precision of the calculations. The fluctuation lifetimes are found to vary by approximately four orders of magnitude over the range of wave numbers investigated, displaying a $k$ dependence consistent with kinetics governed by step-edge mediated diffusion. The values for step stiffness derived from these simulations are compared to step free energies for the same system and temperature obtained in a recent MD-based thermodynamic-integration (TI) study [Freitas, Frolov, and Asta, Phys. Rev. B 95, 155444 (2017)]. Results from the capillary-fluctuation analysis and TI calculations yield statistically significant differences that are discussed within the framework of statistical-mechanical theories for configurational contributions to step free energies.