Vibrational Amplitude Of Surface Atoms Research Articles

Impacts of hot electron diffusion, electron–phonon coupling, and surface atoms on metal surface dynamics revealed by reflection ultrafast electron diffraction

Metals exhibit nonequilibrium electron and lattice subsystems at transient times following femtosecond laser excitation. In the past four decades, various optical spectroscopy and time-resolved diffraction methods have been used to study electron–phonon coupling and the effects of underlying dynamical processes. Here, we take advantage of the surface specificity of reflection ultrafast electron diffraction (UED) to examine the structural dynamics of photoexcited metal surfaces, which are apparently slower in recovery than predicted by thermal diffusion from the profile of absorbed energy. Fast diffusion of hot electrons is found to critically reduce surface excitation and affect the temporal dependence of the increased atomic motions on not only the ultrashort but also sub-nanosecond times. Whereas the two-temperature model with the accepted physical constants of platinum can reproduce the observed surface lattice dynamics, gold is found to exhibit appreciably larger-than-expected dynamic vibrational amplitudes of surface atoms while keeping the commonly used electron–phonon coupling constant. Such surface behavioral difference at transient times can be understood in the context of the different strengths of binding to surface atoms for the two metals. In addition, with the quantitative agreements between diffraction and theoretical results, we provide convincing evidence that surface structural dynamics can be reliably obtained by reflection UED even in the presence of laser-induced transient electric fields.

Size and surface orientation effects on thermal expansion coefficient of one-dimensional silicon nanostructures

We perform classical molecular dynamics simulations based on the Tersoff interatomic potential to investigate the size and surface orientation dependence of lattice constant and thermal expansion coefficient of one-dimensional silicon nanostructures. Three different surface orientations of silicon are considered, i.e., Si(110), Si(111), and Si(100) with 2×1 reconstruction. For each surface orientation, we investigate nanostructures with thicknesses ranging from 0.3 to 5.0 nm. We compute the vibrational amplitude of surface atoms, lattice constant, and thermal expansion coefficient as a function of size and temperature, and compare them for different surface orientations. An analytical expression is developed to compute the variation of the thermal expansion coefficient with size of the nanostructure.

Surface melting of close-packed Mg(0001)

Using molecular dynamics simulations and an analytic embedded-atom method, an investigation of the surface anharmonicity for the close-packed surface of Mg(0001) is presented in the temperature range from 0 K to its bulk melting temperature. The temperature dependences of the surface phonon frequencies, the mean square vibrational amplitudes of surface atoms and the layer structure factor have been calculated. The calculated results are in good agreement with the experimental data available. Surface melting of the closed-packed Mg(0001) is predicted by the calculation of the layer structure factor, and a liquid-like layer is observed from the simulation of its microstructure. The possible mechanism for the anomalous behavior is discussed.

Surface melting of close‐packed Mg(0001), compared with Al(111)

AbstractUsing molecular dynamics simulations and an analytic embedded‐atom method, a comparative study of the surface anharmonicity for the close‐packed surface of Mg(0001) and Al(111) is presented in the temperature range from 0 K to their melting temperatures. The temperature dependences of the surface phonon frequencies, the mean square vibrational amplitudes of surface atoms and the layer structure factor are calculated. The calculated results are in good agreement with the available experimental data. Although with the same atomic arrangement for the top layer, Al(111) preserves its crystalline order in the temperature range considered, and Mg(0001) exhibits surface melting. The possible mechanism for the different melting behaviors of the two surfaces is discussed. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Comparative study of anharmonicity: Ni(111), Cu(111), and Ag(111)

We present a comparative study of the structure and the dynamics of the most close packed surface of Ni, Cu, and Ag from near room temperature up to ${0.9T}_{m},$ using molecular dynamics simulations and interaction potentials from the embedded atom method. Calculated shifts in the surface phonon frequencies, the broadening of their linewidths, and the variations in the mean square vibrational amplitudes of surface atoms, as a function of temperature, indicate that anharmonic effects are small on these surfaces. The surface thermal expansion of these three (111) surfaces is also found to be smaller than that of the respective (100) and (110) surfaces. Additionally, we do not find any premelting or pronounced disordering on these surfaces, in the temperature range considered.

Anharmonic effects on Ag(111): a molecular dynamics study

We have explored the structure and dynamics of Ag(111) in the temperature range 300–1100 K, using molecular dynamics simulations and interaction potentials from the embedded atom method. Calculated shifts in the surface phonon frequencies, the broadening of their line-widths, and the variations in the mean square vibrational amplitudes of surface atoms, with temperature, indicate that anharmonic effects are small up to 900 K, beyond which there is an enhancement. Thermal expansion is found to be about the same as in the bulk, and the surface does not disorder until 1100 K and does not premelt.

Ion-beam crystallography of the GaSb (110) surface

We report the first successful structure determination of a reconstructed compound semiconductor based on mass-resolved RBS. For the GaSb (110) surface blocking directions have been determined for ions backscattered from the Ga atoms and from the Sb atoms in the near-surface region. The reconstruction is characterised by a rotation of the bond between toplayer Sb and Ga atoms. We find a bond rotation angle of (29.5±1.5)°, which is close to a ELEED value recently reported for this surface. The rms vibrational amplitude of surface atoms is enhanced by a factor 1.5 with respect to the bulk value.

Mean Displacement of Surface Atoms in Palladium and Lead Single Crystals

The intensity of specularly reflected [(00) reflection] low-energy (5-500-eV) electrons has been measured as a function of temperature for the (100) and (111) faces of palladium and for the (111) face of lead in the temperature ranges 25°-600°C and 25°-225°C, respectively. From the data, the root-mean-square displacements, 〈u⊥〉, of surface atoms perpendicular to the surface planes and the surface Debye temperatures have been calculated. The mean vibrational amplitudes of surface atoms are 40%→100% larger than for bulk atoms. There is little difference between the surface mean displacements of different crystal orientations; 〈u⊥〉 appears to be relatively insensitive to changes of surface structure or surface density. The experimental results correlate well with those obtained for platinum and silver single-crystal surfaces. It is believed that all monatomic face-centered cubic crystal surfaces should have mean displacements markedly larger than those in the bulk.

Surface atom vibrations

Low energy electron diffraction measurements of the temperature dependence of the intensity of many diffraction beams from the (110) surface of a clean nickel crystal indicate that the mean square vibrational amplitude of surface atoms is greater than that of atoms in the bulk of the crystal. Vibration in the plane of the surface is anisotropic with u 2 [110] ∼ u 2 [001] > u 2 [1 1 ̄ 0] , which in turn are greater than the mean square vibrational amplitude of bulk atoms. The assignment of actual numerical values to these parameters requires additional refinement of the data.