Surface Anharmonicity Research Articles

A study of dynamical evolution of small two-dimensional Copper islands’ diffusion on Ag(111) surface and observed surface effects

We study the diffusion of two-dimensional [Formula: see text] islands on Ag(1[Formula: see text]1[Formula: see text]1) surface using molecular dynamics (MD) simulations. The work is the extension of calculations of monomer and dimer Hayat et al. [Phys. Rev. B 82 (2010) 085411] and trimer results Shah et al. [Phys. Lett. A 378 (2014) 1732]. Simulations carried out at three different temperatures — 300, 500, and 700 K — show the concerted motion to be dominant for the smaller islands (2- to 4-atoms), while the shape-changing multiple-atom processes are responsible for the diffusion of larger islands. Arrhenius plots of the diffusion coefficients reveal that the effective energy barrier is less than [Formula: see text] meV for the largest island size of Cu/Ag(1[Formula: see text]1[Formula: see text]1). There is a scaling of the effective energy barrier with size to some extent, but most notably it remains constant for islands with 4- to 6-atoms. The diffusion coefficient increases within a factor of 10 at the three temperatures 300, 500, and 700 K. The observed anharmonic features of the [Formula: see text] adislands (breakage and pop–up) at Ag(1[Formula: see text]1[Formula: see text]1) surface as well as the surface anharmonicity of the Ag-substrate (fissures, dislocations, vacancy generation, and atomic exchange), are also presented. These findings can serve as an input for kinetic Monte Carlo (KMC) simulations. For the smaller sized islands the variation in the effective energy barrier with the island size is in good agreement with the experimental findings.

Four-phonon scattering significantly reduces intrinsic thermal conductivity of solids

For decades, the three-phonon scattering process has been considered to govern thermal transport in solids, while the role of higher-order four-phonon scattering has been persistently unclear and so ignored. However, recent quantitative calculations of three-phonon scattering have often shown a significant overestimation of thermal conductivity as compared to experimental values. In this Rapid Communication we show that four-phonon scattering is generally important in solids and can remedy such discrepancies. For silicon and diamond, the predicted thermal conductivity is reduced by 30% at 1000 K after including four-phonon scattering, bringing predictions in excellent agreement with measurements. For the projected ultrahigh-thermal conductivity material, zinc-blende BAs, a competitor of diamond as a heat sink material, four-phonon scattering is found to be strikingly strong as three-phonon processes have an extremely limited phase space for scattering. The four-phonon scattering reduces the predicted thermal conductivity from 2200 to 1400 W/m K at room temperature. The reduction at 1000 K is 60%. We also find that optical phonon scattering rates are largely affected, being important in applications such as phonon bottlenecks in equilibrating electronic excitations. Recognizing that four-phonon scattering is expensive to calculate, in the end we provide some guidelines on how to quickly assess the significance of four-phonon scattering, based on energy surface anharmonicity and the scattering phase space. Our work clears the decades-long fundamental question of the significance of higher-order scattering, and points out ways to improve thermoelectrics, thermal barrier coatings, nuclear materials, and radiative heat transfer.

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.

Anharmonic effects on B2–FeAl(1 1 0) surface: A molecular dynamics study

Using molecular dynamics simulations and the analytic embedded-atom method (AEAM), the surface anharmonicity of B2–FeAl(1 1 0) has been studied in the temperature range from 0 K to 1400 K. The temperature dependence of the interlayer spacing, mean square vibrational amplitudes, surface phonon frequencies and line-widths, and layer structure factor have been calculated. The obtained results indicate that the anharmonic effects are small in the temperature range from 0 K to 900 K. The temperature dependences of the interlayer spacing indicates that the rippling effect of the B2–FeAl(1 1 0) surface is exhibited by the contraction of Fe surface atoms and the expansion of Al atoms, which persists at high temperatures. The temperature dependence of the layer structure factors shows that the B2–FeAl(1 1 0) surface does not disorder until the temperature of 1300 K.

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)

Mechanism of adatom formation on Ag(1 1 0) studied by combined quasi-elastic He atom scattering and low energy ion scattering

Two complementary techniques, i.e. low-energy ion scattering in the neutral impact collision ion scattering spectroscopy (NICISS) mode and energy resolved He atom scattering (HAS) are combined to study the adatom formation mechanism on Ag(110). The NICISS spectra have been collected between 300 and 900K along the 〈001〉, 〈11¯2〉 and 〈11¯0〉 azimuthal directions while HAS measurements of the diffuse elastic peak has been performed along the 〈11¯0〉 directions between 190 and 800K. Both techniques are sensitive to surface disorder and HAS data have been corrected by using the NICISS results in particular on the anharmonicity estimated through a two atoms scattering model. In fact, above 500K surface anharmonicity is clearly detected and accompanies the proliferation of thermal induced defects. Without this anharmonic correction the adatom formation energy Ea is too low and similar to the surface diffusion barrier. Instead, including the anharmonicity the estimate, Ea=(0.38±0.03)eV, is in excellent agreement with the predictions of molecular dynamics simulations.

Femtosecond impulsive vibrational spectroscopy in conjugated polymers

We apply the impulsive coherent vibrational spectroscopy technique to the study of the vibrational structure of conjugated polymers and oligomers. Molecular vibrations are directly observed in the time domain using tunable 10 fs light pulses from a recently developed optical parametric amplifier. We present results obtained with the prototypical systems sexithiophene, polidiacetylene and poly( p-phenylenevinylene), observing modes with frequencies up to 2100 cm −1 (16 fs period). We directly measure vibrational dephasing times and gain hints on the potential energy surface anharmonicity.

Vibrational structure of theO 1sionization spectrum ofCO2

The dynamical localization of the $\mathrm{O} 1s$ core holes in the ${\mathrm{CO}}_{2}$ molecule is studied ab initio beyond the linear vibronic coupling model. The vibrational structure of the $\mathrm{O} 1s$ x-ray photoelectron spectrum (XPS) has been calculated employing accurate potential energy surfaces of the ground and ionized diabatic electronic states obtained at the self-consistent field and singles and doubles configuration-interaction (SDCI) methods. A very good agreement of the SDCI computed vibrational structure of the $\mathrm{O} 1s$ XPS with the respective experimental high-resolution spectrum has been obtained. The anharmonicity of the ionic state potential-energy surface induced mostly by the ground-state surface anharmonicity plays a crucial role in the proper description of the vibrational line intensities. The linear model is discussed in detail. The linear model based on the vibronic coupling constants obtained from the geometry change in the ionized state relative to the ground-state reference configuration has been shown to contain a hidden renormalization of the coupling constants. This improves the agreement of the calculated intensities of the vibrational lines in the spectrum with the experiment, compared to the case of the strict linear model. The limitations of this renormalized linear model are discussed. Electron relaxation and correlation considerably affect the vibrational line intensities. The popular equivalent core approximation is tested for ${\mathrm{CO}}_{2}$. The calculation of the $\mathrm{O} 1s$ XPS performed at the SDCI level with and without this approximation is shown to provide almost identical results on the vibrational intensities.

Anharmonicity on Al(100) and Al(111) surfaces

We present a molecular-dynamics analysis of the stable nonmelting (100) and (111) surfaces of Al. A many-body potential derived from first-principles calculations is used. The molecular-dynamics method includes anharmonic effects of all orders. We study static and dynamical properties of the surface. An expansion of the (111) surface and a contraction of the (100) surface results from the calculations. At low temperature, the vertical mean-square vibrational amplitude is larger than the in-plane component, while at higher temperature the in-plane component approaches the vertical one. Both components are at least twice as large as the bulk value. The interactions due to the surface decay very rapidly going into the crystal from the surface, as indicated by the analysis of the Debye-Waller factor. The evaluated linewidths for the Rayleigh surface phonon reproduce quite well the temperature dependence of the He-surface scattering data. The experimental behavior of the energy shifts, as a function of the scattering momentum transfer, presents a minimum inside the Brillouin zone, which is also found by our calculations. The surface energy shifts are about $30%$ larger than the bulk ones at the same temperature. The effect of surface anharmonicity is much larger for the static properties than for the dynamical properties.

The energy relaxation of Si–H vibration in the H/Si(111) system. Relaxation rate and potential energy surface anharmonicity

The vibrational energy relaxation of the Si–H stretching vibration in the H/Si(111) system is investigated by application of the perturbation theory to the anharmonic Si–H oscillator. The eigenfunctions for the 3D motion of an adsorbed H atom are obtained with an ab initio potential energy surface calculated for the H–Si(SiH 3) 3 cluster. The transition matrix elements between the vibrational states involved in the relaxation process are evaluated. The spectrum of the velocity autocorrelation function of the top Si atom appearing in the expression for the relaxation rate is calculated with classical molecular dynamics and corrected for the quantum effects. The energy relaxation channels are indicated and the calculated relaxation rates are compared with experimental data. The calculated slow decay of the H atom excitation is due to a small value of the transition matrix elements. The magnitudes of these matrix elements are shown to be sensitive to the high-order anharmonicity parameters of the potential energy surface.

Dynamics of anharmonic surfaces in harmonic crystals

Explicit expressions are given for the effective equations of motion for surface atoms placed in a general anharmonic potential and attached to semi-infinite harmonic bulk substrates. Three types of one-dimensional substrates are considered: i) continuous dispersionless, ii) discrete with nearest neighbours harmonic interactions, and iii) a substrate showing a strong spatial dispersion due to next-nearest neighbours interactions. The elimination of the harmonic degrees of freedom of the dispersionless substrate i) reduces the problem to the damped Duffing oscillator in the case of an external force applied to the surface atom, and to an extended Duffing oscillator with time-dependent coefficients in the case of scattering of a phonon incoming from the bulk. In both remaining cases [ ii) and iii)]the resulting equations of motion are Volterra integro-differential equations. The equations of motion obtained allow for the study of transitive regimes, of higher harmonics generation and of chaotic behaviour, due to the surface anharmonicity.

Temperature dependence of the Ag(110) surface phonons

We present an experimental study of the S 1 and S 3 phonon modes of Ag(110) between 300 and ∼ 700 K. The study was carried out along the 〈001〉 direction by means of energy-resolved He atom scattering with time-of-flight detection. The energy shifts of the modes were measured over most of the surface Brillouin zone. A non-linear behavior of the S 3 shifts above 600 K was observed for the first time. The surface anharmonicity constants were also evaluated.

A Model for the Thermal Expansion of Ag(111) and other Metal Surfaces

We develop a model to study the thermal expansion of surfaces, wherein phonon frequencies are obtained from ab initio total energy calculations. Anharmonic effects are treated exactly in the direction normal to the surface, and within a quasiharmonic approximation in the plane of the surface. We apply this model to the Ag(111) and Al(111) surfaces, and find that our calculations reproduce the experimental observation of a large and anomalous increase in the surface thermal expansion of Ag(111) at high temperatures [P. Statiris, H.C. Lu and T. Gustafsson, Phys. Rev. Lett. 72, 3574 (1994)]. Surprisingly, we find that this increase can be attributed to a rapid softening of the in-plane phonon frequencies, rather than due to the anharmonicity of the out-of-plane surface phonon modes. This provides evidence for a new mechanism for the enhancement of surface anharmonicity. A comparison with Al(111) shows that the two surfaces behave quite differently, with no evidence for such anomalous behavior on Al(111).

Atomic dynamics and structure of the Ge(111)c(2 x 8) surface.

We present results of a first-principles molecular-dynamics study of the surface structure and atomic dynamics of Ge(111)c(2\ifmmode\times\else\texttimes\fi{}8) at T=0 and T=300 K. The T=0 ground-state structure shows asymmetries between the two adatoms and the two restatoms in the surface unit cell, which are seen experimentally in low-energy electron diffraction. These asymmetries, which are found to survive at T\ensuremath{\sim}300 K, lead to zone folding and splitting of the surface phonon modes. Two pairs of prominent surface modes are identified, mostly localized on the adatoms and second-layer atoms just below. The values of the mean square displacements for the various layers at different temperatures moreover indicate an enhanced surface anharmonicity with respect to the bulk.

Systematic trends in the normal enhancement of the phonon anharmonicity at the surface of metals.

The temperature dependence of the Rayleigh wave frequency measured by He atom scattering for the surfaces Al(001), Al(111), and Cu(001) is compared with bulk data in order to establish the surface enhancement of phonon anharmonicity. A comparison is made also with recent HREELS data for the Cu(110) surface. In all cases the surface anharmonicity is found to be less than or at most of the order of twice the bulk anharmonicity, in agreement with recent calculations of the enhancement of the zero-point mean-square displacements.

Surface vibrations of Ag(100) and Cu(100): A molecular-dynamics study.

We present molecular-dynamics studies of Ag(100) and Cu(100), using interatomic potentials obtained by the embedded-atom method. The low-temperature results for the surface phonon frequencies and polarizations at selected points in the two-dimensional Brillouin zone are in good agreement with experimental data and also with results of first-principles calculations on both systems. The mean-square vibrational amplitudes of the surface atoms are found to be isotropic and much larger than the reported values for the bulk. As a function of increasing temperature, the frequencies of the surface phonons are found to redshift and the peaks to broaden. The variation of the mean-square vibrational amplitude with temperature displays effects of enhanced surface anharmonicity.

Cu(110): disorder or enhanced anharmonicity? A computer simulation study of surface defects and dynamics

By using molecular dynamics and an effective n-body potential adapted to copper, we show the dynamical behavior of (110) surfaces to be greatly affected by the large concentration of defects present at high temperatures. Above T = 1000 K, surface anharmonicity is increased by point defects as do the vibrational amplitudes of atoms pertaining to surface layers. Accounting for thermal attenuation observed in diffraction experiments requires both, thermal disorder and surface anharmonicity to be considered. Surface relaxations are found to decrease on increasing the temperature, in qualitative agreement with recent experiments. At the highest temperature we studied, T = 1233 K, thermally generated adatoms become fully delocalized along the close-packed rows [1̄10], a feature characterizing the early stages of anisotropic surface melting.

Anharmonic broadening of surface phonons in Cu(111)

A first calculation of the anharmonic damping of surface phonons in Cu(111) has been carried out. The slab method is used to simulate the truncation of the crystal. A central potential is adopted to parametrize harmonic and anharmonic interactions. Clear indications of enhanced surface anharmonicity are provided.

Enhanced surface anharmonicity observed in vibrations on Cu(110).

Surface anharmonicity has been measured on Cu(110) by examining the temperature dependence of surface phonons with atomic motion normal to the surface using high-resolution electron-energy-loss spectroscopy. At the Brillouin zone center \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{} the energy of the ${\mathit{MS}}_{7}$ resonance decreases by 3.2 meV and the intrinsic width increased by 8.6 meV as the temperature increases from 21 to 766 K. Energy decrease and width increase are also observed at the Brillouin zone edge Y\ifmmode\bar\else\textasciimacron\fi{} in the ${\mathit{S}}_{3}$ phonon. The percentage energy decrease is the same in both phonons. Direct comparison with bulk-phonon measurements shows that the anharmonicity at the surface is 4.1--4.8 times greater than in the bulk.

High-resolution low-energy electron-diffraction analysis of the Pb(110) roughening transition.

We present a detailed line-shape analysis of the high-resolution low-energy electron-diffraction angular profiles measured from the Pb(110) surface undergoing a roughening transition. Experimentally, we show that the effects of multiple scattering and the thermal diffuse scattering do not make significant contributions to the line shape and therefore do not affect the structural information extracted from the angular intensity distribution of the diffracted beams associated with a surface undergoing the roughening transition. We have measured the effect of anisotropy in the roughening of a low-index plane metal surface. For the Pb(110) surface, the ratio of anisotropic interaction energies is estimated from the measurement to be ${\mathit{J}}_{\mathit{x}}$:${\mathit{J}}_{\mathit{y}}$=3.46:1. In addition, we have also measured an enhanced surface anharmonicity starting around 380 K, which is closely related to the anomalous derelaxation of the top layers previously observed by the high-energy ion-channeling technique. This derelaxation may be the major cause for the roughening transition occurring in the Pb(110) surface.