The inelastic scattering of neutrons by nanoparticles due to acoustic vibrational modes (energy below 10 meV) confined in nanoparticles is calculated using the Zemach-Glauber formalism. Such vibrational modes are commonly observed by light scattering techniques (Brillouin or low-frequency Raman scattering). We also report high resolution inelastic neutron scattering measurements for anatase TiO2 nanoparticles in a loose powder. Factors enabling the observation of such vibrations are discussed. These include a narrow nanoparticle size distribution which minimizes inhomogeneous broadening of the spectrum and the presence of hydrogen atoms oscillating with the nanoparticle surfaces which enhances the number of scattered neutrons.
Classical continuum elastic calculations show that the acoustic vibrational modes of an embedded nanoparticle can be lightly damped even when the longitudinal plane wave acoustic impedances $Z_o=ρv_L$ of the nanoparticle and the matrix are the same. It is not necessary for the matrix to be less dense or softer than the nanoparticle in order to have long lived vibrational modes. Continuum boundary conditions do not always accurately reflect the microscropic nature of the interface between nanoparticle and matrix, and a multi-layer model of the interface reveals the possibility of additional red…
The spectrum of acoustic vibrational modes of an inhomogeneous elastic continuum are analyzed with application to a spherical nanoparticle embedded in an infinite glass block. The relationship of these modes to the discrete vibrational spectrum of a free sphere is studied. The vibrational modes of a sphere with a fixed surface are relevant in some situations. Comparisons are also made to calculations of mode frequency and damping based on complex valued frequency.
Arbitrary waves incident on a solid embedded nanoparticle are studied. The acoustic vibrational frequencies are shown to correspond to the poles of the scattering cross section in the complex frequency plane. The location of the poles is unchanged even if the incident wave is nonplanar. A second approach approximating the infinite matrix as a very large shell surrounding the nanoparticle provides an alternate way of predicting the mode frequencies. The wave function of the vibration is also provided.
The vibrational density of states of silicon nanoparticles in the range from 2.3 to 10.3 nm is studied with the help of molecular-dynamics simulations. From these simulations the vibrational density of states and frequencies of bulk-like vibrational modes at high-symmetry points of the Brillouin-zone have been derived. The results show an increase of the density of states at low frequencies and a transfer of modes from the high-frequency end of the spectrum to the intermediate range. At the same time the peak of transverse optical modes is shifted to higher frequencies. These observations are …
Vibrational mode frequencies and damping are calculated for an elastic sphere embedded in an infinite, homogeneous, isotropic elastic medium. Anisotropic elasticity of the sphere significantly shifts the frequencies in comparison to simplified calculations that assume isotropy. New low frequency Raman light scattering data are presented for silicon spheres grown in a SiO2 glass matrix. Principal features of the Raman spectrum are not correctly described by a simple model of the nanoparticle as a free, isotropic sphere, but require both matrix effects and the anisotropy of the silicon to be tak…
We report results of a systematic study of structural, vibrational and thermodynamical properties of 34-atom bimetallic nanoparticles from the AgnCu34-n family using model interaction potentials as derived from the embedded atom method and in the harmonic approximation of lattice dynamics. Systematic trends in the bond length and dynamical properties can be explained largely on arguments based on local coordination and elemental environment. Thus increase in the number of silver atoms in a given neighborhood introduces a monotonic increase in bond length while increase of the copper content do…
The validity of the linear elasticity theory is examined at the nanometer scale by investigating the vibrational properties of silver and gold nanoparticles whose diameters range from about 1.5 to 4 nm. Comparing the vibration modes calculated by elasticity theory and atomistic simulation based on the Embedded Atom Method, we first show that the anisotropy of the stiffness tensor in elastic calculation is essential to ensure a good agreement between elastic and atomistic models. Second, we illustrate the reduction of the number of vibration modes due to the diminution of the number of atoms wh…
Raman spectrums of nanoparticles of a p-dibromobenzene with size of 300 nanometers and 50 nanometers are measured. It is found that frequencies of lines of stretching vibrations of C-Br at reduction of the sizes of nanoparticles below 300 nanometers are incremented. It is related to magnification of parameters of the lattice and interaction reduction between molecules.
We study theoretically spectrum of radial vibrational modes in composite metal nanostructures such as bimetallic core-shell particles and metal nanoshells with dielectric core in an environment. We calculate frequencies and damping rates of fundamental (breathing) modes for these nanostructures along with those of two higher-order modes. For metal nanoshells, we find that the breathing mode frequency is always lower than the one for solid particles of the same size, while the damping is higher and increases with reduction of the shell thickness. We identify two regimes that can be characterize…
Using Raman scattering, the solid solution nanoparticles of paradibrombenzol/paradihlorbenzol are investigated. It is found that in a spectrum of nanoparticles of solid solution frequencies of spectral lines are reduced in comparison with similar lines of a single crystal with the same concentration of components. Calculations of the lattice oscillations by Dyne's method are performed. It is shown that these modifications of frequencies can be caused by the increase of lattice parameters with the reduction of nanoparticles sizes.
The vibrational density of states (VDOS) of nanoclusters and nanocrystalline materials are derived from molecular-dynamics simulations using empirical tight-binding potentials. The results show that the VDOS inside nanoclusters can be understood as that of the corresponding bulk system compressed by the capillary pressure. At the surface of the nanoparticles the VDOS exhibits a strong enhancement at low energies and shows structures similar to that found near flat crystalline surfaces. For the nanocrystalline materials an increased VDOS is found at high and low phonon energies, in agreement wi…
We have carried out a computational study of the inelastic electron tunneling spectrum (IETS) of the two vibrational modes of a single hydrogen atom on a Cu(100) surface in a scanning tunneling microscopy (STM) junction. This study addresses key issues about vibrational assignment and line shape of observed peaks in IETS within the framework of density functional theory calculations and the Lorente-Persson theory for STM-IETS. We argue that the observation of only a single, broad peak in the STM-IETS [L.J. Lauhon and W. Ho, Phys. Rev. Lett. 85, 4566 (2000)] is not caused by any symmetry restri…
The discrete nature of the vibrational modes of an isolated nanometer-scale solid dramatically modifies its low-energy electron and phonon dynamics from that of a bulk crystal. However, nanocrystals are usually coupled--even if only weakly--to an environment consisting of other nanocrystals, a support matrix, or a solid substrate, and this environmental interaction will modify the vibrational properties at low frequencies. In this paper we investigate the modification of the vibrational modes of an insulating spherical nanoparticle caused by a weak {\it mechanical} coupling to a semi-infinite …
A new method is presented for describing vibrational effects in x-ray absorption spectroscopy (XAS) and resonant inelastic x-ray scattering (RIXS) using a combination of the classical Franck-Condon (FC) approximation and classical trajectories run on the core-excited state. The formulation of RIXS is an extension of the semiclassical Kramers-Heisenberg (SCKH) formalism of Ref. {Ljungberg_2010} to the resonant case, retaining approximately the same computational cost. To overcome difficulties with connecting the absorption and emission processes in RIXS the classical FC approximation is used fo…
To understand the vibrational and configurational entropy effects for the stability of core-shell and solid-solution bimetallic nanoparticles, we theoretically investigated the excess energy of PdPt nanoparticles, adopting the (PdPt)201 model of ca. 2 nm by using the density functional method. The vibrational energy and entropy terms contributed to the total energy of both core-shell and solid-solution nanoparticles. The configurational entropy term was defined only for the solid-solution nanoparticles. Although the absolute values of vibrational energy and entropy terms were much larger than …
Gold nanoparticles emit broad-band upconverted luminescence upon irradiation with pulsed infrared laser radiation. Although the phenomenon is widely observed, considerable disagreement still exists concerning the underlying physics - most notably over the applicability of concepts such as multiphoton absorption, inelastic scattering, and interband and intraband electronic transitions. Here, we study single particles and small clusters of particles by employing a spectrally resolved power-law analysis of the irradiation-dependent emission as a sensitive probe of these physical models. Two regim…
We describe how to treat the interaction of travelling electrons with localised vibrational modes in nanojunctions. We present a multichannel scattering technique which can be applied to calculate the transport properties for realistic systems, and show how it is related to other methods that are useful in particular cases. We apply our technique to describe recent experiments on the conductance through molecular junctions.
We discuss the rich vibrational dynamics of nanometer-scale semiconducting and insulating crystals as probed by localized electronic impurity states, with an emphasis on nanoparticles that are only weakly coupled to their environment. Two principal regimes of electron-phonon dynamics are distinguished, and a brief survey of vibrational-mode broadening mechanisms is presented. Recent work on the effects of mechanical interaction with the environment is discussed.
Recently, two reports have demonstrated the amazing possibility to probe vibrational excitations from nanoparticles with a spatial resolution much smaller than the corresponding free-space phonon wavelength using electron energy loss spectroscopy (EELS). While Lagos et al. evidenced a strong spatial and spectral modulation of the EELS signal over a nanoparticle, Krivanek et al. did not. Here, we show that discrepancies among different EELS experiments as well as their relation to optical near- and far-field optical experiments can be understood by introducing the concept of confined bright and…
Non-equilibrium Effects in Vibrational Modes Pumped by Inelastic Tunneling
State Key Laboratory of Micro-nano Engineering Science, Tsung-Dao Lee Institute & School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院、李政道研究所微纳工程科学国家重点实验室）；SUPA, School of Physics and Astronomy, University of St Andrews（圣安德鲁斯大学物理与天文学院）；Department of Physics, King’s College London（伦敦国王学院物理系）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；Physikalisches Institut, Universität Bonn（波恩大学物理研究所）
We measured the infrared vibrational properties of bulk and nanoparticle WS$_2$ in order to investigate the structure-property relations in these novel materials. In addition to the symmetry-breaking effects of local strain, nanoparticle curvature modifies the local charging environment of the bulk material. Performing a charge analysis on the \emph{xy}-polarized E$_{1u}$ vibrational mode, we find an approximate 1.5:1 intralayer charge difference between the layered 2H material and inorganic fullerene-like (IF) nanoparticles. This effective charge difference may impact the solid-state lubricat…
Hydrogen is a promising fossil-fuel alternative fuel owing to its environmentally neutral emissions and high energy density. However, the need for purified water and external power are critical hindrances to implementation of hydrogen production. The present work reveals the potential to overcome these shortcomings through piezo-photocatalysis of seawater using BaTiO3-x (BTO) nanoparticles. This material was made piezoelectrically active by annealing under different atmospheres, including O2, N2, Ar, and H2, the latter of which caused Ti4+ to Ti(4-x)+ multiple reductions and structural expansi…
The focus in this paper is an analysis of existing state of the arts directed toward the development of the next generation of vibration damping systems. The research work concentrates on an investigation related to nanoparticles/fibres/tubes-reinforced materials and coatings dynamic characterization and modeling of the fundamental phenomena that control relationships between structure and damping/mechanical properties of the materials. We simulated composite materials using finite element and mesh free methods, using a hollow shell representation of the individual nanotube/fiber. Results of t…
A new type of excitations by highly focused electron beams in scanning transmission electron microscopes is predicted for nanoparticles. The calculated electron energy loss spectra of metallic (silver) and insulating (SiO(sub2)) nanoplatelets reveal dramatic enhancement of radiative electromagnetic modes within the light cone, allowed by the breakdown of momentum conservation in the inelastic scattering event. These modes can be accessed with e-beams in the vacuum far-field zone, similarly to the recently developed far-field optics based on surface plasmon resonances.
We theoretically analyzed inelastic effects in the electron transport through molecular junctions originating from electron-vibron interactions. The molecular bridge was simulated by a periodic chain of identical interacting hydrogen-like atoms providing a set of energy states for the electron tunneling. To avoid difficulties inevitably arising when advanced computational techniques are employed to study inelastic electron transport through multilevel bridges, we propose and develop a semiphenomenological approach. The latter is based on the Buttiker's dephasing model within the scattering mat…
A time-dependent approach is used to explore inelastic effects during electron transport through few-level systems. We study a tight-binding chain with one and two sites connected to vibrations. This simple but transparent model gives insight about inelastic effects, their meaning and the approximations currently used to treat them. Our time-dependent approach allows us to trace back the time sequence of vibrational excitation and electronic interference, the ibrationally introduced time delay and the electronic phase shift. We explore a full range of parameters going from weak to strong elect…
A theoretical analysis of inelastic electron tunneling spectroscopy (IETS) experiments conducted on molecular junctions are presented, where the second derivative of the current with respect to voltage is usually plotted as a function of applied bias. Within the nonperturbative computational scheme, adequate for arbitrary parameters of the model, we consider the virtual conduction process in the off-resonance region. Here we study the influence of few crucial factors on the IETS spectra: the strength of the vibronic coupling, the phonon energy, and the device working temperature. It was also s…
Quantum hot carrier spectra in plasmonic catalysis
Beijing Computational Science Research Center（北京计算科学研究中心）；Nankai University（南开大学）；Donostia International Physics Center（多诺西亚国际物理中心）；Imperial College London（伦敦帝国理工学院）
We study the spectrum of vibrational modes in metal nanoparticles with a dielectric core. Vibrational modes are excited by the rapid heating of the particle lattice that takes place after laser excitation, and can be monitored by means of pump-probe spectroscopy as coherent oscillations of transient optical spectra. In nanoshells, the presence of two metal surfaces results in a substantially different energy spectrum of acoustic vibrations than for solid particles. We calculated the energy spectrum as well as the damping of nanoshell vibrational modes. The oscillator strength of fundamental br…
Analysis of the spheroidal modes of vibration of a free elastic sphere show that they can be qualitatively grouped into two categories: primarily longitudinal and primarily transverse. This is not a sharp distinction. However, there is a relatively stark contrast between the two kinds of modes. Primarily transverse modes have a small divergence and have frequencies that are almost functionally independent of the longitudinal speed of sound. Analysis of inelastic light scattering intensity from confined acoustic phonons in nanoparticles requires an understanding of this qualitative distinction …
A new experimental method of determination of equilibrium isotopic properties of substances based on Inelastic Neutron Scattering (INS) is proposed. We present mathematical formalism allowing calculation of beta-factor of single-element solids based on INS-derived Phonon Density of States (PDOS). PDOS data for nanodiamonds of widely different sizes and of macroscopic diamond were determined from Inelastic Neutron Scattering experiment. This allowed determination of heat capacities and, for the first time, \b{eta}-factors for the diamond nanoparticles. We demonstrate considerable size-dependent…
We report first principles density functional perturbation theory calculations and inelastic neutron scattering measurements of the phonon density of states, dispersion relations and electromechanical response of PbTiO3, BaTiO3 and SrTiO3. The phonon density-of-states of the quantum paraelectric SrTiO3 is found to be fundamentally distinct from that of ferroelectric PbTiO3 and BaTiO3 with a large 70-90 meV phonon band-gap. The phonon dispersion and electromechanical response of PbTiO3 reveal giant anisotropies. The interplay of covalent bonding and ferroelectricity, strongly modulates the elec…
We calculate the vibrational density-of-states in an insulating nanoparticle that is in weak mechanical contact with a semi-infinite substrate. The work is motivated by a recent experiment by Yang et al., where the low-energy phonon density-of-states of Y2O3 nanoparticles doped with Eu was measured. Preliminary results presented here, based on the conventional quasiparticle-pole approximation for the phonon propagator, are in reasonable agreement with experiment.
Transmission electron microscopy and spectroscopy currently enable the acquisition of spatially resolved spectral information from a specimen by focusing electron beams down to a sub-Angstrom spot and then analyzing the energy of the inelastically scattered electrons with few-meV energy resolution. This technique has recently been used to experimentally resolve vibrational modes in 2D materials emerging at mid-infrared frequencies. Here, based on first-principles theory, we demonstrate the possibility of identifying single isotope atom impurities in a nanostructure through the trace that they …
We report real space imaging measurements of inelastic Friedel oscillations. The inelastic electron tunneling spectroscopy, using scanning tunneling microscopy, around dimers of dichlorobenze adsorbates on Au(111) surface display clear spatial modulations that we attribute to inelastic scattering at the molecular sites caused by molecular vibrations. Due to local interactions between the adsorbate and the surface states, the molecular vibrations generate a redistribution of the charge density at energies in a narrow range around the inelastic mode. Our experimental findings are supported by th…
We report inelastic neutron scattering measurements of the phonon spectra in a pure powder sample of the multiferroic material BiFeO3. A high-temperature range was covered to unravel the changes in the phonon dynamics across the Neel (T_N ~ 650 K) and Curie (T_C ~ 1100 K) temperatures. Experimental results are accompanied by ab-initio lattice dynamical simulations of phonon density of states to enable microscopic interpretations of the observed data. The calculations reproduce well the observed vibrational features and provide the partial atomic vibrational components. Our results reveal clear…
We propose and theoretically analyze a new vibrational spectroscopy, termed electron- and light-induced stimulated Raman (ELISR) scattering, that combines the high spatial resolution of electron microscopy with the molecular sensitivity of surface-enhanced Raman spectroscopy. With ELISR, electron-beam excitation of plasmonic nanoparticles is utilized as a spectrally-broadband but spatially-confined Stokes beam in the presence of a diffraction-limited pump laser. To characterize this technique, we develop a numerical model and conduct full-field electromagnetic simulations to investigate two di…
Hydrogen arranges at dislocations in palladium to form nanoscale hydrides, changing the vibrational spectra. An ab initio hydrogen potential energy model versus Pd neighbor distances allows us to predict the vibrational excitations for H from absolute zero up to room temperature adjacent to a partial dislocation and with strain. Using the equilibrium distribution of hydrogen with temperature, we predict excitation spectra to explain new incoherent inelastic neutron-scattering measurements. At 0K, dislocation cores trap H to form nanometer-sized hydrides, while increased temperature dissolves t…
The lattice dynamics of coesite has been studied by a combination of diffuse x-ray scattering, inelastic x-ray scattering and an ab initio lattice dynamics calculation. The combined technique gives access to the full lattice dynamics in harmonic description and thus eventually provides detailed information on the elastic properties, the stability and metastability of crystalline systems. The experimentally validated calculation was used for the investigation of eigenvectors, mode character and their influence on the density of vibrational states. High symmetry sections of the reciprocal space …
We report a phonon density of states measurement of $α$-ZnCl$_{2}$ using the coherent inelastic neutron scattering technique and a lattice dynamical calculation in four crystalline phases of ZnCl$_{2}$ using a transferable interatomic potential. The model calculations agree reasonably well with the available experimental data on the structures, specific heat, Raman frequencies and their pressure variation in various crystalline phases. The calculated results have been able to provide a fair description of the vibrational as well as the thermodynamic properties of ZnCl$_{2}$ in all its four pha…
Low frequency acoustic vibration and phonon linewidth for CdTe0.68Se0.32 nanoparticle embedded in borosilicate glass are calculated using two different approaches by considering the elastic continuum model and fixed boundary condition. The presence of medium significantly affects the phonon peaks and results into the broadening of the modes. The linewidth is found to depend inversely on the size, similar to that reported experimentally. The damping time and quality factor have also been calculated. The damping time that is of the order of picoseconds decreases with the decrease in size. High v…
Interactions between elementary excitations are of great interest from a fundamental aspect and for novel applications. While plasmon-exciton have been extensively studied, the interaction mechanisms between acoustic vibrations (phonons) and localized surface plasmons (LSPs) remain quite unexplored. Here, we present a new theoretical framework for the investigation of the interaction between confined acoustic vibrations and LSPs involved in resonant acoustic Raman scattering. We express the Raman scattering process in the framework of Fermi's golden rule and introduce the concept of Raman ener…
The structure and vibrational spectrum of Gd3N@C80 is studied through Raman and inelastic electron tunneling spectroscopy (IETS) as well as density functional theory (DFT) and universal force field (UFF) calculations. Hindered rotations, shown by both theory and experiment, indicate the formation of a Gd3N-C80 bond which reduces the ideal icosahedral symmetry of the C80 cage. The vibrational modes involving the movement of the encapsulated species are a fingerprint of the interaction between the fullerene cage and the core complex. We present Raman data for the Gd3N@C2n (40 < n < 44) family as…
Microscopic description of Raman spectra in nanopowders of nonpolar crystals is accomplished by developing the theory of disorder-induced broadening of optical vibrational eigenmodes. Analytical treatment of this problem is performed, and line shape and width are determined as functions of phonon quantum numbers, nanoparticle shape, size, and the strength of disorder. The results are found to be strongly dependent on either the broadened line is separated or it is overlapped with other lines of the spectrum. Three models of disorder, i.e. weak point-like impurities, weak smooth random potentia…
We present an ab-initio method to simulate the current noise in the presence of electron-vibration interactions in atomic and molecular junctions at finite temperature. Using a combination of nonequilibrium Keldysh Green's function techniques and density functional theory, we study the elastic and inelastic contributions to electron current and shot noise within a wide range of transmission values in systems exhibiting multiple electronic levels and vibrational modes. Within our model we find the upper threshold, at which the inelastic noise contribution changes sign, at a total transmission b…
In a semiconductor-based double quantum well (QW) coupled to a degree of freedom with an internal dynamics, we demonstrate that the electronic motion is controllable within femtoseconds by applying appropriately shaped electromagnetic pulses. In particular, we consider a pulse-driven AlxGa1-xAs based symmetric double QW coupled to uniformly distributed or localized vibrational modes and present analytical results for the lowest two levels. These predictions are assessed and generalized by full-fledged numerical simulations showing that localization and time-stabilization of the driven electron…
We present first-principles calculations of the dI/dV characteristics of an H2 molecule sandwiched between Au and Pt electrodes in the presence of electron-phonon interactions. The conductance is found to decrease by a few percentage at threshold voltages corresponding to the excitation energy of longitudinal vibrations of the H2 molecule. In the case of Pt electrodes, the transverse vibrations can mediate transport through otherwise non-transmitting Pt $d$-channels leading to an increase in the differential conductance even though the hydrogen junction is characterized predominately by a sing…
Using time-resolved pump-probe spectroscopy we have performed the first investigation of the vibrational modes of gold nanoshells. The fundamental isotropic mode launched by a femtosecond pump pulse manifests itself in a pronounced time-domain modulation of the differential transmission probed at the frequency of nanoshell surface plasmon resonance. The modulation amplitude is significantly stronger and the period is longer than in a gold nanoparticle of the same overall size, in agreement with theoretical calculations. This distinct acoustical signature of nanoshells provides a new and effici…
We present a novel {\em ab initio} approach for computing intramolecular charge and energy transfer rates based upon a projection operator scheme that parses out specific internal nuclear motions that accompany the electronic transition. Our approach concentrates the coupling between the electronic and nuclear degrees of freedom into a small number of reduced harmonic modes that can be written as linear combinations of the vibrational normal modes of the molecular system about a given electronic minima. Using a time-convolutionless master-equation approach, parameterized by accurate quantum-ch…
We calculate the inelastic scattering probabilities in the wide band limit of a local polaron model with quadratic coupling to bosons. The central object is a two-particle Green function which is calculated exactly using a purely algebraic approach. Compared with the usual linear interaction term a quadratic interaction term gives higher probabilities for inelastic scattering involving a large number of bosons. As an application we consider the problem hot electron mediated energy transfer at surfaces and use the delta self-consistent field extension of density functional theory to calculate a…
The influence of molecular vibration on the Seebeck coefficient is studied within a simple model. Results of a scattering theory approach are compared to those of a full self-consistent non-equilibrium Green's function scheme. We show, for a reasonable choice of parameters, that inelastic effects have non-negligible influence on the resulting Seebeck coefficient for the junction. We note that the scattering theory approach may fail both quantitatively and qualitatively. Results of calculation with reasonable parameters are in good agreement with recent measurements [P. Reddy et al., Science 31…
The zeolitic imidazole framework ZIF-71 has the potential to outperform other well-studied metal-organic frameworks due to its intrinsic hydrophobicity and large pore size. However, a detailed description of its complex physical phenomena and structural dynamics has been lacking thus far. Herein, we elucidated all vibrational modes of ZIF-71 using high-resolution inelastic neutron scattering and synchrotron radiation infrared spectroscopy in conjunction with density functional theory calculations. We discover low-energy collective modes, such as gate-opening and shearing mechanisms that may af…
Recent advances in our understanding of thermal transport in nanocrystalline systems are responsible for the integration of new technologies into advanced energy systems, including thermoelectric refrigeration systems and renewable energy platforms. However, there is little understanding of heat energy transport mechanisms that govern the thermal properties of disordered nanocomposites. In this work, we explore thermal transport mechanisms in disordered packings of amorphous nanoparticles with and without a polymer filling the interstices in order to quantify the impact of thermal boundary sca…
