Daniel B. Murray

Probing atomic ordering and multiple twinning in metal nanocrystals through their vibrations

Control of nanocrystal (NC) crystallinity currently raises great interest because of its potential benefits in both physics modeling and technological applications. Advances in methods for synthesizing perfect single-crystalline NCs are recent, so that the effect of crystallinity on NC properties has received only limited study and still needs to be properly investigated. Here, we report that crystallinity of gold NCs dramatically modifies their vibrations. Using low-frequency Raman scattering, we clearly demonstrate that single-domain NCs vibrate differently than their multiply twinned counterparts, through the splitting of the quadrupolar vibrations, which is only observed for the former. Using the resonant ultrasound approach, we calculate the vibrational frequencies of a gold sphere and show that elastic anisotropy induces a lift of degeneracy of the quadrupolar mode in good agreement with our experimental measurements. These findings open up challenging perspectives on using Raman spectroscopy to characterize nanocrystallinity.

Vibrations of free and embedded anisotropic elastic spheres: Application to low-frequency Raman scattering of silicon nanoparticles in silica

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

Phonons in an inhomogeneous continuum: Vibrations of an embedded nanoparticle

{\mathrm{SiO}}_{2}

Acoustic vibrations of anisotropic nanoparticles

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 taken into account. Libration, not vibration, is the dominant mechanism.

Forecasting a chaotic time series using an improved metric for embedding space

The spectrum of acoustic vibrational modes of an inhomogeneous elastic continuum is 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.

Long lived acoustic vibrational modes of an embedded nanoparticle

Acoustic vibrations of nanoparticles made of materials with anisotropic elasticity and nanoparticles with nonspherical shapes are theoretically investigated using a homogeneous continuum model. Cubic, hexagonal, and tetragonal symmetries of the elasticity are discussed, as are spheroidal, cuboctahedral, and truncated cuboctahedral shapes. Tools are described to classify the different vibrations and, for example, help identify the modes having a significant low-frequency Raman-scattering cross section. Continuous evolutions of the modes starting from those of an isotropic sphere coupled with the determination of the irreducible representation of the branches permit some qualitative statements to be made about the nature of various modes. For spherical nanoparticles, a more accurate picture is obtained through projections onto the vibrations of an isotropic sphere.

Longitudinal versus transverse spheroidal vibrational modes of an elastic sphere

Abstract A method is presented for improving the accuracy of forecasts of future values of a time series of one variable of a chaotic dynamical system. The metric for the embedding space of time-delay vectors of time series values is obtained from a metric tensor whose components are varied to minimize root mean squared error of forecasts. The improvement of forecasts is demonstrated for time series of the Henon and Ikeda maps, the Lorenz system of coupled differential equations and the Mackey-Glass delay differential equation.

Metal Nanoparticle Ensembles: Tunable Laser Pulses Distinguish Monomer from Dimer Vibrations

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)=rhov(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. A corrected formula for acoustic impedance is provided for the case of longitudinal spherical waves. Continuum boundary conditions do not always accurately reflect the microscopic nature of the interface between the nanoparticle and the matrix, and a multilayer model of the interface reveals the possibility of additional reduction of mode damping.

Vibrations of weakly coupled nanoparticles

Analysis of the spheroidal modes of vibration of a free continuum 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 between different spheroidal modes. In addition, some common misconceptions about spheroidal modes are corrected.

Surface enhanced Raman scattering of silver sensitized cobalt nanoparticles in metal–dielectric nanocomposites

Resonant interaction of laser pulses with plasmons is used to identify vibrations associated with isolated spheres and pairs of contacting spheres in a system of gold nanoparticles. The optical pulses generate coherent mechanical oscillations of both monomers and dimers in the 5-150 GHz range, the amplitudes of which exhibit a strong enhancement when the laser central wavelength is tuned to resonate with the corresponding plasmon. Because of the resonant selection in the excitation process, the widths of the acoustic modes are significantly smaller than broadening caused by the spread in radii in the ensemble.