Longitudinal versus transverse spheroidal vibrational modes of an elastic sphere

Saviot, Lucien; Murray, D. B.

doi:10.1103/physrevb.72.205433

Cited by 41 publications

(33 citation statements)

References 26 publications

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“…25 They also showed that modes of both natures are present in a sequence ͑n , l͒ with fixed l Ͼ 0, whereas for l = 0, all modes have a dominant longitudinal character. The longitudinal or transverse nature of a mode will determine its contribution to the VV Raman and Brillouin terms or to the HV Raman term, respectively.…”

Section: ͑19͒mentioning

confidence: 97%

Brillouin and Raman scattering from the acoustic vibrations of spherical particles with a size comparable to the wavelength of the light

Montagna

2008

Phys. Rev. B

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The inelastic light scattering of the acoustic vibration of spherical nanoparticles has been studied within a continuum approximation, extending the previous models, valid for small particles, to the case of particle sizes comparable with the wavelength of the light. A mechanism appears, i.e. the polarizability modulation related to density changes, which is typical of Brillouin scattering and is negligible for small particles. Furthermore, the contribution of the polarizability modulation induced by the relative displacements of atoms, which produces the Raman scattering in small particles, strongly changes. Spheroidal modes other than the l = 0 and l = 2 ones, the only Raman active in small particles, contribute to both scattering mechanisms. As the size increases, higher l modes with higher n, the index that labels the radial wave vector, become important. In relatively large particles, the active ͑n , l , m͒ spheroidal modes are those with frequency close to that of the Brillouin active vibrations in the bulk material, i.e., nl Ϸ qv L , where q is the exchanged wave vector of the light and v L is the longitudinal sound velocity. Also torsional modes become active and produce depolarized light scattering with properties similar to those of transverse acoustic phonons.

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Section: ͑19͒mentioning

confidence: 97%

Brillouin and Raman scattering from the acoustic vibrations of spherical particles with a size comparable to the wavelength of the light

Montagna

2008

Phys. Rev. B

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“…4 In order to confirm the validity of this simple approach for spherical nanoparticles, we use a method similar to the one used in a previous work. 17 Studying the frequency changes resulting from a continuous variation of the elasticity of the material the sphere is made of provides some insight into the nature of the vibrations. A cubic material has three independent elastic constants C 11 , C 12 and C 44 instead of two for isotropic elasticity for which C 44 = C11−C12…”

Section: Methodsmentioning

confidence: 99%

Simple model for the vibrations of embedded elastically cubic nanocrystals

et al. 2010

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The purpose of this work is to calculate the vibrational modes of an elastically anisotropic sphere embedded in an isotropic matrix. This has important application to understanding the spectra of low-frequency Raman scattering from nanoparticles embedded in a glass matrix. First some low frequency vibrational modes of a free cubically elastic sphere are found to be nearly independent of one combination of elastic constants. This is then exploited to obtain an isotropic approximation for these modes which enables to take into account the surrounding isotropic matrix. This method is then used to quantatively explain recent spectra of gold and copper nanocrystals in glasses.

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“…The lowest energy mode, however, belongs to a set of l ¼ 2 solutions (in the simplest of which, the sphere is deformed to an oblate, then to a prolate spheroid [15]), and has an energy of approximately 40% of that of the l ¼ 0 mode (for a more detailed solution see, for example, Salvador et al [16]). Regardless of the details of the mode, Lamb theory solutions are characterized by a 1=r dependence of the discrete acoustic-phonon energy on the particle radius.…”

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confidence: 99%

Universal Role of Discrete Acoustic Phonons in the Low-Temperature Optical Emission of Colloidal Quantum Dots

et al. 2009

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Multiple energy scales contribute to the radiative properties of colloidal quantum dots, including magnetic interactions, crystal field splitting, Pauli exclusion, and phonons. Identification of the exact physical mechanism which couples first to the dark ground state of colloidal quantum dots, inducing a significant reduction in the radiative lifetime at low temperatures, has thus been under significant debate. Here we present measurements of this phenomenon on a variety of materials as well as on colloidal heterostructures. These show unambiguously that the dominant mechanism is coupling of the ground state to a confined acoustic phonon, and that this mechanism is universal.

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Longitudinal versus transverse spheroidal vibrational modes of an elastic sphere

Cited by 41 publications

References 26 publications

Brillouin and Raman scattering from the acoustic vibrations of spherical particles with a size comparable to the wavelength of the light

Brillouin and Raman scattering from the acoustic vibrations of spherical particles with a size comparable to the wavelength of the light

Simple model for the vibrations of embedded elastically cubic nanocrystals

Universal Role of Discrete Acoustic Phonons in the Low-Temperature Optical Emission of Colloidal Quantum Dots

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