Vibration Eigenmodes and Size of Microcrystallites in Glass: Observation by Very-Low-Frequency Raman Scattering

Abstract

The observation of very-low-frequency bands by Raman scattering in a nucleated cordierite glass is described. The frequency of the maximum of scattering is proportional to the inverse diameter of the particles, which are spherical spinel microcrystallites. It is shown that vibrational surface modes of particles are responsible for this Raman scattering.PACS numbers: 68.35.Ja, 81.20.Qf After the specific-heat measurements of small metal particles, carried out by Novotny, Meincke, and Watson, 1 and Novotny and Meincke, 2 many theoretical researches have been made on the lattice dynamics 3 " 7 of small particles. The vibrations of spherical particles have been studied a century ago by Lamb 8 who discussed the problem of the homogeneous elastic body in a spherical shape. Two types of modes, spheroidal and torsional, are derived from the stress-free boundary condition of a spherical surface. The recent theoretical works of Tamura and co-workers 6,7 are an extension of Lamb's theory and consider various effects surrounding a small particle: matrix effect, surface relaxation effect, local clamping effect, and shape effect.The aim of the latest theoretical studies was principally to interpret the specific-heat measurements. However, it should be possible to observe by infrared absorption or Raman scattering the modes which obey the transition selection rules. Some years ago Hayashi and Kanamori 9 observed the Raman scattering from the surface phonon mode in GaP microcrystals. The energy of the observed modes was between the bulk TO and LO phonon peaks. In the work which is presented in this Letter we were rather interested in the Raman scattering from particle modes, the energies of which fall in the acoustic of the bulk, and which contribute to specific heat.Actually, the first observation of particle modes by Raman scattering at very low frequency in a nucleated glass is presented in this Letter. This Raman spectroscopy follows a detailed study of nucleation and precise characterization of nuclei or microcrystals, carried out partially in our research group. 10,11 The base glass, nucleation of which has been studied, has a composition close to that of the mineral cordierite: 52 Si0 2 , 34.7 A1 2 0 3 , 12.5 MgO, with 0.8 Cr 2 0 3 (wt.%). Nucleation was induced at a temperature higher than 800 °C by Cr 3 + ions which are well known as a good nucleating agent. The characterization of nuclei or microcrystallites was carried out by several techniques. The size of the particles was determined principally by small-angle neutron scattering, 10 and also by small-angle x-ray scattering and electron microscopy. 12 The nature and structure of the microcrystallites were precisely determined by electron paramagnetic resonance, 10 " 13 laser spectroscopy, 11 and electron diffraction. 12 The process of nucleation and crystallization was described as follows. At first there is a diffusion of Cr 3+ ions in the glassy matrix giving rise to a clustering of these ions and the formation of a mixed MgCr 2 0 4 -MgAl 2 04 spinel. Microcr...

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

“…This procedure aims to reveal some dependence of the measured LFRS signal on the NC size, as is usually observed in Raman scattering by the vibrations of NCs (7,8). The Stokes/anti-Stokes low-frequency Raman spectra of all samples are shown in Fig.…”

The complete Raman spectrum of nanometric SnO2 particles

“…Low-frequency bands have been reported for Ag particles embedded in SiO 2 thin films, 29 CdSe nanocrocrystals in glasses, 30 CdS microcrystals, 31,32 MgCr 2 O 4 -MgAl 2 O 4 crystals in glass, 33 and nanosized TiO 2 . 34 Despite the number of publications related to SnO 2 and Raman spectroscopy, however, they have not generally been reported for SnO 2 .…”

High Frequency Acoustics in Colloid-Based Meso- and Nanostructures by Spontaneous Brillouin Light Scattering

“…However, there is a paucity of non-destructive experimental techniques to probe this 'music' of particle vibrations since both high frequency resolution and sensitivity are required to detect the numerous eigenmodes. Raman scattering [83,84] has been utilized to measure few eigenfrequencies of nanoparticles with dimension below 10 nm, whereas Brillouin light scattering (BLS) [45,46,85] and optical pulse-probe techniques [27,28,86] can probe respectively the spontaneous and stimulated vibrations confined in sub-micrometer particles. In the latter technique, the excited acoustic oscillations are observed in the form of modulations of the transient reflectivity of the probe laser, and hence the particles must possess good reflectance, e.g., by introduction of gold shells.…”

“…[51,83] The use of inelastic light scattering to measure vibration eigenmodes of small spherical particles was first performed experimentally by low-frequency Raman scattering (RS). [83] Due to selection rules only two distinct vibration eigenmodes contribute to the RS of spherical particles with diameter (d) much smaller than the wavelength of the probing light (d ≪ λ). [92] For bigger spheres with d ∼ λ, Brillouin light scattering (BLS) in the GHz-range becomes the technique of choice.…”