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...

A model assuming a non-continuous structure of glasses is established to interpret the inelastic neutron scattering and Raman scattering. The 'boson' peak in Raman scattering is related to the vibrational density of states 'excess'. These two related features are a result of vibrations localized in the blobs that compose the glass. Size distributions of the blobs are deduced from neutron and Raman scatterings.

Fabrication of devices from inorganic nanocrystals normally requires that they are self-organized into ordered structures. It has now been demonstrated that nanocrystals are able to self-organize in a 'supra'-crystal with a face-centred cubic (f.c.c.) structure. The physical properties of nanocrystals self-organized into compact arrays are quite different from those of both isolated nanocrystals and the bulk phase. The collective optical and magnetic properties of these nanocrystal assemblies are governed mainly by dipolar interactions. Here, we show that nanocrystals vibrate coherently when they are self-organized in f.c.c. supra-crystals. Hence, a phase relation exists between the vibrations of all of the nanocrystals in a supra-crystal. This vibrational coherence can be observed by a substantial change of the quadrupolar low-frequency Raman scattering peak. Although a change in electronic transport properties has previously been observed on self-organization of silver nanocrystals, vibrational coherence represents the first intrinsic property of f.c.c. supra-crystals.

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