The size dependence of vibrational eigenfrequencies and the mean square vibrational displacement of a small particle

Tamura, Akira; Higeta, K; Ichinokawa, T.

doi:10.1088/0022-3719/16/9/004

Cited by 28 publications

(15 citation statements)

References 11 publications

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“…and for crystals with rigid constraints at their surfaces [269]. A distinguishing feature of these calculations of the DOS, later borne out by experiments, is an enhancement in the number of modes at low energies.…”

Section: Low-energy Vibrations Of Nanostructuresmentioning

confidence: 95%

“…The evidence for lower-dimensional vibrations seems stronger in systems where there is a larger acoustic impedance mismatch between surface atoms and their surroundings, such as between isolated nanocrystals and vacuum. In such cases, however, it may be more appropriate to consider the low energy vibrations as eigenmodes of small particles [267,268,269].…”

Section: Low-energy Vibrations Of Nanostructuresmentioning

confidence: 99%

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Vibrational thermodynamics of materials

Fultz¹

2010

Progress in Materials Science

571

428

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Abstract. The literature on vibrational thermodynamics of materials is reviewed. The emphasis is on metals and alloys, especially on the progress over the last decade in understanding differences in the vibrational entropy of different alloy phases and phase transformations. Some results on carbides, nitrides, oxides, hydrides and lithium-storage materials are also covered.Principles of harmonic phonons in alloys are organized into thermodynamic models for unmixing and ordering transformations on an Ising lattice, and extended for non-harmonic potentials. Owing to the high accuracy required for the phonon frequencies, quantitative predictions of vibrational entropy with analytical models prove elusive. Accurate tools for such calculations or measurements were challenging for many years, but are more accessible today. Ab-initio methods for calculating phonons in solids are summarized. The experimental techniques of calorimetry, inelastic neutron scattering, and inelastic x-ray scattering are explained with enough detail to show the issues of using these methods for investigations of vibrational thermodynamics. The explanations extend to methods of data analysis that affect the accuracy of thermodynamic information.It is sometimes possible to identify the structural and chemical origins of the differences in vibrational entropy of materials, and the number of these assessments is growing. There has been considerable progress in our understanding of the vibrational entropy of mixing in solid solutions, compound formation from pure elements, chemical unmixing of alloys, order-disorder transformations, and martensitic transformations. Systematic trends are available for some of these phase transformations, although more examples are needed, and many results are less reliable at high temperatures. Nanostructures in materials can alter sufficiently the vibrational dynamics to affect thermodynamic stability. Internal stresses in polycrystals of anisotropic materials also contribute to the heat capacity. Lanthanides and actinides show a complex interplay of vibrational, electronic, and magnetic entropy, even at low temperatures.A "quasiharmonic model" is often used to extend the systematics of harmonic phonons to high temperatures by accounting for the effects of thermal expansion against a bulk modulus. Non-harmonic effects beyond the quasiharmonic approximation originate from the interactions of thermally-excited phonons with other phonons, or with the interactions of phonons with electronic excitations. In the classical high temperature limit, the adiabatic electron-phonon coupling can have a surprisingly large effect in metals when temperature causes significant changes in the electron density near the Fermi level. There are useful similarities in how temperature, pressure, and composition alter the conduction electron screening and the interatomic force constants. Phononphonon "anharmonic" interactions arise from those non-harmonic parts of the interatomic potential that cannot be accounted for by the quasiharmonic ...

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Section: Low-energy Vibrations Of Nanostructuresmentioning

confidence: 95%

Section: Low-energy Vibrations Of Nanostructuresmentioning

confidence: 99%

Vibrational thermodynamics of materials

Fultz¹

2010

Progress in Materials Science

571

428

View full text Add to dashboard Cite

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“…[6][7][8][9] These well-defined red or yellow absorptions have been used for millennia to color glass and glazes. [10,11] Over the last decade, most Raman scattering studies on metallic NPs concerned isolated [12][13][14][15][16][17][18][19] or self-organized [20,21] gold and silver NPs because their surface is chemically stable and choosing a laser excitation close to the SPR allows for a strong enhancement of the Raman signal. Some additional studies were conducted on NPs embedded in a glassy matrix.…”

Section: Introductionmentioning

confidence: 99%

Low wavenumber Raman scattering of cobalt nanoparticles self‐organized in 3D superlattices far from surface plasmon resonance

Meziane

Courty

Colomban

et al. 2015

J Raman Spectroscopy

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International audienceWe report the first observation of low wavenumber Raman scattering from cobalt nanoparticles under 514.5nm laser excitation. These 7.4nm diameter particles were self-organized in 3D superlattices, but we assign the Raman signature to vibrations of the individual nanoparticles, according to Lamb’s elastic sphere model. We estimate the relative Raman intensity to be around 500 times lower than it would be for silver nanoparticles, but our results demonstrate that surface plasmon–phonon resonance coupling is not mandatory to observe Lamb’s modes in metal nanoparticles

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“…The distinct peaks which appear between the BP and the Rayleigh line are considered to be due to acoustic phonon modes confined in homogeneous, spherical particles. 5,14,15 The sample annealed at 600°C exhibits a Raman spectrum ( Fig. 1) very similar to that of the as-quenched glass.…”

Section: Methodsmentioning

confidence: 78%

Low‐wavenumber Raman scattering spectroscopy in studies of new gallium‐doped silica glass‐based transparent vitroceramic medium

Ceccato

Maschio

Ferrari³

et al. 2001

J Raman Spectroscopy

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Optically transparent, silica glass-based vitroceramic material doped with gallium oxide was obtained by standard glass fusion and appropriate thermal treatments. Low-wavenumber Raman scattering spectroscopy allowed the determination of the microstructure and in particular the size distribution of nanoparticles embedded in the amorphous matrix. The nanocrystal growth was accurately controlled by heat treatment conditions. Transmission electron microscopy and X-ray diffraction measurements revealed the presence of a single crystalline phase, spherical-shaped nanoaggregates, homogeneously distributed in the transparent composite medium.

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The size dependence of vibrational eigenfrequencies and the mean square vibrational displacement of a small particle

Cited by 28 publications

References 11 publications

Vibrational thermodynamics of materials

Vibrational thermodynamics of materials

Low wavenumber Raman scattering of cobalt nanoparticles self‐organized in 3D superlattices far from surface plasmon resonance

Low‐wavenumber Raman scattering spectroscopy in studies of new gallium‐doped silica glass‐based transparent vitroceramic medium

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