Phonon Dispersion of Diamond Measured by Inelastic X-Ray Scattering

Schwoerer-Böhning, M.; Macrander, A. T.; Arms, D. A.

doi:10.1103/physrevlett.80.5572

Cited by 108 publications

(67 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…While being similar to some existing facilities [8][9][10][14][15][16], it will provide new capabilities due both to the design of the beamline and the high flux available from the SPring-8 storage ring.…”

Section: Resultsmentioning

confidence: 99%

“…Other monochromator designs (e.g. [25]) were considered, and are used for IXS at APS [9,10]. However, the difficulties associated with accommodating the finite (though small) angular divergence of the X-ray beam reduce the throughput of these designs as compared to a single back reflecting crystal: relative losses of about a factor of two were expected at low (ϳ15 keV) energies and a factor of 4 or more at higher energies (above 20 keV).…”

Section: Inelastic X-ray Scatteringmentioning

confidence: 99%

“…Pioneering work in IXS was done at HASYLAB in Hamburg, Germany [7] while the utility of the technique as a probe of condensed matter physics was demonstrated at ESRF [8]. More recently an IXS instrument at APS has begun to provide results [9,10], and a second beamline for these measurements has been built at ESRF [11]. In the field of nuclear resonant scattering of synchrotron radiation, first work was also done at HASYLAB [12].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An X-ray scattering beamline for studying dynamics

Baron

Tanaka

Goto

et al. 2000

Journal of Physics and Chemistry of Solids

251

118

View full text Add to dashboard Cite

Section: Resultsmentioning

confidence: 99%

Section: Inelastic X-ray Scatteringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An X-ray scattering beamline for studying dynamics

Baron

Tanaka

Goto

et al. 2000

Journal of Physics and Chemistry of Solids

251

118

View full text Add to dashboard Cite

“…They comprise an excellent model system due to the high phonon dispersion, simplicity of the first order spectrum, and the availability of samples with different crystallite size. In addition, the phonon dispersion of diamond is well studied, which allows us to compare the calculated frequencies with high-quality experimental data [8,[11][12][13][14] .…”

mentioning

confidence: 99%

Quantum‐chemical perspective of nanoscale Raman spectroscopy with the three‐dimensional phonon confinement model

Korepanov

Hamaguchi

2017

J Raman Spectroscopy

View full text Add to dashboard Cite

Raman spectroscopy of crystalline/molecular systems is well backed with quantum chemical calculations and group theory, making it a unique characterization tool. For the "intermediate" case of nanoscale systems, however, the use of Raman spectroscopy is limited by the lack of such theoretical bases. Here, we suggest to couple a scaled quantum-mechanical (SQM) calculation with the phonon confinement model (PCM) to construct a universal and physically consistent basis for nanoscale Raman spectroscopy. Unlike the commonly used one-dimensional dispersion PCM, we take into account the confinement along all the three dimensions of the k-space. We apply it to diamond nanoparticles of sub-50nm size, a system with pronounced anisotropy of dispersion for which the use of three-dimensional dispersion is a requisite. The model excellently reproduces sizesensitive spectral features, including the peak position, bandwidth and asymmetry of the sp 3 C-C Raman band. This fundamental approach can be easily generalized to other nanocrystalline solids to hopefully contribute the future development of quantitative nanoscale Raman spectroscopy. Keywords: phonon confinement, nanoparticlesThe continuously growing interest to nanoscale matter drives a strong demand for fast, noninvasive and statistically reliable characterization methods. This makes Raman spectroscopy an indispensable tool for nanoscience. The difficult challenge of Raman spectroscopy of nanoscale materials is to establish a consistent way to link the Raman pattern to the characteristic size of the crystallites. The straightforward approach is to directly calculate the normal modes of nanoparticles as big molecules [1,2] . This requires assumptions of the shape, size and symmetry. The calculated spectra are the set of narrow lines. Since the number of normal modes for nanoparticles is in the order of thousands, such calculations do not seem to be routinely availbale for real systems. The other common approach is the elastic sphere model (ESM), in which the nanoparticle is approximated by a homogeneous isotropic freestanding elastic sphere. The vibrations of such system can be easily derived from first principles calculations [3] . For the nanoparticles of other shapes, as well as systems with the size smaller than ~5nm, the applicability of ESM is limited. For more details on ESM the reader is referred to the review [4] . The third general approach starts from the Raman spectrum of a bulk crystal, for which the selection rules allow only the phonons close to the Brillouin zone (BZ) center. Nano-size crystallites lack the translational symmetry and the quasimomentum preservation does not hold. As a result, BZ points away from the center can also contribute to the Raman spectra. To what extent the selection rule breaks depends on the size of the crystallite. This effect is named the "phonon confinement" after the work of Richter [5] , who first suggested the physical model for describing it. The approach by Richter's is to multiply the phonon wavefunction of the crystal φ...

show abstract

“…In this work we used 4th degree 3D polynomials, symmetrized according to the symmetry of the Brillouin zone. The data on the phonon dispersion were taken from inelastic neutron scattering 5,15,16 and inelastic X-ray scattering 4, 17 experiments (total 220 points). Due to the symmetry, we need accurate description of the phonon dispersion only inside a narrow sector of the first BZ between [100], [111], and [110] directions; for the other points, we simply use rotation and/or translation into this sector.…”

mentioning

confidence: 99%

Communication: Three-dimensional model for phonon confinement in small particles: Quantitative bandshape analysis of size-dependent Raman spectra of nanodiamonds

Korepanov

Witek

Okajima

et al. 2014

The Journal of Chemical Physics

View full text Add to dashboard Cite

Raman spectroscopy of nano-scale materials is facing a challenge of developing a physically sound quantitative approach for the phonon confinement effect, which profoundly affects the phonon Raman band shapes of small particles. We have developed a new approach based on 3-dimensional phonon dispersion functions. It analyzes the Raman band shapes quantitatively in terms of the particle size distributions. To test the model, we have successfully obtained good fits of the observed phonon Raman spectra of diamond nanoparticles in the size range from 1 to 100 nm.

show abstract

Phonon Dispersion of Diamond Measured by Inelastic X-Ray Scattering

Cited by 108 publications

References 16 publications

An X-ray scattering beamline for studying dynamics

An X-ray scattering beamline for studying dynamics

Quantum‐chemical perspective of nanoscale Raman spectroscopy with the three‐dimensional phonon confinement model

Communication: Three-dimensional model for phonon confinement in small particles: Quantitative bandshape analysis of size-dependent Raman spectra of nanodiamonds

Contact Info

Product

Resources

About