Overbending of the longitudinal optical phonon branch in diamond as evidenced by inelastic neutron and x-ray scattering

Kulda, J.; Kainzmaier, H.; Strauch, D.; Dörner, B.; Lorenzen, M.; Krisch, M.

doi:10.1103/physrevb.66.241202

Cited by 48 publications

(41 citation statements)

References 25 publications

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“…This effect, called overbending, has been observed in diamond as well. 24 In graphite, it has been predicted to result from a Kohn anomaly, i.e., the frequency at the Γ point is lowered due to interaction of the phonon with the electronic system. 11,12 Another Kohn anomaly in graphite can be found for the TOderived phonon branch at the K-point (fully symmetric A ′ 1 (K 1 ) mode).…”

Section: Resultsmentioning

confidence: 99%

Phonon dispersion of graphite by inelastic x-ray scattering

et al. 2007

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We present the full in-plane phonon dispersion of graphite obtained from inelastic x-ray scattering, including the optical and acoustic branches, as well as the mid-frequency range between the K and M points in the Brillouin zone, where experimental data have been unavailable so far. The existence of a Kohn anomaly at the K point is further supported. We fit a fifth-nearest neighbour force-constants model to the experimental data, making improved force-constants calculations of the phonon dispersion in both graphite and carbon nanotubes available.

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Section: Resultsmentioning

confidence: 99%

Phonon dispersion of graphite by inelastic x-ray scattering

et al. 2007

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“…Lines: scaled quantum-mechanical calculation results, circles: X-ray scattering data [8,13] ; squares: neutron scattering data [11,12] ; diamonds: neutron scattering data [14] .…”

Section: Figmentioning

confidence: 99%

“…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] .…”

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confidence: 99%

“…under which the 3D dispersion function was replaced with an averaged 1D dispersion curve. However, in case of distinct anisotropy of phonon dispersion like over-bending [8] , one-dimensional approximation curve leads to very arbitrary results. A typical example is diamond, for which several groups suggested different 1D dispersion curves, neither of which can really approximate the 3D function [9] .…”

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

Korepanov

Hamaguchi

2017

J Raman Spectroscopy

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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...

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“…This 1D approach is not applicable if the material shows a strong anisotropy of phonon dispersion. Well known example having such anisotropy is diamond, in which over-bending of the longitudinal phonon branch has been observed even for low wave vector: 4 while two of the optical phonon branches have a "downward" curvature near the BZ center, the third one has an "upward" curvature. Obviously, effective 1D function cannot represent well for such materials.…”

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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

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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.

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Overbending of the longitudinal optical phonon branch in diamond as evidenced by inelastic neutron and x-ray scattering

Cited by 48 publications

References 25 publications

Phonon dispersion of graphite by inelastic x-ray scattering

Phonon dispersion of graphite by inelastic x-ray scattering

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

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