Lattice Vibrations in Diamond

Yarnell, J. L.; Warren, J.L.; Wenzel, R. G.

doi:10.1103/physrevlett.13.13

Cited by 29 publications

(12 citation statements)

References 6 publications

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“…These works and others done over the next few years, were extensively reported in review articles [60 -63] In these years also comparable results began to appear [48,57] from other laboratories. The field was now a field in being and not merely in development.…”

Section: Phonons Dispersion Curves and Interatomic Forcessupporting

confidence: 65%

Slow neutron spectroscopy and the grand atlas of the physical world

Brockhouse¹

1995

Rev. Mod. Phys.

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On October 12, 1994, telephone communications from Stockholm ensured that I would have the privilege of giving a Nobel Lecture, for which I must thank all those involved in arranging for this great and surprising event of my life. But I had to go back some thirty to forty-five years, first in memory and then in the entropy of my files and library. The lecture was given on December 8, 1994 (and subsequently on several occasions). This written version covers the same ground, though sometimes in different order, with a little additional material from my preparations, which time prevented including in the spoken lecture. In August 1950, when I joined the Physics Division of the Chalk River Nuclear Laboratory, it was 18 years since the identification of the neutron as being emitted in some radioactive processes and 14 years since verification of the supposition that neutrons would exhibit wave-particle duality. A considerable body of theory was available in the open literature-which was still small enough so that one person could have read all that was then available. There had been significant measurements of total cross sections using neutron beams produced by cyclotrons. Self-sustaining reactors employing the neutron-induced fission of uranium had been demonstrated and full-scale models which emitted potent beams of both fast and slow neutrons had been constructed. Slow neutron beams from reactors were already in use at several laboratories (including Chalk River) for studies of crystals and other forms of matter. The works of E.O. Wollan and C.G. Shull at the Oak Ridge National Laboratory were particularly significant because they included the first studies of a number of phenomena and because they already presented values of scattering power for neutrons of a substantial number of elements. This history is discussed in the lecture of my senior colleague and co-winner of the 1994 Nobel Prize in Physics, Clifford Shull. To 1951, some studies had been made of the elastic scattering of monochromatic slow neutrons by specimens in the form of powdered crystals (the neutron analog of Debye-Scherrer patterns for X-rays), which led to improved crystallographic understanding of the substances involved. And there

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Section: Phonons Dispersion Curves and Interatomic Forcessupporting

confidence: 65%

Slow neutron spectroscopy and the grand atlas of the physical world

Brockhouse¹

1995

Rev. Mod. Phys.

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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%

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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“…Note that the lattice constant of diamond is 0.3567 nm. 5 In order to describe real samples, whose size is typically far from being monodisperse, one must take into account the particle size distribution (PSD) ρ(σ ), which makes the working formula as follows:…”

mentioning

confidence: 99%

“…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

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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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Lattice Vibrations in Diamond

Cited by 29 publications

References 6 publications

Slow neutron spectroscopy and the grand atlas of the physical world

Slow neutron spectroscopy and the grand atlas of the physical world

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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