Phonon dispersion branches in α quartz

Dörner, B.; Grimm, H.; Rżany, H.

doi:10.1088/0022-3719/13/36/014

Cited by 88 publications

(18 citation statements)

References 11 publications

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“…For simplicity, we assume that there is a dominant vibrational mode, the Si-O stretch mode, and we thus neglect the influence of lower-frequency phonon resonances [18]. The justification of this assumption is that the absorption spectrum of crystal quartz [19] shows a dominant feature at the frequency of the Si-O stretch mode and a very much weaker feature at lower frequency.…”

Section: Numerical Examplesmentioning

confidence: 99%

Prediction of an extremely large nonlinear refractive index for crystals at terahertz frequencies

et al. 2015

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We develop a simple analytical model for calculating the vibrational contribution to the nonlinear refractive index n2 (Kerr coefficient) of a crystal in terms of known crystalline parameters such as the linear refractive index, the coefficient of thermal expansion, atomic density, and the reduced mass and the natural oscillation frequency of the vibrational modes of the crystal lattice. We show that the value of this contribution in the terahertz spectral region can exceed the value of the nonlinear refractive index n2 in the visible and near-IR spectral ranges (which is largely electronic in origin) by several orders of magnitude. For example, for crystal quartz the value of the Kerr coefficient in the low-frequency limit is n2 = 2.2 × 10 −9 esu or equivalently is 4.4 × 10 −16 m 2 /W, which is very much larger than its value of 3 × 10 −20 m 2 /W in the visible range. Furthermore, we present an analysis of the dispersion of n2 in the terahertz spectral range and show that even larger values of n2 occur for frequencies close to the vibrational resonances.

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Section: Numerical Examplesmentioning

confidence: 99%

Prediction of an extremely large nonlinear refractive index for crystals at terahertz frequencies

et al. 2015

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“…The lattice dynamics of quartz has been extensively studied, including a considerable number of measurements in the proximity of the G point by ultrasound techniques [6], Raman [7,8] and infrared spectroscopy [9] -to mention only a few publications -and extensive investigations of the phonon dispersion in high-symmetry directions based on inelastic neutron scattering (INS) [10,11] and inelastic X-ray scattering (IXS) [12] have been presented. On the other hand, a full experimental study of the lattice dynamics, including not only phonon dispersion curves, but also phonon eigenvectors for arbitrary momentum transfers, is still missing.…”

Section: Introductionmentioning

confidence: 99%

New insights into the lattice dynamics ofα-quartz

Bosak¹,

Krisch

Chernyshov

et al. 2012

Zeitschrift für Kristallographie

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“…Investigations of these properties have a long history. The atomic structure and vibrational properties of perfect alpha-quartz have been the subject of extensive and productive studies, both experimental [2][3][4][5] and theoretical [6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Interstitial-oxygen induced localized vibrational properties in alpha-quartz

Kislov

Zatsepin

2013

Journal of Non-Crystalline Solids

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Local configurations and localized vibrations of oxygen interstitials in different charged states in alpha-quartz are investigated by computer calculations. First-principle potentials of the Buckingham type have been used in numerical modeling. The study of the lattice dynamics in defective crystal is performed using the phonon local density of states. Frequencies of localized vibrations induced by oxygen interstitials are determined. It is shown that the atomic configuration, type, number and frequency of localized vibrations depend on the sign and magnitude of the interstitial atom charge.

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Phonon dispersion branches in α quartz

Cited by 88 publications

References 11 publications

Prediction of an extremely large nonlinear refractive index for crystals at terahertz frequencies

Prediction of an extremely large nonlinear refractive index for crystals at terahertz frequencies

New insights into the lattice dynamics ofα-quartz

Interstitial-oxygen induced localized vibrational properties in alpha-quartz

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