On Geodesically Convex Functions on Symmetric Spaces

Akhiezer, Dmitri

doi:10.1002/1522-2616(200107)227:1<5::aid-mana5>3.0.co;2-g

Cited by 2 publications

(3 citation statements)

References 5 publications

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“…This explains the T -dependence of α observed in most sonic and ultrasonic experiments. However, the T -dependence of the sound velocity in glasses such as As 2 S 3 and As 2 Se 3 8 cannot be explained by this model: the behavior observed there is very similar to the decrease of sound velocity in crystals, where it is assigned to relaxation of thermal phonons by anharmonic interactions 9,10 . This suggests that, even if the nature of thermal modes in glasses is unknown, and certainly different from propagating plane-wave phonons, a similar anharmonic mechanism can be present 11,12 .…”

Section: Introductionmentioning

confidence: 94%

“…However, the T dependence of the sound velocity in glasses such as As 2 S 3 and As 2 Se 3 8 cannot be explained by this model: The behavior observed there is very similar to the decrease of sound velocity in crystals, where it is assigned to relaxation of thermal phonons by anharmonic interactions. 9,10 This suggests that even if the nature of thermal modes in glasses is unknown, and certainly different from propagating plane-wave phonons, a similar anharmonic mechanism can be present. 11,12 In fact, we have observed that Brillouin scattering measurements of α in vitreous silica at frequencies in the hypersonic range cannot be described satisfactorily by the TAR mechanism alone.…”

Section: Introductionmentioning

confidence: 99%

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Acoustic damping and dispersion in vitreous germanium oxide

2012

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New Brillouin scattering measurements of velocity and attenuation of sound in the hypersonic regime are presented. The data are analyzed together with the literature results at sonic and ultrasonic frequencies. As usual, thermally activated relaxation of structural entities describes the attenuation at sonic and ultrasonic frequencies. As already shown in vitreous silica, we conclude that the damping by network viscosity, resulting from relaxation of thermal phonons, must be taken into account to describe the attenuation at hypersonic frequencies. In addition, the bare velocity obtained by subtracting to the experimental data the effect of the two above mechanisms is constant for temperatures below 250 K, but increases almost linearly above, up to the glass transition temperature. This might indicate the presence of a progressive local polyamorphic transition, as already suggested for vitreous silica.Comment: 14 pages, 8 figure

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Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Acoustic damping and dispersion in vitreous germanium oxide

2012

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“…The study of temperature-dependent ultrasonic attenuation plays a very important role in understanding the interaction of ultrasonic waves with crystals. Changes in ultrasonic attenuation with temperature can be used to infer information about the interaction of ultrasonic waves with individual phonons in the region ωτ 1 [9], where ω is the angular frequency and τ is the thermal relaxation time. Different causes can be attributed to the attenuation of ultrasonic waves propagating through them: of these, important causes of acoustical dissipation are phonon-phonon (p-p) interaction, thermoelastic loss, dislocation damping due to screw and edge dislocations, scattering from grain boundaries (dominant in polycrystalline materials), etc.…”

Section: Introductionmentioning

confidence: 99%

Ultrasonic attenuation due to phonon–phonon interaction, thermoelastic loss and dislocation damping in transition metal carbides

Singh

et al. 2008

J. Phys.: Condens. Matter

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Temperature dependent ultrasonic attenuation due to phonon-phonon (p-p) interaction, thermoelastic loss and dislocation damping due to screw and edge dislocations have been investigated in fcc (NaCl B1 type) structured group IVb and Vb monocarbides (transition metal carbides, namely TiC, ZrC, HfC, VC, NbC and TaC) in the temperature range 50-500 K, along the three crystallographic directions of propagation, namely [100], [110] and [111] for longitudinal and shear modes of propagation. The second-and third-order elastic moduli (SOEM and TOEM) obtained at different temperatures using the electrostatic and Born repulsive potentials and taking interactions up to next-nearest neighbours, have been used to obtain Gruneisen numbers, acoustic coupling constants and their ratios along different directions of propagation and polarization for longitudinal and shear modes of wave propagation. Temperature variation of the phonon relaxation time shows exponential decay. The results have been discussed and compared with available data.

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On Geodesically Convex Functions on Symmetric Spaces

Cited by 2 publications

References 5 publications

Acoustic damping and dispersion in vitreous germanium oxide

Acoustic damping and dispersion in vitreous germanium oxide

Ultrasonic attenuation due to phonon–phonon interaction, thermoelastic loss and dislocation damping in transition metal carbides

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