On the Theory of Dispersion of X-Rays

Kronig, R. de L.

doi:10.1364/josa.12.000547

Cited by 1,613 publications

(188 citation statements)

References 12 publications

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“…1b tan d as functions of f. The presented curves refer to the reference temperature T 0 ¼ 20 C. They were obtained by shifting the measured frequency segments along the frequency axis in order to obtain as smooth master curves as possible. Their quality is underlined, since storage modulus ReEðf Þ and loss modulus ImE ¼ ðr 0 =e 0 Þ sin d are related via the Kramers-Kronig relation [18], which must hold for any linear response function [21]. The glass transition temperatures T g are defined in this context as the temperature where tan dðTÞ is maximal when testing at a test frequency f ¼ 0:01 Hz.…”

Section: Hardness and Viscoelasticity Of The Rubber Tread Compoundsmentioning

confidence: 99%

Rubber Friction on Ice: Experiments and Modeling

et al. 2016

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Rubber friction on ice is studied both experimentally and theoretically. The friction tests involve three different rubber tread compounds and four ice surfaces exhibiting different roughness characteristics. Tests are carried out at four different ambient air temperatures ranging from À5 to À13 C, under three different nominal pressures ranging from 0.15 to 0:45 MPa, and at the sliding speed 0.65 m/s. The viscoelastic properties of all the rubber compounds are characterized using dynamic mechanical analysis. The surface topography of all ice surfaces is measured optically. This provides access to standard roughness quantities and to the surface roughness power spectra. As for modeling, we consider two important contributions to rubber friction on ice: (1) a contribution from the viscoelasticity of the rubber activated by ice asperities scratching the rubber surface and (2) an adhesive contribution from shearing the area of real contact between rubber and ice. At first, a macroscopic empirical formula for the friction coefficient is fitted to our test results, yielding a satisfactory correlation. In order to get insight into microscopic features of rubber friction on ice, we also apply the Persson rubber friction and contact mechanics theory. We discuss the role of temperature-dependent plastic smoothing of the ice surfaces and of frictional heating-induced formation of a meltwater film between rubber and ice. The elaborate model exhibits very satisfactory predictive capabilities. The study shows the importance of combining advanced testing and state-ofthe-art modeling regarding rubber friction on ice.

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Section: Hardness and Viscoelasticity Of The Rubber Tread Compoundsmentioning

confidence: 99%

Rubber Friction on Ice: Experiments and Modeling

et al. 2016

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“…In 1927 H. Kramers [9] and in 1926 R. Kroning [4] formulated relations between real and imaginary parts of complex function:…”

Section: A Dispersion Relations In Accordance With Cipmentioning

confidence: 99%

“…The CIP data of Ni0.55Zn0.45Fe2O4 ferrite measured by Islam R. (Fig. 8) is cut at about f = 10 4 Hz. More to it -the ′′ ( ) part shows high increase of amplitude at lower frequencies, but, at the same time, ′ ( ) part does not show any additional changes of amplitude.…”

Section: A Cip Spectra Reconstruction With the Help Of Spectra Modelingmentioning

confidence: 99%

The Use of Kramers-Kronig Relations for Verification of Quality of Ferrite Magnetic Spectra

Ponomarenko

Solovjova

Grizāns

2015

Electrical, Control and Communication Engineering

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-The complex initial permeability (CIP) as a function of frequency is one of the main properties of ferrites. This characteristic (CIP) is measured experimentally, therefore there can be found noisy, doubtful or incomplete parts of the spectrum. Thus there is a need for a method of evaluation of quality of CIP. In this article for evaluation of the quality of experimental CIP spectra of polycrystalline ferrite materials the KKR (KramersKronig relations) are used. In order to apply KKR to experimentally measured data (i.e. data with finite limits) the method of transforming these integral relations into summation relations with finite limits is developed and described. This method can be used only for CIP given over the wide frequency rage, so that the imaginary part of CIP is fully presented. Using KKR with the help of CIP spectra model (based on the effects coming from polycrystal grain sizes and defects distribution) partly removes aforementioned limit. Thus with the help of the model we can also make CIP spectra reconstruction (in cases when CIP is noisy or incomplete) and CIP spectra decomposition.

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“…The goal of a complete linear-response opticalspectroscopy experiment in zero field is to determine the real and the imaginary parts of the dielectric function. While certain techniques, such as spectroscopic ellipsometry or time-domain spectroscopy, can provide experimental access to both of them, other methods rely on the Kramers-Kronig (KK) relations [4][5][6][7] due to a limited set of measured optical quantities. A widespread technique of this kind is reflectance spectroscopy, where one measures the absolute reflectivity R(ω) in a broad range of frequencies and determines the phase θ(ω) of the complex reflectivity coefficient 8 :…”

Section: Introductionmentioning

confidence: 99%

Magneto-optical Kramers-Kronig analysis

Levallois

Nedoliuk

Crassee

et al. 2015

Review of Scientific Instruments

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We describe a simple magneto-optical experiment and introduce a magneto-optical KramersKronig analysis (MOKKA) that together allow extracting the complex dielectric function for leftand right-handed circular polarizations in a broad range of frequencies without actually generating circularly polarized light. The experiment consists of measuring reflectivity and Kerr rotation, or alternatively transmission and Faraday rotation, at normal incidence using only standard broadband polarizers without retarders or quarter-wave plates. In a common case, where the magneto-optical rotation is small (below ∼ 0.2 rad), a fast measurement protocol can be realized, where the polarizers are fixed at 45 • with respect to each other. Apart from the time-effectiveness, the advantage of this protocol is that it can be implemented at ultra-high magnetic fields and in other situations, where an in-situ polarizer rotation is difficult. Overall, the proposed technique can be regarded as a magnetooptical generalization of the conventional Kramers-Kronig analysis of reflectivity on bulk samples and the Kramers-Kronig constrained variational analysis of more complex types of spectral data. We demonstrate the application of this method to the textbook semimetals bismuth and graphite and also use it to obtain handedness-resolved magneto-absorption spectra of graphene on SiC.

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On the Theory of Dispersion of X-Rays

Cited by 1,613 publications

References 12 publications

Rubber Friction on Ice: Experiments and Modeling

Rubber Friction on Ice: Experiments and Modeling

The Use of Kramers-Kronig Relations for Verification of Quality of Ferrite Magnetic Spectra

Magneto-optical Kramers-Kronig analysis

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