X-ray polarization: General formalism and polarization analysis

Detlefs, C.; Rı́o, M. Sánchez del; Mazzoli, Claudio

doi:10.1140/epjst/e2012-01630-3

Cited by 32 publications

(24 citation statements)

References 42 publications

(59 reference statements)

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“…Measuring the linear component of the polarization light is rather common, but the precise access to the full polarization state is not easy [16]. Few methods are able to give such information.…”

Section: Polarization Effectmentioning

confidence: 99%

Chirality, birefringence, and polarization effects inα-quartzstudied by resonant elastic x-ray scattering

et al. 2014

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We show that enantiomers are extremely sensitive to the quality of the light polarization in resonant elastic x-ray scattering experiments. In α-quartz, the (001) reflection shows a very strong sensitivity to a small fraction of linear component included in nominally circularly polarized light. This fraction induces an important phase difference between the angular dependence of the recorded intensity from each enantiomer. We are thus able to model all aspects of the resonant scattering and determine the dominant physics, extract the crystal chirality, and obtain very precise values for the Stokes polarization parameters. Effects of birefringence and of higher-order electric transitions are also quantified and it is shown that in comparison they are negligible.

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Section: Polarization Effectmentioning

confidence: 99%

Chirality, birefringence, and polarization effects inα-quartzstudied by resonant elastic x-ray scattering

et al. 2014

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“…With coherent and linearly polarized X-rays from synchrotron sources and upcoming free electron laser sources, however, practically no limitation for the maximum scattering vector in the Q-range relevant for mesoscale objects exists. Employing X-ray photon correlation spectroscopy with polarization analysis, 70 a sufficiently large range of scattering vectors can be accessed to address both translational diffusion and rotational diffusion of anisotropic particles. From the first cumulants determined over a sufficiently large range of scattering vectors, the quantities ⟨D tr ⟩, ∆D tr , and D rot relevant for the diffusion of anisotropic particles can be obtained experimentally.…”

Section: Discussionmentioning

confidence: 99%

Depolarized light scattering from prolate anisotropic particles: The influence of the particle shape on the field autocorrelation function

Passow

Hagen

Löwen

et al. 2015

The Journal of Chemical Physics

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We provide a theoretical analysis for the intermediate scattering function typically measured in depolarized dynamic light scattering experiments. We calculate the field autocorrelation function g1(VH)(Q,t) in dependence on the wave vector Q and the time t explicitly in a vertical-horizontal scattering geometry for differently shaped solids of revolution. The shape of prolate cylinders, spherocylinders, spindles, and double cones with variable aspect ratio is expanded in rotational invariants flm(r). By Fourier transform of these expansion coefficients, a formal multipole expansion of the scattering function is obtained, which is used to calculate the weighting coefficients appearing in the depolarized scattering function. In addition to translational and rotational diffusion, especially the translational-rotational coupling of shape-anisotropic objects is considered. From the short-time behavior of the intermediate scattering function, the first cumulants Γ(Q) are calculated. In a depolarized scattering experiment, they deviate from the simple proportionality to Q(2). The coefficients flm(Q) strongly depend on the geometry and aspect ratio of the particles. The time dependence, in addition, is governed by the translational and rotational diffusion tensors, which are calculated by means of bead models for differently shaped particles in dependence on their aspect ratio. Therefore, our analysis shows how details of the particle shape--beyond their aspect ratio--can be determined by a precise scattering experiment. This is of high relevance in understanding smart materials which involve suspensions of anisotropic colloidal particles.

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“…. In 2012, further reviews appeared on the occasion of the Resonant Elastic X‐ray Scattering workshop 2011 concerning the development within the last 20 years in general and with specific focus on actinide systems , theoretical aspects as well as polarization analysis .…”

Section: History and Present Statusmentioning

confidence: 99%

Probing a crystal's short‐range structure and local orbitals by Resonant X‐ray Diffraction methods

Zschornak

Richter

Nentwich

et al. 2014

Crystal Research and Technology

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Diffraction Anomalous Fine Structure (DAFS) combines the long‐range, crystallographic sensitivity of X‐ray diffraction with the short‐range sensitivity of X‐ray Absorption Spectroscopy (XAS). In comparison to other spectroscopic methods, DAFS can additionally distinguish phases of different translational symmetry by choice of momentum transfer, or isolate spectra from chemically identical atoms on various Wyckoff sites of a crystal's structure using crystallographic weights. The Anisotropy of Anomalous Scattering (AAS) extends the concept of isotropically scattering atoms to a more general case, where the atom's scattering characteristics depend on the polarization as well as the wavevector of the incident and scattered X‐rays. These can be written as tensors that reflect the local site symmetries of the resonant atom. Forbidden Reflection Near‐Edge Diffraction (FRED) is an elegant way to measure AAS by using reflections that are extinguished in the special case of isotropically scattering atoms. They can only be observed due to the non‐isotropic contributions at photon energies in the vicinity of an absorption edge where electronic transitions occur. Combining the site selectivity of DAFS with the information accessible through AAS allows probing the short‐range order and local orbitals of selected atoms in a crystal structure of a chosen phase. The present condensed review gives a brief overview on the pioneer work, the theory and sensitivities as well as selected recent applications of these powerful and promising Resonant X‐ray Diffraction (RXD) methods. Additionally, some recent work of the authors is included exemplarily for the model structure rutile TiO2 presenting the progress in measurement and interpretation.

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X-ray polarization: General formalism and polarization analysis

Cited by 32 publications

References 42 publications

Chirality, birefringence, and polarization effects inα-quartzstudied by resonant elastic x-ray scattering

Chirality, birefringence, and polarization effects inα-quartzstudied by resonant elastic x-ray scattering

Depolarized light scattering from prolate anisotropic particles: The influence of the particle shape on the field autocorrelation function

Probing a crystal's short‐range structure and local orbitals by Resonant X‐ray Diffraction methods

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