scholarly journals Reciprocal Space Expansion in the Analysis of X-Ray Scattering Intensities from Liquid Carbon Tetrachloride

1986 ◽  
Vol 59 (1) ◽  
pp. 117-120 ◽  
Author(s):  
Keiko Nishikawa ◽  
Takao Iijima
Keyword(s):  
Carbon Tetrachloride ◽  
Reciprocal Space ◽  
Liquid Carbon ◽  
X Ray ◽  
X Ray Scattering ◽  
Space Expansion ◽  
Ray Scattering

Six-dimensional real and reciprocal space small-angle X-ray scattering tomography

Nature ◽  
2015 ◽  
Vol 527 (7578) ◽  
pp. 353-356 ◽  
Author(s):  
Florian Schaff ◽  
Martin Bech ◽  
Paul Zaslansky ◽  
Christoph Jud ◽  
Marianne Liebi ◽  
...  
Keyword(s):  
Small Angle ◽  
Reciprocal Space ◽  
X Ray ◽  
X Ray Scattering ◽  
Ray Scattering

scholarly journals 3D nanoscale analysis of bone healing around degrading Mg implants studied by X-ray scattering tensor tomography

2020 ◽  
Author(s):  
Marianne Liebi ◽  
Viviane Lutz-Bueno ◽  
Manuel Guizar-Sicairos ◽  
Bernd M. Schönbauer ◽  
Johannes Eichler ◽  
...  
Keyword(s):  
Bone Healing ◽  
Orthopedic Implants ◽  
Reciprocal Space ◽  
Bone Implant ◽  
X Ray ◽  
Implant Materials ◽  
Tensor Tomography ◽  
X Ray Scattering ◽  
The Impact ◽  
Ray Scattering

AbstractThe nanostructural adaptation of bone is crucial for its compatibility with orthopedic implants. The bone’s nanostructure determines its mechanical properties, however little is known about its temporal and spatial adaptation in degrading implants. This study presents insights into this adaptation by applying electron microscopy, elemental analysis, and small-angle X-ray scattering tensor-tomography (SASTT). We extend the SASTT reconstruction to multiple radii of the reciprocal space vector q, providing a 3D reciprocal-space map per voxel. Each scattering curve is spatially linked to one voxel in the volume, and properties such as the thickness of the mineral particles are quantified. This reconstruction provides information on nanostructural adaptation during healing around a degrading ZX10 magnesium implant over the course of 18 months, using a sham as control. The nanostructural adaptation process is observed to start with an initially fast interfacial organization towards the implant direction, followed by a substantial reorganization of the volume around the implant, and an adaptation in the later degradation stages. The study sheds light on the complex bone-implant interaction in 3D, allowing a more guided approach towards the design of future implant materials, which are expected to be of great interest for further clinical studies on the bone-implant interaction.TOC text and figureDegrading Magnesium implants are mechanically and chemically well adapted orthopedic implant materials and ensure a gradual load transfer during bone healing due to their degradation. The impact of the implant degradation on the bone nanostructure is however not fully understood. This study unveils the processes 3D and shows different stages of bone healing.

scholarly journals Validation study of small-angle X-ray scattering tensor tomography

2020 ◽  
Vol 27 (3) ◽  
pp. 779-787 ◽  
Author(s):  
Manuel Guizar-Sicairos ◽  
Marios Georgiadis ◽  
Marianne Liebi
Keyword(s):  
Small Angle ◽  
Structural Information ◽  
Anisotropic Scattering ◽  
Reciprocal Space ◽  
Separate Analysis ◽  
X Ray ◽  
Tensor Tomography ◽  
X Ray Scattering ◽  
Dot Product ◽  
Ray Scattering

Small-angle scattering tensor tomography (SASTT) is a recently developed technique able to tomographically reconstruct the 3D reciprocal space from voxels within a bulk volume. SASTT extends the concept of X-ray computed tomography, which typically reconstructs scalar values, by reconstructing a tensor per voxel, which represents the local nanostructure 3D organization. In this study, the nanostructure orientation in a human trabecular-bone sample obtained by SASTT was validated by sectioning the sample and using 3D scanning small-angle X-ray scattering (3D sSAXS) to measure and analyze the orientation from single voxels within each thin section. Besides the presence of cutting artefacts from the slicing process, the nanostructure orientations obtained with the two independent methods were in good agreement, as quantified with the absolute value of the dot product calculated between the nanostructure main orientations obtained in each voxel. The average dot product per voxel over the full sample containing over 10 000 voxels was 0.84, and in six slices, in which fewer cutting artefacts were observed, the dot product increased to 0.91. In addition, SAXS tensor tomography not only yields orientation information but can also reconstruct the full 3D reciprocal-space map. It is shown that the measured anisotropic scattering for individual voxels was reproduced from the SASTT reconstruction in each voxel of the 3D sample. The scattering curves along different 3D directions are validated with data from single voxels, demonstrating SASTT's potential for a separate analysis of nanostructure orientation and structural information from the angle-dependent intensity distribution.

scholarly journals Aperiodic atomic ordering in PMN recovered from the anomalous x-ray scattering

2014 ◽  
Vol 70 (a1) ◽  
pp. C1758-C1758
Author(s):  
Miloš Kopecký ◽  
Jiří Kub ◽  
Jan Fábry ◽  
Zbyněk Šourek
Keyword(s):  
Absorption Edge ◽  
Diffuse Scattering ◽  
Imaging Techniques ◽  
Relaxor Ferroelectrics ◽  
Reciprocal Space ◽  
Anomalous Scattering ◽  
Space Images ◽  
X Ray ◽  
X Ray Scattering ◽  
Ray Scattering

Various imaging techniques with atomic resolutions have been developed to study 3D arrangement of atoms in sub-nanometer and nanometer scale. The method presented is based on the measurement of the anomalous portion of x-ray scattering in large volume of the reciprocal space. It can be shown that, by analogy to x-ray holography with atomic resolution, the anomalous diffuse scattering provides information on both the amplitude and the phase of the scattered wave. The sample was PbMg1/3Nb2/3O3 (PMN), which belongs to relaxor ferroelectrics. Although the short and intermediate range chemical ordering is responsible for its relaxor behaviour, the real arrangement of cations remains unclear so far. The intensities of x-ray scattering in a large 3D volume of the reciprocal space were measured using an intense x-ray radiation generated by the synchrotron facility. Anomalous x-ray scattering has been obtained as a difference of intensity maps collected at two energies. The energy E1 just below the Nb K absorption edge was chosen in order to get a strong anomalous component in the scattering from Nb atoms. The data acquired at the energy E2 far from the absorption edge were used as the reference. The measured 3D pattern of anomalous scattering, including both discrete diffraction peaks and continuous x-ray diffuse scattering, allows us to reconstruct numerically an average environment around Nb atoms. The reconstructed real-space images clearly show a systematic local ordering of Mg2+ and Nb5+ cations. This ordering is more significant close to the central reference Nb atom but it is still apparent at the distance of about 3 nm giving thus an idea on the average size of ordered regions. More distant sites are occupied randomly with probabilities of occurrence of Mg2+ and Nb5+ cations given by their relative fraction in the sample. It is possible to determine conditioned probabilities of site occupancies by the given type of atom provided that the central site is occupied by Nb and to get information on the structure model of the ordered regions in the crystal.

scholarly journals Small-angle X-ray scattering tensor tomography: model of the three-dimensional reciprocal-space map, reconstruction algorithm and angular sampling requirements

2018 ◽  
Vol 74 (1) ◽  
pp. 12-24 ◽  
Author(s):  
Marianne Liebi ◽  
Marios Georgiadis ◽  
Joachim Kohlbrecher ◽  
Mirko Holler ◽  
Jörg Raabe ◽  
...  
Keyword(s):  
Small Angle ◽  
Three Dimensional ◽  
Reconstruction Algorithm ◽  
Reciprocal Space ◽  
Mathematical Framework ◽  
X Ray ◽  
Tensor Tomography ◽  
X Ray Scattering ◽  
Degree Of Orientation ◽  
Ray Scattering

Small-angle X-ray scattering tensor tomography, which allows reconstruction of the local three-dimensional reciprocal-space map within a three-dimensional sample as introduced by Liebiet al.[Nature(2015),527, 349–352], is described in more detail with regard to the mathematical framework and the optimization algorithm. For the case of trabecular bone samples from vertebrae it is shown that the model of the three-dimensional reciprocal-space map using spherical harmonics can adequately describe the measured data. The method enables the determination of nanostructure orientation and degree of orientation as demonstrated previously in a single momentum transferqrange. This article presents a reconstruction of the complete reciprocal-space map for the case of bone over extended ranges ofq. In addition, it is shown that uniform angular sampling and advanced regularization strategies help to reduce the amount of data required.

scholarly journals Healing X-ray scattering images

IUCrJ ◽  
2017 ◽  
Vol 4 (4) ◽  
pp. 455-465 ◽  
Author(s):  
Jiliang Liu ◽  
Julien Lhermitte ◽  
Ye Tian ◽  
Zheng Zhang ◽  
Dantong Yu ◽  
...  
Keyword(s):  
Statistical Tests ◽  
Reciprocal Space ◽  
Saxs Data ◽  
X Ray ◽  
X Ray Scattering ◽  
Experimental Configuration ◽  
Angle Data ◽  
Space Data ◽  
Ray Scattering

X-ray scattering images contain numerous gaps and defects arising from detector limitations and experimental configuration. We present a method to heal X-ray scattering images, filling gaps in the data and removing defects in a physically meaningful manner. Unlike generic inpainting methods, this method is closely tuned to the expected structure of reciprocal-space data. In particular, we exploit statistical tests and symmetry analysis to identify the structure of an image; we then copy, average and interpolate measured data into gaps in a way that respects the identified structure and symmetry. Importantly, the underlying analysis methods provide useful characterization of structures present in the image, including the identification of diffuseversussharp features, anisotropy and symmetry. The presented method leverages known characteristics of reciprocal space, enabling physically reasonable reconstruction even with large image gaps. The method will correspondingly fail for images that violate these underlying assumptions. The method assumes point symmetry and is thus applicable to small-angle X-ray scattering (SAXS) data, but only to a subset of wide-angle data. Our method succeeds in filling gaps and healing defects in experimental images, including extending data beyond the original detector borders.

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