scholarly journals Small-Angle Scattering from Fractional Brownian Surfaces

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2042
Author(s):  
Eugen Mircea Anitas
Keyword(s):  
Small Angle ◽  
Structural Parameters ◽  
Small Angle Scattering ◽  
Distribution Functions ◽  
Advanced Materials ◽  
Two Phase ◽  
Amorphous Phases ◽  
Angle Scattering ◽  
Recent Developments ◽  
New Generation

Recent developments in nanotechnology have allowed the fabrication of a new generation of advanced materials with various fractal-like geometries. Fractional Brownian surfaces (fBs) are often used as models to simulate and characterize these complex geometries, such as the surface of particles in dilute particulate systems (e.g., colloids) or the interfaces in non-particulate two-phase systems (e.g., semicrystalline polymers with crystalline and amorphous phases). However, for such systems, a realistic simulation involves parameters averaged over a macroscopic volume. Here, a method based on small-angle scattering technique is proposed to extract the main structural parameters of surfaces/interfaces from experimental data. It involves the analysis of scattering intensities and the corresponding pair distance distribution functions. This allows the extraction of information with respect to the overall size, fractal dimension, Hurst and spectral exponents. The method is applied to several classes of fBs, and it is shown that the obtained numerical values of the structural parameters are in very good agreement with theoretical ones.

scholarly journals Classifying and analyzing small-angle scattering data using weighted k nearest neighbors machine learning techniques

2020 ◽  
Vol 53 (2) ◽  
pp. 326-334
Author(s):  
Richard K. Archibald ◽  
Mathieu Doucet ◽  
Travis Johnston ◽  
Steven R. Young ◽  
Erika Yang ◽  
...  
Keyword(s):  
Machine Learning ◽  
Small Angle ◽  
Structural Parameters ◽  
Nearest Neighbors ◽  
Small Angle Scattering ◽  
Machine Learning Techniques ◽  
Stochastic Gradient Descent ◽  
Scattering Data ◽  
Gradient Descent Method ◽  
Angle Scattering

A consistent challenge for both new and expert practitioners of small-angle scattering (SAS) lies in determining how to analyze the data, given the limited information content of said data and the large number of models that can be employed. Machine learning (ML) methods are powerful tools for classifying data that have found diverse applications in many fields of science. Here, ML methods are applied to the problem of classifying SAS data for the most appropriate model to use for data analysis. The approach employed is built around the method of weighted k nearest neighbors (wKNN), and utilizes a subset of the models implemented in the SasView package (https://www.sasview.org/) for generating a well defined set of training and testing data. The prediction rate of the wKNN method implemented here using a subset of SasView models is reasonably good for many of the models, but has difficulty with others, notably those based on spherical structures. A novel expansion of the wKNN method was also developed, which uses Gaussian processes to produce local surrogate models for the classification, and this significantly improves the classification accuracy. Further, by integrating a stochastic gradient descent method during post-processing, it is possible to leverage the local surrogate model both to classify the SAS data with high accuracy and to predict the structural parameters that best describe the data. The linking of data classification and model fitting has the potential to facilitate the translation of measured data into results for both novice and expert practitioners of SAS.

scholarly journals Uniqueness of models from small-angle scattering data: the impact of a hydration shell and complementary NMR restraints

2015 ◽  
Vol 71 (1) ◽  
pp. 57-66 ◽  
Author(s):  
Henry S. Kim ◽  
Frank Gabel
Keyword(s):  
Small Angle ◽  
Hydration Shell ◽  
Small Angle Scattering ◽  
Conformational Space ◽  
Scattering Data ◽  
Body System ◽  
Angle Scattering ◽  
Recent Developments ◽  
The Impact ◽  
Nmr Restraints

Small-angle scattering (SAS) has witnessed a breathtaking renaissance and expansion over the past 15 years regarding the determination of biomacromolecular structures in solution. While important issues such as sample quality, good experimental practice and guidelines for data analysis, interpretation, presentation, publication and deposition are increasingly being recognized, crucial topics such as the uniqueness, precision and accuracy of the structural models obtained by SAS are still only poorly understood and addressed. The present article provides an overview of recent developments in these fields with a focus on the influence of complementary NMR restraints and of a hydration shell on the uniqueness of biomacromolecular models. As a first topic, the impact of incorporating NMR orientational restraints in addition to SAS distance restraints is discussed using a quantitative visual representation that illustrates how the possible conformational space of a two-body system is reduced as a function of the available data. As a second topic, the impact of a hydration shell on modelling parameters of a two-body system is illustrated, in particular on its inter-body distance. Finally, practical recommendations are provided to take both effects into account and promising future perspectives of SAS approaches are discussed.

Small Angle Scattering from Nanocrystalline Pd

1988 ◽  
Vol 132 ◽  
Author(s):  
G. Wallner ◽  
E. Jorra ◽  
H. Franz ◽  
J. Peisl ◽  
R. Birringer ◽  
...  
Keyword(s):  
Crystallite Size ◽  
Size Distribution ◽  
Small Angle ◽  
Volume Fraction ◽  
Structural Parameters ◽  
Spatial Arrangement ◽  
Small Angle Scattering ◽  
X Rays ◽  
Angle Scattering ◽  
Log Normal

ABSTRACTThe microstructure of nanocrystalline Pd was investigated by small angle scattering of neutrons and X-rays. The samples were prepared by compacting small crystallites produced by evaporation and condensation in an inert gas atmosphere. The strong scattering signal is interpreted to arise from crystallites embedded in a matrix of incoherent interfaces. Size distributions were deduced from the scattering curves. They consist of two parts: the crystallite size distribution dictated by the production process, and a structureless contribution due to the correlation in the spatial arrangement of the crystallites. The crystallite size distribution may be described by a log-normal distribution centred at R=2nm. The characteristic form of the correlation contribution arises from the dense packing of non-spherical crystallites. From the scattering cross-section in absolute units the volume fraction vc of crystallites was obtained as vc≈0.3, and the mean atomic density ρi in the interfaces as ρi≈0.52. The change of structural parameters during thermal annealing of the samples was studied. Up to high temperatures an appreciable volume fraction of crystallites with nearly unchanged size remains along with large particles.

Interpretation of small-angle scattering data of inhomogeneous ellipsoids

2004 ◽  
Vol 37 (5) ◽  
pp. 815-822 ◽  
Author(s):  
Gerhard Fritz ◽  
Alexander Bergmann
Keyword(s):  
Cross Sections ◽  
Small Angle ◽  
Theoretical Calculations ◽  
Negative Contrast ◽  
Small Angle Scattering ◽  
Distribution Functions ◽  
Distance Distribution ◽  
Scattering Data ◽  
Elliptical Cross ◽  
Angle Scattering

Small-angle scattering data of inhomogeneous ellipsoidal particles are discussed in terms of their pair distance distribution functionsp(r). Special attention is given to the determination of core and shell thicknesses and axis ratios as well as to large distances within the particles, since cross terms between parts of positive and negative contrast within the particle can produce misleading results, similar to homogeneous particles or Janus particles. Cross-section pair distance distribution functionspc(r) of cylinders with elliptical cross sections show similar behaviour. Theoretical calculations are compared with small-angle X-ray and neutron scattering (SAXS and SANS) data of cetyltrimethylammonium bromide in aqueous KCl solutions.

Small-angle scattering behavior of thread-like and film-like systems

2016 ◽  
Vol 49 (1) ◽  
pp. 260-276 ◽  
Author(s):  
Salvino Ciccariello ◽  
Pietro Riello ◽  
Alvise Benedetti
Keyword(s):  
Small Angle ◽  
Large Scale ◽  
Probability Function ◽  
Structural Parameters ◽  
Small Angle Scattering ◽  
Constant Thickness ◽  
Small Scale ◽  
Linear Segment ◽  
Angle Scattering ◽  
The Right

Film-like and thread-like systems are, respectively, defined by the property that one of the constituting homogenous phases has a constant thickness (δ) or a constant normal cross section (of largest chord δ). The stick probability function of this phase, in the limit δ → 0, naturally leads to the definition of the correlation function (CF) of a surface or of a curve. This CF closely approximates the generating stick probability function in the range of distances larger than δ. The surface and the curve CFs, respectively, behave as 1/rand as 1/r2asrapproaches zero. This result implies that the relevant small-angle scattering intensities behave as {\cal P}_{{\cal S}}/q^2 or as {\cal P}_{{\cal C}}/q in the intermediate range of the scattering vector magnitude (q) and as {\cal P}/q^4 in the outermostqrange. Similarly to {\cal P}, pre-factors {\cal P}_{{\cal S}} and {\cal P}_{{\cal C}} simply depend on some structural parameters. Depending on the scale resolution it may happen that a given sample looks thread like at large scale, film like at small scale and particulate at a finer scale. An explicit example is reported. As a practical illustration of the above results, the surface and the curve CFs of some simple geometrical shapes have been explicitly evaluated. In particular, the CF of the right circular cylinder is evaluated. Its limits, as the height or the diameter the cylinder approaches zero, are shown to coincide with the CFs of a circle and of a linear segment, respectively.

scholarly journals Small-angle scattering from multiphase fractals

2014 ◽  
Vol 47 (1) ◽  
pp. 198-206 ◽  
Author(s):  
A. Yu. Cherny ◽  
E. M. Anitas ◽  
V. A. Osipov ◽  
A. I. Kuklin
Keyword(s):  
Power Law ◽  
Small Angle ◽  
Small Angle Scattering ◽  
Variation Method ◽  
Multiphase System ◽  
Model Parameters ◽  
Contrast Variation ◽  
Crossover Point ◽  
Two Phase ◽  
Angle Scattering

Small-angle scattering (SAS) intensities observed experimentally are often characterized by the presence of successive power-law regimes with various scattering exponents whose values vary from −4 to −1. This usually indicates multiple fractal structures of the sample characterized by different size scales. The existing models explaining the crossover positions (that is, the points where the power-law scattering exponent changes) involve only one contrast parameter, which depends solely on the ratio of the fractal sizes. Here, a model that describes SAS from a multiphase system with a few contrast parameters is described, and it is shown that the crossover position depends on the scattering length density of each phase. The Stuhrmann contrast variation method is generalized and applied to experimental curves in the vicinity of the crossover point beyond the Guinier region. The contrast variation is applied not to the intensity itself but to the model parameters, which can be found by fitting the experimental data with the suggested interpolation formula. The model supplements the existing two-phase models and gives the simple condition of their inapplicability: if the crossover point depends on the contrast then a two-phase model is not relevant. The developed analysis allows one to answer the qualitative question of whether one fractal `absorbs' another one or they are both immersed in a surrounding homogeneous medium like a solvent or solid matrix. The models can be applied to experimental SAS data where the absolute value of the scattering exponent of the first power-law regime is higher than that of the subsequent second power-law regime, that is, the scattering curve is `convex' near the crossover point. As is shown, the crossover position can be very sensitive to contrast variation, which influences significantly the length of the fractal range.

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