Modelling of high-symmetry nanoscale particles by small-angle scattering

2013 ◽  
Vol 47 (1) ◽  
pp. 84-94 ◽  
Author(s):  
Cassio Alves ◽  
Jan Skov Pedersen ◽  
Cristiano Luis Pinto Oliveira
Keyword(s):  
Small Angle ◽  
Structural Parameters ◽  
Small Angle Scattering ◽  
High Symmetry ◽  
Scattering Intensity ◽  
Angle Scattering ◽  
Small Set ◽  
Debye Formula ◽  
Definition Of ◽  
Theoretical Scattering

A versatile procedure to build high-symmetry objects and to calculate their corresponding small-angle scattering intensity is presented. Starting from a set of vertex positions, available from a large and extensible database, it is possible to build several types of bodies using spherical subunits. A fast implementation, based on the Debye formula using a histogram of distance, is then used to compute the theoretical scattering intensity. Since the model is built from the definition of a small set of parameters, it is possible to perform an optimization of structural parameters against experimental data. Finally, affine size polydispersities can be easily included by the rescaling of the histogram of the positions used in the calculations. Several examples of the calculations are presented, demonstrating the method and its applicability.

Contrast variation in small-angle scattering experiments on polydisperse and superparamagnetic systems: basic functions approach

2007 ◽  
Vol 40 (1) ◽  
pp. 56-70 ◽  
Author(s):  
Mikhail V. Avdeev
Keyword(s):  
Small Angle ◽  
Magnetic Particles ◽  
Scattering Length ◽  
Small Angle Scattering ◽  
Contrast Variation ◽  
Match Point ◽  
Scattering Intensity ◽  
Scattering Length Density ◽  
Angle Scattering ◽  
Basic Functions

The development of the basic functions approach [Stuhrmann (1995).Modern Aspects of Small-Angle Scattering, edited by H. Brumberger, pp. 221–254. Dordrecht: Kluwer Academic Publishers] for the contrast variation technique in small-angle scattering from systems of polydisperse and superparamagnetic non-interacting particles is presented. For polydisperse systems the modified contrast is introduced as the difference between the effective mean scattering length density (corresponding to the minimum of the scattering intensity as the function of the scattering length density of the solvent) and the density of the solvent. Then, the general expression for the scattering intensity is written in the classical way through the modified basic functions. It is shown that the shape scattering from the particle volume can be reliably obtained. Modifications of classical expressions describing changes in integral parameters of the scattering (intensity at zero angle, radius of gyration, Porod integral) with the contrast are analyzed. In comparison with the monodisperse case, the residual scattering in the minimum of intensity as a function of contrast (effective match point) in polydisperse systems makes it possible to treat the Guinier region of scattering curves around the effective match point quite precisely from the statistical viewpoint. However, limitations of such treatment exist, which are emphasized in the paper. In addition, the effect of magnetic scattering in small-angle neutron scattering from superparamagnetic nanoparticles is considered in the context of the basic functions approach. Conceptually, modifications of the integral parameters of the scattering in this case are similar to those obtained for polydisperse multicomponent particles. Various cases are considered, including monodisperse non-homogeneous and homogeneous magnetic particles, and polydisperse non-homogeneous and homogeneous magnetic particles. The developed approach is verified for two models representing the main types of magnetic fluids – systems of polydisperse superparamagnetic particles located in liquid carriers.

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 Laterally Resolved Small-Angle Scattering Intensity from Lipid Bilayer Simulations: An Exact and a Limited-Range Treatment

2020 ◽  
Vol 16 (8) ◽  
pp. 5287-5300 ◽  
Author(s):  
Mitchell W. Dorrell ◽  
Frederick A. Heberle ◽  
John Katsaras ◽  
Lutz Maibaum ◽  
Edward Lyman ◽  
...  
Keyword(s):  
Lipid Bilayer ◽  
Small Angle ◽  
Limited Range ◽  
Small Angle Scattering ◽  
Scattering Intensity ◽  
Angle Scattering

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.

Rapid and accurate calculation of small-angle scattering profiles using the golden ratio

2013 ◽  
Vol 46 (4) ◽  
pp. 1171-1177 ◽  
Author(s):  
Max C. Watson ◽  
Joseph E. Curtis
Keyword(s):  
Small Angle ◽  
Golden Ratio ◽  
Expansion Method ◽  
Multipole Expansion ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Approximation Technique ◽  
Scattering Intensity ◽  
Angle Scattering ◽  
Multipole Expansion Method

Calculating the scattering intensity of anN-atom system is a numerically exhaustingO(N2) task. A simple approximation technique that scales linearly with the number of atoms is presented. Using an exact expression for the scattering intensityI(q) at a given wavevectorq, the rotationally averaged intensityI(q) is computed by evaluatingI(q) in several scattering directions. The orientations of theqvectors are taken from a quasi-uniform spherical grid generated by the golden ratio. Using various biomolecules as examples, this technique is compared with an established multipole expansion method. For a given level of speed, the technique is more accurate than the multipole expansion for anisotropically shaped molecules, while comparable in accuracy for globular shapes. The processing time scales sub-linearly inNwhen the atoms are identical and lie on a lattice. The procedure is easily implemented and should accelerate the analysis of small-angle scattering data.

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 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 Lipid Bilayer Structure Refinement with SAXS/SANS Based Restrained Ensemble Molecular Dynamics

2021 ◽  
Author(s):  
Yevhen Cherniavskyi ◽  
Svetlana Baoukina ◽  
Bryan W. Holland ◽  
D. Peter Tieleman
Keyword(s):  
Molecular Dynamics ◽  
Lipid Bilayers ◽  
Small Angle ◽  
Structure Refinement ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Bilayer Structure ◽  
Lipid Molecule ◽  
Scattering Intensity ◽  
Angle Scattering

Small-angle scattering is a powerful technique that can probe the structure of lipid bilayers on the nanometer scale. Retrieving the real space structure of lipid bilayers from the scattering intensity can be a challenging task, as their fluid nature results in a liquid-like scattering pattern which is hard to interpret. The standard approach to this problem is to describe the bilayer structure as a sum of density distributions of separate components of the lipid molecule and then to fit the parameters of the distributions against experimental data. The accuracy of the density-based analysis is partially limited by the choice of the functions used to describe component distributions, especially in the case of multi-component bilayers. The number of parameters in the model is balanced by the need for an accurate description of the underlying bilayer structure and the risk of overfitting the data. Here, we present an alternative method for the interpretation of small-angle scattering intensity data for lipid bilayers. The method is based on restrained ensemble molecular dynamics simulations that allow direct incorporation of the scattering data into the simulations in the form of a restraining potential. This approach combines the information implicitly contained in the simulation force field with structural data from the scattering intensity and is free from prior assumptions regarding the bilayer structure.<br>

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