Fractal Pores or a Distribution of Pore sizes: Alternative Interpretations of Power-Law Small-Angle Scattering

1986 ◽  
Vol 73 ◽  
Author(s):  
Paul W. Schmidt
Keyword(s):  
Fractal Dimension ◽  
Neutron Scattering ◽  
Power Law ◽  
Small Angle ◽  
Scattered Intensity ◽  
X Ray ◽  
Number Distribution ◽  
Angle Scattering ◽  
Q Values ◽  
Boundary Surfaces

ABSTRACTThe intensity I(q) of the small-angle x-ray or neutron scattering has been calculated for a system of randomly oriented, independently scatter-ing pores with a number distribution of pore diameters which has the form of a power law. As has already been shown, [P. W. Schmidt, J. Appl. Cryst. 15, 567–569 (1982)], when the number distribution of the maximum diameters a of the pores is proportional to a−γ, I(q) is proportional to q−(7−γ), where q = 4πλ−1sin(θ/2), θ is the scattering angle, and λ is the wavelength. The coefficient of the power-law intensity has been expressed in terms of some of the constants which determine the diameter distribu-tion. Equations have been obtained for the scattered intensity I(q) at q values larger and smaller than those at which power-law scattering occurs. The intensity scattered by this system is compared with the intensity from a system of pores with fractal pore-boundary surfaces which have a fractal dimension D.

Experimental Evidence of Clusters in Molten Alloys of the Eutectic Aluminum-Tin System by Means of a X-Ray-high Temperature-small Angle Scattering Apparatus

1970 ◽  
Vol 25 (7) ◽  
pp. 1085-1091 ◽  
Author(s):  
R. Hezel ◽  
S. Steeb
Keyword(s):  
High Temperature ◽  
Small Angle ◽  
Short Range ◽  
Eutectic System ◽  
Wide Angle ◽  
Molten Metals ◽  
Scattered Intensity ◽  
Solid Materials ◽  
X Ray ◽  
Angle Scattering

An apparatus for measuring X-Ray small- and wide angle scattering of solid materials and especially of molten metals with temperatures up to 1100 °C is described. Alloys of the eutectic system Al -Sn with tin-contents up to 30 At.-% are investigated. The influence of surface oxide layers on the scattered intensity is discussed. Correlation functions as well as the Guinier approximation yielded inhomogeneities with mean diameters up to 10 Å in the investigated melts. Therefore the dimensions of these so-called short range segregation zones correspond to those of the first coordination sphere

Theory, practice and prospects of X-ray and neutron scattering for lignocellulosic biomass characterization: towards understanding biomass pretreatment

2015 ◽  
Vol 8 (2) ◽  
pp. 436-455 ◽  
Author(s):  
Gang Cheng ◽  
Xin Zhang ◽  
Blake Simmons ◽  
Seema Singh
Keyword(s):  
Neutron Scattering ◽  
Detailed Analysis ◽  
Lignocellulosic Biomass ◽  
Small Angle ◽  
Small Angle Scattering ◽  
Biomass Pretreatment ◽  
Biomass Recalcitrance ◽  
X Ray ◽  
Angle Scattering ◽  
Biomass Characterization

We present a detailed analysis of application of wide and small angle scattering techniques to study the structures of cellulose and lignin which are relevant to biomass recalcitrance.

Small-angle scattering: a view on the properties, structures and structural changes of biological macromolecules in solution

2003 ◽  
Vol 36 (2) ◽  
pp. 147-227 ◽  
Author(s):  
Michel H. J. Koch ◽  
Patrice Vachette ◽  
Dmitri I. Svergun
Keyword(s):  
High Resolution ◽  
Neutron Scattering ◽  
Small Angle ◽  
Structure Factor ◽  
Structural Changes ◽  
Biological Macromolecules ◽  
Time Resolved ◽  
Scattering Intensity ◽  
X Ray ◽  
Angle Scattering

1. Introduction 1482. Basics of X-ray and neutron scattering 1492.1 Elastic scattering of electromagnetic radiation by a single electron 1492.2 Scattering by assemblies of electrons 1512.3 Anomalous scattering and long wavelengths 1532.4 Neutron scattering 1532.5 Transmission and attenuation 1553. Small-angle scattering from solutions 1563.1 Instrumentation 1563.2 The experimental scattering pattern 1573.3 Basic scattering functions 1593.4 Global structural parameters 1613.4.1 Monodisperse systems 1613.4.2 Polydisperse systems and mixtures 1633.5 Characteristic functions 1644. Modelling 1664.1 Spherical harmonics 1664.2 Shannon sampling 1694.3 Shape determination 1704.3.1 Modelling with few parameters: molecular envelopes 1714.3.2 Modelling with many parameters: bead models 1734.4 Modelling domain structure and missing parts of high-resolution models 1784.5 Computing scattering patterns from atomic models 1844.6 Rigid-body refinement 1875. Applications 1905.1 Contrast variation studies of ribosomes 1905.2 Structural changes and catalytic activity of the allosteric enzyme ATCase 1916. Interactions between molecules in solution 2036.1 Linearizing the problem for moderate interactions: the second virial coefficient 2046.2 Determination of the structure factor 2057. Time-resolved measurements 2118. Conclusions 2159. Acknowledgements 21610. References 216A self-contained presentation of the main concepts and methods for interpretation of X-ray and neutron-scattering patterns of biological macromolecules in solution, including a reminder of the basics of X-ray and neutron scattering and a brief overview of relevant aspects of modern instrumentation, is given. For monodisperse solutions the experimental data yield the scattering intensity of the macromolecules, which depends on the contrast between the solvent and the particles as well as on their shape and internal scattering density fluctuations, and the structure factor, which is related to the interactions between macromolecules. After a brief analysis of the information content of the scattering intensity, the two main approaches for modelling the shape and/or structure of macromolecules and the global minimization schemes used in the calculations are presented. The first approach is based, in its more advanced version, on the spherical harmonics approximation and relies on few parameters, whereas the second one uses bead models with thousands of parameters. Extensions of bead modelling can be used to model domain structure and missing parts in high-resolution structures. Methods for computing the scattering patterns from atomic models including the contribution of the hydration shell are discussed and examples are given, which also illustrate that significant differences sometimes exist between crystal and solution structures. These differences are in some cases explainable in terms of rigid-body motions of parts of the structures. Results of two extensive studies – on ribosomes and on the allosteric protein aspartate transcarbamoylase – illustrate the application of the various methods. The unique bridge between equilibrium structures and thermodynamic or kinetic aspects provided by scattering techniques is illustrated by modelling of intermolecular interactions, including crystallization, based on an analysis of the structure factor and recent time-resolved work on assembly and protein folding.

scholarly journals Small-Angle X-Ray and Neutron Scattering on Photosynthetic Membranes

2021 ◽  
Vol 9 ◽  
Author(s):  
Dainius Jakubauskas ◽  
Kell Mortensen ◽  
Poul Erik Jensen ◽  
Jacob J. K. Kirkensgaard
Keyword(s):  
Neutron Scattering ◽  
Small Angle ◽  
Environmental Changes ◽  
Data Interpretation ◽  
Photosynthetic Membrane ◽  
Noninvasive Methods ◽  
X Ray ◽  
Angle Scattering ◽  
Active Research

Ultrastructural membrane arrangements in living cells and their dynamic remodeling in response to environmental changes remain an area of active research but are also subject to large uncertainty. The use of noninvasive methods such as X-ray and neutron scattering provides an attractive complimentary source of information to direct imaging because in vivo systems can be probed in near-natural conditions. However, without solid underlying structural modeling to properly interpret the indirect information extracted, scattering provides at best qualitative information and at worst direct misinterpretations. Here we review the current state of small-angle scattering applied to photosynthetic membrane systems with particular focus on data interpretation and modeling.

Quantification of the information in small-angle scattering data

2014 ◽  
Vol 47 (6) ◽  
pp. 2000-2010 ◽  
Author(s):  
Martin Cramer Pedersen ◽  
Steen Laugesen Hansen ◽  
Bo Markussen ◽  
Lise Arleth ◽  
Kell Mortensen
Keyword(s):  
Data Analysis ◽  
Neutron Scattering ◽  
Ray Tracing ◽  
Information Content ◽  
Small Angle ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
X Ray ◽  
Angle Scattering ◽  
Wide Range

Small-angle X-ray and neutron scattering have become increasingly popular owing to improvements in instrumentation and developments in data analysis, sample handling and sample preparation. For some time, it has been suggested that a more systematic approach to the quantification of the information content in small-angle scattering data would allow for a more optimal experiment planning and a more reliable data analysis. In the present article, it is shown how ray-tracing techniques in combination with a statistically rigorous data analysis provide an appropriate platform for such a systematic quantification of the information content in scattering data. As examples of applications, it is shown how the exposure time at different instrumental settings or contrast situations can be optimally prioritized in an experiment. Also, the gain in information by combining small-angle X-ray and neutron scattering is assessed. While solution small-angle scattering data of proteins and protein–lipid complexes are used as examples in the present case study, the approach is generalizable to a wide range of other samples and experimental techniques. The source code for the algorithms and ray-tracing components developed for this study has been made available on-line.

Small-angle scattering studies of the pore structure of polymer-modified portland cement pastes

1990 ◽  
Vol 5 (6) ◽  
pp. 1281-1284 ◽  
Author(s):  
V. M. Castaño ◽  
P. W. Schmidt ◽  
H. G. Hörnis
Keyword(s):  
Portland Cement ◽  
Neutron Scattering ◽  
Pore Structure ◽  
Small Angle ◽  
Small Angle Scattering ◽  
Cement Pastes ◽  
X Ray ◽  
Angle Scattering ◽  
Gel Porosity

Small-angle x-ray and neutron scattering experiments were performed in several polymer-containing portland cement pastes with the same w/c ratio. The nature of the results is discussed in terms of the role of the polymer upon the properties of the materials. A comparison with other works seems to indicate that the capillary pores are strongly affected whereas the gel porosity remains unchanged by the polymer solutions.

scholarly journals H2O/D2O Contrast Variation for Ultra-Small-Angle Neutron Scattering to Minimize Multiple Scattering Effects of Colloidal Particle Suspensions

2018 ◽  
Vol 2 (3) ◽  
pp. 37 ◽  
Author(s):  
Akira Otsuki ◽  
Liliana de Campo ◽  
Christopher Garvey ◽  
Christine Rehm
Keyword(s):  
Neutron Scattering ◽  
Multiple Scattering ◽  
Small Angle ◽  
Small Angle Neutron Scattering ◽  
Colloidal Particle ◽  
Scattered Intensity ◽  
Particle Suspensions ◽  
Scattering Effects ◽  
Multiple Scattering Effects ◽  
Q Values

This study investigated the use of solvent contrast (H2O/D2O ratio) as a means to optimize the ultra-small-angle neutron scattering (USANS) signal. By optimizing the signal, it was possible to reduce the undesirable effects of coherent multiple scattering while still maintaining a measurable scattered intensity. This result will further enable the use of USANS as a probe of the interactions between colloidal particles and their structures within concentrated suspensions as well as particle dispersion/aggregation. As a model system, we prepared silica colloidal particle suspensions at different solid concentrations. USANS curves were measured using the classical Bonse–Hart double crystal diffractometer while varying the scattering length density of the aqueous phase, thus varying the contrast to the silica particles. As a means of assessing the impact of multiple scattering effects on different q-values, we analyzed the scattered intensity at different contrasts at three different q values. The data were then used to determine the match point of the silica particle suspensions from the expected square root dependence of the scattered intensity with solvent composition, to analyze any differences associated with the solid concentration change, and to determine the optimum H2O/D2O ratio in terms of high transmission (TSAS > 80%) and high enough scattering intensity associated with the contrast of the system. Through this investigation series, we confirmed that adjusting the contrast of the solvent (H2O/D2O) is a good methodology to reduce multiple scattering while maintaining a strong enough scattering signal from a concentrated suspension of silica particles for both USANS and rheometric USANS (rheo-USANS) experiments.

Butterfly Patterns: an Anomaly Common to the Neutron Scattering Spectra of Elongated Rubbers, Melts and Gels:

1991 ◽  
Vol 248 ◽  
Author(s):  
J. Bastide ◽  
F. Boue ◽  
R. Oeser ◽  
E. Mendes ◽  
F. Zielinski ◽  
...  
Keyword(s):  
Neutron Scattering ◽  
Small Angle ◽  
Small Proportion ◽  
Small Angle Neutron Scattering ◽  
Scattered Intensity ◽  
Extension Ratio ◽  
Scattering Spectra ◽  
First Time ◽  
Direction Opposite ◽  
Q Values

AbstractA totally unexpected phenomenon has been observed for the first time a few years ago when studying, by small angle neutron scattering, rubbery networks containing a small proportion of uncrosslinked labelled (deuterated) chains [1].When such a system is elongated, the scattered intensity strongly increases with the extension ratio λ for q vectors parallel to the stretching direction (and for low q values). Conversely, in the direction perpendicular to the elongation axis, the scattered intensity slightly decreases at low q for small extension ratios and then remains approximately constant when λ is further increased. The changes which are observed occur therefore in a direction opposite to the “conventional” one, i.e. that corresponding to chains effectively linked by at least two chemical junctions to the network and thus oriented on an average along the direction of stretching.

Characterization of H defects in the aluminium–hydrogen system using small-angle scattering techniques

2001 ◽  
Vol 34 (2) ◽  
pp. 119-129 ◽  
Author(s):  
C. E. Buckley ◽  
H. K. Birnbaum ◽  
J. S. Lin ◽  
S. Spooner ◽  
D. Bellmann ◽  
...  
Keyword(s):  
Neutron Scattering ◽  
Small Angle ◽  
Inelastic Neutron Scattering ◽  
Lattice Parameter ◽  
Inelastic Neutron ◽  
X Ray ◽  
Gas Plasma ◽  
Angle Scattering ◽  
Almost All ◽  
Relative Change

Aluminium foils (99.99% purity) and single crystals (99.999% purity) were charged with hydrogen using a gas plasma method and electrochemical methods, resulting in the introduction of a large amount of hydrogen. X-ray diffraction measurements indicated that within experimental error there was a zero change in lattice parameter after plasma charging. This result is contradictory to almost all other face-centred cubic (f.c.c.) materials, which exhibit a lattice expansion when the hydrogen enters the lattice interstitially. It is hypothesized that the hydrogen does not enter the lattice as an interstitial solute, but instead forms an H–vacancy complex at the surface that diffuses into the volume and then clusters to form H2bubbles. Small- and ultra-small-angle neutron scattering (SANS, USANS) and small-angle X-ray scattering (SAXS) were primarily employed to study the nature and agglomeration of the H–vacancy complexes in the Al–H system. The SAXS results were ambiguous owing to double Bragg scattering, but the SANS and USANS investigation, coupled with results from inelastic neutron scattering, and transmission and scanning electron microscopy, revealed the existence of a large size distribution of hydrogen bubbles on the surface and in the bulk of the Al–H system. The relative change in lattice parameter is calculated from the pressure in a bubble of average volume and is compared with the experimentally determined value.

scholarly journals GENFIT: software for the analysis of small-angle X-ray and neutron scattering data of macromolecules in solution

2014 ◽  
Vol 47 (3) ◽  
pp. 1132-1139 ◽  
Author(s):  
Francesco Spinozzi ◽  
Claudio Ferrero ◽  
Maria Grazia Ortore ◽  
Alejandro De Maria Antolinos ◽  
Paolo Mariani
Keyword(s):  
Neutron Scattering ◽  
Small Angle ◽  
Heterogeneous Systems ◽  
Software Tool ◽  
Scattering Data ◽  
Model Parameters ◽  
X Ray ◽  
High Data ◽  
Link Functions ◽  
Angle Scattering

Many research topics in the fields of condensed matter and the life sciences are based on small-angle X-ray and neutron scattering techniques. With the current rapid progress in source brilliance and detector technology, high data fluxes of ever-increasing quality are produced. In order to exploit such a huge quantity of data and richness of information, wider and more sophisticated approaches to data analysis are needed. Presented here isGENFIT, a new software tool able to fit small-angle scattering data of randomly oriented macromolecular or nanosized systems according to a wide list of models, including form and structure factors. Batches of curves can be analysed simultaneously in terms of common fitting parameters or by expressing the model parametersviaphysical or phenomenological link functions. The models can also be combined, enabling the user to describe complex heterogeneous systems.

Sign in / Sign up

Export Citation Format

Share Document