Quantitative analysis of the nonlinear relationship between neutron or x-ray reflectance and the scattering-length-density profile

1995 ◽  
Vol 52 (2) ◽  
pp. 1938-1952 ◽  
Author(s):  
Xiao-Lin Zhou
Keyword(s):  
Quantitative Analysis ◽  
Density Profile ◽  
Scattering Length ◽  
Nonlinear Relationship ◽  
X Ray ◽  
Scattering Length Density

String Fit: a new structurally oriented X-ray and neutron reflectivity evaluation technique

2001 ◽  
Vol 34 (3) ◽  
pp. 239-251 ◽  
Author(s):  
Erich Politsch
Keyword(s):  
Density Profile ◽  
Ad Hoc ◽  
Structural Characteristics ◽  
Scattering Length ◽  
Radius Of Gyration ◽  
Data Sets ◽  
Molecular Conformations ◽  
X Ray ◽  
Scattering Length Density ◽  
Molecular Arrangement

A novel method for the analysis of neutron and X-ray reflectivity measurements is presented. In contrast to existing methods, the new data fitting approach is structurally oriented and therefore only requires information about the chemical structure of studied molecules and no otherad hocassumptions. Apart from the inversion of reflectivity into scattering length density profile, the inversion of scattering length density profile into molecular arrangement is addressed systematically for non-trivial molecular conformations for the first time. This includes the calculation of structural characteristics, such as radius of gyration or chain order parameters, based on measured reflectograms. Another important option is the possibility to evaluate simultaneously neutron and X-ray reflectograms of a given sample. For better convergence, especially for complex simultaneous evaluations, an effective extension of the normally used least-squares deviation function is introduced. Different simulated molecular ensembles are used to illustrate the features of the new approach; typically, excellent agreement between the simulated starting and final deduced data sets is achieved.

Model-independent determination of the surface scattering-length-density profile from specular reflectivity data

1992 ◽  
Vol 25 (2) ◽  
pp. 129-145 ◽  
Author(s):  
J. S. Pedersen
Keyword(s):  
Density Profile ◽  
Fourier Transformation ◽  
Scattering Length ◽  
Simulated Data ◽  
Limited Range ◽  
Square Root ◽  
Scattering Length Density ◽  
Angle Scattering ◽  
Specular Reflectivity ◽  
Reflectivity Data

An approach for analysing neutron and X-ray specular reflectivity data from stratified media having variation in the scattering-length density near the surface is described. The method has its origin in small-angle scattering and it is composed of two steps: (i) indirect Fourier transformation [Glatter (1977). J. Appl. Cryst. 10, 415–421] giving the profile correlation function p(z) of the derivative dρ/dz of the scattering-length density; (ii) square-root deconvolution [Glatter (1981). J. Appl. Cryst. 14, 101–108] giving dρ/dz and ρ, the scattering-length-density profile. The only requirement for applying the method is that the scattering-length density varies only in a limited range. In nearly all cases the approach does not require any knowledge of the chemical composition of the surface layer and consequently incorporates a certain degree of objectivity. The method gives the smoothest profile which agrees with the experimental reflectivity data. The method is tested on simulated reflectivity data for a series of different surface profiles and subsequently used for analysing experimental data on fluorocarbon amphiphiles in water and salt solutions. The tests on simulated data show that the indirect Fourier transformation gives correlation functions agreeing very well with the corresponding functions of the original profiles. It is further demonstrated that the square-root deconvolution gives reliable results for the scattering-length-density profiles.

scholarly journals Joint small-angle X-ray and neutron scattering data analysis of asymmetric lipid vesicles

2017 ◽  
Vol 50 (2) ◽  
pp. 419-429 ◽  
Author(s):  
Barbara Eicher ◽  
Frederick A. Heberle ◽  
Drew Marquardt ◽  
Gerald N. Rechberger ◽  
John Katsaras ◽  
...  
Keyword(s):  
Density Profile ◽  
Small Angle ◽  
Scattering Length ◽  
Lipid Vesicles ◽  
Computational Effort ◽  
Scattering Data ◽  
Joint Analysis ◽  
Melting Transition ◽  
X Ray ◽  
The Individual

Low- and high-resolution models describing the internal transbilayer structure of asymmetric lipid vesicles have been developed. These models can be used for the joint analysis of small-angle neutron and X-ray scattering data. The models describe the underlying scattering length density/electron density profiles either in terms of slabs or through the so-called scattering density profile, previously applied to symmetric lipid vesicles. Both models yield structural details of asymmetric membranes, such as the individual area per lipid, and the hydrocarbon thickness of the inner and outer bilayer leaflets. The scattering density profile model, however, comes at a cost of increased computational effort but results in greater structural resolution, showing a slightly lower packing of lipids in the outer bilayer leaflet of ∼120 nm diameter palmitoyloleoyl phosphatidylcholine (POPC) vesicles, compared to the inner leaflet. Analysis of asymmetric dipalmitoyl phosphatidylcholine/POPC vesicles did not reveal evidence of transbilayer coupling between the inner and outer leaflets at 323 K, i.e. above the melting transition temperature of the two lipids.

Scattering length density profile of Ni film under controlled corrosion: A study in neutron reflectometry

Pramana ◽  
2008 ◽  
Vol 71 (5) ◽  
pp. 1097-1101 ◽  
Author(s):  
Surendra Singh ◽  
A. K. Poswal ◽  
S. K. Ghosh ◽  
Saibal Basu
Keyword(s):  
Density Profile ◽  
Scattering Length ◽  
Neutron Reflectometry ◽  
Scattering Length Density

scholarly journals Carbonaceous Materials Investigated by Small-Angle X-ray and Neutron Scattering

2020 ◽  
Vol 6 (4) ◽  
pp. 82
Author(s):  
Eneli Härk ◽  
Matthias Ballauff
Keyword(s):  
Neutron Scattering ◽  
Small Angle ◽  
Small Angle Neutron Scattering ◽  
Carbon Nanomaterials ◽  
Scattering Length ◽  
Carbonaceous Materials ◽  
X Ray ◽  
Scattering Length Density ◽  
X Ray Scattering ◽  
Ray Scattering

Carbonaceous nanomaterials have become important materials with widespread applications in battery systems and supercapacitors. The application of these materials requires precise knowledge of their nanostructure. In particular, the porosity of the materials together with the shape of the pores and the total internal surface must be known accurately. Small-angle X-ray scattering (SAXS) and small-angle neutron scattering (SANS) present the methods of choice for this purpose. Here we review our recent investigations using SAXS and SANS. We first describe the theoretical basis of the analysis of carbonaceous material by small-angle scattering. The evaluation of the small-angle data relies on the powerful concept of the chord length distribution (CLD) which we explain in detail. As an example of such an evaluation, we use recent analysis by SAXS of carbide-derived carbons. Moreover, we present our SAXS analysis on commercially produced activated carbons (ACN, RP-20) and provide a comparison with small-angle neutron scattering data. This comparison demonstrates the wealth of additional information that would not be obtained by the application of either method alone. SANS allows us to change the contrast, and we summarize the main results using different contrast matching agents. The pores of the carbon nanomaterials can be filled gradually by deuterated p-xylene, which leads to a precise analysis of the pore size distribution. The X-ray scattering length density of carbon can be matched by the scattering length density of sulfur, which allows us to see the gradual filling of the nanopores by sulfur in a melt-impregnation procedure. This process is important for the application of carbonaceous materials as cathodes in lithium/sulfur batteries. All studies summarized in this review underscore the great power and precision with which carbon nanomaterials can be analyzed by SAXS and SANS.

REFLEX: a program for the analysis of specular X-ray and neutron reflectivity data

2019 ◽  
Vol 52 (1) ◽  
pp. 201-213 ◽  
Author(s):  
Guillaume Vignaud ◽  
Alain Gibaud
Keyword(s):  
Physical Properties ◽  
Density Profile ◽  
Scattering Length ◽  
Electron Density Profile ◽  
Neutron Reflectivity ◽  
X Rays ◽  
X Ray ◽  
Spin Polarized ◽  
Reflectivity Data ◽  
Footprint Effect

The use of X-ray and neutron reflectivity has been generalized worldwide for scientists who want to determine specific physical properties (such as electron-density profile, scattering-length density, roughness and thickness) of films less than 200 nm thick deposited on a substrate. This paper describes a freeware program named REFLEX, which is a standalone program dedicated to the simulation and analysis of X-ray and neutron reflectivity from multilayers. This program was first written two decades ago and has been constantly improved since, but never published until now. The latest version of REFLEX covers generalized types of calculation of reflectivity curves including both neutron and X-ray reflectivity. In the case of X-rays, the program can deal with both s and p polarization, which is quite important in the soft X-ray region where the two polarizations can yield different results. Neutron reflectivity is calculated within the framework of non-spin-polarized neutrons. REFLEX has also been designed to include any type of fluid (such as supercritical CO2) on top of the analysed film and includes corrections of the footprint effect for analysis on an absolute scale.

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