Fitting a free-form scattering length density profile to reflectivity data using temperature-proportional quenching

2006 ◽  
Vol 125 (24) ◽  
pp. 244702 ◽  
Author(s):  
Charles F. Laub ◽  
Tonya L. Kuhl
Keyword(s):  
Density Profile ◽  
Scattering Length ◽  
Free Form ◽  
Scattering Length Density ◽  
Reflectivity Data

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.

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.

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

Unbiased analysis of neutron and X-ray reflectivity data by an evolution strategy

2002 ◽  
Vol 35 (3) ◽  
pp. 347-355 ◽  
Author(s):  
Erich Politsch ◽  
Gregor Cevc
Keyword(s):  
Scattering Length ◽  
Evolution Strategy ◽  
Free Form ◽  
The Novel ◽  
Maximum Information ◽  
X Ray ◽  
Long Wavelength ◽  
Novel Approach ◽  
Reflectivity Data ◽  
Maximum Information Entropy

A new method for the unbiased determination of scattering length density (SLD) profiles from neutron or X-ray reflectograms is presented, based on an evolution strategy. In contrast to existing methods, the new approach uses no constraints that could influence the fit result improperly. While it is widely agreed that SLD profile oscillations with small wavelength and small amplitude cannot be resolved, randomly occurring long-wavelength oscillations have been neglected to date despite the fact that such oscillations can tremendously affect the calculated SLD profile. No easy remedy exists for this problem within the framework of conventional reflectogram analysis methods. The analytical approach proposed in this work offers a solution based on the recognition that each perturbation which leads to an indistinguishable reflectivity has a negative pendant. Averaging of numerous different, randomly perturbed, profiles therefore cancels out random deviations and accentuates reliable features. Moreover, the resulting averaged free-form fit has maximum (information) entropy. The performance of the novel approach is demonstrated by analysing complex molecular arrangements at an air–water interface and comparing the results with prior evaluations.

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.

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.

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