X-Ray Reflection Analysis Programs

Adrian R. Rennie
Department of Physics and Astronomy, Uppsala University

Introduction List of programs Web Resources on X-ray reflection

Introduction

The absorption of X-rays by matter is more often significant than that of neutrons and the effect can be important when calculating reflectivity. The absorption is included by adding an imaginary component to the scattering length density. Programs for calculation of neutron reflection may often ignore this term as it can be some orders of magnitued smaller than the real component. The simplification of fewer parameters can be greatly advantageous for users. The programs listed below have been adapted to include explicitly the input of the imaginary component of the scattering length or scattering length density.

A separate, more extensive list of programs that are intended primarily for analysis of neutron reflectometry data is available at www.reflectometry.net/refprog.htm. Most of the programs described below are intended for the analysis of data that concerns molecules at interfaces that can be characterised by known volumes and scattering properties. In many cases it is convenient to consider separate hydrophobic and hydrophilic parts. For surfactants these are known colloquially as 'tails' and 'head groups'. The fitting in terms of physical and molecular properties such as area per molecule at an interface and number of solvent molecules usually leads to better minimisation of residuals.

Some general programs that allow analysis of structures in terms of a few arbitrary multilayers have also been provided (xspots and xmspots). There is a wide variety of software available for such analysis and a separate catalogue of programs provided by other authors for either X-ray or neutron reflection analysis can be found at: www.reflectometry.net/reflect.htm.

A very crude indication of the importance of the absorption and the imaginary part of the scattering length can be seen in the plots of the ratio of the imaginary part, bi, to the real part br. If this is not small, it will be necessary to include the extra term in the calculation of the refractive index.

plot of bi/br against atomic number for X-rays

Plot of bi/br against atomic number, Z, for X-rays, CuKa radiation.

plot of bi/br against atomic number for X-rays

Plot of bi/br against atomic number, Z, for neutrons (assumes natural isotopic abundance and wavelength of 6 Å).

It is clear that for only a few light elements such as lithium and boron is the ratio for neutron scattering above 0.01. This accounts for the separate development of simplified software for the analysis of neutron reflectivity data for soft matter.

List of Programs

Name Purpose Single/Multiple Data Sets Version Date
xjakt Fit a two layer model defined by scattering lengths and volumes of heads, tails and solvent and area per molecule in the layer. The total thickness and number of solvent molecules are further parameters. The variant xyacht fits the tail region thickness. An account of the models in these programs is provided in the description of jakt. Single 1.1 27 June 2015
xmboat Fit a two layer model for a surface active molecule at a solution interface. The structure is defined by scattering lengths and volumes of heads, tails, counter ions and the solvent as well as the area per molecule in the layer. The tail thickness and number of solvent molecules associated with the heads are further parameters. Multiple 1.1 27 June 2015
xmjakt Fit a two layer model defined by scattering lengths and volumes of heads, tails and solvent and area per molecule in the layer. The total thickness and number of solvent molecules are further parameters. The variant xyacht fits the tail region thickness. An account of the models in these programs is provided in the description of mjakt. Multiple 1.1 27 June 2015
xmyacht Fit a two layer model defined by scattering lengths and volumes of heads, tails and solvent and area per molecule in the layer. The total thickness and number of solvent molecules are further parameters. The variant xjakt fits the total thickness. An account of the models in these programs is provided in the description of myacht. Multiple 1.1 27 June 2015
xmono This fits a model of a monolayer of molecules at a solution interface. The surface layer is parameterised by the volume, scattering length and area per molecule. The thickness an roughness are further parameters. This model is equivalent to that in mono but includes the imaginary parts of the scattering lengths. Single 1.1 27 June 2015
xmspots This is a generalised multilayer fitting program for layers at an interface with measurements of multiple data sets. The surface can be composed of up to three regions with a different total number of layers. Apart from the inclusion of the imaginary part of the scattering length density as input parameters, the model is as described in spots. Multiple 1.1 27 June 2015
xspots This is a multilayer fitting program for layers at an interface that can calculate the reflectivity for an interface with regions that are covered with different surface structures. The interface can be composed of up to three regions with a different total number of layers. Apart from the inclusion of the imaginary part of the scattering length density as input parameters, the model is as described in spots. Single 1.2 27 June 2015
xyacht Fit a two layer model defined by scattering lengths and volumes of heads, tails and solvent and area per molecule in the layer. The total thickness and number of solvent molecules are further parameters. The variant xyacht fits the tail region thickness. An account of the models in these programs is provided in the description of yacht. Single 1.1 27 June 2015

It is recommended to run the programs using clickfit or clickfit_m and the utility 'Prop' available from the ILL. Instruction for download and use of Prop are available from the ILL WWW site. Prop is installed but Clickfit and the fitting programs only need to be copied to suitable directories. The programs that are marked 'single' in the list above can be uded to fit individual data files or to fit automatically sequences of data files. They should be started with clickfit. The programs that are marked as 'multiple' can be used for simultaneous fits of several data sets measured for the same sample. This can, for example, be used to constrain a model to both X-ray and neutron data. This requires the use of clickfit_m.

Web Resources for X-Reflectivity

The following links provide information about X-ray scattering, reflectivity analysis and tools for calculation of contrast. In particular it may be necessary to consider the variation of scattering and absorption with energy or wavelength when calculating the scattering length density for some materials.

Thanks

I am grateful to Dr Ron Ghosh for provision of the Fitfun package and the clickfit interface that is used with the software. His help with the development of the programs is much appreciated.

Introduction List of programs Web Resources on X-ray reflection

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Return to www.reflectometry.net for other resources about reflection and reflectometry.


Please address any comments or report any errors to Professor Adrian R. Rennie at:

Materials Physics, Uppsala University, Sweden.

Adrian.Rennie@physics.uu.se

© Copyright - Programs and Description - A. R. Rennie Last updated 1 November 2015