Iterative reconstruction of a refractive-index profile from x-ray or neutron reflectivity measurements

anaklasis: a compact software package for model-based analysis of specular neutron and X-ray reflectometry data sets

A new software package (anaklasis) for model-based analysis of specular neutron and X-ray reflectivity is introduced. Key features include a user-friendly compact interfacial model definition scheme and a complete set of methods for co-refining data and estimating parameter uncertainty.

anaklasis constitutes a set of open-source Python scripts that facilitate a range of specular neutron and X-ray reflectivity calculations, involving the generation of theoretical curves and the comparison/fitting of interfacial model reflectivity against experimental data sets. The primary focus of the software is twofold: on one hand to offer a more natural framework for model definition, requiring minimum coding literacy, and on the other hand to include advanced analysis methods that have been proposed in recent work. Particular attention is given to the ability to co-refine reflectivity data and to the estimation of model-parameter uncertainty and covariance using bootstrap analysis and Markov chain Monte Carlo sampling. The compactness and simplicity of model definition together with the streamlined analysis do not present a steep learning curve for the user, an aspect that may accelerate the generation of reproducible, easily readable and statistically accurate reports in future neutron and X-ray reflectivity related literature.

Recent Progresses in Nanometer Scale Analysis of Buried Layers and Interfaces in Thin Films by X-rays and Neutrons

In the early 1960s, scientists achieved the breakthroughs in the fields of solid surfaces and artificial layered structures. The advancement of surface science has been supported by the advent of ultra-high vacuum technologies, newly discovered and established scanning probe microscopy with atomic resolution, as well as some other advanced surface-sensitive spectroscopy and microscopy. On the other hand, it has been well recognized that a number of functions are related to the structures of the interfaces, which are the thin planes connecting different materials, most likely by layering thin films. Despite the scientific significance, so far, research on such buried layers and interfaces has been limited, because the probing depth of almost all existing sophisticated analytical methods is limited to the top surface. The present article describes the recent progress in the nanometer scale analysis of buried layers and interfaces, particularly by using X-rays and neutrons. The methods are essentially promising to non-destructively probe such buried structures in thin films. The latest scientific research has been reviewed, and includes applications to bio-chemical, organic, electronic, magnetic, spintronic, self-organizing and complicated systems as well as buried liquid-liquid and solid-liquid interfaces. Some emerging analytical techniques and instruments, which provide new attractive features such as imaging and real time analysis, are also discussed.

Multifitting: software for the reflectometric reconstruction of multilayer nanofilms

Multifitting is a computer program designed specifically for modeling the optical properties (reflection, transmission, absorption) of multilayer films consisting of an arbitrary number of layers in a wide range of wavelengths. Multifitting allows a user to calculate the reflectometric curves for a given structure (direct problem) and to find the parameters of the films from the experimentally obtained curves (inverse problem), either manually or automatically. Key features of Multifitting are the ability to work simultaneously with an arbitrary number of experimental curves and an ergonomic graphical user interface that is designed for intensive daily use in the diagnosis of thin films. Multifitting is positioned by the author as the successor to the IMD program, which has become the standard tool in research and technology groups synthesizing and studying thin-film coatings.

Model-independent recovery of interfacial structure from multi-contrast neutron reflectivity data

An indirect Fourier transform/simulated annealing method exploits the information content of multiple solvent contrast neutron reflectivity data and permits the model-independent recovery of interfacial structure at the air/liquid and solid/liquid interface.

Neutron specular reflectivity at soft interfaces provides sub-nanometre information concerning the molecular distribution of thin films, while the application of contrast variation can highlight the scattering from different parts of the system and lead to an overall reduction in fitting ambiguity. Traditional modelling approaches involve the construction of a trial scattering length density profile based on initial speculation and the subsequent refinement of its parameters through minimization of the discrepancy between the calculated and measured reflectivity. In practice this might produce an artificial bias towards specific sets of solutions. On the other hand, direct inversion of reflectivity data, despite its ability to provide a unique solution, is subject to limitations and experimental complications. Presented here is an integrated indirect Fourier transform/simulated annealing method that, when applied to multiple solvent contrast reflectivity data and within the limits of finite spatial resolution, leads to reliable reconstructions of the interfacial structure without the need for any a priori assumptions. The generality of the method permits its straightforward application in common experimental contrast-variation investigations at the solid/liquid and air/liquid interface.

Surface induced smectic order in ionic liquids - an X-ray reflectivity study of [C22C1im]+[NTf2]. Phys Chem Chem Phys 2018;19:26651-26661. [PMID: 28960006 DOI: 10.1039/c7cp04852a]

Surface induced smectic order was found for the ionic liquid 1-methyl-3-docosylimidazolium bis(trifluoromethlysulfonyl)imide by X-ray reflectivity and grazing incidence scattering experiments. Near the free liquid surface, an ordered structure of alternating layers composed of polar and non-polar moieties is observed. This leads to an oscillatory interfacial profile perpendicular to the liquid surface with a periodicity of 3.7 nm. Small angle X-ray scattering and polarized light microscopy measurements suggest that the observed surface structure is related to fluctuations into a metastable liquid crystalline SmA₂ phase that was found by supercooling the bulk liquid. The observed surface ordering persists up to 157 °C, i.e. more than 88 K above the bulk melting temperature of 68.1 °C. Close to the bulk melting point, we find a thickness of the ordered layer of L = 30 nm. The dependency of L(τ) = Λ ln(τ/τ₁) vs. reduced temperature τ follows a logarithmic growth law. In agreement with theory, the pre-factor Λ is governed by the correlation length of the isotropic bulk phase.

Extended model for the reconstruction of periodic multilayers from extreme ultraviolet and X-ray reflectivity data

An extended model for the reconstruction of multilayer nanostructures from reflectometry data in the X-ray and extreme ultraviolet ranges is proposed. In contrast to the standard model approach, where the transitional region is defined in advance as a specific function, the transition layer is sought as a linear combination of several functions at once in the extended model. This allows one to describe a much wider class of multilayer structures with different dominant physical mechanisms for the formation of transition regions. The extended model occupies an intermediate position between the classical model approach and the so-called model-free methods. The efficiency of the described method is illustrated in detail in numerical simulations and in a real experiment on the annealing of a multilayer Mo/Be mirror.

Element specific monolayer depth profiling

The electronic phase behavior and functionality of interfaces and surfaces in complex materials are strongly correlated to chemical composition profiles, stoichiometry and intermixing. Here a novel analysis scheme for resonant X-ray reflectivity maps is introduced to determine such profiles, which is element specific and non-destructive, and which exhibits atomic-layer resolution and a probing depth of hundreds of nanometers.