Advice on describing Bayesian analysis of neutron and X-ray reflectometry

As a result of the availability of modern software and hardware, Bayesian analysis is becoming more popular in neutron and X-ray reflectometry analysis. The understandability and replicability of these analyses may be harmed by inconsistencies in how the probability distributions central to Bayesian methods are represented in the literature. Herein advice is provided on how to report the results of Bayesian analysis as applied to neutron and X-ray reflectometry. This includes the clear reporting of initial starting conditions, the prior probabilities, the results of any analysis and the posterior probabilities that are the Bayesian equivalent of the error bar, to enable replicability and improve understanding. It is believed that this advice, grounded in the authors' experience working in the field, will enable greater analytical reproducibility in the work of the reflectometry community, and improve the quality and usability of results.

Faster and lower-dose X-ray reflectivity measurements enabled by physics-informed modeling and artificial intelligence co-refinement

An approach is presented for analysis of real-time X-ray reflectivity (XRR) process data not just as a function of the magnitude of the reciprocal-space vector q, as is commonly done, but as a function of both q and time. The real-space structures extracted from the XRR curves are restricted to be solutions of a physics-informed growth model and use state-of-the-art convolutional neural networks (CNNs) and differential evolution fitting to co-refine multiple time-dependent XRR curves R(q, t) of a thin film growth experiment. Thereby it becomes possible to correctly analyze XRR data with a fidelity corresponding to standard fits of individual XRR curves, even if they are sparsely sampled, with a sevenfold reduction of XRR data points, or if the data are noisy due to a 200-fold reduction in counting times. The approach of using a CNN analysis and of including prior information through a kinetic model is not limited to growth studies but can be easily extended to other kinetic X-ray or neutron reflectivity data to enable faster measurements with less beam damage.

Structural investigation of sulfobetaines and phospholipid monolayers at the air-water interface

Mixtures of sulfobetaine based lipids with phosphocholine phospholipids are of interest in order to study the interactions between zwitterionic surfactants and the phospholipids present in cell membranes. In this study we have investigated the structure of mixed monolayers of sulfobetaines and phosphocholine phospholipids. The sulfobetaine used has a single 18-carbon tail, and is referred to as SB3-18, and the phospholipid used is DMPC. Surface pressure-area isotherms of the samples were used to determine whether any phase transitions were present during the compression of the monolayers. Neutron and X-ray reflectometry were then used to investigate the structure of these monolayers perpendicular to the interface. We found that the average headgroup and tail layer thickness was reasonably consistent across all mixtures, with a variation of less than 3 Å reported in the total thickness of the monolayers at each surface pressure. However, by selective deuteration of the two components of the monolayers, it was found that the two components have different tail layer thicknesses. For the mixture with equal compositions of DMPC and SB3-18 or with a higher composition of DMPC the tail tilts were found to be constant, resulting in a greater tail layer thickness for SB3-18 due to its longer tail. For the mixture higher in SB3-18 this was not the case, the tail tilt angle for the two components was found to be different and DMPC was found to have a greater tail layer thickness than SB3-18 as a result.

A general approach to maximise information density in neutron reflectometry analysis

Neutron and x-ray reflectometry are powerful techniques facilitating the study of the structure of interfacial materials. The analysis of these techniques is ill-posed in nature requiring the application of model-dependent methods. This can lead to the over- and under- analysis of experimental data when too many or too few parameters are allowed to vary in the model. In this work, we outline a robust and generic framework for the determination of the set of free parameters that are capable of maximising the information density of the model. This framework involves the determination of the Bayesian evidence for each permutation of free parameters; and is applied to a simple phospholipid monolayer. We believe this framework should become an important component in reflectometry data analysis and hope others more regularly consider the relative evidence for their analytical models.