Understanding the properties of thin films is crucial for their application in materials science, from gaining insights into physical phenomena at the nanoscale to advancing applied technologies. An effective method for analyzing these properties is X-ray diffraction (XRD), which provides detailed information about the crystal structures of materials.Among the features observed in the XRD patterns, Laue oscillations, or diffraction intensity oscillations near the main diffraction peaks, offer insights into the thickness, surface roughness, and layering of thin films.Despite their potential, Laue oscillations have not been fully utilized in quantitative analyses owing to difficulties such as the nonlinearity of the data, involvement of both discrete and continuous parameters, and risk of converging on incorrect local minima in conventional curve-fitting methods.

This study presents a novel approach to address these challenges using Bayesian statistics and the replica exchange Monte Carlo (REMC) method.Bayesian statistics enable precise parameter estimation and qualify the uncertainty associated with these estimates, which is essential for reliable data interpretation. The Markov Chain Monte Carlo (MCMC) method is a powerful statistical tool for exploring complex parameter spaces and computing Bayesian posterior distributions.REMC, an extension of MCMC, enhances convergence efficiency by running multiple MCMC simulations at different energy levels (or “temperatures”) and allowing exchanges between them. This approach mitigates the risk of stagnation in the local optima by enabling detailed exploration of the parameter space.

A key strength of this flexible Bayesian framework is its ability to evaluate different statistical models, such as those based on Gaussian and Poisson noise, directly from experimental data. This data-driven methodology allows for selecting the most appropriate noise models that best capture the data.In addition to the numerical comparison of Bayes factors, this process provides researchers with an intuitive understanding of the analysis results and builds confidence in conclusions by displaying the predictive distribution.More importantly, the principles and benefits of this methodology extend beyond Laue oscillation analysis, providing a generalizable framework for analyzing experimental data across diverse scientific fields.

To demonstrate the effectiveness of this approach, real experimental data from iron selenide (FeSe) thin films were analyzed.The results demonstrate that this method enables accurate quantitative analysis of Laue oscillations, including thickness and surface roughness, while providing comprehensive uncertainty assessment.By integrating Bayes factor-based decision-making and qualitative validation with predictive distributions, this study establishes a robust and adaptable strategy for experimental analysis across various scientific disciplines.
(Written by Yuki Sakishita on behalf of all the authors.)

Share this topic

Fields