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In this study, we added vacancies adjacent to a Si/Ge interface to create a disordered structure. The structure was then relaxed using various strategies. We applied Procrustes shape analysis for disorder quantification and identifying different local atomic environments.

Feature extraction and a neural network model are applied to predict the defect types and concentrations in experimental TiO$_2$ samples. A dataset of TiO$_2$ structures with vacancies and interstitials of oxygen and titanium is built and the structures are relaxed using energy minimization. The features of the calculated pair distribution functions (PDFs) of these defected structures are extracted using linear methods (principal component analysis, non-negative matrix factorization) and non-linear methods (autoencoder, convolutional neural network). The extracted features are used as the inputs to a neural network that maps the feature weights to the concentration of each defect type. The performance of this machine learning pipeline is validated by predicting the defect concentrations based on experimentally-measured TiO$_2$ PDFs and comparing the results to brute-force predictions. A physics-based initialization of the autoencoder has the highest accuracy in predicting the defect concentrations. This model incorporates physical interpretability and predictability of material properties, enabling a more efficient material characterization process with scattering data.

A workflow is presented for performing pair distribution function (PDF) analysis of defected materials using structures generated from atomistic simulations. A large collection of structures, which differ in the types and concentrations of defects present, are obtained through energy minimization with an empirical interatomic potential. Each of the structures is refined against an experimental PDF. The structures with the lowest goodness of fit $R_w$ values are taken as being representative of the experimental structure. The workflow is applied to anatase titanium dioxide ($a$-TiO$_2$) and tetragonal zirconium dioxide ($t$-ZrO$_2$) synthesized in the presence of microwave radiation, a low temperature process that generates disorder. The results suggest that titanium vacancies and interstitials are the dominant defects in $a$-TiO$_2$, while oxygen vacancies dominate in $t$-ZrO$_2$. Analysis of the atomic displacement parameters extracted from the PDF refinement and mean squared displacements calculated from molecular dynamics simulations indicate that while these two quantities are closely related, it is challenging to make quantitative comparisons between them. The workflow can be applied to other materials systems, including nanoparticles.

We investigate the effect of pore size and shape on the thermal conductivity of a series of idealized metal-organic frameworks (MOFs) containing adsorbed gas using molecular simulations., We investigate the effect of pore size and shape on the thermal conductivity of a series of idealized metal-organic frameworks (MOFs) containing adsorbed gas using molecular simulations. With no gas present, the thermal conductivity decreases with increasing pore size. In the presence of adsorbed gas, MOFs with smaller pores experience reduced thermal conductivity due to phonon scattering introduced by gas–crystal interactions. In contrast, for larger pores (>1.7 nm), the adsorbed gas does not significantly affect thermal conductivity. This difference is due to the decreased probability of gas–crystal collisions in larger pore structures. In contrast to MOFs with simple cubic pores, the thermal conductivity in structures with triangular and hexagonal pore channels exhibits significant anisotropy. For different pore geometries at the same atomic density, hexagonal channel MOFs have both the highest and lowest thermal conductivities, along and across the channel direction, respectively. In the triangular and hexagonal channeled structures, the presence of gas molecules has different effects on thermal conductivity along different crystallographic directions.