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Register a new userDescribing condensed matter from atomically resolved imaging data: from structure to generative and causal models
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The development of high-resolution imaging methods such as electron and scanning probe microscopy and atomic probe tomography have provided a wealth of information on structure and functionalities of solids. The availability of this data in turn necessitates development of approaches to derive quantitative physical information, much like the development of scattering methods in the early XX century which have given one of the most powerful tools in condensed matter physics arsenal. Here, we argue that this transition requires adapting classical macroscopic definitions, that can in turn enable fundamentally new opportunities in understanding physics and chemistry. For example, many macroscopic definitions such as symmetry can be introduced locally only in a Bayesian sense, balancing the prior knowledge of materials physics and experimental data to yield posterior probability distributions. At the same time, a wealth of local data allows fundamentally new approaches for the description of solids based on construction of statistical and physical generative models, akin to Ginzburg-Landau thermodynamic models. Finally, we note that availability of observational data opens pathways towards exploring causal mechanisms underpinning solid structure and functionality.
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Atomic structures and adatom geometries of surfaces encode information about the thermodynamics and kinetics of the processes that lead to their formation, and which can be captured by a generative physical model. Here we develop a workflow based on a machine learning-based analysis of scanning tunneling microscopy images to reconstruct the atomic and adatom positions, and a Bayesian optimization procedure to minimize statistical distance between the chosen physical models and experimental observations. We optimize the parameters of a 2- and 3-parameter Ising model describing surface ordering and use the derived generative model to make predictions across the parameter space. For concentration dependence, we compare the predicted morphologies at different adatom concentrations with the dissimilar regions on the sample surfaces that serendipitously had different adatom concentrations. The proposed workflow is universal and can be used to reconstruct the thermodynamic models and associated uncertainties from the experimental observations of materials microstructures. The code used in the manuscript is available at https://github.com/saimani5/Adatom_interactions.
Exploration of structure-property relationships as a function of dopant concentration is commonly based on mean field theories for solid solutions. However, such theories that work well for semiconductors tend to fail in materials with strong correlations, either in electronic behavior or chemical segregation. In these cases, the details of atomic arrangements are generally not explored and analyzed. The knowledge of the generative physics and chemistry of the material can obviate this problem, since defect configuration libraries as stochastic representation of atomic level structures can be generated, or parameters of mesoscopic thermodynamic models can be derived. To obtain such information for improved predictions, we use data from atomically resolved microscopic images that visualize complex structural correlations within the system and translate them into statistical mechanical models of structure formation. Given the significant uncertainties about the microscopic aspects of the materials processing history along with the limited number of available images, we combine model optimization techniques with the principles of statistical hypothesis testing. We demonstrate the approach on data from a series of atomically-resolved scanning transmission electron microscopy images of Mo$_x$Re$_{1-x}$S$_2$ at varying ratios of Mo/Re stoichiometries, for which we propose an effective interaction model that is then used to generate atomic configurations and make testable predictions at a range of concentrations and formation temperatures.
An approach for the analysis of atomically resolved scanning transmission electron microscopy data with multiple ferroic variants in the presence of imaging non-idealities and chemical variabilities based on a rotationally invariant variational autoencoder (rVAE) is presented. We show that an optimal local descriptor for the analysis is a sub-image centered at specific atomic units, since materials and microscope distortions preclude the use of an ideal lattice as a reference point. The applicability of unsupervised clustering and dimensionality reduction methods is explored and are shown to produce clusters dominated by chemical and microscope effects, with a large number of classes required to establish the presence of rotational variants. Comparatively, the rVAE allows extraction of the angle corresponding to the orientation of ferroic variants explicitly, enabling straightforward identification of the ferroic variants as regions with constant or smoothly changing latent variables and sharp orientational changes. This approach allows further exploration of the chemical variability by separating the rotational degrees of freedom via rVAE and searching for remaining variability in the system. The code used in the manuscript is available at https://github.com/saimani5/ferroelectric_domains_rVAE.
Atom probe tomography (APT) helps elucidate the link between the nanoscale chemical variations and physical properties, but it has limited structural resolution. Field ion microscopy (FIM), a predecessor technique to APT, is capable of attaining atomic resolution along certain sets of crystallographic planes albeit at the expense of elemental identification. We demonstrate how two commercially-available atom probe instruments, one with a straight flight path and one fitted with a reflectron-lens, can be used to acquire time-of-flight mass spectrometry data concomitant with a FIM experiment. We outline various experimental protocols making use of temporal and spatial correlations to best discriminate field evaporated signals from the large field ionised background signal, demonstrating an unsophisticated yet efficient data mining strategy to provide this discrimination. We discuss the remaining experimental challenges that need be addressed, notably concerned with accurate detection and identification of individual field evaporated ions contained within the high field ionised flux that contributes to a FIM image. Our hybrid experimental approach can, in principle, exhibit true atomic resolution with elemental discrimination capabilities, neither of which atom probe nor field ion microscopy can individually fully deliver - thereby making this new approach, here broadly termed analytical field ion microscope (aFIM), unique.
Materials characterization remains a significant, time-consuming undertaking. Generally speaking, spectroscopic techniques are used in conjunction with empirical and ab-initio calculations in order to elucidate structure. These experimental and computational methods typically require significant human input and interpretation, particularly with regards to novel materials. Recently, the application of data mining and machine learning to problems in material science have shown great promise in reducing this overhead. In the work presented here, several aspects of machine learning are explored with regards to characterizing a model material, titania, using solid-state Nuclear Magnetic Resonance (NMR). Specifically, a large dataset is generated, corresponding to NMR $^{47}$Ti spectra, using ab-initio calculations for generated TiO$_2$ structures. Principal Components Analysis (PCA) reveals that input spectra may be compressed by more than 90%, before being used for subsequent machine learning. Two key methods are used to learn the complex mapping between structural details and input NMR spectra, demonstrating excellent accuracy when presented with test sample spectra. This work compares Support Vector Regression (SVR) and Artificial Neural Networks (ANNs), as one step towards the construction of an expert system for solid state materials characterization.
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