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The wealth of properties in functional materials at the nanoscale has attracted tremendous interest over the last decades, spurring the development of ever more precise and ingenious characterization techniques. In ferroelectrics, for instance, scanning probe microscopy based techniques have been used in conjunction with advanced optical methods to probe the structure and properties of nanoscale domain walls, revealing complex behaviours such as chirality, electronic conduction or localised modulation of mechanical response. However, due to the different nature of the characterization methods, only limited and indirect correlation has been achieved between them, even when the same spatial areas were probed. Here, we propose a fast and unbiased analysis method for heterogeneous spatial data sets, enabling quantitative correlative multi-technique studies of functional materials. The method, based on a combination of data stacking, distortion correction, and machine learning, enables a precise mesoscale analysis. When applied to a data set containing scanning probe microscopy piezoresponse and second harmonic generation polarimetry measurements, our workflow reveals behaviours that could not be seen by usual manual analysis, and the origin of which is only explainable by using the quantitative correlation between the two data sets.

Piezoresponse force microscopy (PFM) is routinely used to probe the nanoscale electromechanical response of ferroelectric and piezoelectric materials. However, many challenges remain in the interpretation of the recovered signal. Specifically, many non‐ferroelectric contributions affect the measured response, ranging from electrostatics, to charge injection and trapping, and topographic cross‐talk. Recently, machine learning (ML) has been utilized to identify multiple contributors within complex data systems, such as PFM response. A substantial advancement in ML approaches for PFM techniques is offered by dimensional stacking, enabling encoding of physical and/or chemical correlations within the materials' response across different data dimensions spanning varying ranges. However, dimensional stacking requires appropriate scaling for each dimension (before ML analysis) to minimize undesired information loss. Here, the impact of clustering globally and locally scaled parameters in polarization switching experiments via resonant PFM (RPFM) are discussed. Specifically, dimensional stacking of scaled parameters can mask or enhance ferroelectric and non‐ferroelectric behaviors, and aid identification of various physical phenomena contributing to the measured RPFM response. This study highlights the importance of data curation for ML, and its role in identifying signal contributors to scanning probe microscopy (SPM)‐based techniques with multidimensional data, such as resonant and/or spectroscopic SPM.

Despite remarkable advances in characterization techniques of functional materials yielding an ever growing amount of data, the interplay between the physical and chemical phenomena underpinning materials’ functionalities is still often poorly understood. Dimensional reduction techniques have been used to tackle the challenge of understanding materials’ behavior, leveraging the very large amount of data available. Here, we present a method for applying physical and chemical constraints to dimensional reduction analysis, through dimensional stacking. Compared to traditional, uncorrelated techniques, this approach enables a direct and simultaneous assessment of behaviors across all measurement parameters, through stacking of data along specific dimensions as required by physical or chemical correlations. The proposed method is applied to the nanoscale electromechanical relaxation response in (1 − x)PMN-xPT solid solutions, enabling a direct comparison of electric field- and chemical composition-dependent contributors. A poling-like, and a relaxation-like behavior with a domain glass state are identified, and their evolution is tracked across the phase diagram. The proposed dimensional stacking technique, guided by the knowledge of the underlying physics of correlated systems, is valid for the analysis of any multidimensional dataset, opening a spectrum of possibilities for multidisciplinary use.

Machine‐learning techniques are more and more often applied to the analysis of complex behaviors in materials research. Frequently used to identify fundamental behaviors within large and multidimensional datasets, these techniques are strictly based on mathematical models. Thus, without inherent physical or chemical meaning or constraints, they are prone to biased interpretation. The interpretability of machine‐learning results in materials science, specifically materials’ functionalities, can be vastly improved through physical insights and careful data handling. The use of techniques such as dimensional stacking can provide the much needed physical and chemical constraints, while proper understanding of the assumptions imposed by model parameters can help avoid overinterpretation. These concepts are illustrated by application to recently reported ferroelectric switching experiments in PbZr_0.2Ti_0.8O₃thin films. Through systematic analysis and introduction of physical constraints, it is argued that the behaviors present are not necessarily due to exotic mechanisms previously suggested, but rather well described by classical ferroelectric switching superimposed by non‐ferroelectric phenomena, such as electrochemical deformation, electrostatic interactions, and/or charge injection.