Insights into cation ordering of double perovskite oxides from machine learning and causal relations

This work investigates the origins of cation ordering of double perovskites using first-principles theory computations combined with machine learning (ML) and causal relations. We have considered various oxidation states of A, A', B, and B' from the family of transition metal ions to construct a diverse compositional space. A conventional framework employing traditional ML classification algorithms such as Random Forest (RF) coupled with appropriate features including geometry-driven and key structural modes leads to highly accurate prediction (~98%) of A-site cation ordering. We have evaluated the accuracy of ML models by entailing analyses of decision paths, assignments of probabilistic confidence bound, and finally introducing a direct non-Gaussian acyclic structural equation model to investigate causality. Our study suggests that the structural modes are the most important features for classifying layered, columnar and rock-salt ordering. For clear layered ordering, the charge difference between the A and A' is the most important feature which in turn depends on the B, B' charge separation. Based on the outputs from ML models, we have designed functional forms with these features to derive energy differences forming clear layered ordering. The trilinear coupling between tilt, rotation, and A-site antiferroelectric displacement in Landau free-energy expansion becomes the necessary condition behind the formation of A-site cation ordering

AtomAI: A Deep Learning Framework for Analysis of Image and Spectroscopy Data in (Scanning) Transmission Electron Microscopy and Beyond

AtomAI is an open-source software package bridging instrument-specific Python libraries, deep learning, and simulation tools into a single ecosystem. AtomAI allows direct applications of the deep convolutional neural networks for atomic and mesoscopic image segmentation converting image and spectroscopy data into class-based local descriptors for downstream tasks such as statistical and graph analysis. For atomically-resolved imaging data, the output is types and positions of atomic species, with an option for subsequent refinement. AtomAI further allows the implementation of a broad range of image and spectrum analysis functions, including invariant variational autoencoders (VAEs). The latter consists of VAEs with rotational and (optionally) translational invariance for unsupervised and class-conditioned disentanglement of categorical and continuous data representations. In addition, AtomAI provides utilities for mapping structure-property relationships via im2spec and spec2im type of encoder-decoder models. Finally, AtomAI allows seamless connection to the first principles modeling with a Python interface, including molecular dynamics and density functional theory calculations on the inferred atomic position. While the majority of applications to date were based on atomically resolved electron microscopy, the flexibility of AtomAI allows straightforward extension towards the analysis of mesoscopic imaging data once the labels and feature identification workflows are established/available. The source code and example notebooks are available at https://github.com/pycroscopy/atomai

Describing condensed matter from atomically resolved imaging data: from structure to generative and causal models

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

Bridging microscopy with molecular dynamics and quantum simulations: An AtomAI based pipeline

Recent advances in (scanning) transmission electron microscopy have enabled routine generation of large volumes of high-veracity structural data on 2D and 3D materials, naturally offering the challenge of using these as starting inputs for atomistic simulations. In this fashion, theory will address experimentally emerging structures, as opposed to the full range of theoretically possible atomic configurations. However, this challenge is highly non-trivial due to the extreme disparity between intrinsic time scales accessible to modern simulations and microscopy, as well as latencies of microscopy and simulations per se. Addressing this issue requires as a first step bridging the instrumental data flow and physics-based simulation environment, to enable the selection of regions of interest and exploring them using physical simulations. Here we report the development of the machine learning workflow that directly bridges the instrument data stream into Python-based molecular dynamics and density functional theory environments using pre-trained neural networks to convert imaging data to physical descriptors. The pathways to ensure the structural stability and compensate for the observational biases universally present in the data are identified in the workflow. This approach is used for a graphene system to reconstruct optimized geometry and simulate temperature-dependent dynamics including adsorption of Cr as an ad-atom and graphene healing effects. However, it is universal and can be used for other material systems

Anomalous Polarization Reversal in Strained Thin Films of CuInP2_2S6_6

Strain-induced transitions of polarization reversal in thin films of a ferrielectric CuInP$_2$S$_6$ (CIPS) with ideally-conductive electrodes is explored using the Landau-Ginzburg-Devonshire (LGD) approach with an eighth-order free energy expansion in polarization powers. Due to multiple potential wells, the height and position of which are temperature- and strain-dependent, the energy profiles of CIPS can flatten in the vicinity of the non-zero polarization states. This behavior differentiates these materials from classical ferroelectrics with the first or second order ferroelectric-paraelectric phase transition, for which potential energy profiles can be shallow or flat near the transition point only, corresponding to zero spontaneous polarization. Thereby we reveal an unusually strong effect of the mismatch strain on the out-of-plane polarization reversal, hysteresis loops shape, dielectric susceptibility, and piezoelectric response of CIPS films. In particular, by varying the sign of the mismatch strain and its magnitude in a narrow range, quasi-static hysteresis-less paraelectric curves can transform into double, triple, and other types of pinched and single hysteresis loops. The strain effect on the polarization reversal is opposite, i.e., "anomalous", in comparison with many other ferroelectric films in that the out-of-plane remanent polarization and coercive field increases strongly for tensile strains, meanwhile the polarization decreases or vanish for compressive strains. We explain the effect by "inverted" signs of linear and nonlinear electrostriction coupling coefficients of CIPS and their strong temperature dependence. For definite values of temperature and mismatch strain, the low-frequency hysteresis loops of polarization may exhibit negative slope in the relatively narrow range of external field amplitude and frequency.Comment: 26 pages, including 8 figures and 1 Appendi

Direct Fabrication of Atomically Defined Pores in MXenes

Controlled fabrication of nanopores in atomically thin two-dimensional material offers the means to create robust membranes needed for ion transport, nanofiltration, and DNA sensing. Techniques for creating nanopores have relied upon either plasma etching or direct irradiation using electrons or ions; however, aberration-corrected scanning transmission electron microscopy (STEM) offers the advantage of combining a highly energetic, sub-angstrom sized electron beam for atomic manipulation along with atomic resolution imaging. Here, we utilize a method for automated nanopore fabrication with real-time atomic visualization to enhance our mechanistic understanding of beam-induced transformations. Additionally, an electron beam simulation technique, Electron-Beam Simulator (E-BeamSim) was developed to observe the atomic movements and interactions resulting from electron beam irradiation. Using the 2D MXene Ti3C2Tx, we explore the influence of temperature on nanopore fabrication by tracking atomic transformation pathways and find that at room temperature, electron beam irradiation induces random displacement of atoms and results in a pileup of titanium atoms at the nanopore edge. This pileup was confirmed and demonstrated in E-BeamSim simulations around the small, milled area in the MXene monolayer. At elevated temperatures, the surface functional groups on MXene are effectively removed, and the mobility of atoms increases, which results in atomic transformations that lead to the selective removal of atoms layer by layer. Through controllable manufacture using e-beam milling fabrication, the production and then characterization of the fabricated defects can be better understood for future work. This work can lead to the development of defect engineering techniques within functionalized MXene layers.Comment: Experimental and simulations on the electron beam interactions with MXene monolayers to form nanopores as a function of temperatur

Bending-induced isostructural transitions in ultrathin layers of van der Waals ferrielectrics

Using Landau-Ginzburg-Devonshire (LGD) phenomenological approach we analyze the bending-induced re-distribution of electric polarization and field, elastic stresses and strains inside ultrathin layers of van der Waals ferrielectrics. We consider a CuInP2S6 (CIPS) thin layer with fixed edges and suspended central part, the bending of which is induced by external forces. The unique aspect of CIPS is the existence of two ferrielectric states, FI1 and FI2, corresponding to big and small polarization values, which arise due to the specific four-well potential of the eighth-order LGD functional. When the CIPS layer is flat, the single-domain FI1 state is stable in the central part of the layer, and the FI2 states are stable near the fixed edges. With an increase of the layer bending below the critical value, the sizes of the FI2 states near the fixed edges decreases, and the size of the FI1 region increases. When the bending exceeds the critical value, the edge FI2 states disappear being substituted by the FI1 state, but they appear abruptly near the inflection regions and expand as the bending increases. The bending-induced isostructural FI1-FI2 transition is specific for the bended van der Waals ferrielectrics described by the eighth (or higher) order LGD functional with consideration of linear and nonlinear electrostriction couplings. The isostructural transition, which is revealed in the vicinity of room temperature, can significantly reduce the coercive voltage of ferroelectric polarization reversal in CIPS nanoflakes, allowing for the curvature-engineering control of various flexible nanodevices.Comment: 26 pages, 7 figures and Appendices A-