Neighbors Map: an Efficient Atomic Descriptor for Structural Analysis

Accurate structural analysis is essential to gain physical knowledge and understanding of atomic-scale processes in materials from atomistic simulations. However, traditional analysis methods often reach their limits when applied to crystalline systems with thermal fluctuations, defect-induced distortions, partial vitrification, etc. In order to enhance the means of structural analysis, we present a novel descriptor for encoding atomic environments into 2D images, based on a pixelated representation of graph-like architecture with weighted edge connections of neighboring atoms. This descriptor is well adapted for Convolutional Neural Networks and enables accurate structural analysis at a low computational cost. In this paper, we showcase a series of applications, including the classification of crystalline structures in distorted systems, tracking phase transformations up to the melting temperature, and analyzing liquid-to-amorphous transitions in pure metals and alloys. This work provides the foundation for robust and efficient structural analysis in materials science, opening up new possibilities for studying complex structural processes, which can not be described with traditional approaches

Efficient and transferable machine learning potentials for the simulation of crystal defects in bcc Fe and W

Data-driven, or machine learning (ML), approaches have become viable alternatives to semiempirical methods to construct interatomic potentials, due to their capacity to accurately interpolate and extrapolate from first-principles simulations if the training database and descriptor representation of atomic structures are carefully chosen. Here, we present highly accurate interatomic potentials suitable for the study of dislocations, point defects, and their clusters in bcc iron and tungsten, constructed using a linear or quadratic input-output mapping from descriptor space. The proposed quadratic formulation, called quadratic noise ML, differs from previous approaches, being strongly preconditioned by the linear solution. The developed potentials are compared to a wide range of existing ML and semiempirical potentials, and are shown to have sufficient accuracy to distinguish changes in the exchange-correlation functional or pseudopotential in the underlying reference data, while retaining excellent transferability. The flexibility of the underlying approach is able to target properties almost unattainable by traditional methods, such as the negative divacancy binding energy in W or the shape and the magnitude of the Peierls barrier of the 1 2 ⟨ 111 ⟩ screw dislocation in both metals. We also show how the developed potentials can be used to target important observables that require large time-and-space scales unattainable with first-principles methods, though we emphasize the importance of thoughtful database design and degrees of nonlinearity of the descriptor space to achieve the appropriate passage of information to large-scale calculations. As a demonstration, we perform direct atomistic calculations of the relative stability of 1 2 ⟨ 111 ⟩ dislocations loops and three-dimensional C15 clusters in Fe and find the crossover between the formation energies of the two classes of interstitial defects occurs at around 40 self-interstitial atoms. We also compute the kink-pair formation energy of the 1 2 ⟨ 111 ⟩ screw dislocation in Fe and W, finding good agreement with density functional theory informed line tension models that indirectly measure those quantities. Finally, we exploit the excellent finite-temperature properties to compute vacancy formation free energies with full anharmonicity in thermal vibrations. The presented potentials thus open up many avenues for systematic investigation of free-energy landscape of defects with ab initio accuracy

Prediction of mechanical twinning in magnesium silicate post-perovskite

The plastic properties of MgSiO(3) post-perovskite are considered to be one of the key issues necessary for understanding the seismic anisotropy at the bottom of the mantle in the so-called D" layer. Although plastic slip in MgSiO(3) post-perovskite has attracted considerable attention, the twinning mechanism has not been addressed, despite some experimental evidence from low-pressure analogues. On the basis of a numerical mechanical model, we present a twin nucleation model for post-perovskite involving the emission of 1/6 partial dislocations. Relying on first-principles calculations with no adjustable parameters, we show that {110} twin wall formation resulting from the interaction of multiple twin dislocations occurs at a twinning stress comparable in magnitude to the most readily occurring slip system in post-perovskite. Because dislocation activities and twinning are competitive strain-producing mechanisms, twinning should be considered in future models of crystallographic preferred orientations in post-perovskite to better interpret seismic anisotropy in the lowermost lower mantle

Calculation of dislocation binding to helium-vacancy defects in tungsten using hybrid ab initio-machine learning methods

Calculations of dislocation-defect interactions are essential to model metallic strength, but the required system sizes are at or beyond ab initio limits. Current estimates thus have extrapolation or finite size errors that are very challenging to quantify. Hybrid methods offer a solution, embedding small ab initio simulations in an empirical medium. However, current implementations can only match mild elastic deformations at the ab initio boundary. We describe a robust method to employ linear-in-descriptor machine learning potentials as a highly flexible embedding medium, precisely matching dislocation migration pathways whilst keeping at least the elastic properties constant. This advanced coupling allows dislocations to cross the ab initio boundary in fully three dimensional defect geometries. Investigating helium and vacancy segregation to edge and screw dislocations in tungsten, we find long-range relaxations qualitatively change impurity-induced core reconstructions compared to those in short periodic supercells, even when multiple helium atoms are present. We also show that helium-vacancy complexes, considered to be the dominant configuration at low temperatures, have only a very weak binding to screw dislocations. These results are discussed in the context of recent experimental and theoretical studies. More generally, our approach opens a vast range of mechanisms to ab initio investigation and provides new reference data to both validate and improve interatomic potentials

Reinforcing materials modelling by encoding the structures of defects in crystalline solids into distortion scores

International audienceThis work revises the concept of defects in crystalline solids and proposes a universal strategy for their characterization at the atomic scale using outlier detection based on statistical distances. The proposed strategy provides a generic measure that describes the distortion score of local atomic environments. This score facilitates automatic defect localization and enables a stratified description of defects, which allows to distinguish the zones with different levels of distortion within the structure.This work proposes applications for advanced materials modelling ranging from the surrogate concept for the energy per atom to the relevant information selection for evaluation of energy barriers from the mean force.Moreover, this concept can serve for design of robust interatomic machine learning potentials and high-throughput analysis of their databases. The proposed definition of defects opens up many perspectives for materials design and characterisation, promoting thereby the development of novel techniques in materials science

Robust crystal structure identification at extreme conditions using a density-independent spectral descriptor and supervised learning

The increased time- and length-scale of classical molecular dynamics simulations have led to raw data flows surpassing storage capacities, necessitating on-the-fly integration of structural analysis algorithms. As a result, algorithms must be computationally efficient, accurate, and stable at finite temperature to reliably extract the relevant features of the data at simulation time. In this work, we leverage spectral descriptors to encode local atomic environments and build crystal structure classification models. In addition to the classical way spectral descriptors are computed, i.e. over a fixed radius neighborhood sphere around a central atom, we propose an extension to make them independent from the material's density. Models are trained on defect-free crystal structures with moderate thermal noise and elastic deformation, using the linear discriminant analysis (LDA) method for dimensionality reduction and logistic regression (LR) for subsequent classification. The proposed classification model is intentionally designed to be simple, incorporating only a limited number of parameters. This deliberate simplicity enables the model to be trained effectively even when working with small databases. Despite the limited training data, the model still demonstrates inherent transferability, making it applicable to a broader range of scenarios and datasets. The accuracy of our models in extreme conditions is compared to traditional algorithms from the literature, namely adaptive common neighbor analysis (a-CNA), polyhedral template matching (PTM) and diamond structure identification (IDS). Finally, we showcase two applications of our method: tracking a solid-solid BCC-to-HCP phase transformation in Zirconium at high pressure up to high temperature, and visualizing stress-induced dislocation loop expansion in single crystal FCC Aluminum containing a Frank-Read source, at high temperature