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

A perfect crystal is a purely theoretical concept. Real-world crystals contain imperfections, also called defects, which influence the properties of materials. In this study, we revise the concept of defects and propose a universal strategy for their characterization using statistical distances.

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The ability of crystalline materials to fulfill a set of design criteria is controlled by static and kinetic properties of defects in the material. Identification and characterization of defects provide the crucial information for interpretation of simulations and experiments that bridge the gap between atomic- and micrometer-scales. But what is actually a concept of defects at the atomic scale? Where does the defect start and where does it end? How to define the spreading of the defect within the crystalline lattice and to understand its impact on the energy landscape of materials? In this study, we try to answer these questions using machine learning (ML) methods and introduce a novel concept of the distortion scores of local atomic environments to reinforce the modern methods of materials modeling.

We propose the distortion score of local atomic environments that describes a statistical distance from a reference structure, which, for example, can be a perfect crystal structure. Based on these distortion scores, we identify structural defects as atoms-outliers deviating from the reference structure. This score facilitates automatic localization of defects and enables their stratified description, which allows to distinguish the zones with different levels of distortion within the structure. The method is well adapted for the detection of structural defects and for monitoring their trajectories, as well as for tracking the structural changes during phase transitions or crystallization. 

Interestingly, when computing the distortion scores with respect to the underlying perfect crystal structure, there is conjecture between the computed scores and the local atomic energy (i.e., the proposed distortion score exhibits a correlation with the local atomic energy). Taking into account that the distortion scores are computed solely from the geometrical information, this conjecture appeared surprising for us. Trying to better understand the origin of this correlation, we found that, from a mathematical point of view, there is a similitude between the formalism that describes the local atomic energy of materials in quantum mechanics (QM) and the statistical distances based on the sample covariance matrix. Inspired by the QM formalism, we propose a panel of statistical distances that allow for a good agreement with the local energies. This finding opens up many perspectives in the field of computational materials science.  In the paper, we demonstrate the applications ranging from the surrogate concept for the energy per atom to the selection of the relevant structural information for the evaluation of energy barriers (Figure 1). The proposed definition of defects serves to reinforce not only the performance of traditional approaches but also of modern ML methods in materials science. In this work, we have demonstrated how the new concept of distortion scores can be applied for the design and improvement of ML interatomic potentials. 

 Figure 1. Proposed applications of the distortion scores for materials modeling

In perspective, the notion of distortion scores based on statistical distances can be extended beyond the structural properties of defects and numerical methods of materials characterization. The present concept can be useful for the organization and classification of multivariate data provided by experimental techniques, where the atomic coordinates are provided, such as atom probe or transmission electron microscopy tomography.  

For more information, please check out our paper:

Goryaeva, A.M., Lapointe, C., Dai, C., Dérès, J., Maillet, J.B., Marinica, M.C.  Reinforcing materials modelling by encoding the structures of defects in crystalline solids into distortion scores. Nat Commun 11, 4691 (2020). https://doi.org/10.1038/s41467-020-18282-2

Alexandra Goryaeva

postdoc, CEA Paris-Saclay

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