Deep Bayesian local crystallography

Sergei V Kalinin,Mani Valleti,Rama K Vasudevan,Maxim Ziatdinov,Raphael P Hermann,Junjie Zhang,Hong Zheng,Wenrui Zhang,Gyula Eres,Mark P Oxley

doi:10.1038/s41524-021-00621-6

Abstract

The advent of high-resolution electron and scanning probe microscopy imaging has opened the floodgates for acquiring atomically resolved images of bulk materials, 2D materials, and surfaces. This plethora of data contains an immense volume of information on materials structures, structural distortions, and physical functionalities. Harnessing this knowledge regarding local physical phenomena necessitates the development of the mathematical frameworks for extraction of relevant information. However, the analysis of atomically resolved images is often based on the adaptation of concepts from macroscopic physics, notably translational and point group symmetries and symmetry lowering phenomena. Here, we explore the bottom-up definition of structural units and symmetry in atomically resolved data using a Bayesian framework. We demonstrate the need for a Bayesian definition of symmetry using a simple toy model and demonstrate how this definition can be extended to the experimental data using deep learning networks in a Bayesian setting, namely rotationally invariant variational autoencoders.

Highlights

Macroscopic symmetry is one of the central concepts in the modern condensed matter physics and materials science[1,2,3,4,5,6]
Symmetry concepts arrived with the advent of X-ray methods developed by Bragg, and for almost a century remained the primary and natural language of physics
Symmetry-based descriptors have emerged as a foundational element of condensed matter physics and materials science alike

Summary

Introduction

Macroscopic symmetry is one of the central concepts in the modern condensed matter physics and materials science[1,2,3,4,5,6]. Symmetry concepts arrived with the advent of X-ray methods developed by Bragg, and for almost a century remained the primary and natural language of physics. Symmetry-based descriptors have emerged as a foundational element of condensed matter physics and materials science alike. The natural counterpart of symmetry-based descriptors is the concept of physical building blocks. Systems such as Penrose structures[8,9,10,11,12,13] possess well-defined building blocks but undefined translation symmetry. The amenability of symmetry-based descriptors have led to much deeper insights into the structure and functionalities of materials with translational symmetries compared to (partially) disordered systems[23,24,25]

Objectives

Methods

Results