Three-dimensional coordinates of individual atoms in materials revealed by electron tomography

TL;DR

This paper demonstrates a novel electron tomography method that accurately determines the 3D positions of individual atoms in materials with high precision, without assuming crystallinity, enabling detailed atomic-scale analysis.

Contribution

The authors introduce a technique to locate thousands of individual atoms in 3D with ~19 pm precision, surpassing traditional crystallography limitations.

Findings

Achieved atomic coordinate determination with ~19 pm precision.

Measured atomic displacement and strain tensors at ~1 nm^3 resolution.

Validated results with density functional theory and molecular dynamics simulations.

Abstract

Crystallography, the primary method for determining the three-dimensional (3D) atomic positions in crystals, has been fundamental to the development of many fields of science. However, the atomic positions obtained from crystallography represent a global average of many unit cells in a crystal. Here, we report, for the first time, the determination of the 3D coordinates of thousands of individual atoms and a point defect in a material by electron tomography with a precision of ~19 picometers, where the crystallinity of the material is not assumed. From the coordinates of these individual atoms, we measure the atomic displacement field and the full strain tensor with a 3D resolution of ~1nm^3 and a precision of ~10^-3, which are further verified by density functional theory calculations and molecular dynamics simulations. The ability to precisely localize the 3D coordinates of individual atoms in materials without assuming crystallinity is expected to find important applications in materials science, nanoscience, physics and chemistry.