Determining Three-Dimensional Atomic Coordinates in Materials via Electron Tomography
The paper presents a significant advancement in electron tomography, highlighting the ability to determine the three-dimensional coordinates of individual atoms in materials without assuming crystallinity. This is achieved using a combination of aberration-corrected scanning transmission electron microscopy (STEM) and equal slope tomography (EST). The authors have demonstrated the capability of this methodology by determining the positions of 3,769 individual tungsten atoms, achieving a precision of approximately 19 picometers.
Historically, crystallography has been the cornerstone for resolving atomic positions in materials, providing average positions across many unit cells. However, individual atomic resolution, particularly in non-crystalline materials, has remained a challenge since Richard Feynman's 1959 call to locate individual atoms using electron microscopy. This paper addresses that challenge by integrating advanced STEM imaging with EST reconstruction, enabling unprecedented precision in localizing atoms individually.
The experimental workflow entailed acquiring 62 tilt images of a tungsten needle using an aberration-corrected STEM running in annular dark field mode. These images underwent a series of preprocessing steps to correct for drift and scan distortions before being reconstructed into a 3D representation using EST. The authors employed two noise reduction schemes—Wiener filtering and a sparsity-based denoising algorithm—to improve the reconstruction's quality and reliability. Atom tracing was then performed, resulting in the identification of 3,641 common atoms from independent reconstructions and an additional 128 atoms that passed further validation.
The paper's emphasis on measuring the atomic displacement field and full strain tensor holds particular relevance for materials characterization, offering 3D spatial resolution of ~1 nm and precision of ~10-3. Such precision, confirmed through density functional theory (DFT) calculations and molecular dynamics (MD) simulations, allows for a detailed understanding of strain and defects within materials. The authors highlighted the role of surface tungsten carbide (WC) and carbon diffusion in altering the atomic structure, demonstrating the practical implications of their methodology in assessing material properties.
This technique goes beyond existing methods that primarily apply to crystalline samples and provides a direct imaging capability for materials with diverse structural morphologies, including amorphous states. The implications of these findings extend to fields such as nanoscience, materials engineering, and chemistry, where understanding atomic-level phenomena is crucial. As the methodology is refined and adapted to other materials, it promises to enhance our capacity to characterize and innovate across various scientific and engineering disciplines.
Looking ahead, the potential applications of this research are vast. Not only does it hold promise for enhancing the precision of strain measurements in nanostructures and devices, but it also opens new avenues for the investigation of defects and interfaces, enabling a deeper understanding and control over material properties and functionalities. Moreover, as computational techniques continue to evolve and complement experimental methods, the integration of these insights with larger-scale models could pave the way for novel material design strategies.