Atomic electron tomography: 3D structures without crystals
Authors: Miao Jianwei , Ercius Peter , Billinge Simon J. L. 
Published: September 2016

BACKGROUND
To understand material properties and functionality at the most fundamental level, one must know the three-dimensional (3D) positions of atoms with high precision. For crystalline materials, x-ray crystallography has provided this information since the pioneering work of Max von Laue, William Henry Bragg, and William Lawrence Bragg around 100 years ago. But perfect crystals are rare in nature. Real materials often contain defects, surface reconstructions, nanoscale heterogeneities, and disorders, which strongly influence material properties and performance. Completely different approaches from crystallography are needed to determine the 3D atomic arrangement of crystal defects and noncrystalline systems. Although single-particle cryo–electron microscopy (cryo-EM) has been under rapid development for 3D structure determination of macromolecules with identical or similar conformations at near-atomic resolution, this method cannot be generally applied to the physical sciences for the following three reasons. First, most materials do not have identical copies and cannot be averaged to achieve atomic resolution. Second, a priori knowledge of the peptide sequence and stereochemistry in protein molecules greatly facilitates their 3D atomic structure determination, but this knowledge is not applicable to physical science samples. Third, unlike in biological specimens, the presence of diffraction and phase contrast in the transmission electron microscopy images of most materials poses a challenge for tomographic reconstruction.These difficulties have made the objective of solving the 3D atomic structure of crystal defects and noncrystalline systems a major challenge for structural characterization in the physical sciences.

ADVANCES
Major developments in aberration-corrected electron microscopes, advanced detectors, data acquisition methods, powerful 3D image reconstruction, and atom-tracing algorithms have placed one method—atomic electron tomography (AET)—on the cusp of this breakthrough. In recent years, AET has been used to image the 3D structure of grain boundaries and stacking faults and the 3D core structure of edge and screw dislocations at atomic resolution. This technique has also revealed the existence of atomic steps at 3D twin boundaries that are hidden in conventional 2D projections. Furthermore, the combination of AET and atom-tracing algorithms has enabled the determination of the coordinates of individual atoms and point defects in materials with a 3D precision of ~19 pm, allowing direct measurements of 3D atomic displacements and the full strain tensor. Finally, the single-particle reconstruction method developed in cryo-EM has been applied for 3D structure determination of small (≤2-nm) gold nanoparticles and heterogeneous platinum nanocrystals at atomic-scale resolution.

OUTLOOK
The future research frontiers of AET involve increasing the sample complexity (including real materials with different atomic species and disordered systems), image contrast (determining the 3D atomic positions of both heavy and light elements), detection sensitivity (revealing individual atoms at surfaces and interfaces), and data acquisition speed (probing the dynamics of individual atoms and defects). The ability to precisely determine all atomic coordinates and species in real materials without assuming crystallinity will transform our understanding of structure-property relationships at the most fundamental level. For instance, using atomic coordinates as inputs to first-principles calculations, it is possible to compute the effect on the material properties of each defect and atomic reorganization, giving precious clues about how to modify and engineer materials at the atomic level to yield better performance in a device. Catalysis involves atoms interacting on nanoparticle surfaces in poorly understood ways, and the mechanisms of particle growth in synthesis reactors or in devices under load are largely unknown. Breakthroughs in our ability to reliably measure this information in 3D will have effects across disciplines from electronics and catalysis to energy conversion.

Atomic electron tomography (AET) and its transformative impact on the physical sciences.

(
Top
) Schematic diagram of AET, in which 2D images are measured with an advanced electron microscope by tilting a sample to many different orientations. The 3D structure of the sample is iteratively reconstructed from the images, and the coordinates of individual atoms are localized. (
Bottom
) AET enables 3D imaging of crystal defects—such as grain boundaries, stacking faults, dislocations, and point defects—at atomic resolution. The ability to precisely determine the 3D coordinates of individual atoms allows direct measurements of atomic displacements and the full strain tensor in materials.