Determining atomic coordinates in 3D by atomic electron tomography
Authors: Ercius Peter , Xu Rui , Chen Chien‐Chun , Wu Li , Scott Mary , Theis Wolfgang , Ophus Colin , Park Jungwon , Elmlund Hans , Zett Alex , Alivisatos A. Paul , Miao Jianwei 
Published: December 2016

At a basic level, materials properties depend on the three‐dimensional arrangement of atoms, and it is necessary to determine their coordinates to make correlative measurements of structure and functionality from basic principles. Traditional 3D reconstruction techniques (such as X‐ray crystallography and single‐particle Cryo‐Em) continue to provide critical insights into structure/property relationships but average over many identical structures. This will blur out the defects inherent to inhomogeneous nanoengineered materials important to their functionality. Aberration‐corrected HR‐TEM and HAADF‐STEM are now indispensable techniques in materials science to examine the atomic structure of materials systems with sub‐Å resolution and single atom sensitivity. Combining these new tools with powerful iterative 3D reconstruction and peak finding algorithms for electron tomography is opening a new field with the ability to determine atomic coordinates of all atoms in a structure without the assumption of crystallinity. This talk will cover recent develops and future directions of Atomic Electron Tomography (AET), which will be critical to our understanding of the atomic structure of complex materials systems.
HAADF‐STEM and the equally sloped tomography method were recently used to determine the atomic coordinates of 3,769 atoms in 9 atomic layers at the apex of an etched tungsten needle (Figure 1) [1]. A tungsten point defect was unambiguously located in the material for the first time in three‐dimensions. Comparing the experimental positions to the ideal bcc tungsten lattice produces the atomic displacement field with ±19 pm precision. Kernel density estimation applied to the differentiation of the displacement field was used to calculate the 6 components of the strain tensor with ~1 nm 3D spatial resolution indicating expansion along the [011] axis (x‐axis) and compression along the [100] axis (y‐axis). It was determined by experiments, DFT simulations and MD simulations that the strain in the lattice was due to a surface layer of tungsten carbide and sub‐surface carbon. This result shows the capabilities of AET to measure atomic coordinates of inhomogeneous objects without the assumption of crystallinity providing and the capability of directly measuring materials properties.
Measurements of material structure in their native environment are now being accomplished using in‐situ TEM, but has been limited by the thickness of the SiN windows and the contained liquid volume. A recent advance in this field was the introduction of the graphene liquid cell (GLC) to minimize the combined window/liquid thickness allowing observation of the growth and coalescence of colloidal Pt nanoparticles at atomic resolution [2]. It was discovered that stable NPs in the GLC were randomly rotating thus providing many orientations that could be reconstructed using methods developed in single‐particle Cryo‐Em. A direct electron detector and aberration‐corrected HR‐TEM were combined with a GLC in a technique called 3D SINGLE (3D Structure Identification of Nanoparticles by Graphene Liquid Cell EM) to determine the atomic‐scale facets, lattice plane orientations and multi‐twinned grain structure of a Pt nanoparticle in liquid with 2.10 Å resolution (Figure 2) [3]. The particle is constructed of three distinct regions: a central disk region of well‐ordered {111} atomic planes with conical protrusions attached on each side connected by screw dislocations.