[Paper Review] Solving Complex Nanostructures With Ptychographic Atomic Electron Tomography

Philipp Pelz, Sinéad M. Griffin+7 more|arXiv (Cornell University)|Jun 17, 2022

Advanced Electron Microscopy Techniques and Applications49 references4 citations

TL;DR

This paper introduces ptychographic atomic electron tomography (PAET), a method combining ptychographic phase contrast imaging with electron tomography to achieve sub-atomic resolution 3D structural determination of beam-sensitive and light-element-containing nanomaterials. Using mixed-state ptychography on a double-walled carbon nanotube with a Zr-Te core, the authors resolve the full Zr₁₁Te₅₀ structure with 17 pm precision, identifying a previously unobserved ZrTe₂ phase.

ABSTRACT

Transmission electron microscopy (TEM) is a potent technique for the determination of three-dimensional atomic scale structure of samples in structural biology and materials science. In structural biology, three-dimensional structures of proteins are routinely determined using phase-contrast single-particle cryo-electron microscopy from thousands of identical proteins, and reconstructions have reached atomic resolution for specific proteins. In materials science, three-dimensional atomic structures of complex nanomaterials have been determined using a combination of annular dark field (ADF) scanning transmission electron microscopic (STEM) tomography and subpixel localization of atomic peaks, in a method termed atomic electron tomography (AET). However, neither of these methods can determine the three-dimensional atomic structure of heterogeneous nanomaterials containing light elements. Here, we perform mixed-state electron ptychography from 34.5 million diffraction patterns to reconstruct a high-resolution tilt series of a double wall-carbon nanotube (DW-CNT), encapsulating a complex $\mathrm{ZrTe}$ sandwich structure. Class averaging of the resulting reconstructions and subpixel localization of the atomic peaks in the reconstructed volume reveals the complex three-dimensional atomic structure of the core-shell heterostructure with 17 picometer precision. From these measurements, we solve the full $\mathrm{Zr_{11}Te_{50}}$ structure, which contains a previously unobserved $\mathrm{ZrTe_{2}}$ phase in the core. The experimental realization of ptychographic atomic electron tomography (PAET) will allow for structural determination of a wide range of nanomaterials which are beam-sensitive or contain light elements.

Motivation & Objective

• To overcome the limitations of conventional atomic electron tomography (AET) in imaging beam-sensitive and light-element-containing nanomaterials.
• To develop a phase-contrast electron tomography method that preserves structural integrity while achieving atomic resolution.
• To enable the structural determination of complex, heterogeneous nanostructures such as core-shell heterostructures with light elements.
• To validate the method on a double-walled carbon nanotube encapsulating a complex Zr-Te compound with unknown phases.

Proposed method

• Employed mixed-state electron ptychography on a 4D STEM dataset acquired across a tilt series of a double-walled carbon nanotube (DW-CNT) with a Zr-Te core.
• Used the LSQML algorithm for iterative reconstruction of the complex wavefunction and phase-contrast projections from 34.5 million diffraction patterns.
• Applied class averaging and subpixel localization of atomic peaks in the reconstructed 3D volume to determine atomic positions with 17 pm precision.
• Combined experimental reconstructions with simulated datasets using the PRISM algorithm to validate structural fidelity under partial spatial and temporal coherence.
• Performed density functional theory (DFT) calculations using the optB86b-vdW functional to validate the stability and chemical assignment of atomic species.
• Used symmetry indicators and band structure analysis to characterize the topological nature of the Zr-Te phases.

Experimental results

Research questions

• RQ1 Can ptychographic phase contrast imaging enable high-resolution 3D atomic structure determination of beam-sensitive and light-element-containing nanomaterials?
• RQ2 What is the three-dimensional atomic arrangement of the Zr-Te core within a double-walled carbon nanotube, including previously unobserved phases?
• RQ3 To what extent can subpixel localization and class averaging resolve atomic positions with 17 pm precision in complex heterogeneous nanostructures?
• RQ4 How does the experimental ptychographic reconstruction compare to simulated data under realistic coherence and probe conditions?
• RQ5 What is the thermodynamic stability and chemical assignment of the Zr-Te phases, particularly the newly identified ZrTe₂ phase?

Key findings

• The method achieved a 3D atomic resolution of 17 pm in the reconstructed volume, with a median position error of 10 pm between experimental and simulated coordinates.
• The full Zr₁₁Te₅₀ structure was solved, revealing a previously unobserved ZrTe₂ phase in the core, confirmed by DFT calculations.
• The reconstructed 3D volume showed minimal structural damage after the tilt series, with only minor defects visible post-imaging.
• Class-averaged ptychographic reconstructions showed high signal-to-noise ratio and matched well with simulated data, validating the method's accuracy.
• DFT calculations using the optB86b-vdW functional produced lattice parameters for bulk ZrTe₅ that closely matched experimental values at 10 K.
• Chemical assignment of atoms was confirmed by comparing nearest-neighbor environments and DFT energy minimization, assigning Zr to columns with >4 nearest neighbors and Te to those with ≤4.