Codes for: Solving Complex Nanostructures With Ptychographic Atomic Electron Tomography

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 \SI{17}{\pico\meter} 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.