In scanning transmission electron microscopy (STEM), real space image quantification allows the counting of the number of atoms in a crystallographic projection, perpendicular to the electron probe. Atom counting is an established method in high-angle annular dark-field (HAADF) imaging and has applications that include the estimation of 3D shapes in metallic nanoparticles [1-2], or local composition variations in high-Z materials with known, constant thickness [3]. The incoherent nature of the HAADF contrast yields a monotonic increase of the image counts with Z, and this allows us to directly interpret image contrast at atomic columns positions as the number of atoms in projection. However, HAADF is only valid for atom counting of heavy elements that scatter strongly at high-angle. Phase imaging techniques are more appropriate for counting light elements because they ensure the collection of weak scattering signals at low angles. Phase methods recover the phase of the electron wavefunction scattered by both light and heavy elements; however, this phase is not directly quantifiable due to coherence [4]. Here, we present a novel approach to phase quantification, based on the combination of HAADF atom counting and electron ptychography. Electron ptychography is a 4D STEM phase technique whereby we recover the complex exit wavefunction from a set of 2D coherent electron diffraction patterns collected over a 2D image grid. Unlike other phase recovery techniques, electron ptychography has the unique advantage that it can be performed simultaneously with HAADF imaging. This allows for atom counting of heavy elements which can be used as means to rescale the ptychographic phase and count the light elements [5-6]. Herein, we apply this novel quantitative ptychographic approach to determine the local sub-stoichiometric composition of CeO_2-x nanoparticles. Fig. 1 (a) illustrates a schematic of the 4D STEM ptychographic method, where the Ce atom count in (b), obtained from the simultaneously recorded HAADF image, is used to calibrate the ptychographic phase in (c) to count O atoms.

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Knowing the 3D atomic structures of materials or biomolecules is crucial for understanding their functions. X-ray diffraction is currently the most important technique for determination of 3D atomic structures, but requires large crystals which are often difficult to obtain. Electrons, similar to X-rays and neutrons, are powerful source for diffraction experiments. Due to the strong interactions between electrons and matter, crystals that are considered as powder in X-ray crystallography can be treated as single crystals by 3D electron diffraction methods [1]. This enables structure determination of materials and organic molecules from micron- to nanometer-sized 3D crystals that are too small for conventional X-ray diffraction. Furthermore, by taking the advantages of the unique properties of electron scattering, it is possible to determine the charge states of atoms/ions [2] and the absolute structure of chiral crystals [3].

Over the past decades, a number of 3D ED methods have been developed for structure determination. At the early stages of 3D ED method development, tilting of the crystal was done manually, while diffraction patterns were collected on negative film. It could take years before sufficient data were obtained and processed in order to determine the crystal structure. The computerization of TEMs and the development of CCD detectors allowed software to be developed that can semi-automatically collect 3D ED data in less than an hour [1]. Thanks to the recent advancement in CMOS and hybrid detector technology, it is now feasible to collect diffraction data in movie mode while continuously rotating the crystal (continuous rotation election diffraction, cRED, also known as MicroED [4] in structural biology). Benefiting from these technological advances, structure determination can now be accomplished within a few hours. Recently, fully automated serial rotation electron diffraction data collection and processing has been realized by our group [5].

By using 3D ED / MicroED methods, we have solved more than 200 novel crystal structures of small inorganic compounds [6] (including zeolite, MOF, COF and minerals) and biomolecules [7,8] (pharmaceuticals, small organic molecules, peptides and proteins) in the past 7 years. Recently, we have solved two novel protein [9,10] structures with 3D ED/MicroED and shown that it is feasible to use MicroED for structure based drug discovery [11]. We aim to further improve these methods, develop new methods and more importantly spread them to labs around the world.

[1] Gemmi M., Mugnaioli E., Gorelik T. E., Kolb U., Palatinus L., Boullay P., Hovmöller S. & Abrahams J. P. (2019). ACS Cent. Sci. 5, 1315–1329.

[2] Yonekura K., Kato K., Ogasawara M., Tomita M. & Toyoshima C. (2015). Proc. Natl. Acad. Sci. 112, 3368–3373.

[3] Brázda P., Palatinus L. & Babor M. (2019). Science. 364, 667–669.

[4] Shi D., Nannenga B. L., Iadanza M. G. & Gonen T. (2013). eLife. 2, e01345.

[5] Wang B., Zou X. & Smeets S. (2019). IUCrJ. 6, 854–867.

[6] Huang Z., Willhammar T. & Zou X. (2021). Chem. Sci. 12, 1206–1219.

[7] Clabbers M. T. B. & Xu H. (2020). Drug Discov. Today Technol., S1740674920300354.

[8] Clabbers M. T. B. & Xu H. (2021). Acta Crystallogr. Sect. Struct. Biol. 77, 313–324.

[9] Xu H., Lebrette H., Clabbers M. T. B., Zhao J., Griese J. J., Zou X. & Högbom M. (2019). Sci. Adv. 5, eaax4621.

[10] Clabbers M. T. B., Holmes S., Muusse T. W., Vajjhala P., Thygesen S. J., Malde A. K., Hunter D. J. B., Croll T. I., Flueckiger L., Nanson J. D., Rahaman H., Aquila A., Hunter M. S., Liang M., Yoon C. H., Zhao J., Zatsepin N. A., Abbey B., Sierecki E., Gambin Y., Stacey K. J., Darmanin C., Kobe B., Xu H. & Ve T. Nat. Commun. (In Press)

[11] Clabbers M. T. B., Fisher S. Z., Coinçon M., Zou X. & Xu H. (2020). Commun. Biol. 3, 417.

The project is supported by the Knut and Alice Wallenberg Foundation (2018.0237, X.Z.), the Swedish Research Council (2017-05333, H.X.; 2019-00815, X.Z.) and the Science for Life Laboratory through the pilot project grant Electron Nanocrystallography, and MicroED@SciLifeLab.

Quantitative convergent-beam electron diffraction (QCBED) has become renowned for its accuracy and precision when it comes to measuring bonding electrostatic potentials and electron densities [1 – 3]. Density functional theory (DFT) needs no introduction because of its ubiquity in materials science and crystallography. It is efficient but compromised in accuracy by the approximations needed to make it less computationally expensive than many-body wave-function calculations. It is also feared by some that DFT is becoming over-parametrised in the bid to deal with the shortcomings of approximations and is therefore “straying from the path toward the exact functional” [4].

We have integrated DFT into QCBED in such a way that allows DFT model parameters, including parameters associated with density functionals, to be refined by fitting DFT-calculated convergent-beam electron diffraction (CBED) patterns to experimental CBED patterns from a real material. We call this QCBED-DFT [5] and illustrate the basic principle of the method in Fig. 1 below.

We will present a number of experimental measurements of density functional parameters such as the Hubbard energy, U, in some strongly correlated electron materials, NiO and CeB₆, from our recently published work [5], as well as some new, unpublished trials.

[1] Zuo, J. -M., Kim, M., O’Keeffe, M. & Spence, J. C. H. (1999). Nature 401, 49.

[2] Nakashima, P. N. H., Smith, A. E., Etheridge, J. & Muddle, B. C. (2011). Science 331, 1583.

[3] A. Genoni, L. Bučinský, N. Claiser, J. Contreras‐García, B. Dittrich, P.M. Dominiak, E. Espinosa, C. Gatti, P. Giannozzi, J. Gillet, D. Jayatilaka, P. Macchi, A.Ø. Madsen, L. Massa, C.F. Matta, K.M. Merz Jr, P.N.H. Nakashima, H. Ott, U. Ryde, K. Schwarz, M. Sierka, S. Grabowsky (2018). Chem. Eur. J. 24, 10881.

[4] Medvedev, M. G., Bushmarinov, I. S., Sun, J., Perdew, J. P. & Lyssenko, K. A. (2017). Science 355, 49.

[5] Peng, D. & Nakashima, P. N. H. (2021). Phys. Rev. Lett. 126, in press.

We thank the late Prof. Andrew Johnson. We are grateful to the Monash Centre for Electron Microscopy where the CBED data were collected. Many thanks to Prof. Joanne Etheridge for her valuable advice throughout this work. PN thanks the Australian Research Council for funding (FT110100427 & DP210100308).

3D electron diffraction (3D ED) undergoes rapid development in the past years. Structure solution is relatively easy, dynamical refinement provides accurate structure models and also absolute structure determination [1], but the accuracy of the lattice parameters remains a problem despite some effort. Lattice parameters obtained by 3D ED have at least an order of magnitude lower accuracy than single crystal x-ray data and the comparison is even worse with powder x-ray data. The reasons causing this poor accuracy are instrument-induced geometrical distortions present in the data and, in case of beam sensitive samples, crystal damage induced by the electron beam. In 2D diffraction patterns, distortions caused by aberrations of electromagnetic lenses are well known and have been analysed several times [2], but the precession assisted data collection induces new distortion, which were never analysed and we quantify and describe them for the first time. For mathematical description, we split the total in-plane difference between the expected and observed position of the diffraction maxima into radial and tangential (Dr and Dt) contributions, which are then described by circular harmonics - function of diffraction vector length r and azimuth j of the diffraction maximum (eq. 1).

Parameters j_r,n, j_t,n, r_n,m and t_n,m need to be determined either by the calibration of the microscope or by the refinement against the diffraction data. This general approach allowed us to compensate for all observed distortions, not only the classical pincushion-barrel, spiral and elliptical. The distortions depend on excitation of the lenses and can be calibrated. Tools for distortion refinement are incorporated in software PETS 2 [3] and distortion refinement workflow may be found in Jana Cookbook example Borane [4].

The effects of geometrical distortions in 3D ED data was so far only marginally analysed [3]. Here we analyse the effects of both the distortions in the plane of diffraction image and also the errors in the crystal orientation. The effect of the accumulated electron dose is also significant (Figure 1). Measurements of anti-B₁₈H₂₂ molecular crystal shows that the beam damage results in lattice parameters increase by about 1.5(5)‰ per accumulated dose of 1 e^-.Å^-2.

Recent developments in the ability to control the shape of metal nanocrystals using wet chemistry synthesis techniques have drawn significant attention for potential applications in plasmonics, photonics and catalysis. It is conjectured that shape control can be achieved by controlling the nanocrystal surface structure, primarily using surfactants and metal additives. For example, various shapes of Au nanoparticles, including rods, cubes, decahedra and octahedra, can be grown selectively using a trace amount of Ag [1] or Cu [2] additives. Understanding the underlying mechanisms of shape control by metal additives is therefore vital for the further engineering of nanocrystals. However, the establishment of atomic structure models of metal additives on the nanocrystal surface, that are just a few atoms wide, is still challenging.

For this aim, there are three essential requirements of the characterisation technique: (1) sufficient chemical sensitivity to distinguish surface additives; (2) spatial resolution at the atomic scale; (3) avoidance of damage to the surface structure from the probe.

Scanning transmission electron microscopy (STEM) has been widely used as a powerful means of resolving atomistic structures of nanocrystals. In this study, we studied the structure of Cu additives on the surface of Au nanocubes using conventional energy dispersive X-ray spectroscopy STEM (EDX-STEM) and high-angle annular dark filed STEM (HAADF-STEM), as well as four-dimensional STEM (4D-STEM) tuned specifically for the detection of surface adatoms.

EDX-STEM mapping reveals the presence of Cu on the {100} surfaces of Au nanocubes. However, the high electron dose required to achieve meaningful statistics can damage the structure during acquisition so a quantitative, high resolution analysis of an undamaged surface is not possible.

HAADF-STEM collects electrons at high angles by an annular detector and presents intensity sensitive to the atomic number (Z), however, it is also sensitive to other material parameters such as thickness and local environments (such as vacuum) [3,4]. We observe the intensity to drop at the nanoparticle atomic surface layer in the HAADF-STEM image but cannot distinguish whether this is due exclusively to the presence of (lower Z) Cu atoms or just fewer atoms on the surface layer. Furthermore, this is a dose-inefficient technique, using only those electrons scattered to high angles, and surface modification can be observed during acquisition.

4D-STEM using a fast pixelated detector records the full diffraction patterns at each probe position during the STEM experiment. The collected 4D datasets enable us to investigate features in diffraction patterns that are specifically related to different material parameters [4]. This method has the advantages of a lower dose than EDX-STEM and access to much more specimen information than HAADF-STEM. In this work, we developed an iterative method by starting with an ideal nanocube model with uniform thickness and with/without surface Cu layers. Dynamic diffraction conditions and scattering angles sensitive to the presence of Cu additives were identified based on the comprehensive dynamical scattering 4D-STEM simulations of this initial model. We then collected experimental 4D-STEM datasets using our optimised imaging conditions, from which Cu adatoms on the surface were evident with excellent contrast. In the next step, a matching of experimental diffraction patterns with simulated diffraction patterns was conducted to determine the realistic surface thickness profile. These allowed us to further refine the nanocube model using the observed surface structure of Cu adatoms and fitted thickness profile for the ultimate 4D-STEM simulations. Excellent agreement was achieved in both qualitative and quantitative comparisons between 4D-STEM simulations and 4D-STEM experiments over various imaging models (which each correspond to different diffraction physics). This suggests that the refined nanocube surface model represents the actual structure of Cu additives on the surface of Au nanocubes. This provides an approach for identifying the type and arrangement of the critical surface atoms that play an important role in controlling the growth and shape of nanoparticles.

[1] Personick, Michelle L., et al. Nano letters 11.8 (2011): 3394-3398. [2] Sun, Jianhua, et al. Crystal Growth and Design 8.3 (2008): 906-910.[3] LeBeau, James M., et al. 100.20 (2008): 206101. [4] Cowley, John. M. Surface Science 114.2-3 (1982): 587-606.[4] Ophus, Colin. Microscopy and Microanalysis 25.3 (2019): 563-582.

Keywords: Metal nanocrystals; Metal additives; Surface structure; 4D-STEM; STEM simulation

This work was carried out on the microscopes at the Monash Centre for Electron Microscopy funded by ARC grant number (LE0454166). This work was supported by ARC funding Discovery Project number DP160104679.

One of major crystallographic challenges is how to determine the structure of severely distorted crystal lattices, such as at a dislocation core and in high entropy alloys where distortion is non-uniform. Here we propose a new 4D scanning transmission electron microscopy (4D-STEM) based technique, called Cepstral STEM, for imaging disordered crystals using electron diffuse scattering. Local fluctuations of diffuse scattering are captured by scanning electron nanodiffraction (SEND) using a coherent probe. The harmonic signals in electron diffuse scattering are detected through Cepstral analysis and used for imaging. By integrating Cepstral analysis with 4D-STEM, we demonstrate that information about the distortive part of electron scattering potential can be separated and imaged at nm spatial resolution. We apply our technique to the analysis of a dislocation core in SiGe and lattice distortions in high entropy alloy [1].

[1] Yu-Tsun Shao, Renliang Yuan, Haw-Wen Hsiao, Qun Yang, Yang Hu, and Jian-Min Zuo, "Cepstral scanning transmission electron microscopy imaging of severe lattice distortions", Ultramicroscopy, 113252 (2021).