Day 1 - Monday, October 23, 2017
Determining 3D Atomic Structure Through Advanced S/TEM Imaging and Analysis.
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 blurs 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) at the Molecular Foundry, which will be critical to our understanding of the atomic structure of complex materials systems.
Electron cryo-tomography in the life sciences.
All living organisms on earth are a complex mixture of proteins, lipids, carbohydrates and nucleic acids which come together in an ordered way to execute essential biological processes necessary for life. As structural cell biologists we want to understand how these processes occur at the resolution of protein structure. Electron cryo-tomography with sub-tomogram averaging is the perfect technique to achieve this aim. Conceived in the 1974 by Walter Hoppe from the Max Planck Institute in Munich (later Martinsried), electron cryo-tomography has undergone rapid development in the last 10 years, making it an extremely powerful and desirable technology. In my talk, I will be describing how we perform electron cryo-tomography, the type of questions we can address, and the recent success stories as well as continuing challenges that still need to be addressed.
Three-dimensional imaging of point defects using quantitative STEM.
Previously, we have shown that HAADF-STEM can provide three-dimensional information of the location of individual dopant atoms in SrTiO3 from a single image. The number of dopant atoms in a column and the depth position information are extracted using quantitative STEM, by comparing the experimental column intensities with calculations for all possible dopant configurations, and determining the most probable dopant position given an experimentally determined noise function. This method is limited by inherent experimental noise (detector noise, sample instability under the beam, sample contamination, surface amorphous layers, sample imperfections, etc.), in particular, when intensity differences between different configurations are small. The contrast and interpretability can be improved using variable-angle HAADF-STEM (VA-HAADF). A key feature of VA-HAADF is that it utilizes information provided by the angular dependence of the scattering in HAADF. The acquisition of multiple variable angle data and use of compound probabilities significantly improved the accuracy and precision of both the number of dopants as well as the their position(s). Configurations that are ambiguous in one detector regime can be resolved in the other. Detecting vacancies in STEM images is even more challenging than dopant atoms that have a large atomic number difference with the host. We have combined VA-HAADF and rigid registration methods to detect Sr vacancies in SrTiO3 and their associated local atom relaxations. Lattice relaxation around the vacancies are detected with picometer precision. Finally, we will discuss recent results on the effects of doping in a Mott insulator materials on the global and local atomic structure.
Imaging electric polarization and probing ferroelectric domain dynamics by advanced electron microscopy.
As advances in transmission electron microscopy (TEM) have enabled the determination of the three-dimensional structure and local properties of materials with the sub-angstrom resolution, the recent development of in situ TEM techniques allows one to follow the dynamic response of nanostructured materials to applied fields. In this talk, I will present our recent TEM studies of the polarization ordering and dynamic domain switching behaviors of ferroelectric/multiferroic thin films. It was found that the charged domain walls can be created or erased by applying a bias, and the resistance of the local film strongly depends on the characteristics of the charged domain walls. It will also be show that the surface monolayer of conducting oxide can induce a giant spontaneous polarization in ultrathin multiferroelectric films and that a peculiar rumpled nanodomain structure, which is in analog to morphotropic phase boundaries (MPB), is formed. Finally, it will be demonstrated that small defects in ferroelectric thin films can act as nano-building-blocks for the emergence of novel topological states of polarization ordering, namely, polarization vortex/anivortex/hedgehog/antihedgehog nanodomain arrays. I will also give an overview of new research opportunities concerning domains in ferroelectric/multiferroic materials.
Atomic Electron Tomography: Adding a New Dimension to See Individual Atoms in Materials.
To understand material properties and functionality at the fundamental level, one must know the 3D positions of atoms with high precision. For crystalline materials, crystallography has provided this information since the pioneering work of Max von Laue, William Henry Bragg, and William Lawrence Bragg over a century ago. However, perfect crystals are rare in nature. Real materials often contain crystal defects, surface reconstructions, nanoscale heterogeneities, and disorders, which strongly influence material properties and performance. Here, we will present atomic electron tomography (AET) for 3D structure determination of crystal defects and disordered materials at the single-atom level. Using a Fourier based iterative algorithm, we first demonstrated electron tomography at 2.4-Å resolution without assuming crystallinity in 2012. We then applied AET to image the 3D structure of grain boundaries and stacking faults and the 3D core structure of edge and screw dislocations at atomic resolution. Furthermore, in combination of AET and atom tracing algorithms, we localized 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. More recently, we determined the 3D coordinates of 6,569 Fe and 16,627 Pt atoms in an FePt nanoparticle, and correlated chemical order/disorder and crystal defects with material properties at the individual atomic level. We identified rich structural variety with unprecedented 3D detail including atomic composition, grain boundaries, anti-phase boundaries, anti-site point defects and swap defects. We showed that the experimentally measured coordinates and chemical species with 22 pm precision can be used as direct input for density functional theory calculations of material properties such as atomic spin and orbital magnetic moments and local magnetocrystalline anisotropy. Looking forward, AET will not only advance our ability in 3D atomic structure determination of crystal defects and disordered materials, but also transform our understanding of materials properties and functionality at the individual atomic level.
1. J. Miao et al., Science 353, aaf2157 (2016).
2. J. Miao, et al., Phys. Rev. B. 72, 052103 (2005).
3. M. C. Scott et al., Nature 483, 444–447 (2012).
4. C. C. Chen et al., Nature 496, 74–77 (2013).
5. R. Xu et al., Nature Mater. 14, 1099-1103 (2015).
6. Y. Yang et al., Nature 542, 75-79 (2017).
7. A. Pryor Jr. et al., Sci. Rep. 7, 10409 (2017).
Low dose atomic resolution tomography and dynamics of nano-objects.
The latest generation of aberration-corrected Transmission Electron Microscopes (TEM) have a resolution and sensitivity that is sufficient to detect even single light atoms from the periodic table of elements and to pinpoint their position with a lateral precision that reaches the wavelength of the imaging electrons. However the depth (z) information remains less certain. For the study of beam-sensitive crystalline nanoparticles such as catalysts and bio-organic structures there is a need for a tomographic method for fast characterization of the shape of pristine particles at atomic resolution . In this presentation we describe a quantitative parameterless 3D reconstruction method that uses the exit wave obtained from only one viewing direction parallel to the atomic columns. In this configuration the strong dynamical scattering yields a signal that is stronger than the incoherent signal in HAADF STEM which allows to minimize the exposure of the object to the incident beam. The method is based on the “channeling” theory  which has all the ingredients for a full 3D quantification of the atomic structure since it is not influenced by channeling in neighboring columns up to thicknesses of tens of nm, so that the exit wave can be analyzed column by column. Furthermore the atoms of a column act as weak lenses, which focus the electron wave periodically with depth so that the exit wave of a column is a very sensitive peaked fingerprint of the “weigth” of the column. Every pixel in the exit wave function is a complex number. The theory of channeling is simple  and provides a way to interpret the exit wave, which can be visualized graphically by plotting the complex values of the pixels in complex 2D space. From the Argand plot of a column we can deduce the position of the column, the defocus distance (with sub-Angstrom precision), the total mass of the column and the residual aberrations . By combining this information we can then reconstruct the object in 3D including profile of top and bottom surface with single atom sensitivity. We have applied this successfully to nanoparticles of Ge, MgO, Au . We also developed a fast method to visualize the vertical position of atoms in a thin sheet and applied it to study the dynamics of thin graphene sheet in real time. We will also show how the approach can be expanded beyond periodic materials to include non-periodic molecular structures and applied it to visoalise a network of randomly oriented oleic acid molecules. And finally will show a new a new tomographic imaging method for biological macromolecules using hollow cone dark field (HCDF) imaging with thermal diffuse scattered electrons that gives about a 4 times contrast increase as compared to bright field imaging. We demonstrate a 3D reconstruction of a stained GroEL particle with HCDF with about 13.5 Å resolution but using a strongly reduced number of images.
1 ) CF Kisielowski, et al., R., Phys Rev. B 88, (2013) 024305
2) Van Dyck, and M. Op de Beeck, Ultramicroscopy 64 (1996), 99-107.
3) A. Wang, F.R. Chen, S. Van Aert,D. Van Dyck, Ultramicr. 110 (2010) 527-534.
4) D. Van Dyck, J.R Jinschek , F.R Chen, Nature 486 (2012), 243-246
5) F.R Chen, C Kisielowski, D. Van Dyck Micron 86 (2015) 59-65
The materials data bank: serving the physical sciences community.
Model-based iterative reconstructions of magnetization and magnetic vector potential for nanoscale magnetic particles.
Vector field tomography refers to the reconstruction of one or more components of a 3D vector field. For magnetic nano-particles, there are several relevant 3D fields: the magnetization M, the magnetic induction B, the demagnetization field H, and the magnetic vector potential A. Among these, the magnetization, i.e., the magnetic moment density as a function of position, is the most fundamental quantity and all others can be derived from it using well-known magnetostatics relations. In this contribution, we begin by reviewing those aspects of Lorentz microscopy that are of importance to the tomographic reconstruction process. Then we describe two applications of the more general approach known as model-based iterative reconstruction (MBIR), which is based on Bayesian concepts. To reconstruct the magnetic vector potential, we combine a forward model for image formation in the TEM with a prior model to formulate the tomographic reconstruction problem as a maximum a-posteriori probability estimation problem (MAP). We define a MAP cost function which we minimize iteratively to determine the magnetic vector potential A. We will present comparisons between simulated and experimental data sets to show that the MBIR approach fields quantifiably better reconstructions that the more traditional vector field tomography approaches based on filtered back-projection.
To reconstruct the magnetization in 3D, we employ a similar forward model and combine it with a prior model that enforces sparsity in the reconstructed magnetic field. The optimization of the cost function is then implemented using the alternate direction method of multipliers (ADMM) theory. Using simulated and real data, we show that our algorithm accurately reconstructs both the magnetization and the magnetic vector potential. Once both M and A are known, it is in principle possible to derive the magnetic induction B and the demagnetization field H; this, in turn, can lead to the extraction of the position dependent demagnetization tensor field. We will present some preliminary results and thoughts concerning this tensor field.
Visualization of Three-Dimensional Magnetization in Magnetic Nanostructures.
Confinement of magnetic structures geometrically as well as energetically leads to novel and unexpected behavior. With advances in fabrication and lithography tools, magnetic structures can be made in complex, confined three-dimensional (3D) geometries at the nanoscale as well as patterned into a variety of interacting lattices. In order to control their behavior, it is necessary to understand the fundamental physics of such interactions along with the influence of physical shape of the nanostructures in 3D.
Lorentz transmission electron microscopy (LTEM) has been extensively used for characterizing magnetization and domains in magnetic structures as it offers a high spatial resolution along with direct visualization of the magnetization. LTEM combined with phase retrieval, can be used to obtain quantitative information about the magnetization and interactions between nanostructures. In this work, we will present results using a dedicated Lorentz microscope equipped with a spherical aberration corrector which offers a highest spatial resolution of 0.5 nm while maintaining the sample in a field free region. We will present a brief introduction to the vector field tomography technique for 3D visualization of magnetization and demonstrate its application to various magnetic systems such as domain walls in shape memory alloys , domains in magnetic heterostructures  and magnetic nanowires .
Figure 1 (a) 3D reconstruction of the Bx component of magnetic induction in Fe-Pd alloy sample indicating the difference between the foil normal and the domain wall direction, (b) 3D reconstruction of complete magnetic induction in and around a Ni nanowire using a single projection.
 C. Phatak, A. K. Petford-Long, and M. De Graef, “Recent advances in Lorentz microscopy,” Curr. Opin. Solid State Mater. Sci., 20(2), 107–114 (2016).
 S. Zhang, A. Petford-long, and C. Phatak, “Three dimensional magnetic field reconstruction of artificial Skyrmion heterostructures,” Microsc. Microanal., 21 (S3), 1959–1960 (2015).
 C. Phatak, L. de Knoop, F. Houdellier, C. Gatel, M. J. Hÿtch, and A. Masseboeuf, “Quantitative 3D electromagnetic field determination of 1D nanostructures from single projection.,” Ultramicroscopy, 164, 24–30 (2016).
Day 2 - Tuesday, October 24, 2017
Utilizing multiple scattering in recovering 3D structural information from TEM data.
One of the very challenging goals in transmission electron microscopy is the
reconstruction of the position and type of every atom in the sample being transmitted by
the electron beam. A number of different approaches for reaching this goal have been
developed, e.g. a combination of model-based interpretations of HAADF-STEM images
of different projections [1,2], compressed-sensing- enhanced tomographic
reconstructions , or straight-forward conventional tomography  – all based on a
monotonous or even linear interpretation of HAADF-STEM image intensities.
While the HAADF-STEM signal is comparatively monotonous with the projected
scattering strength, the HAADF-STEM scattering cross section for a single atom is very
small, especially for low atomic numbers. It is therefore important to extend 3D atomic-
resolution imaging also to imaging modes that are sensitive to the phase shift imposed
by the scattering atom on the wave function of the transmitted electron. However,
multiple elastic scattering, makes the application of linear imaging impossible the
interpretation of such data.
We will present our recently developed approaches to utilize multiple scattering of
electrons to retrieve the three-dimensional distribution of the electrostatic potential of an
arrangement of atoms from a series of HRTEM images , ptychography, or scanning
confocal TEM data . The inversion of multiple scattering also solves the phase
problem in electron crystallography . Along with this recent progress in inverting
multiple scattering novel reconstruction algorithms for atomic-resolution HAADF-STEM
tomography will also be presented .
 S. Van Aert, Nature 470, 374 (2011)
 S. Bals, et al. Nano Lett. 11, 3420 (2011)
 B. Goris et al. Nature Materials 11, 930 (2012)
 C.-C. Chen et al. Nature 496, 74 (2013)
 W. Van den Broek and C.T. Koch, Phys. Rev. Lett. 109, 245502 (2012)
 W. Van den Broek and C.T. Koch, Phys. Rev. B 87, 184108 (2013)
 F. Wang, R.S. Pennington, C.T. Koch, Phys. Rev. Lett. 117, 015501 (2016)
 W. Van den Broek, et al. (2017) in preparation
Exit Wavefunction Reconstruction - current status and future prospects.
Exit wavefunction reconstruction is now firmly established as an important computational method for extracting quantitative information from high-resolution TEM images. The essence of the method is to seek solutions that invert the forward high-resolution phase contrast imaging process to recover the complex wavefunction at the exit surface (or other location) of the specimen from a suitably conditioned dataset of real image intensities.
This approach was originally proposed by Schiske  and subsequently extended by the groups of van Dyck and co-workers in Antwerp  and Saxton and Kirkland  in Cambridge using different input image geometries. For the former a series of axial images was used to extend the directly interpretable resolution limit from that set by the limits of spherical aberration to that imposed by partial coherence, whereas the latter used a tilt azimuth dataset, which enabled super-resolution beyond the axial limit. More recently alternative data sets including ptychography  have also been used for phase retrieval.
This lecture will firstly compare the advantages of the various geometries with respect to recovery of both low and high spatial frequencies and to dose efficiency. I will also discuss the parallel developments in accurate aberration measurement which are required to suitably define the restoration filters used, with respect to approximations in the forward imaging process.
Finally, I will discuss recent advances in which the restored wavefunction can be used to directly infer 3D structural data from local (atomistic) variations in the phase for weakly scattering objects and propose ways in which this could be extended to more general strong objects.
 Schiske P. (1973). In Hawkes P. (Ed.), Image Processing and Computer Aided Design in Electron Optics, London: Academic Press, p. 82.
 van Dyck D. & Coene W. (1984). Ultramicroscopy 15, 29.
 Kirkland A.I., Saxton W.O., Chau K.L., Tsuno K. & Kawasaki M. (1995). Ultramicroscopy 57, 355.
 Gao, S., Wang, P., Zhang, F., Martinez, G.T., Nellist, P.D., Pan, X. and Kirkland, A.I. (2017). Nature Comm., 8, 163.
Phase contrast imaging and simulation in STEM for applications in tomography.
Scanning Transmission Electron Microscopy (STEM) is a very flexible characterization instrument, capable of performing a wide range of imaging, diffraction, and spectroscopic studies, including 3D atomic electron tomography. With the introduction of extremely high speed direct electron detectors, we can now record a full 2D image of the diffracted electron probe at a 2D grid of probe positions, producing a four-dimensional dataset we refer to as a 4D-STEM experiment. In this talk I will describe new (and old) forms of phase contrast imaging made possible 4D-STEM experiments and probe-structuring instrumentation, differential phase contrast (DPC), matched illumination and detector interferometry (MIDI)-STEM, ptychography, and multi-beam STEM holography.
In the second part of this talk, I will present a new algorithm and code for STEM image simulation. Image simulation for scanning transmission electron microscopy at atomic resolution for samples with realistic dimensions can require very large computation times using existing simulation algorithms. We present a new algorithm named PRISM that combines features of the two most commonly used algorithms, namely the Bloch wave and multislice methods. PRISM uses a Fourier interpolation factor f that has typical values of 4–20 for atomic resolution simulations. We show that in many cases PRISM can provide a speedup that scales with f^4 compared to multislice simulations, with a negligible loss of accuracy. I will also present a software package called Prismatic for parallelized simulation of image formation in STEM using both the PRISM and multislice methods. By distributing the workload between multiple CUDA-enabled GPUs and multicore processors, accelerations as high as 1000x for PRISM and 15x for multislice are achieved relative to traditional multislice implementations. Prismatic is freely available both as an open-source CUDA/C++ package with a graphical user interface for Windows and OSX, and as a Python package.
Correlation and modulation in structure.
Correlation and modulation at different length scale are very important phenomena to describe spatial variations/deviations of atoms from a periodic lattice (crystalline) and thereby understand growth and stability of crystals. For the case of large deviations, various approaches might be adopted. About ten years ago, Prof Archie Howie wrote a Chapter on “Extrapolating from Fifty Years Dislocation Imaging-Reaching into the cores” , and a question was posed “where are the atoms?” in icosahedral crystals . Now Electron Image
Tomography (EIT) is beginning to be able to give answers. In this workshop, most of the discussion will be made from the approaches of EIT. However I will try to review the importance of 3D electron diffraction (ED) information. We can vividly observe the effect of structure modulations and correlation on ED intensity distributions over all 3D reciprocal space. This type of structure modulation can be described by “density modulation” and “phase modulation” through a crystal structure factor, and these modulations are normally coupled. Information obtained through (3D-EDT) will give a unique value for not only obtaining a structure solution but also various deviations especially “phase modulation”. These will play an important role in understanding pairwise interaction between/among atoms.
In this conceptual talk I will discuss the usefulness and advantages of 3D-EDT for the study of modulations/correlations by taking examples of fcc-based alloys both commensurate and incommensurate , incommensurate microporous SiO 2 crystal with AlPO 4 -5 type structure  and zeolite intergrowths . Dr Peter Oleynikov will present some recent experimental results obtained by 3D-EDT as well as its technical aspects.
 Turning Points in Solid-State, Materials and Surface Science, Royal Society Chemistry 2008, eds by Keneth DM Harris and Peter P Edwards, Chap. 41.
 Icosahedral Crystals: Where Are the Atoms ? Per Bak, PRL, 56, 1986, 861.
 Study of the Incommensurate Tw-Dimensional Antiphase Structure of Au 3+ Zn by High Voltage, High Resolution Electron Microscopy, Osamu Terasaki, J Phys Soc Jpn, 51, 1982, 2159
 Incommensurate modulation in the microporous silica SSZ-24, Z. Liu et. Al, Chem, European Journal, 8
First woven covalent organic framework solved using electron crystallography.
Making fabric by weaving is known as one of the oldest and most enduring methods. Nevertheless such an important design concept still needs to be emulated in extended chemical structures. Linking molecules into weaving structures would be of a great help to create materials with exceptional mechanical properties and dynamics. For this purpose a woven covalent organic framework-505 (COF-505) has been synthesized using a designed strategy . However, COF-505 is not well crystallized, which gives rise to a poorly resolved PXRD pattern. Therefore, approaches based on electron crystallography methods have been used. The structure of this COF has been solved by a combination of 3D electron diffraction tomography (3D EDT, ), high-resolution TEM imaging and structure modeling.
3D EDT dataset was collected from a single sub-micron crystal in a tilting range of –41.3° to +69.1°. The reconstructed 3D reciprocal lattice was identified as a C-centered orthorhombic Bravais lattice with the unit cell parameters of a = 18.9 Å, b = 21.3 Å, c = 30.8 Å, and V = 12399 Å3, which have been used to index reflections observed in both PXRD pattern and Fourier diffractograms of HRTEM images. The derived reflection conditions were summarized as hkl: h+k = 2n; hk0: h, k = 2n; h0l: h = 2n and 0kl: k = 2n, leading to five possible space groups (s.g.): Cm2a (39), Cc2a (41), Cmca (64), Cmma (67) and Ccca (68). Cm2a, Cmma and Ccca were excluded because their projected plane group symmetries along [1-10] do not coincide with those of the experimental HRTEM images (pgg). Furthermore, by performing Fourier analysis of the HRTEM images and imposing symmetry to the reflections, Cu(I) positions were determined from the reconstructed 3D potential map (Fig. 1). The structure of COF-505 was built in Materials Studio by putting Cu(PDB)2 units at copper positions and connecting them through biphenyl (reacted BZ) molecules (Fig. 2). The chemical composition was determined by the elemental analysis, which indicated that the unit-cell framework is constructed by 8 Cu(PDB)2 and 16 biphenyl units. However, symmetry operations of the s.g. Cmca require two PDB units connected to one copper onto a mirror plane perpendicular to the a–axis that is not the energetically favorable geometry. The final s.g. determined as Cc2a and was used to build and optimize a structure model. The PXRD pattern calculated from the model is consistent with the experimental pattern of activated COF-505.
Figure 1. Electron microscopy studies of COF-505. (A) HRTEM image of COF-505 taken with the [1‑10] incidence. (B) 2D reciprocal plane of the reconstructed 3D reciprocal lattice of COF-505 (3D-EDT data). (C) 2D projected potential map obtained by imposing pgg plane symmetry on Fig 1A. (D) Reconstructed 3D electrostatic potential map (threshold: 0.8).
Figure 2. Crystal structure of COF-505. The weaving structure (left) of COF-505 consists of chemically identical helices (right, marked in blue and yellow as they are of opposite chirality) with the pitch of 14.2 Å. The yellow helices propagate in the [1-10] direction, while the blue helices propagate in the  direction with copper (I) ions as the points-of-registry.
 Y. Liu, Y. Ma, Y. Zhao, X. Sun, F. Gandara, H. Furukawa, Z. Liu, H. Zhu, C. Zhu, K. Suenaga, P. Oleynikov, A. S. Alshammari, X. Zhang, O. Terasaki, O. M. Yaghi. Weaving of organic threads into a crystalline covalent organic framework. Science, 351 (2016) 365–369.
 M. Gemmi, P. Oleynikov. Scanning reciprocal space for solving unknown structures: energy filtered diffraction tomography and rotation diffraction tomography methods. Z. Krist. 228 (2013) 51–58.
Correlative Microscopy of Three-Dimensional Nanostructures.
Microstructure in general is defined by the type, structure, number, shape, and topological arrangements of phases and/or lattice defects. Microstructure determination by electron microscopy typically is carried in projection and in 2D. Characterization of complex nanostructures, however, requires three-dimensional (3D) structure and composition determination. Transmission electron diffraction (TED) and the related imaging are appropriate techniques for 3D nanostructure determination because they are highly sensitive to local atomic structure. Similarly, recent developments in the technology of multi-detector EDS or ultraviolet laser assisted local-electrode atom probe tomography (APT) have made 3D composition determination possible. Thus, there is a great potential in combining the above approaches together. Here, I will describe the
progresses we have made in 1) atomic scale structure, strain and composition determination in semiconductor nanostructures  using a combination of aberration corrected scanning transmission electron microscopy (STEM), X-ray diffraction and APT, and 2) the diffraction based determination of 3D nanostructured TiN thin-films . Future developments that combine atomic scale defects determination and 3D nanostructure determination will be discussed.
Fig. Reconstructed nanosized columnar grains and their orientations in sputter deposited TiN thin film. Side (a), front (b) and top view (c) of the 3D morphologies of reconstructed grains. (A Sigma-9 grain is indicated by the arrows) (d) Orientations of the seven grains. Each cube is labelled by the color used to represent the grain. From Ref. 2
 H. Kim et al., Journal of Applied Physics 113 (10), 103511 (2013).
 Y. F. Meng and J. M. Zuo, IUCrJ 3, 300 (2016).
From atom probe tomography imaging to microstructural quantification.
One of the currently most limiting factors limiting the impact of atom probe tomography on advancing the understanding of materials microstructures is the lack of a robust theoretical structure justifying the reconstructed images and chemical analyses. The fact that the evaporated structure is only known from the reconstruction and thus entirely depends on the underlying theoretical assumptions used in the reconstruction algorithm makes a systematic quantification of chemical and spatial errors and uncertainties in general very hard to impossible. Efforts to overcome these limitations exist both on the experimental and the modeling sides. Forward modeling, for example, focuses on the evaporation process and the resulting evaporation sequences on the atomistic scale, and the direct comparison between experimentally acquired and virtually generated data allows quantification of errors in reconstructed samples. In this talk, we show that the effect of local surface structure as well as density variations in the material can be modeled by ab-initio modeling of evaporation fields based on the so-called “Müller model”, and discuss possible extensions that will allow a more comprehensive modeling of metallic samples with full structural complexity.