Transport of intensity phase retrieval of arbitrary wave fields including vortices.

The phase problem can be considered as one of the cornerstones of quantum mechanics intimately connected to the detection process and the uncertainty relation. The latter impose fundamental limits on the manifold phase reconstruction schemes invented to date, in particular, at small magnitudes of the quantum wave. Here, we show that a rigorous solution of the transport of intensity reconstruction (TIE) scheme in terms of a linear elliptic partial differential equation for the phase provides reconstructions even in the presence of wave zeros if particular boundary conditions are given. We furthermore discuss how partial coherence hampers phase reconstruction and show that a modified version of the TIE reconstructs the curl-free current density at arbitrary (in)coherence. Our results open the way for TIE-based phase retrieval of arbitrary wave fields, eventually containing zeros such as phase vortices.

Observation of the Larmor and Gouy rotations with electron vortex beams.

Electron vortex beams carrying intrinsic orbital angular momentum (OAM) are produced in electron microscopes where they are controlled and focused by using magnetic lenses. We observe various rotational phenomena arising from the interaction between the OAM and magnetic lenses. First, the Zeeman coupling, proportional to the OAM and magnetic field strength, produces an OAM-independent Larmor rotation of a mode superposition inside the lens. Second, when passing through the focal plane, the electron beam acquires an additional Gouy phase dependent on the absolute value of the OAM. This brings about the Gouy rotation of the superposition image proportional to the sign of the OAM. A combination of the Larmor and Gouy effects can result in the addition (or subtraction) of rotations, depending on the OAM sign. This behavior is unique to electron vortex beams and has no optical counterpart, as Larmor rotation occurs only for charged particles. Our experimental results are in agreement with recent theoretical predictions.

Experimental evidence for oxygen sublattice control in polar infinite layer SrCuO2.

A recent theoretical study [Phys. Rev. B 85, 121411(R) (2012)] predicted a thickness limit below which ideal polar cuprates turn nonpolar driven by the associated electrostatic instability. Here we demonstrate this possibility by inducing a structural transformation from the bulk planar to chainlike structure upon reducing the SrCuO2 repeat thickness in SrCuO2/SrTiO3 superlattices with unit-cell precision. Our results, based on structural investigation by x-ray diffraction and high resolution scanning transmission electron microscopy, demonstrate that the oxygen sublattice can essentially be built by design. In addition, the electronic structure of the chainlike structure, as studied by x-ray absorption spectroscopy, shows the signature for preferential hole occupation in the Cu 3d(3z2-r2) orbital, which is different from the planar case.

Nanoscale investigation of the degradation mechanism of a historical chrome yellow paint by quantitative electron energy loss spectroscopy mapping of chromium species.

Getting the picture: The investigation of 100 year old chrome yellow paint by transmission electron microscopy and spectroscopy has led to the identification of four types of core-shell particles. This nanoscale investigation has allowed a mechanism to be proposed for the darkening of some bright yellow colors in Van Gogh's paintings (e.g. in Falling leaves (Les Alyscamps), 1888).

Convexity constraints on linear background models for electron energy-loss spectra.

In this paper convexity constraints are derived for a background model of electron energy loss spectra (EELS) that is linear in the fitting parameters. The model outperforms a power-law both on experimental and simulated backgrounds, especially for wide energy ranges, and thus improves elemental quantification results. Owing to the model's linearity, the constraints can be imposed through fitting by quadratic programming. This has important advantages over conventional nonlinear power-law fitting such as high speed and a guaranteed unique solution without need for initial parameters. As such, the need for user input is significantly reduced, which is essential for unsupervised treatment of large datasets. This is demonstrated on a demanding spectrum image of a semiconductor device sample with a high number of elements over a wide energy range.

Absence of a pressure gap and atomistic mechanism of the oxidation of pure Co nanoparticles.

Understanding chemical reactivity and magnetism of 3d transition metal nanoparticles is of fundamental interest for applications in fields ranging from spintronics to catalysis. Here, we present an atomistic picture of the early stage of the oxidation mechanism and its impact on the magnetism of Co nanoparticles. Our experiments reveal a two-step process characterized by (i) the initial formation of small CoO crystallites across the nanoparticle surface, until their coalescence leads to structural completion of the oxide shell passivating the metallic core; (ii) progressive conversion of the CoO shell to Co3O4 and void formation due to the nanoscale Kirkendall effect. The Co nanoparticles remain highly reactive toward oxygen during phase (i), demonstrating the absence of a pressure gap whereby a low reactivity at low pressures is postulated. Our results provide an important benchmark for the development of theoretical models for the chemical reactivity in catalysis and magnetism during metal oxidation at the nanoscale.

Artificial construction of the layered Ruddlesden-Popper manganite La2Sr2Mn3O10 by reflection high energy electron diffraction monitored pulsed laser deposition.

Pulsed laser deposition has been used to artificially construct the n = 3 Ruddlesden-Popper structure La(2)Sr(2)Mn(3)O(10) in epitaxial thin film form by sequentially layering La(1-x)Sr(x)MnO(3) and SrO unit cells aided by in situ reflection high energy electron diffraction monitoring. The interval deposition technique was used to promote two-dimensional SrO growth. X-ray diffraction and cross-sectional transmission electron microscopy indicated that the trilayer structure had been formed. A site ordering was found to differ from that expected thermodynamically, with the smaller Sr(2+) predominantly on the R site due to kinetic trapping of the deposited cation sequence. A dependence of the out-of-plane lattice parameter on growth pressure was interpreted as changing the oxygen content of the films. Magnetic and transport measurements on fully oxygenated films indicated a frustrated magnetic ground state characterized as a spin glass-like magnetic phase with the glass temperature T(g) ≈ 34 K. The magnetic frustration has a clear in-plane (ab) magnetic anisotropy, which is maintained up to temperatures of 150 K. Density functional theory calculations suggest competing antiferromagnetic and ferromagnetic long-range orders, which are proposed as the origin of the low-temperature glassy state.

Well shaped Mn3O4 nano-octahedra with anomalous magnetic behavior and enhanced photodecomposition properties.

Very uniform and well shaped Mn3O4 nano-octahedra are synthesized using a simple hydrothermal method under the help of polyethylene glycol (PEG200) as a reductant and shape-directing agent. The nano-octahedra formation mechanism is monitored. The shape and crystal orientation of the nanoparticles is reconstructed by scanning electron microscopy and electron tomography, which reveals that the nano-octahedra only selectively expose {101} facets at the external surfaces. The magnetic testing demonstrates that the Mn3O4 nano-octahedra exhibit anomalous magnetic properties: the Mn3O4 nano-octahedra around 150 nm show a similar Curie temperature and blocking temperature to Mn3O4 nanoparticles with 10 nm size because of the vertical axis of [001] plane and the exposed {101} facets. With these Mn3O4 nano-octahedra as a catalyst, the photodecomposition of rhodamine B is evaluated and it is found that the photodecomposition activity of Mn3O4 nano-octahedra is much superior to that of commercial Mn3O4 powders. The anomalous magnetic properties and high superior photodecomposition activity of well shaped Mn3O4 nano-octahedra should be related to the special shape of the nanoparticles and the abundantly exposed {101} facets at the external surfaces. Therefore, the shape preference can largely broaden the application of the Mn3O4 nano-octahedra.

2D atomic mapping of oxidation states in transition metal oxides by scanning transmission electron microscopy and electron energy-loss spectroscopy.

Using a combination of high-angle annular dark-field scanning transmission electron microscopy and atomically resolved electron energy-loss spectroscopy in an aberration-corrected transmission electron microscope we demonstrate the possibility of 2D atom by atom valence mapping in the mixed valence compound Mn3O4. The Mn L(2,3) energy-loss near-edge structures from Mn2+ and Mn3+ cation sites are similar to those of MnO and Mn2O3 references. Comparison with simulations shows that even though a local interpretation is valid here, intermixing of the inelastic signal plays a significant role. This type of experiment should be applicable to challenging topics in materials science, such as the investigation of charge ordering or single atom column oxidation states in, e.g., dislocations.

Image simulation of high resolution energy filtered TEM images.

Inelastic image simulation software is presented, implementing the double channeling approximation which takes into account the combination of multiple elastic and single inelastic scattering in a crystal. The approach is described with a density matrix formalism. Two applications in high resolution energy filtered (EFTEM) transmission electron microscopy (TEM) images are presented: thickness-defocus maps for SrTiO(3) and exit plane intensities for an (LaAlO(3))(3)(SrTiO(3))(3) multilayer system. Both systems show a severe breakdown in direct interpretability which becomes worse for higher acceleration voltages, thicker samples and lower excitation edge energies. Since this effect already occurs in the exit plane intensity, it is a fundamental limit and image simulations in EFTEM are indispensable just as they are indispensable for elastic high resolution TEM images.

EELS of niobium and stoichiometric niobium-oxide phases--Part I: plasmon and near-edges fine structure.

A comprehensive electron energy-loss spectroscopy study of niobium (Nb) and stable Nb-oxide phases (NbO, NbO2, Nb2O5) was carried out. In this work (Part I), the plasmons and energy-loss near-edge structures (ELNES) of all relevant Nb edges (Nb-N2,3, Nb-M4,5, Nb-M2,3, Nb-M1, and Nb-L2,3) up to energy losses of about 2600 eV and the O-K edge are analyzed with respect to achieving characteristic fingerprints of Nb in different formal oxidation states (0 for metallic Nb, +2 for NbO, +4 for NbO2, and +5 for Nb2O5). Chemical shifts of the Nb-N2,3, Nb-M4,5, Nb-M2,3, and Nb-L2,3 edges are extracted from the spectra that amount to about 4 eV as the oxidation state increases from 0 for Nb to +5 for Nb2O5. Four different microscopes, including a 200 keV ZEISS Libra with monochromator, were used. The corresponding wide range of experimental parameters with respect to the primary electron energy, convergence, and collection semi-angles as well as energy resolution allows an assessment of the influence of the experimental setup on the ELNES of the different edges. Finally, the intensity of the Nb-L2,3 white-line edges is correlated with niobium 4d-state occupancy in the different reference materials.

Fringe contrast in inelastic LACBED holography.

We discuss diffraction holography in a scattering geometry reported by Herring [Ultramicroscopy 104 (2005) 261, Ultramicroscopy 106 (2006) 960] and interpreted in terms of the density matrix of the fast electrons. Whereas the previous description used an approximation replacing the LACBED by a CBED geometry and consequently left some doubts about the conclusions (namely the non-detectability of the MDFF) we now fully include the Fresnel propagator and the biprism operator in order to calculate the density matrix of the inelastically scattered electrons in LACBED geometry. We show that a defocus on the biprism with respect to the sample does not cause a significant effect on the fringe patterns that are formed when the discs are exactly overlapping. An important difference to the CBED geometry is however that the fringe contrast decreases when the shear deviates from a reciprocal lattice vector. This should enable to measure the spatial coherence for smaller shears than is possible in image holography.

The Fresnel effect of a defocused biprism on the fringes in inelastic holography.

We present energy filtered holography experiments on a thin foil of Al. By propagating the reduced density matrix of the probe electron through the microscope, we quantitatively predict the fringe contrast as a function of energy loss. Fringe contrast simulations include the effect of Fresnel fringes created at the edges of the defocused biprism, the effect of partial coherence in combination with inelastic scattering, and the effect of a finite energy distribution of the incoming beam.

Demonstration of a 2 × 2 programmable phase plate for electrons.

First results on the experimental realisation of a 2 × 2 programmable phase plate for electrons are presented. The design consists of an array of electrostatic elements that influence the phase of electron waves passing through 4 separately controllable aperture holes. This functionality is demonstrated in a conventional transmission electron microscope operating at 300 kV and results are in very close agreement with theoretical predictions. The dynamic creation of a set of electron probes with different phase symmetry is demonstrated, thereby bringing adaptive optics in TEM one step closer to reality. The limitations of the current design and how to overcome these in the future are discussed. Simulations show how further evolved versions of the current proof of concept might open new and exciting application prospects for beam shaping and aberration correction.

Exploring possibilities of band gap measurement with off-axis EELS in TEM.

A technique to measure the band gap of dielectric materials with high refractive index by means of energy electron loss spectroscopy (EELS) is presented. The technique relies on the use of a circular (Bessel) aperture and suppresses Cherenkov losses and surface-guided light modes by enforcing a momentum transfer selection. The technique also strongly suppresses the elastic zero loss peak, making the acquisition, interpretation and signal to noise ratio of low loss spectra considerably better, especially for excitations in the first few eV of the EELS spectrum. Simulations of the low loss inelastic electron scattering probabilities demonstrate the beneficial influence of the Bessel aperture in this setup even for high accelerating voltages. The importance of selecting the optimal experimental convergence and collection angles is highlighted. The effect of the created off-axis acquisition conditions on the selection of the transitions from valence to conduction bands is discussed in detail on a simplified isotropic two band model. This opens the opportunity for deliberately selecting certain transitions by carefully tuning the microscope parameters. The suggested approach is experimentally demonstrated and provides good signal to noise ratio and interpretable band gap signals on reference samples of diamond, GaN and AlN while offering spatial resolution in the nm range.

Probing the symmetry of the potential of localized surface plasmon resonances with phase-shaped electron beams.

Plasmonics, the science and technology of the interaction of light with metallic objects, is fundamentally changing the way we can detect, generate and manipulate light. Although the field is progressing swiftly, thanks to the availability of nanoscale manufacturing and analysis methods, fundamental properties such as the plasmonic excitations' symmetries cannot be accessed directly, leading to a partial, sometimes incorrect, understanding of their properties. Here we overcome this limitation by deliberately shaping the wave function of an electron beam to match a plasmonic excitations' symmetry in a modified transmission electron microscope. We show experimentally and theoretically that this offers selective detection of specific plasmon modes within metallic nanoparticles, while excluding modes with other symmetries. This method resembles the widespread use of polarized light for the selective excitation of plasmon modes with the advantage of locally probing the response of individual plasmonic objects and a far wider range of symmetry selection criteria.