Search Results (110 total)

Complete understanding of atomic resolution high-angle annular dark-field (Z-contrast) images requires quantitative agreement between simulations and experiments. We show that intensity variations can be placed on an absolute scale by normalizing the measured image intensities to the incident beam. We construct fractional intensity images of a SrTiO₃ single crystal for regions of different thickness up to 120 nm. Experimental images are compared directly with image simulations. Provided that spatial incoherence is taken into account in the simulations, almost perfect agreement is found between simulation and experiment.

We consider the elastic scattering of a fast incident electron both prior and subsequent to its involvement in an atomic inner-shell ionization (core-loss) event in a crystal. By using numerical simulations, it is shown that elastic scattering subsequent to ionization can strongly affect the qualitative features of atomic resolution core-loss images of crystals recorded in the scanning transmission electron microscope (STEM). This conclusion holds even for a thin crystal foil and for a relatively large detector, which is matched to the probe-forming aperture in an aberration-corrected STEM. Such a conclusion is potentially very important for the interpretation of experimental core-loss images. We also introduce an approximate model that incorporates the effects of elastic scattering subsequent to ionization in the case of a small detector.

We contrast the two situations in which either a light beam is incident on a moving medium or a moving optical image is incident on a stationary medium. The principle of relativity suggests that the effects on the light of propagating through the medium should be similar. We find, however, that there are subtle differences which we can understand in terms of the relative alignment of the Poynting and wave vectors. Our analysis and experiments investigate both translational motion and rotation.

The phase of the mean-field wave function of a Bose-Einstein condensate can be recovered from a time series of images. We adapt an iterative retrieval method that has been successful in linear electron and optical imaging systems to solve the nonlinear Gross-Pitaevskii equation. We address a number of issues related to the successful application of this method to the nonlinear system, including the retrieval of wave functions with nonzero net topological charge (i.e., containing vortices) and the effects of repulsive and attractive interactions in the condensate on the convergence properties of the method. Recovering the phase from the continuity-of-density equation is also investigated. An understanding of these issues is of importance for the practical implementation of phase retrieval to Bose-Einstein condensates.

The simultaneous measurement of structural and chemical information at the atomic scale provides fundamental insights into the connection between form and function in materials science and nanotechnology. We demonstrate structural and chemical mapping in Bi_0.5Sr_0.5MnO₃ using an aberration-corrected scanning transmission electron microscope. Two-dimensional mapping is made possible by an adapted method for fast acquisition of electron energy-loss spectra. The experimental data are supported by simulations, which help to explain the less intuitive features.

Core-loss electron energy loss spectroscopy is a powerful experimental tool with the potential to provide atomic-resolution information about electronic structure at defects and interfaces in materials and nanostructures. Interpretation, however, is nonintuitive. Comparison of experimental and simulated compositional maps in LaMnO₃ shows good agreement, apart from an overall scaling of image contrast, and shows that the shape and width of spectroscopic images do not show a simple variation with binding energy, as commonly assumed, or with the size of the orbital excited. For the low lying La N_4,5 edge with threshold at around 99  eV, delocalization does not preclude atomic resolution, but reduces the image contrast. The image width remains comparable to that of the much higher lying O K edge with threshold at around 532  eV. Both edges show a volcanolike feature, a dip at the column position not previously seen experimentally. In the case of the O K edge, this represents an experimental verification of nonlocal inelastic scattering effects in electron energy loss spectroscopy imaging. In the case of the N_4,5 edge, the volcanolike feature is due to dynamical channeling and absorption of the probe through the specimen thickness. Simulation is therefore critical to the interpretation of atomic-resolution elemental maps.

Atom column intensities of silicon single crystals oriented along different crystallographic orientations are compared in experimental and simulated high-angle annular dark-field images in scanning transmission electron microscopy. The intensity of a background, measured between the columns, is also evaluated and found to be largely independent of the column spacing. The contrast is lower in the experiments, and it has been suggested previously that this follows because the background is higher in the experiments. We explore the extent to which the comparison of experimental atom column intensities with image simulations is aided by subtraction of the background for these data. We also explore an alternative view: simple simulations overestimate the contrast because spatial incoherence and associated instabilities are not taken into account. The results do not distinguish between these approaches, which need not be in opposition, and we describe experiments which might further clarify matters.

We observe, using phase maps obtained from a focal series of images, the evolution in time of a gold-vacuum interface. What is seen is the reconfiguration and removal of whole columns of gold atoms (typically containing three to nine atoms) at the interface. These structural changes are discussed with reference to the variation in binding energy along the interface.

Momentum-transfer-resolved electron spectroscopy is a technique for examining the electronic structure of materials and requires the use of detectors accepting a small range of momentum transfers. For crystalline specimens, it is necessary to consider the channeling behavior of the fast electrons both before and after inelastic scattering to adequately describe the signals produced. Using oxygen K-shell core loss in NiO as a case study, we examine channeling in high-angular-resolution electron-channeling electron spectroscopy. The roles of nonlocality and sample thickness as they relate to the channeling effect are explored. Particular attention is given to the behavior arising from the channeling of the scattered electrons, as compared with models in which only the incident electrons channel. Calculations allowing for the channeling of both the incident and the scattered electrons are computationally demanding and we explore approximations that can be made for detectors with small acceptance angles.

We show how an effective nonlocality in imaging can lead to the sampling of a spatial region which is not significantly illuminated by an imaging probe. The nonlocality is embodied in the effective nonlocal potential describing inelastic scattering which occurs when coupled channel Schrödinger equations are reduced to a single integro-differential equation. The context in which this prediction will be illustrated is atomic resolution imaging based on energy-loss spectroscopy in scanning transmission electron microscopy.

It is commonly understood that the retrieval of a complex-valued object from its diffraction pattern using a support constraint is a difficult problem, the more so if the support is symmetric. In this Letter we show that, for just such a symmetric support, use of an iterative algorithm in which the basic iteration is specified by a difference map converges routinely. All that is required is sufficient oversampling in the diffraction pattern coupled with judicious choices of the parameters defining the difference map.

We present a detailed study of a simple scalar field model that yields nonsingular cosmological solutions. We study both the qualitative dynamics of the homogeneous and isotropic background and the evolution of inhomogeneous linear perturbations. We calculate the spectrum of perturbations generated on super-Hubble scales during the collapse phase from initial vacuum fluctuations on small scales and then evolve these numerically through the bounce. We show there is a gauge in which perturbations remain well-defined and small throughout the bounce, even though perturbations in other commonly used gauges become large or ill-defined. We show that the comoving curvature perturbation calculated during the collapse phase provides a good estimate of the resulting large-scale adiabatic perturbation in the expanding phase while the Bardeen metric potential is dominated by what becomes a decaying mode after the bounce. We show that a power-law collapse phase with scale factor proportional to (-t)^2/3 can yield a scale-invariant spectrum of adiabatic scalar perturbations in the expanding phase, but the amplitude of tensor perturbations places important constraints on the allowed initial conditions.

The ability to localize, identify, and measure the electronic environment of individual atoms will provide fundamental insights into many issues in materials science, physics, and nanotechnology. We demonstrate, using an aberration-corrected scanning transmission electron microscope, the spectroscopic imaging of single La atoms inside CaTiO₃. Dynamical simulations confirm that the spectroscopic information is spatially confined around the scattering atom. Furthermore, we show how the depth of the atom within the crystal may be estimated.

The “delocalization” of inelastic scattering is an important issue for the ultimate spatial resolution of innershell spectroscopy in the electron microscope. It is demonstrated in a nonlocal model for electron energy loss spectroscopy (EELS) that delocalization of scanning transmission electron microscopy (STEM) images for single, isolated atoms is primarily determined by the width of the probe, even for light atoms. We present experimental data and theoretical simulations for Ti L-shell EELS in a [100] SrTiO₃ crystal showing that, in this case, delocalization is not significantly increased by dynamical propagation. Issues relating to the use of aberration correctors in the STEM geometry are discussed.

The ultrasensitive differential scanning calorimetry is used to observe the glass transition in thin (1–400 nm) spin-cast films of polystyrene, poly (2-vinyl pyridine) and poly (methyl methacrylate) on a platinum surface. A pronounced glass transition is observed even at a thickness as small as 1–3 nm. Using the high heating (20–200  K/ms) and cooling (1–2  K/ms in glass transition region) rates which are typical for this technique, we do not observe appreciable dependence of the glass transition temperature over the thickness range from hundreds of nanometers down to 3 nm thick films. The evolution of calorimetric data with film thickness is discussed in terms of broadening of transition dynamics and loss of transition contrast.

We investigate the orbital angular momentum correlation of a photon pair created in a spontaneous parametric down-conversion process. We show how the conservation of the orbital angular momentum in this process results from phase matching in the nonlinear crystal.

We explain that, unlike the spin angular momentum of a light beam which is always intrinsic, the orbital angular momentum may be either extrinsic or intrinsic. Numerical calculations of both spin and orbital angular momentum are confirmed by means of experiments with particles trapped off axis in optical tweezers, where the size of the particle means it interacts with only a fraction of the beam profile. Orbital angular momentum is intrinsic only when the interaction with matter is about an axis where there is no net transverse momentum.

We show that aberration corrections can be made in any arbitrary linear imaging system provided the aberrations are well characterized and at least one of these aberrations can be independently varied in a well-controlled manner. We derive a generalization of the Schrödinger equation for wave propagation in aberration space assuming forward scattering. Transport equations in aberration space are derived. A general iterative algorithm which can retrieve the phase, and is robust in the presence of noise, is also derived. This is demonstrated using simulated data pertinent to electron microscopy, from a series of images with differing spherical aberration.

We discuss retrieval of the phase of quantum-mechanical and classical wave fields in the presence of first-order vortices. A practical method of phase retrieval is demonstrated which is robust in the presence of noise. Conditions for the uniqueness of the retrieved phase are discussed and we show that determination of the phase in a given plane requires a series of at least three two-dimensional intensity images at different propagation distances. The method is applicable to a wide range of scenarios such as the imaging of imperfect crystals, quantitative determination of the strength of vortex filaments in high-temperature superconductors, and x-ray and electron holography.

We report a study of the thermodynamic properties of indium clusters on a SiN _x surface during the early stages of thin film growth using a sensitive nanocalorimetry technique. The measurements reveal the presence of abnormal discontinuities in the heat of melting below 100 °C. These discontinuities, for which temperature separation corresponds to a spatial periodicity equal to the thickness of an indium monolayer, are found to be related to the atomic “magic numbers,” i.e., the number of atoms necessary to form a complete shell of atoms at particle surface.

The melting behavior of 0.1–10-nm-thick discontinuous indium films formed by evaporation on amorphous silicon nitride is investigated by an ultrasensitive thin-film scanning calorimetry technique. The films consist of ensembles of nanostructures for which the size dependence of the melting temperature and latent heat of fusion are determined. The relationship between the nanostructure radius and the corresponding melting point and latent heat is deduced solely from experimental results (i.e., with no assumed model) by comparing the calorimetric measurements to the particle size distributions obtained by transmission electron microscopy. It is shown that the melting point of the investigated indium nanostructures decreases as much as 110 K for particles with a radius of 2 nm. The experimental results are discussed in terms of existing melting point depression models. Excellent agreement with the homogeneous melting model is observed.

Jones matrices describe the polarization, or spin angular momentum, of a light beam as it passes through an optical system. We devise an equivalent of the Jones matrix formulation for light possessing orbital angular momentum. The matrices are then developed to account for light that has both spin and orbital angular momentum.

A numerical model is used to investigate the conversion efficiency of second-harmonic generation with “nondiffracting” Bessel beams. We experimentally validate the model and show, in contrast to a previous prediction, that the conversion efficiency is always less than for Boyd-Kleinman focused Gaussian beams.

During the 1960s there was much discussion about the transition from a quantal to a classical description of ion-beam channeling. There is no reason why a quantal model should not be used. However, no such calculations have been attempted. We present a fully quantum mechanical model for Rutherford backscattering of an ion beam from a thin crystalline lattice. Good agreement with experimental Rutherford backscattering angular scans is demonstrated. The transition from the quantal to the classical model is discussed.

We investigate the spontaneous parametric down-conversion for light beams possessing orbital angular momentum. The experimental results indicate that the orbital angular momentum is not conserved within the classical light fields. This is in contrast to second harmonic generation where the conservation of orbital angular momentum leads to a well-defined mode transformation. We attribute this difference in behavior to the loss of spatial coherence within each of the down-converted fields.