Abstract: In order to interpret the amplitude and phase of the exit wave in terms of mass and position of the atoms, one has to invert the dynamic scattering of the electrons in the object so as to obtain a starting structure which can then be used as a seed for further quantitative structure refinement. This is especially challenging in case of a zone axis condition when the interaction of the electrons with the atom column is very strong. Based on the channelling theory we will show that the channelling map not only yields a circle on the Argand plot but also a circular defocus curve for every column. The former gives the number of atoms in each column, while the latter provides the defocus value for each column, which reveals the surface roughness at the exit plane with single atom sensitivity.

Abstract: The effects of amorphous layers on the quality of exit wave restorations have been investigated. Two independently developed software implementations for exit wave restoration have been used to simulated focal series of images of SrTiO3 with amorphous carbon layers incorporated. The restored exit waves have been compared both qualitatively and quantitatively. We have shown that amorphous layers have a strong impact on the quantitative measurements of atomic column positions, however, the error in the position measurements is still in the picometer range.

Abstract: The charge-coupled devices used in electron microscopy are coated with a scintillating crystal that gives rise to a severe modulation transfer function (MTF). Exact knowledge of the MTF is imperative for a good correspondence between image simulation and experiment. We present a practical method to measure the MTF above the Nyquist frequency from the beam blocker's shadow image. The image processing has been fully automated and the program is made public. The method is successfully tested on three cameras with various beam blocker shapes.

Abstract: In this paper, it has been investigated how to measure atom column positions as accurately and precisely as possible using a focal series of images. In theory, it is expected that the precision would considerably improve using a maximum likelihood estimator based on the full series of focal images. As such, the theoretical lower bound on the variances of the unknown atom column positions can be attained. However, this approach is numerically demanding. Therefore, maximum likelihood estimation has been compared with the results obtained by fitting a model to a reconstructed exit wave rather than to the full series of focal images. Hence, a real space model-based exit wave reconstruction technique based on the channelling theory is introduced. Simulations show that the reconstructed complex exit wave contains the same amount of information concerning the atom column positions as the full series of focal images. Only for thin samples, which act as weak phase objects, this information can be retrieved from the phase of the reconstructed complex exit wave.

Abstract: Scheelite related compounds (A',A '') [(B',B '')O-4], with B', B '' = W and/or Mo are promising new light-emitting materials for photonic applications, including phosphor converted LEDs (light-emitting diodes). In this paper, the creation and ordering of A-cation vacancies and the effect of cation substitutions in the scheelite-type framework are investigated as a factor for controlling the scheelite-type structure and luminescent properties. CaGd2(1-x)Eu2x(MoO4)(4(1-y))(WO4)(4y) (0 <= x <= 1, 0 <= y <= 1) solid solutions with scheelite-type structure were synthesized by a solid state method, and their structures were investigated using a combination of transmission electron microscopy techniques and powder X-ray diffraction. Within this series all complex molybdenum oxides have (3 + 2)D incommensurately modulated structures with superspace group I4(1)/a(alpha,beta,0)00(-beta,alpha,0)00, while the structures of all tungstates are (3 + 1)D incommensurately modulated with superspace group I2/b(alpha beta 0)00. In both cases the modulation arises because of cation-vacancy ordering at the A site. The prominent structural motif is formed by columns of A-site vacancies running along the c-axis. These vacant columns occur in rows of two or three aligned along the [110] direction of the scheelite subcell. The replacement of the smaller Gd3+ by the larger Eu3+ at the A-sublattice does not affect the nature of the incommensurate modulation, but an increasing replacement of Mo6+ by W6+ switches the modulation from (3 + 2)D to (3 + 1)D regime. Thus, these solid solutions can be considered as a model system where the incommensurate modulation can be monitored as a function of cation nature while the number of cation vacancies at the A sites remain constant upon the isovalent cation replacement. All compounds' luminescent properties were measured, and the optical properties were related to the structural properties of the materials. CaGd2(1-x)(MoO4)(4(1-y))(WO4)(4y) phosphors emit intense red light dominated by the D-5(0)-F-7(2) transition at 612 nm, along with other transitions from the D-5(1) and D-5(0) excited states. The intensity of the 5D0-7F2 transition reaches a maximum at x = 0.5 for y = 0 and 1.

Abstract: A widely used performance criterion in high-resolution transmission electron microscopy (HRTEM) is the information limit. It corresponds to the inverse of the maximum spatial object frequency that is linearly transmitted with sufficient intensity from the exit plane of the object to the image plane and is limited due to partial temporal coherence. In practice, the information limit is often measured from a diffractogram or from Young's fringes assuming a weak phase object scattering beyond the inverse of the information limit. However, for an aberration corrected electron microscope, with an information limit in the sub-angstrom range, weak phase objects are no longer applicable since they do not scatter sufficiently in this range. Therefore, one relies on more strongly scattering objects such as crystals of heavy atoms observed along a low index zone axis. In that case, dynamical scattering becomes important such that the non-linear and linear interaction may be equally important. The non-linear interaction may then set the experimental cut-off frequency observed in a diffractogram. The goal of this paper is to quantify both the linear and the non-linear information transfer in terms of closed form analytical expressions. Whereas the cut-off frequency set by the linear transfer can be directly related with the attainable resolution, information from the non-linear transfer can only be extracted using quantitative, model-based methods. In contrast to the historic definition of the information limit depending on microscope parameters only, the expressions derived in this paper explicitly incorporate their dependence on the structure parameters as well. In order to emphasize this dependence and to distinguish from the usual information limit, the expressions derived for the inverse cut-off frequencies will be referred to as the linear and non-linear structural information limit. The present findings confirm the well-known result that partial temporal coherence has different effects on the transfer of the linear and non-linear terms, such that the non-linear imaging contributions are damped less than the linear imaging contributions at high spatial frequencies. This will be important when coherent aberrations such as spherical aberration and defocus are reduced.

Abstract: Reconstructed exit waves are useful to quantify unknown structure parameters such as the position and composition of the atom columns at atomic scale. Existing techniques provide a complex wave in a flat plane which is close to the plane where the electrons leave the atom columns. However, due to local deviation in the flatness of the exit surface, there will be an offset between the plane of reconstruction and the actual exit of a specific atom column. Using the channelling theory, it has been shown that this defocus offset can in principle be determined atom column-by-atom column. As such, the surface roughness could be quantified at atomic scale. However, the outcome strongly depends on the initial plane of reconstruction especially in a crystalline structure. If this plane is further away from the true exit, the waves of the atom columns become delocalized and interfere mutually which strongly complicates the interpretation of the exit wave in terms of the local structure. In this paper, we will study the delocalization with defocus using the channelling theory in a more systematic way.

Abstract: Statistical parameter estimation theory is proposed as a method to quantify electron microscopy images. It aims at obtaining precise and accurate values for the unknown structure parameters including, for example, atomic column positions and types. In this theory, observations are purely considered as data planes, from which structure parameters have to be determined using a parametric model describing the images. The method enables us to measure positions of atomic columns with a precision of the order of a few picometers even though the resolution of the electron microscope is one or two orders of magnitude larger. Moreover, small differences in averaged atomic number, which cannot be distinguished visually, can be quantified using high-angle annular dark field scanning transmission electron microscopy images. Finally, it is shown how to optimize the experimental design so as to attain the highest precision. As an example, the optimization of the probe size for nanoparticle radius measurements is considered. It is also shown how to quantitatively balance signal-to-noise ratio and resolution by adjusting the probe size.

Abstract: An extension to model-based electron energy loss spectroscopy (EELS) quantification is reported to improve the possibility of modelling fine structure changes in electron energy loss spectra. An equalisation function is used in the energy loss near edge structure (ELNES) region to model the differences between a single atom differential cross section and the cross section for an atom in a crystal. The equalisation function can be shown to approximate the relative density of unoccupied states for the given excitation edge. On a set of 200 experimental h-BN spectra, this technique leads to statistically acceptable models resulting into unbiased estimates of relative concentrations and making the estimated precisions come very close to the Cramer-Rao lower bound (CRLB). The method greatly expands the useability of model-based EELS quantification to spectra with pronounced fine structure. Another benefit of this model is that one also gets an estimate of the unoccupied density of states for a given excitation edge, without having to do background removal and deconvolution, making the outcome intrinsically more reliable and less noisy. (c) 2006 Elsevier B.V. All rights reserved.