Abstract: Various low temperature treatments of Ni50.6Ti49.4 have shown an unexpected effect on the martensitic start temperature. Periodic diffuse intensity distributions in reciprocal space indicate the formation of short pure Ni strings along the <111> directions in the B2 ordered lattice, precursing the formation of Ni4Ti3 precipitates formed at higher annealing temperatures.

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: The idea of this Review is to introduce newly developed possibilities of advanced electron microscopy to the materials science community. Over the last decade, electron microscopy has evolved into a full analytical tool, able to provide atomic scale information on the position, nature, and even the valency atoms. This information is classically obtained in two dimensions (2D), but can now also be obtained in 3D. We show examples of applications in the field of nanoparticles and interfaces.

Abstract: In this paper, we investigate how precise atoms of a small nanocluster can ultimately be located in three dimensions (3D) from a tilt series of images acquired using annular dark field (ADF) scanning transmission electron microscopy (STEM). Therefore, we derive an expression for the statistical precision with which the 3D atomic position coordinates can be estimated in a quantitative analysis. Evaluating this statistical precision as a function of the microscope settings also allows us to derive the optimal experimental design. In this manner, the optimal angular tilt range, required electron dose, optimal detector angles, and number of projection images can be determined.

Abstract: We propose an improved image simulation procedure for atomic-resolution annular dark-field scanning transmission electron microscopy (STEM) based on the multislice formulation, which takes thermal diffuse scattering fully into account. The improvement with regard to the classical frozen phonon approach is realized by separating the lattice configuration statistics from the dynamical scattering so as to avoid repetitive calculations. As an example, the influence of phonon scattering on the image contrast is calculated and investigated. STEM image simulation of crystals can be applied with reasonable computing times to problems involving a large number of atoms and thick or large supercells.

Abstract: A non-destructive method for measuring the thickness of thin amorphous films composed of light elements has been developed. The method employs the statistics of the phase of the electron exit wave function. The accuracy of this method has been checked numerically by the multislice method and compared with that based on the mean inner potential.

Abstract: A model-based method is proposed to relatively quantify the chemical composition of atomic columns using high angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) images. The method is based on a quantification of the total intensity of the scattered electrons for the individual atomic columns using statistical parameter estimation theory. In order to apply this theory, a model is required describing the image contrast of the HAADF STEM images. Therefore, a simple, effective incoherent model has been assumed which takes the probe intensity profile into account. The scattered intensities can then be estimated by fitting this model to an experimental HAADF STEM image. These estimates are used as a performance measure to distinguish between different atomic column types and to identify the nature of unknown columns with good accuracy and precision using statistical hypothesis testing. The reliability of the method is supported by means of simulated HAADF STEM images as well as a combination of experimental images and electron energy-loss spectra. It is experimentally shown that statistically meaningful information on the composition of individual columns can be obtained even if the difference in averaged atomic number Z is only 3. Using this method, quantitative mapping at atomic resolution using HAADF STEM images only has become possible without the need of simultaneously recorded electron energy loss spectra.

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.