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The surface energy, particularly for nanoparticles, is one of the most important quantities in understanding the thermodynamics of particles. Therefore, it is astonishing that there is still great uncertainty about its value. The uncertainty increases if one questions its dependence on particle size. Different approaches, such as classical thermodynamics calculations, molecular dynamics simulations, and ab initio calculations, exist to predict this quantity. Generally, considerations based on classical thermodynamics lead to the prediction of decreasing values of the surface energy with decreasing particle size. This phenomenon is caused by the reduced number of next neighbors of surface atoms with decreasing particle size, a phenomenon that is partly compensated by the reduction of the binding energy between the atoms with decreasing particle size. Furthermore, this compensating effect may be expected by the formation of a disordered or quasi-liquid layer at the surface. The atomistic approach, based either on molecular dynamics simulations or ab initio calculations, generally leads to values with an opposite tendency. However, it is shown that this result is based on an insufficient definition of the particle size. A more realistic definition of the particle size is possible only by a detailed analysis of the electronic structure obtained from initio calculations. Except for minor variations caused by changes in the structure, only a minor dependence of the surface energy on the particle size is found. The main conclusion of this work is that surface energy values for the equivalent bulk materials should be used if detailed data for nanoparticles are not available.

The possibility of focusing images by the autocorrelation function is explained. It can be shown that these techniques are less sensitive to disturbances by noise than others. Furthermore, focusing criteria derived from autocorrelation functions have different responses to image contrast. It has been shown that these focusing criteria can be determined using binary images and applying the laws of stochastic ergodic metrology. This leads to a large reduction in computing time. Moreover, an attempt was made to focus by means of binary images determined by simple segmentation. The experimental results show that such a focus criterion operates quite well. The criterion offers the advantage that brightness levels in the image can be chosen selectively for focusing.

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Nanocrystalline maghemite, γ–Fe2O3, can be synthesized in a microwave plasma using FeCl3 or Fe3(CO)12 as the precursor. Electron microscopy revealed particle sizes in the range of 5 to 10 nm. In general, this material is superparamagnetic. The magnetic properties are strongly dependent on the precursor. In both cases the production process leads to a highly disordered material with the consequence of a low magnetization. The assumption of a disordered structure is also supported by electron energy loss (EEL) and Mössbauer spectroscopy. The structure of this material shows a nearly identical number of cations on tetrahedral and octahedral lattice sites.

A systematic study is presented of the properties of autofocus criteria. Special importance is attributed to their behaviour with respect to noise, working range and image sharpness, whose reproducibility has been investigated. It can be demonstrated that autofocus algorithms have either a large working range and do not focus in an unambiguous way or vice versa. From considerations of the properties of autofocus algorithms two novel algorithms have been developed which are insensitive to noise. One of these algorithms is characterized by a particularly large working range, whereas the other is capable of achieving maximum sharpness in a reproducible manner.

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