Geometric approach to the phenomenological theory of phase transitions of the second kind

Geometrical approach to the phenomenological theory of phase transitions of the second kind at constant pressure $P$ and variable temperature $T$ is proposed. Equilibrium states of a system at zero external field and fixed $P$ and $T$ are described by points in three-dimensional space with coordinates $\eta$, the order parameter, $T$, the temperature and $\phi$, the thermodynamic potential. These points form the so-called zero field curve in the $(\eta, T, \phi)$ space. Its branch point coincides with the critical point of the system. The small parameter of the theory is the distance from the critical point along the zero-field curve. It is emphasized that no explicit functional dependency of $\phi$ on $\eta$ and $T$ is imposed. It is shown that using $(\eta, T, \phi)$ space one cannot overcome well-known difficulties of the Landau theory of phase transitions and describe non-analytical behavior of real systems in the vicinity of the critical point. This becomes possible only if one increases the dimensionality of the space, taking into account the dependency of the thermodynamic potential not only on $\eta$ and $T$, but also on near (local) order parameters $\lambda_{i}$. In this case under certain conditions it is possible to describe anomalous increase of the specific heat when the temperature of the system approaches the critical point from above as well as from below the critical temperature $T_{c}$.Comment: 20 pages. 2 figures. Requires elsart package available at ftp://ftp.shsu.edu/tex-archive/macros/latex209/contrib/elsevier

Modelling of elastic properties of sintered porous materials

Models for prediction of the elastic characteristics of natural and synthetic porous materials are re-examined and new models are introduced. First, the Vavakin–Salganik (VS) model for materials with isolated spherical pores is extended in order to take into account various statistical distributions of pore sizes. It is shown that the predictions of the extended VS model are in good agreement with experimental data for porous materials with isolated pores such as foamed titanium, porous glass and sandstone. However, the model is in a considerable disagreement with the experimental data for materials sintered from metal powders. The disagreement is explained by the presence of merged and open pores whose shapes cannot be well approximated as spheres. Using the theory of geometrical probabilities, the amount of pores that are close enough to overlap is estimated, and a model is introduced where merging pores are modelled as corresponding ellipsoids. Another modification is proposed to take into account open pores. This modification is based on the classical Rabotnov–Kachanov approach to damage accumulation in the loaded material. Finally, predictions given by the above models, and their combination is compared with experiments. A good agreement is observed between the combined model and the available experimental data for a variety of sintered materials

Coherent X-Ray Diffraction Imaging of Nanostructures

We present here an overview of Coherent X-ray Diffraction Imaging (CXDI) with its application to nanostructures. This imaging approach has become especially important recently due to advent of X-ray Free-Electron Lasers (XFEL) and its applications to the fast developing technique of serial X-ray crystallography. We start with the basic description of coherent scattering on the finite size crystals. The difference between conventional crystallography applied to large samples and coherent scattering on the finite size samples is outlined. The formalism of coherent scattering from a finite size crystal with a strain field is considered. Partially coherent illumination of a crystalline sample is developed. Recent experimental examples demonstrating applications of CXDI to the study of crystalline structures on the nanoscale, including experiments at FELs, are also presented