Studies of some problems related to atomic ordering, molecular motion and pair distribution function

In this thesis the results of my work on three out of four projects on which I was working during my Ph.D. under supervision of Prof. M. F. Thorpe are summarized.; The first project was devoted to the study of properties of a model that was developed to reproduce the ordering of ions in layered double hydroxides. In the model two types of positive ions occupy the sites of triangular lattice. The ordering of ions is assumed to occur due to the long-range Coulomb interaction. The charge neutrality is provided by the negative background charge, which is assumed to be the same at every site of the lattice. General properties of the model in 1d and 2d were studied and the phase diagrams were obtained. The obtained results predict multiple phase separations in this system of charges that can, in particularly, affect the stability of the layered double hydroxides.; Some properties of the atomic pair distribution function (PDF) were studied during my work on the second project. Traditionally PDF was used to study atomic ordering at small distances, while it was assumed that at large distances PDF is featureless. Puzzled by the observation that PDF calculated for the crystalline Ni does not decay at large distances we studied the behavior, in particularly the origin of decay, of PDF at large distances. The obtained results potentially could be used to measure the amount of imperfections in crystalline materials and to test instrumental resolution in X-ray and neutron diffraction experiments.; During my work on the third project we were developing a technique that would allow accurate calculation of PDF for the flexible molecules. Since quantum mechanical calculations are complicated and computationally demanding in calculations of PDF for molecules in liquid or gaseous phases, classical methods, like molecular dynamics are usually employed. Thus, quantum mechanical effects, like zero-point atomic motion, are usually ignored. However, it is necessary to take into account the effect of atomic zero-point motion if there is a desire to extract fine structural details from the PDF. We developed a method that allows incorporation of the effect of atomic zero-point motion into the results of classical MD simulations without performing full quantum mechanical calculations. This technique could be used to correct classically calculated PDFs and thus to achieve better agreement between modeled and experimental PDFs.