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In particularly we studied possible orderings and phase transitions in a model system of two types on ions (long-range Coulomb interaction) on 2D triangular lattice. This work is related to the charge ordering that occur in systems of Ni, Al double hydroxides in whichit can be assumed that ions of Ni and Al occupy the sites of triangular lattice.This work included analytical calculations as well as numerical Monte Carlo simulations.

Other works related to the properties of atomic Pair Distribution Function (PDF) that can be obtained by Fourier transform of the scattering intensity in X-ray or neutron diffraction experiments. In particularly, in calculation of PDF it is usually assumed that peaks that occur in PDF at average interatomic distances in solid materials have gaussian lineshape. We studied the validity of this approximation and possible deviations from this gaussian lineshape. We also studied the role of finite experimental resolution and possible ways (improvements) of how it cold be taken into account in order to achieve better agreement between measures and calculated PDFs.

Another project was about behavior of PDF at large distances. PDF traditionally was used to study atomic correlations in amorphous materials or liquids at small distances. In such materials as distance increases amplitude of peaks in PDF quickly decrease and thus experimental PDF at large distances is featureless. The same behavior with a slower rate of decay of PDF with distance was commonly assumed (but not studied) for the crystalline structures. Puzzled by observation that PDF calculated for the face centered cubic (fcc) structure of Ni does not exhibit decay with increase of the distance we studied behavior of PDF at large distances. Some rather surprising results were obtained.

My final project concerns accurate calculation of PDF function for flexible molecules. Previously in the group of Prof. M.F. Thorpe was developed technique for a very accurate calculation of PDF for crystalline and amorphous materials. This technique allows to achieve extremely good agreement between experimental and modeled PDF up to the distance 20-30 Å. The idea was to develop a technique that would allow to calculate PDF for flexible molecules (read proteins) as accurately as for amorphous and crystalline materials. In traditional calculation of PDF for relatively complex molecules Monte Carlo (MC) or Molecular Dynamics (MD) techniques are used. Quantum calculations, like Car-Parinello techniques, are too slow to model the properties of complex molecules. Thus quantum effects are usually ignored in calculations of PDF for complex molecules. We found a way and developed a technique that allows to incorporate QM effects into results of classical MD simulations. This can potentially significantly improve agreement between modeled and experimental PDF especially at small distances.

Masters Program

More information could be found in my resume, in my publications (publications 1-4) and conferences (conferences 1-2) lists and in my master’s thesis that is eventually happened to be in Russian (downloadable in PDF format).

During my M.S. program at Novosibirsk State University I was modeling electronic properties of linear chain of fullerenes. It is known that if in fullerite crystal (crystal structure formed by fullerene molecules) introduced a metal atom (donor) that donates electrons to the structure, then under some conditions fullerene molecules can polymerize. Such structures exhibit pressure dependent conductivity. We tried to model this behavior by solving Shroedinger equation for electrons in Bohr-Oppengeimer (nuclei move much slower than electrons so that in calculation of electronic structure it can be assumed that nuclei are motionless) approximation. On the other hand, if electronic structure is known, the forces that act on nuclei could be found. By solving this two problems self-consistently we were able to find how electronic charge distribution (polarons) and carbon-carbon bond lengths depend on the distance between the centers of fullerene molecules (pressure). We found that at some distance (pressure) there occurs sharp redistribution of electronic charge on the surface of the molecule. This is in agreement with experimental evidence of metal to week insulator transition that was observed.