Ab-initio determination of x-ray absorption near edge structure (xanes) spectra in an ultrasoft and norm conserving pseudopotentials scheme

X-ray absorption spectroscopy (XAS) is a powerful means of investigation of structural and electronic properties in condensed -matter physics. Analysis of the near edge part of the XAS spectrum, the so – called X-ray Absorption Near Edge Structure (XANES), can typically provide the following information on the photoexcited atom: - Oxidation state and coordination environment. - Speciation of transition metal compounds. - Conduction band DOS projected on the excited atomic species (PDOS). Analysis of XANES spectra is greatly aided by simulations; in the most common scheme the multiple scattering framework is used with the muffin tin approximation for the scattering potential and the spectral simulation is based on a hypothetical, reference structure. This approach has the advantage of requiring relatively little computing power but in many cases the assumed structure is quite different from the actual system measured and the muffin tin approximation is not adequate for low symmetry structures or highly directional bonds. It is therefore very interesting and justified to develop alternative methods. In one approach, the spectral simulation is based on atomic coordinates obtained from a DFT (Density Functional Theory) optimized structure. In another approach, which is the object of this thesis, the XANES spectrum is calculated directly based on an ab – initio DFT calculation of the atomic and electronic structure. This method takes full advantage of the real many-electron final wavefunction that can be computed with DFT algorithms that include a core-hole in the absorbing atom to compute the final cross section. To calculate the many-electron final wavefunction the Projector Augmented Wave method (PAW) is used. In this scheme, the absorption cross section is written in function of several contributions as the many-electrons function of the finale state; it is calculated starting from pseudo-wavefunction and performing a reconstruction of the real-wavefunction by using a transform operator which contains some parameters, called partial waves and projector waves. The aim of my thesis is to apply and test the PAW methodology to the calculation of the XANES cross section. I have focused on iron and silicon structures and on some biological molecules target (myoglobin and cytochrome c). Finally other inorganic and biological systems could be taken into account for future applications of this methodology, which could become an important improvement with respect to the multiscattering approach.

Study of the calibration method of pressure-velocity probes and its application in a field of progressive plane waves

This dissertation presents a calibration procedure for a pressure velocity probe. The dissertation is divided into four main chapters. The first chapter is divided into six main sections. In the firsts two, the wave equation in fluids and the velocity of sound in gases are calculated, the third section contains a general solution of the wave equation in the case of plane acoustic waves. Section four and five report the definition of the acoustic impedance and admittance, and the practical units the sound level is measured with, i.e. the decibel scale. Finally, the last section of the chapter is about the theory linked to the frequency analysis of a sound wave and includes the analysis of sound in bands and the discrete Fourier analysis, with the definition of some important functions. The second chapter describes different reference field calibration procedures that are used to calibrate the P-V probes, between them the progressive plane wave method, which is that has been used in this work. Finally, the last section of the chapter contains a description of the working principles of the two transducers that have been used, with a focus on the velocity one. The third chapter of the dissertation is devoted to the explanation of the calibration set up and the instruments used for the data acquisition and analysis. Since software routines were extremely important, this chapter includes a dedicated section on them and the proprietary routines most used are thoroughly explained. Finally, there is the description of the work that has been done, which is identified with three different phases, where the data acquired and the results obtained are presented. All the graphs and data reported were obtained through the Matlab® routine. As for the last chapter, it briefly presents all the work that has been done as well as an excursus on a new probe and on the way the procedure implemented in this dissertation could be applied in the case of a general field.