This thesis has detailed the extensive analysis of the XAS and RIXS spectra of LiFePO4 and FePO4, with the primary focus on LiFePO4. One of the primary motivations for this study was to understand the electronic structure of the two compounds and, in particular, shed some light on the nature of electron correlation within the samples. Two classes of band structure calculations have come to light. One solution uses the Hubbard U parameter, and this solution exhibits a band gap of about 4 eV. Other solutions that use standard DFT electron correlation functionals yield band gaps between 0 and 1.0 eV. <p>The RIXS spectra of LiFePO4 and FePO4 were analyzed using Voigt function fitting, an uncommon practice for RIXS spectra. Each of the spectra was fit to a series of Voigt functions in an attempt to localize the peaks within the spectra. These peaks were determined to be RIXS events, and the energetic centers of these peaks were compared to a small band gap band structure calculation. The results of the RIXS analysis strongly indicate that the small gap solution is correct. This was a surprising result, given that LiFePO4 is an ionic, insulating transition metal oxide, showing all of the usual traits of a Mott-type insulator. <p>This contradiction was explained in terms of polaron formation. Polarons can severely distort the lattice, which changes the local charge density. This changes the local DOS such that the DOS probed by XAS or RIXS experiments is not necessarily in the ground state. In particular, polaron formation can reduce the band gap. Thus, the agreement between the small gap solution and experiment is false, in the sense that the physical assumptions that formed the basis of the small gap calculations do not reflect reality. Polaronic distortion was also tentatively put forward as an explanation for the discrepancy between partial fluorescence yield, total fluorescence yield, and total electron yield measurements of the XAS spectra of LiFePO4 and FePO4.

This thesis has detailed the extensive analysis of the XAS and RIXS spectra of LiFePO4 and FePO4, with the primary focus on LiFePO4. One of the primary motivations for this study was to understand the electronic structure of the two compounds and, in particular, shed some light on the nature of electron correlation within the samples. Two classes of band structure calculations have come to light. One solution uses the Hubbard U parameter, and this solution exhibits a band gap of about 4 eV. Other solutions that use standard DFT electron correlation functionals yield band gaps between 0 and 1.0 eV. <p>The RIXS spectra of LiFePO4 and FePO4 were analyzed using Voigt function fitting, an uncommon practice for RIXS spectra. Each of the spectra was fit to a series of Voigt functions in an attempt to localize the peaks within the spectra. These peaks were determined to be RIXS events, and the energetic centers of these peaks were compared to a small band gap band structure calculation. The results of the RIXS analysis strongly indicate that the small gap solution is correct. This was a surprising result, given that LiFePO4 is an ionic, insulating transition metal oxide, showing all of the usual traits of a Mott-type insulator. <p>This contradiction was explained in terms of polaron formation. Polarons can severely distort the lattice, which changes the local charge density. This changes the local DOS such that the DOS probed by XAS or RIXS experiments is not necessarily in the ground state. In particular, polaron formation can reduce the band gap. Thus, the agreement between the small gap solution and experiment is false, in the sense that the physical assumptions that formed the basis of the small gap calculations do not reflect reality. Polaronic distortion was also tentatively put forward as an explanation for the discrepancy between partial fluorescence yield, total fluorescence yield, and total electron yield measurements of the XAS spectra of LiFePO4 and FePO4.