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.

Este trabalho é um estudo das dispersões metrológicas em aproximações de funções tidas como não conhecidas ou não totalmente conhecidas. A metodologia alternativa para esse fim são as redes neurais artificiais do tipo Multilayer Perceptrons (MLP), aqui utilizadas como aproximadoras de funções. As funções aproximadas são curvas de calibração decorrentes de indicações de instrumentos ou sistemas de medição numa calibração. Essas curvas levam consigo propriedades metrológicas e possuem, neste trabalho, papel de ponte entre os elementos considerados da teoria metrológica e os elementos considerados da teoria da Inteligência Computacional: as Multilayer Perceptrons (MLPs). Uma balança externa de medição de esforços aerodinâmicos e uma Língua Eletrônica (LE), aplicada na medição da concentração de cátions, foram os meios de aplicação dos conceitos dessa metodologia alternativa. As proposições desta tese visam implementar melhorias na exatidão do ajuste das curvas de calibração por meio da consideração dos seguintes fatores: grandezas de influências, incertezas nos Valores Objetivos (VOs), tendência de medição de erros sistemáticos ocultos ou não solvidos e indicadores de desempenho metrológicos. A indicação da qualidade na medição ou a indicação da competência metrológica de um laboratório de calibração é estabelecida pelos valores das incertezas, e a curva de calibração é o ponto de partida para os cálculos desses valores. Visto que o estabelecimento dessa curva é uma das dificuldades para o cálculo das incertezas e a própria curva é uma fonte de incerteza, sua aproximação requer uma a cuidadosa e meticulosa metodologia, daí a importância estratégica deste trabalho. As dispersões metrológicas possuem conotação de incertezas nas medições e elas são a base para a determinação de seu valor numérico; assim, os indicadores de desempenho podem representar essas dispersões e a recíproca também é verdadeira: a incerteza padrão pode ser um dos indicadores de desempenho. Sintetizando, nesta tese é mostrado de que forma a teoria da inteligência computacional adentra na teoria da metrologia e vice versa, nas esferas dos elementos aqui considerados. / The present study investigates metrological dispersions in fitting partially or totally unknown functions. An alternative method is the application of a multilayer perceptron neural network used here to fit functions. The fitting functions are calibration curves from calibration indications of measurement systems or instruments. These curves hold metrological properties and establish a link between elements of Metrological theory and elements of Computing Intelligence theory: the Multilayer Perceptrons. An external balance of aerodynamic forces and moments and an electronic tongue applied in the measurement of cation concentrations were the measurement systems used to apply the concepts of this alternative methodology. This thesis proposes improvements in the accuracy of fitting calibration curves considering the following factors: influence quantities, uncertainties about target values, tendency of hidden or not solved systematic errors and metrological performance functions. The measurement quality indicator or the laboratory metrological competence indicator is established by uncertainty values and the calibration curve is the starting point for the calculation of these values. The establishment of this curve is one of the difficulties in assessing uncertainties and the curve itself is an uncertainty source. Therefore, a careful and meticulous methodology is necessary in curve approximation, which explains the strategic importance of this work. Metrological dispersions have connotation of uncertainty in measurements and are the basis for calculating their numerical values, the performance functions can represent metrological dispersions and the opposite is also true: the standard uncertainty can be a performance function. Making a synthesis, this thesis demonstrates how computing intelligence theory takes into account the metrological theory and vice versa, in the elements of these theories that were discussed in the present study.

Este trabalho é um estudo das dispersões metrológicas em aproximações de funções tidas como não conhecidas ou não totalmente conhecidas. A metodologia alternativa para esse fim são as redes neurais artificiais do tipo Multilayer Perceptrons (MLP), aqui utilizadas como aproximadoras de funções. As funções aproximadas são curvas de calibração decorrentes de indicações de instrumentos ou sistemas de medição numa calibração. Essas curvas levam consigo propriedades metrológicas e possuem, neste trabalho, papel de ponte entre os elementos considerados da teoria metrológica e os elementos considerados da teoria da Inteligência Computacional: as Multilayer Perceptrons (MLPs). Uma balança externa de medição de esforços aerodinâmicos e uma Língua Eletrônica (LE), aplicada na medição da concentração de cátions, foram os meios de aplicação dos conceitos dessa metodologia alternativa. As proposições desta tese visam implementar melhorias na exatidão do ajuste das curvas de calibração por meio da consideração dos seguintes fatores: grandezas de influências, incertezas nos Valores Objetivos (VOs), tendência de medição de erros sistemáticos ocultos ou não solvidos e indicadores de desempenho metrológicos. A indicação da qualidade na medição ou a indicação da competência metrológica de um laboratório de calibração é estabelecida pelos valores das incertezas, e a curva de calibração é o ponto de partida para os cálculos desses valores. Visto que o estabelecimento dessa curva é uma das dificuldades para o cálculo das incertezas e a própria curva é uma fonte de incerteza, sua aproximação requer uma a cuidadosa e meticulosa metodologia, daí a importância estratégica deste trabalho. As dispersões metrológicas possuem conotação de incertezas nas medições e elas são a base para a determinação de seu valor numérico; assim, os indicadores de desempenho podem representar essas dispersões e a recíproca também é verdadeira: a incerteza padrão pode ser um dos indicadores de desempenho. Sintetizando, nesta tese é mostrado de que forma a teoria da inteligência computacional adentra na teoria da metrologia e vice versa, nas esferas dos elementos aqui considerados. / The present study investigates metrological dispersions in fitting partially or totally unknown functions. An alternative method is the application of a multilayer perceptron neural network used here to fit functions. The fitting functions are calibration curves from calibration indications of measurement systems or instruments. These curves hold metrological properties and establish a link between elements of Metrological theory and elements of Computing Intelligence theory: the Multilayer Perceptrons. An external balance of aerodynamic forces and moments and an electronic tongue applied in the measurement of cation concentrations were the measurement systems used to apply the concepts of this alternative methodology. This thesis proposes improvements in the accuracy of fitting calibration curves considering the following factors: influence quantities, uncertainties about target values, tendency of hidden or not solved systematic errors and metrological performance functions. The measurement quality indicator or the laboratory metrological competence indicator is established by uncertainty values and the calibration curve is the starting point for the calculation of these values. The establishment of this curve is one of the difficulties in assessing uncertainties and the curve itself is an uncertainty source. Therefore, a careful and meticulous methodology is necessary in curve approximation, which explains the strategic importance of this work. Metrological dispersions have connotation of uncertainty in measurements and are the basis for calculating their numerical values, the performance functions can represent metrological dispersions and the opposite is also true: the standard uncertainty can be a performance function. Making a synthesis, this thesis demonstrates how computing intelligence theory takes into account the metrological theory and vice versa, in the elements of these theories that were discussed in the present study.