Wannierfunctions are a superposition of the Blochorbitals in a Brillouin zone belonging to a manifold of energy bands. These Wannier functions have several uses regarding the analysis of the crystal on a local level. Since the Bloch orbital has a gauge indeterminacy and the Wannier functions therefore is strongly non-unique, the natural choice is the maximally localized Wannier funcition. These can be calculated from the standard Bloch orbital using unitary transformation by a steepest descent algorithm as proposed by Nicola Marzari and David Vanderbilt. Here the argument for this algorithm is discussed and explained.

This thesis employs experimental and theoretical methods to characterise carbon nitride solids and proposes a generalstructural model for amorphous carbon nitride (a-C:N). It finds that a-C:N deposited by several methods is essentially identical, with similar bonding environments for carbon and nitrogen atoms. Using evidence from several techniques, the saturation of nitrogen in an sp2 carbon matrix is discussed. The experimental studies on a range of carbon nitride solids show no evidence for a crystalline form of carbon nitride. In addition to the experimental characterisation of a-C:N, ab initio molecular dynamics were used to investigate bonding and structure in carbon nitride. These simulations show that the most common form of nitrogen bonding was three-fold sites with a lone pair of electrons. Two-fold nitrogen sites were also found in agreement with experimental findings. An increase of nitrogen in a-C:N decreases the sp3-carbon fraction, but this is not localised on the nitrogen and the effect is most severe at high densities. A simulation of a low density/high nitrogen content network shows that the nitrogen saturation seen experimentally may be due to the formation of N2 dimers and C-N molecules which are easily driven out of the structure. The ab initio simulations also explore the nature of charged nitrogen and carbon sites in a-C:N. An analysis based on Wannier Function centres provided further information about the bonding and allowed for a detailed classification of these sites. The removal of electrons from the networks caused structural changes that could explain the two-state conductivity in ta-C:N memory devices. Finally, a theoretical study of the electron energy-loss near-edge structure (ELNES) calculated using multiple scattering theory is presented. The calculated ELNES of diamond, graphite and boron, silicon and carbon nitride structures compare well to experiment and supports the experimental finding that no crystalline carbon nitride had (or has) been produced. These ELNES calculations will however, provide a means of identifying crystalline beta-C3N4 should it be synthesised.

This thesis employs experimental and theoretical methods to characterise carbon nitride solids and proposes a generalstructural model for amorphous carbon nitride (a-C:N). It finds that a-C:N deposited by several methods is essentially identical, with similar bonding environments for carbon and nitrogen atoms. Using evidence from several techniques, the saturation of nitrogen in an sp2 carbon matrix is discussed. The experimental studies on a range of carbon nitride solids show no evidence for a crystalline form of carbon nitride. In addition to the experimental characterisation of a-C:N, ab initio molecular dynamics were used to investigate bonding and structure in carbon nitride. These simulations show that the most common form of nitrogen bonding was three-fold sites with a lone pair of electrons. Two-fold nitrogen sites were also found in agreement with experimental findings. An increase of nitrogen in a-C:N decreases the sp3-carbon fraction, but this is not localised on the nitrogen and the effect is most severe at high densities. A simulation of a low density/high nitrogen content network shows that the nitrogen saturation seen experimentally may be due to the formation of N2 dimers and C-N molecules which are easily driven out of the structure. The ab initio simulations also explore the nature of charged nitrogen and carbon sites in a-C:N. An analysis based on Wannier Function centres provided further information about the bonding and allowed for a detailed classification of these sites. The removal of electrons from the networks caused structural changes that could explain the two-state conductivity in ta-C:N memory devices. Finally, a theoretical study of the electron energy-loss near-edge structure (ELNES) calculated using multiple scattering theory is presented. The calculated ELNES of diamond, graphite and boron, silicon and carbon nitride structures compare well to experiment and supports the experimental finding that no crystalline carbon nitride had (or has) been produced. These ELNES calculations will however, provide a means of identifying crystalline beta-C3N4 should it be synthesised.

Made available in DSpace on 2014-06-11T19:23:29Z (GMT). No. of bitstreams: 0 Previous issue date: 2007-12-18Bitstream added on 2014-06-13T19:50:17Z : No. of bitstreams: 1 nacbar_dr_me_bauru.pdf: 1169690 bytes, checksum: c7a661675601c87b8e63ac301a1c144c (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / São calculadas e analisadas as funções de Wannier de localização máxima para elétrons em cristais unidimensionais. Essas funções formam uma base apropriada para descrever estados eletrônicos em materiais sólidos. Para cristais com simetria de inversão é utilizado o método desenvolvido por Bruno-Alfonso e Hai [J. Phys: Condensed Matter 15, 6701 (2003)]. Cada banda de energia é classificada segundo a simetria das funções de Bloch nos pontos 'gama' e 'qui' da zona de Brillouin. Para cada classe de banda a fase das funções de Bloch é escolhida para que as funções de Wannier tenham localização máxima. A simetria da últimas é determinda pelo tipo de banda. São apresentados resultados analíticos e numéricos para o modelo de Kronig-Penney obtidos através da técnica da matriz de transferência e do método tight binding. Posteriormente, apresenta-se um novo procedimento para calcular funções de Wannier de localização máxima em cristais sem simetria de inversão. Para isso são utilizadas técnicas do Cálculo Variacional. A teoria é aplicada para obter e analisar funções de Wannier de elétrons de condução em duas superredes de materiais semicondutores. Uma dessas estruturas tem simetria de inversão e a outra, não. O comportamento assintótico das funções de Wannier é predito analiticamente e verificado através dos cálculos numéricos. As funções de Wannier de localização máxima mostram um decaimento exponencial multiplicado por um decaimento em lei de potência, ambos isotrópicos. O mesmo acontece com parte das funções que não tem localização máxima. Porém, há outras que que apresentam decaimento exponecial reduzido e anisotropia em seu decaimento em lei de potência. Esses resultados novos são explicados levando em conta pontos de ramificação da continuação analítica das funções de Bloch sobre o plano de vetor de onda complexo. / The maximally localized Wannier functions of electrons in one-dimensional crystals are calculated and analyzed. Those functions form a suitable basis to describe localized states in solid materials. For crystals with inversion symmetry we use the procedure of Bruno-Alfonso and Hai [J. Phys: Condensed Matter 15, 6701 (2003)]. Each energy band is classified according to the symmetry of the Bloch functions at the points 'gama' e 'qui' of the Brillouin zone. For each band class, the phase of the Bloch functions in chosen to give the maximally localized Wannier functions. The symmmetry of those functions depends on the band class. Analytical and numerical results are presented for the Kronig-Penney model. Those result are obtained through the tight-binding method or a transfer-matrix technique. A new procedure to calculate the maximally localized Wannier functions in crystals without inversion symmetry is established. This involves techniques of the Variational Calculus. The theory is applied to obtain the Wannier functions of conduction electrons in superlattices of semiconductor materials. One of the superlattices presents inversion symmetry, but the other does not. The asymptotic behavior of the Wannier functions is predicted analytically and verified through numerical calculations. The maximally localized Wannier functions display an isotropic exponetial decal times an isotropic power-law decay. The same applies to a class of non-optimal Wannier functions. However, there is another class of non-optimal Wannier functions with reduced exponential decay and anisotropic power-law decay. Such new results are explained by taking into account branch points in the analytical continuation of the Bloch functions into the plane of complex wave vector.

Orientador: Alexys Bruno Alfonso / Banca: Guo-Qiang Hai / Banca: Aguinaldo Robinson de Souza / O Programa de Pós-Graduação em Ciência e Tecnologia de Materiais, PosMat, tem caráter institucional e integra as atividades de pesquisa em materiais de diversos campi da Unesp / Resumo: São calculadas e analisadas as funções de Wannier de localização máxima para elétrons em cristais unidimensionais. Essas funções formam uma base apropriada para descrever estados eletrônicos em materiais sólidos. Para cristais com simetria de inversão é utilizado o método desenvolvido por Bruno-Alfonso e Hai [J. Phys: Condensed Matter 15, 6701 (2003)]. Cada banda de energia é classificada segundo a simetria das funções de Bloch nos pontos 'gama' e 'qui' da zona de Brillouin. Para cada classe de banda a fase das funções de Bloch é escolhida para que as funções de Wannier tenham localização máxima. A simetria da últimas é determinda pelo tipo de banda. São apresentados resultados analíticos e numéricos para o modelo de Kronig-Penney obtidos através da técnica da matriz de transferência e do método tight binding. Posteriormente, apresenta-se um novo procedimento para calcular funções de Wannier de localização máxima em cristais sem simetria de inversão. Para isso são utilizadas técnicas do Cálculo Variacional. A teoria é aplicada para obter e analisar funções de Wannier de elétrons de condução em duas superredes de materiais semicondutores. Uma dessas estruturas tem simetria de inversão e a outra, não. O comportamento assintótico das funções de Wannier é predito analiticamente e verificado através dos cálculos numéricos. As funções de Wannier de localização máxima mostram um decaimento exponencial multiplicado por um decaimento em lei de potência, ambos isotrópicos. O mesmo acontece com parte das funções que não tem localização máxima. Porém, há outras que que apresentam decaimento exponecial reduzido e anisotropia em seu decaimento em lei de potência. Esses resultados novos são explicados levando em conta pontos de ramificação da continuação analítica das funções de Bloch sobre o plano de vetor de onda complexo. / Abstract: The maximally localized Wannier functions of electrons in one-dimensional crystals are calculated and analyzed. Those functions form a suitable basis to describe localized states in solid materials. For crystals with inversion symmetry we use the procedure of Bruno-Alfonso and Hai [J. Phys: Condensed Matter 15, 6701 (2003)]. Each energy band is classified according to the symmetry of the Bloch functions at the points 'gama' e 'qui' of the Brillouin zone. For each band class, the phase of the Bloch functions in chosen to give the maximally localized Wannier functions. The symmmetry of those functions depends on the band class. Analytical and numerical results are presented for the Kronig-Penney model. Those result are obtained through the tight-binding method or a transfer-matrix technique. A new procedure to calculate the maximally localized Wannier functions in crystals without inversion symmetry is established. This involves techniques of the Variational Calculus. The theory is applied to obtain the Wannier functions of conduction electrons in superlattices of semiconductor materials. One of the superlattices presents inversion symmetry, but the other does not. The asymptotic behavior of the Wannier functions is predicted analytically and verified through numerical calculations. The maximally localized Wannier functions display an isotropic exponetial decal times an isotropic power-law decay. The same applies to a class of non-optimal Wannier functions. However, there is another class of non-optimal Wannier functions with reduced exponential decay and anisotropic power-law decay. Such new results are explained by taking into account branch points in the analytical continuation of the Bloch functions into the plane of complex wave vector. / Mestre