DISSERTAÇÃO DE MESTRADO - PROGRAMA DE PÓS-GRADUAÇÃO EM FISICA
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Item Caracterização estrutural, vibracional e térmica de microbastões de AgVO3(Universidade Federal do Maranhão, 2023-10-11) MIRANDA, Antonio Werbeson; MENEZES, Alan Silva de; http://lattes.cnpq.br/0383834501086115; MOURA, João Victor Barbosa; http://lattes.cnpq.br/0208481199560436; MOURA, João Victor Barbosa; http://lattes.cnpq.br/0208481199560436; MENEZES, Alan Silva de; http://lattes.cnpq.br/0383834501086115; SANTOS, Clenilton Costa dos; http://lattes.cnpq.br/9192468880980905; LIMA, Cleânio da Luz; http://lattes.cnpq.br/3755429557895237In this work we present a study of the structural and phonon properties of silver vanadates in the α-AgVO3 and β-AgVO3 structures. The samples were synthesized by the coprecipitation method and characterized by X-ray Diffraction (XRD), Raman Spectroscopy and Scanning Electron Microscopy (SEM). The α-AgVO3 and β-AgVO3 crystals have rod morphology with micrometric diameter. XRD analyzes together with Rietveld refinement confirmed that the α- AgVO3 sample crystallized in the monoclinic structure of space group C2/c, Z = 8, with the lattice parameters a = 10.4499(8) Å, b = 9, 9256 (5) Å, c = 5.5260 (4) Å, β = 99.647 (8) °, V = 565.07 (7) Å3 , while the β-AgVO3 sample was obtained in the monoclinic structure of space group C1/ m1, Z = 8, with the lattice parameters a = 18.1177 (3) Å, b = 3.58232 (8) Å, c = 8.0389 (2) Å, β = 104.437 (1) °, V = 505.27 (2) Å3 . XRD experiments at low temperatures (298 – 12 K) demonstrated thermal stability of the α-AgVO3 and β-AgVO3 phases and uniaxial negative thermal expansion in the b direction of the β-AgVO3 microcrystals. Raman Spectroscopy and XRD experiments at high temperatures (298 – 673 K) demonstrate that α- AgVO3 microrods exhibit two temperature-induced phase transitions at 413 and 513 K during heating (α → α' → β'), and a transition at 433 K to the β-AgVO3 phase during return to room temperature (β' → β). The β-AgVO3 microrods show a structural transition from the monoclinic phase to a triclinic phase at 473 K (β → β’). The temperature-induced structural modifications in the α-AgVO3 and β-AgVO3 phases, as well as the uniaxial negative thermal expansion in the β-AgVO3 phase are not yet demonstrated in the literature.Item Estudo de plasmas magnetizados na eletrodinâmica de Maxwell-Carroll-Field-Jackiw(Universidade Federal do Maranhão, 2021-07-17) RIBEIRO, Filipe dos Santos; FERREIRA JUNIOR, Manoel Messias; http://lattes.cnpq.br/5263880569990712; FERREIRA JUNIOR, Manoel Messias; http://lattes.cnpq.br/5263880569990712; SANTOS, Frederico Elias Passos dos; http://lattes.cnpq.br/8422758837336123; SANTOS FILHO, Adalto Rodrigues Gomes dos; http://lattes.cnpq.br/9485040610659823; POCHA JUNIOR, Roldão da; http://lattes.cnpq.br/6017951215928479The present work addresses, in a simpli ed way, Appleton's model for magnetized plas mas in the context of the usual Maxwell theory and Maxwell-Carroll-Field-Jackiw (MCFJ) electrodynamics, endowed with a xed 4-vector of Lorentz symmetry violation. We begin by reviewing the essential aspects of electromagnetic (EM) wave propagation in plasmas, analy zing the scattering relations, refractive index, propagation modes, and the birefringence e ect. In the sequel, we revisit some basic aspects of Carroll, Field, and Jackiw's electrodynamics, such as the derivation of the modi ed Maxwell equations and extended scattering relations, which leads to birefringence in vacuum. Finally, we study Appleton's model in the context of MCFJ electrodynamics in order to verify the e ects of the CPT- odd term on the propaga ting modes. Using the same procedure, we nd the relations of scattering, refractive index, propagating modes, and the birefringence e ect. We highlight how the CFJ term alters the propagation indices and acts on the propagating modes.Item Dinâmica de sólitons vetoriais em condensados de Bose-Einstein com interação spin-órbita(Universidade Federal do Maranhão, 2019-03-08) FLORIAN, Cesar Antonio Ibañez; MEZA, Luis Enrique Arroyo; 233535318-74; http://lattes.cnpq.br/1755968991106692; CASTRO, Luis Rafael Benito; 231815238-10; http://lattes.cnpq.br/5687023539793609; HOTT, Marcelo Batista; http://lattes.cnpq.br/0212227705231604; SILVA, Edilberto Oliveira; http://lattes.cnpq.br/3258989322547560; MEZA, Luis Arroyo; http://lattes.cnpq.br/1755968991106692; CASTRO, Luis Rafael Benito; http://lattes.cnpq.br/5687023539793609Nowadays, the experimental realization of a Bose-Einstein condensate (BEC) of atoms with spin-orbit interaction (SOC) has aroused a new interest in studying the intriguing and interesting properties of the system. For example, a BEC of 87Rb atoms (with atomic hyper ne state f = 1) trapped in cigar form (quasi-one-dimensional) can be subjected to an external magnetic eld, which causes the Zeeman e ect on the states of its constituent atoms. Then, through of an arrangement of Raman-type laser and a certain frequency of the lasers, it is possible to induce a transition between the sub-levels mf = 1 and mf = 0, thus leading to spin-orbita coupling, between the hyper ne sub-levels, and a mixture of states for each sub-level. In this dissertation, we study several dynamics of the bright-bright vector soliton, in (1 + 1) space-time dimensions, which are created in a BEC of two internal state atoms, with and without spin-orbit coupling, governed by two equations of Gross-Pitaevskii coupled. To solve the coupled equations, we employed the variational approximation, being used recently for this type of system. In both cases, with and without spin-orbit coupling, we present exact analytical solutions, which solve the equations of motion with di erent polynomial potentials. From the analytical solutions, we study the precession of the system pseudo-spin vector S = 1=2, the unbalance of the pseudo-spin Sz of the soliton, the phase di erence between the soliton components (internal dynamics of soliton), in addition, we also study the movement of the center of mass of the system, and the evolution of the linear momentum of the system (external dynamics of the soliton). We explicitly show the in uence of external potential on the pseudo-spin precission of the system. Finally, we study numerically the stability conditions of the bright-bright soliton solutions, obtained in this work, under small disturbances in their initial condition.Item Vórtices BPS no modelo de Maxwell- CP(2) com estrutura interna(Universidade Federal do Maranhão, 2019-04-23) ANDRADE, João Luís Brandão; SANTOS, Carlos Eduardo da Hora; 943294943-53; http://lattes.cnpq.br/3418148094049270; SANTOS, Carlos Eduardo da Hora; 943294943-53; http://lattes.cnpq.br/3418148094049270; SIFUENTES, Rodolfo Alván Casana; http://lattes.cnpq.br/6508618435773438; SIMAS, Fabiano de Carvalho; http://lattes.cnpq.br/1410695036306945In this dissertation, I present the original BPS vortices (Bogomol'nyi-Prasad-Sommer)eld) inherent in a gauge model Maxwell-CP(2) from the general scenario CP (N-1) (in which N = 3, with N corresponding to the number of components of the CP (2) field), when subjected to the presence of an additional, real and neutral scalar field. Then, focusing on radially symmetrical structures, we construct a first-order structure for the model, using the Bogomol'nyi procedure. From the minimization of the total energy, we obtain general expressions for the minimum energy of the model, whose value has an extra contribution due to the presence of the neutral field, and for the respective first order equations (BPS equations), in which both the minimum energy while the BPS equations depend directly on the functional structure of the dielectric function. The introduction of the scalar field, which interacts with the electromagnetic sector via an unusual dielectric function, produces significant modifications in the shape of the resulting BPS vortices, such changes being understood as the manifestation of internal structures originated by the presence of the additional neutral field.Item Armadilhamento de Campos de Spin-0 em um Anel imerso em (3,1) dimensões(Universidade Federal do Maranhão, 2011-08-29) SIMAS, Fabiano de Carvalho; SANTOS FILHO, Adalto Rodrigues Gomes dos; 136440738-80; http://lattes.cnpq.br/9485040610659823In this work we consider rings constructed with a scalar field ϕ with radial symmetry embedded in the (3, 1) Minkowski spacetime. Such topological defects have radius and thickness related to the energy density and can be attained from a lagrangian density explicitly dependent with the distance,which can be interpreted as an effective theory from a more fundamental model. Neglecting the backreaction on a weak scalar field Φ coupled with the strong field ϕ, a standard mode decomposition leads to a standard action for one-dimensional Klein-Gordon fields living along the ring axis and a two-dimensional Schr¨odinger-like equation, describing massive spin-0 particles. A specific choice of the coupling between the scalar fields Φ and ϕ is able to transform the Schr¨odinger-like equation in a one-dimensional form depending on the radial distance. The interaction is compatible with a repulsive character of the core of the ring and with the presence of resonances around the ring radius. The presence of tachyonic and physical modes are described in a phase space diagram, which is confronted with the numerical analysis of the massive modes. It is found that, for the scale of rings considered, larger radius favor the localization process, and for small radius the leaking of the massive modes is compatible with a repulsive interaction acting between the rings walls and the massive spin-0 particles.Item Síntese e Determinação da Estrutura do Complexo NI(II)(L-TREONINA)2(H2O)2 por Difração de raios - X em Monocristais(Universidade Federal do Maranhão, 2015-08-21) Melo, Ezequiel Borges; MENEZES, Alan Silva de; 642.782.713-87Amino acids, having both the carboxylic group and amine group, may act as bidentate ligands and, depending on its radical group can also act as tridentate ligands. Amino acids complexed with transition metals have attracted the interest of chemists and physicists because of its possible applications and physical properties. L-threonine complexes with Cu+2 (Cu(II)(L-Threonine)2(H2O)), Co+2 (Co(II)(L-Threonine)2(H2O)2) e Zn+2 (Zn(II)(L-Threonine)2(H2O)2) transition metals already exist in the literature and their crystalline structures are different. However, L-threonine complexed with Ni+2 was not found in the literature. Thus, in this study, we used the amino acid L-threonine as a ligand and Ni+2 ion as the transition metal to obtain the crystal of L-threonine complexed with Ni. For that we used the Slow Evaporation crystal growth method, where a solution containing L-threonine and NiCl2.6H2O with molar ratio (2:1) and NaOH to get a basic pH, is allowed to stand for promoting the crystal growth. To get the crystal structure of this material, X-ray diffraction measures were carried in a APEX2 DUO diffractometer of the Crystallography Laboratory in the Physics Institute of UFG. The data analysis and the resolution of the structure were performed the package Bruker SHELXTL and also using the mechanism of structural determination by Direct Methods, one of the most used ways to overcome the phase problem in the structure determination of small molecules. L-threonine complexed with Ni has the chemical formula Ni(II)(L-Treonina)2(H2O)2 and crystallizes in the orthorhombic system with space group C2221. Thus, we identified that the Ni(II)(L-Treonina)2(H2O)2 crystal has a very similar crystalline structure as Co(II)(L-Treonina)2(H2O)2. Furthermore, the knowledge of the structure of this material opens up a range studies can be performed on it.Item Aspectos clássicos da eletrodinâmica de Maxwell suplementada pelo termo CPT-par do setor de gauge do Modelo Padrão Estendido(Universidade Federal do Maranhão, 2009-07-06) Pinheiro, Paulo Rogério Dias; FERREIRA JUNIOR, Manoel Messias; 021.133.087-62The possibility of spontaneous breaking of Lorentz symmetry in the context of string theory appeared in 1990´s as an element capable to direct new ways for developing physics at Planck scale. Possible breaking of Lorentz invariance is seen as a characteristic of the physics beyond the usual Model Standard, that forbids such breaking in its structure. The observation of Lorentz breaking (LV) at lower energies can be seen as an evidence of occurrence of Lorentz spontaneous breaking at Planck scale, with important consequence for the development of the quantum gravitation theory. This work aims at studying the LV effects in a regime of low energies, more necessarily in the context of the Maxwell electrodynamics, in the presence of the CPT-even term (W∝υρφF∝υFρφ) of the standard model extension. In the first part of the work, we deal with the electrodynamics stemming from the parity-odd sector of the tensor W∝υρφ, where the electric and magnetic sectors are connected by the breaking parameter (violating vector k). The method of Green is then used to yield the classic solutions for this electrodynamics. It is observed that Lorentz-violating coefficients contribute in first order for the electric and magnetic sectors. An experiment of feasible accomplishment in laboratory is considered for stipulating an upper bound for the background magnitude (k < 10−16). In the sequel we deal with the electrodynamics stemming from the parity-even sector of the tensor W∝υρφ. The solutions for the electric and magnetic sector are attained similarly by the Green method. With such solutions, we are able to impose an upper bound on the parameters: (eκe−)ib < 2.9 × 10−20. Finally, we evaluate the gauge propagator of this theory, both for the parity-even and the parity-odd sectors. We then use it to analyze the stability, causality and unitary of this model. Keywords: Maxwell electrodynamics, Lorentz symmetry, Classical solutions,Item Estudo da consistência e soluções clássicas da eletrodinâmica de Maxwell-Carroll-Field- Jackiw-Proca(Universidade Federal do Maranhão, 2008-08-21) Santos, Carlos Eduardo da Hora; FERREIRA JUNIOR, Manoel Messias; 021.133.087-62In this work, we investigate some significant aspects of the Maxwell-Carroll-Field- Jackiw-Proca (MCFJP) electrodynamics. This electrodynamics is built through the im- plementation of the Carroll-Field-Jackiw(CFJ) term on the Proca Lagrangian. The CFJ term is the CPT odd term of the gauge sector of the Standard Model Extension. First, we verify under which circumstances this model yields a consistent Quantum Field The- ory (QFT) capable of describing the interactions mediated by photons. In this sense, the propagator ‹Aα(k)Av (k)› is carried out, with the dispersion relations and associated propagation modes being determined. Then, we verify which of these modes are stable, causal and unitary. Only when the theory is causal, stable and unitary, we can say that it can be consistently quantized. It follows that the MCFJP electrodynamics is consistent only for a purely space-like background field, Vα = (0; v). A posteriori, we investigate the classical solutions (static and stationary) of MCFJP electrodynamics. The starting point is the wave equation for the gauge field A (r), which through the use of Green Method, yields explicit expressions for A (k). For a purely time-like background field, Vα= (v0; 0), an exponentially decreasing solution for the electric sector is obtained, equal to the Maxwell-Proca solution. Therefore, the background does not promote any change in electric sectors of the MCFJP and MCFJ electrodynamics. On the other hand, the magnetic sector is changed: for stationary currents, it displays an oscillating behavior [in Maxwell-Proca (MP) electrodynamics, these solutions have an exponentially decreasing behavior]. In the limitMA!0, we obtain the stationary field B(r) ofMCFJ electrodynam- ics (oscillating behavior), which is compatible with the emission of Cerenkov radiation. For a purely space-like background, V = (0; v), we obtain stationary solutions at second order in v, assuming v2 M2 A ; and v jj r. It appears that both magnetic and electric sectors display exponentially decreasing solutions, which recover those ones of the MP electrodynamics in the limit v → 0.Item Propriedades térmicas, dielétricas e vibracionais de Ormosil's baseados em DPMS e TEOS dopados com MDS(Universidade Federal do Maranhão, 2008-05-21) Pinto, Raffael Costa de Figueiredo; PASCHOAL, Carlos William de Araújo; 461.412.863-72In this work have been investigated the dielectric and vibrational properties of the ORMOSIL membranes based on PDMS and TEOS doped with MDS using the Di erential Scanning Calorimetry (DSC), impedance, Raman and infrareds spectroscopy technics. Such membranes are hybrid organic-inorganic materials with potential application in PEMFC (Proton Exchange Membrane Fuel Cell) and were doped with concentrations 0%(Pure Membrane), 5%, 10%, 20% e 30% of MDS. The thermal measurements were performed in the range from room temperature and 550 oC. The results showed that, after the MDS inclusion, the membranes absorb water. Besides, then thermal stability of the membranes decreased with the MDS inclusion. The dielectrics measurements were performed in temperature range of 313K-373K. The results showed that room temperature conductivity increases linearly with the frequency, until 353K, suggesting a hopping conduction and leaving this linear behavior above 353K. Besides, it was observed that conductivity doesn't increases linearly with MDS concentration, but increases until maximal value for 20% MDS concentration and decreases again for 30% MDS concentration de ning a synergetic e ect, which probably is associate with con gurational arrange of microcristallites MDS. Another feature of that membranes is a relaxation process visible in the electrical module graphics which appear just in doped membranes, being however, due to the MDS. The vibrational properties of hybrids membranes were obtained through Raman scattering and infrared. The results con rmed the presence of Si¡O¡Si, Si¡C, Si¡OH, C2H5, Si¡CH3, CH3, CH2, C¡H, S=O and S¡O groups. Where the S=O and S¡O groups are presents just in MDS compound. Consequently, their respective peaks appear only in the doped membrane spectra.Item Transições de fase em monocristais de Na2ThF6(Universidade Federal do Maranhão, 2008-05-20) Melo, Wanessa David Canêdo; PASCHOAL, Carlos William de Araújo; 461.412.863-72In this work we have studied possible phase transitions in Na2ThF6 single crystals using Di erential Scanning Calorimetry (DSC), Raman and Impedance spectroscopies and static simulations. The polarized Raman spectroscopy measurements were performed in the temperature range from 10 K up to 770 K and DSC measurements from 298 K up to 823 K. The results indicate that the Na2ThF6 single crystal are structurally stable in the temperature ranging from 50 K up to 770 K. Below 50 K, a mode with A1 symmetry disappear indicating a possible phase transition. Besides, the bandwidth of the main Raman modes increases with the temperature showing a behavior like Ahrrenius with activation energies of 0,17 eV and 0,16 eV. The Impedance spectroscopy measurements were performed in the temperature range between 298K and 773K in the clivage (311) crystalline plane. The results indicate an increase in the ionic conductivity at high temperatures showing a conduction mechanism with activation energy of 0,28 eV. The imaginary part of the dielectric constant and conductivity present an anomaly at around 735 K, possibly associated to a superionic behavior. The static simulations were performed using the GULP code in the hydrostatic pressure range between room pressure and 20 GPa, showing that the z coordinate of the Na+ ion tends to value 1=2 at around 6 GPa, indicating a possible structural phase transition induced by hydrostatic pressure. The ferroic characteristic of this transition was de ned according to the changes observed for the piezoelectric and compliance tensors.Item Simulações atomísticas em trifluoretos (REF3) e óxidos metálicos mistos (Re(TiTa)06) de terras-raras(Universidade Federal do Maranhão, 2006-02-22) Diniz, Eduardo Moraes; PASCHOAL, Carlos William de Araújo; 461.412.863-72In this work static atomistic simulations were performed to investigate two systems: rare-earth trifluorides, REF3, with tysonite structure (RE = La, Ce, Pr and Nd) and rare-earth mixed metallic oxides, RE(TiTa)O6, with RE = Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Y, Er and Yb. In the rare-earth trifluorides was investigated the pressure induced structural phase transition identified by X-ray powder difraction in RE = La and Ce. The results shown that the crystalline structure is possibly tetragonal, in concordance with quantum mechanical calculations. For this, an interionic potential set that describes better the structural data of each compound and the physical observable was obtained. Besides, it was observed that critical pressure values were closed. The study involving the rare-earth mixed metallic oxides was focused in determining their bulk and structural properties. Thus, firstly a set of reliable interionic potentials was looked for to reproduce the crystalline structure and the physical observable, trough the investigation of three methodologies for obtaining interionic potentials, assuming the methodology that reproduces more reliable the dielectric constants. Furthermore, others bulk properties as lattice energy formation, elastic constants and bulk modulii were calculated. All then shown a rare-earth ionic radii dependence that revealed the morphotropic phase boundary between aeschynite and euxenite crystalline structures presented by these crystals.Item Espalhamento quântico unidimensional via mecânica quântica supersimétrica(Universidade Federal do Maranhão, 2017-03-03) Soares, Camila Correia; CASTRO, Luis Rafael Benito; 231.815.238-10In this work, we study the formalism of the supersimmetric quantum mechanics (SUSY QM) starting with hamiltonian fatorization method of the bosonic harmonic oscillator (BHO) by means of ladders operators and we extended to hamiltonian of oscillators in general, inclusive of the fermionic harmonic oscillator (FHO), with their respective properties. We show that the SUSY QM for bound states, connect hamiltonians, potentials, and eigenvalues energy of different systems which are called supersymmetric partners. In the case scattering states, we notice that SUSY QM applies only in shape invariant potentials (SIPs). Despite this restriction, the SIPs are commonly used in literature by its wide applicability as in particles physics as in condensed matter. Therefore, we study the scattering states to the problem of massive relativistic fermions under the influence of modified Pöschl-Teller potential (PT), which is shape invariant. We calculate the transmission (T) and reflection (R) coefficients, just knowing the superpotential, which was carried out in a simple and elegant form. Thus, the study of the quantum scattering via SUSY QM becomes a powerful tool in the calculations of T and R.Item PROPRIEDADES VIBRACIONAIS E TRANSIÇÃO DE FASE DO PIROCLORO Bi₂Sn₂O₇(Universidade Federal do Maranhão, 2012-03-28) Silva, Rosivaldo Xavier da; PASCHOAL, Carlos William de Araújo; CPF:46161286372; Batista, Jerias Alves; CPF:30447984549; http://lattes.cnpq.br/1319645549100341In this work we investigated the vibrational, structural and dielectric properties of pyrochlore Bi2Sn2O7 (BSO) by Raman spectroscopy, differential scanning calorimetry (DSC) and infrared specular reflectance. The Raman spectrum of BSO was obtained as a function of temperature in the range from 23°C to 427°C. It was observed 18 broad Raman bands at room temperature (α phase) which have been classified according to the literature. The investigation of the evolution of the position, width, integrated area and intensity on the Raman modes depending on the temperature allowed estimating the temperature of the structural transition BSO α ( ) → β ( ) by approximately 127°C. The thermogram obtained by DSC under heating rates of 10K/min and 20K/min showed a peak with onset enthalpy at 98°C. Such peak was associated with the loss of structural domains discussed in the literature. Furthermore, theoretical calculations indicate that the observed peak is related to a displacive phase transition. The infrared reflectance spectrum was obtained at room temperature in the range 60 4000 cm-1, whose setting allowed us to identify the frequencies of transverse and longitudinal optical phonons which were also classified based on the literature. It was estimated the static dielectric constant, the dielectric losses tanδј and quality factor Q for the BSO in the microwave region. The dispersion parameters numerically obtained by Kramers - Kronig show to be in agreement with results obtained from the reflectance fitting.Item Estudo de Primeiros Princípios de Bundles de Nanotubos de Nitreto de Boro sob Pressão Hidrostática(Universidade Federal do Maranhão, 2007-08-21) Coutinho, Samir Silva; GUERINI, Silvete Coradi; CPF:59914424015In this work were studied the electronic, vibrations and structural properties of boron nitride nanotube bundles (16,0), (12,0) and (8,0), when submitted to the hydrostatic pressure changes. To study such properties, we used the ab initio method employing density functional theory in the approach of the generalized gradient approximation. All the simulations were performed using of the siesta code. The obtained results showed that the circular cross section of each one of the studied bundles undergoes a deformation (elliptic) when applied pressure reaches the value of P > 1,0 GPa for the bundle (16,0), P > 2,0 GPa for the bundle (12,0) and for values greater then 6,5 GPa for the bundle (8,0). For each pressure interval it was calculated the percent relative volume, cohesive energy, modes of vibrations and the band structures. The analysis of the electronic properties, through the band structures, indicates that the characteristics semiconducting of boron nitride nanotubes is preserved during the pressure increasing.Item PROPRIEDADES VIBRACIONAIS E DIELÉTRICAS DA MULITA Bi2Mn4O10(Universidade Federal do Maranhão, 2010-11-30) Silva Júnior, Flávio Moura e; PASCHOAL, Carlos William de Araújo; CPF:46161286372In this work we investigated the vibrational properties of ceramics Bi2Mn4O10 (BMO) at room temperature by the Raman and Infrared spectroscopies, the phonons were classified by FG matrix method of Wilson. The dielectric properties of the material, in turn, were studied using the impedance spectroscopy in a range of 22 ° C to 275 ° C. Furthermore, static atomistic simulations were performed at BMO in the range 0.0 to 10 GPa with a step of 0.5 GPa. Concerning the Raman modes, ten out forty eight modes predicted by the group theory, were observed in our experimental spectrum while the spectrum of the imaginary part of inverse dielectric constant, we observe 19 LO modes active in infrared. By using the method of FG Wilson saw that the modes in the range of 600-760 cm-1 are stretching into the ab plane to the octahedral chains MnO6. Libration and bending modes were predicted to 400-570 cm-1 and 300-400 cm-1, respectively. It was further observed that the low-frequency modes are mainly due to translations of the Bi ions. The analysis of the impedance spectroscopy measurements led to the conclusion that the relaxing process of BMO are associated with conductive mechanisms, these being due to movement of polarons. The frequencies, for which the imaginary parts of the module (M '' ) and impedance ( Z '' ) exhibit a maximum, obeyed the Arrhenius law in its dependence on the reciprocal temperature, and the calculated activation energies were 0.57 eV and 0.63 eV for each case, respectively. The frequency dependent peaks that appeared in the Bode plot of the real part of dielectric constant were attributed to thermal relaxation processes associated with activated jumps of polarons. The simulations showed that the compound is quite stable, showing no structural phase transition in the pressure range investigatedItem PROPRIEDADES DIELÉTRICAS DO Bi2Sn2O7 PURO E DOPADO COM MANGANÊS(Universidade Federal do Maranhão, 2010-11-26) Almeida, Rafael Mendonça; PASCHOAL, Carlos William de Araújo; CPF:46161286372; Feio, Waldeci Paraguassu; CPF:57387540268; http://lattes.cnpq.br/3512689932467320In this work we have investigated the dielectric and ionic properties of the pure Bi2Sn2O7 (BSO) and manganese doped ceramics in the temperature range from 23°C to 326°C. Amongst the main results of the BSO it is worthwhile to point out the PTCR ef-fect when it was analysed the temperature dependence of the electrical resistance. Furthermore, in both samples, the imaginary electrical modulus relaxational peaks are related to conductive processes, but only the BSO shows an anomaly in the tempera-ture range investigated. This anomaly is expressed with a displacement of the peaks to the region of low frequencies, as the temperature rises from the ambient value until 100°C, and after to the region of high frequencies, when the temperature changes from 100°C to 326°C. This dynamic of the data allowed to estimate the phase transition value as being equal to 121.5°C. It was also observed that this transition is possibly ferroic because the capacitance dependence with temperature shows a Curie like behaviour. By other side, the analysis of the real part of the electrical permittivity with temperature highlighted that the BSO phase transition point is located some-where around 125°C, while the one from BSO:Mn is around 120°C. The conductivity dependence with the reciprocal temperature showed an Arrhenius like behaviour and, from the mathematical adjustment at high temperatures, it was possible to estimate an activation energy of 1.26 eV. It was also found that the manganese doping inhibited the effect observed in the graphs of versus frequency, favored the conduction me-chanism of the system and preclude the PTCR effect. Analyzing the temperature de-pendence of the dielectric loss it was realized that this quantity also presents an ano-maly at around 120°C that can be assigned to the structural phase transition. Studying the real part of the admittance as function of the frequency, one could segregate the contributions from the bulk and grain boundary of the system and observe that the response of the last one exhibits a peak at 120°C, probably due to the transi-tion. Regarding the manganese ion substitution in the BSO structure, two hypotheses are proposed. It is believed that in both, the tin ion occurs with an oxidation state equal to 2+ and, but substituting either in the tin ion site or in the bismuth ion site, and releasing oxygen vacancies.Item Alguns resultados exatos a Temperatura Finita da Eletrodinâmica CPT-par do Modelo Padrão Estendido(Universidade Federal do Maranhão, 2010-04-30) Silva, Madson Rubem Oliveira; CASANA SIFUENTES, Rodolfo Alván; CPF:05159396764; http://lattes.cnpq.br/6508618435773438Maxwell s electrodynamics is a field theory which contains in its structure three fundamental physical symmetries: The Lorentz symmetry, the CPT-symmetry and the local gauge symmetry. The Lorentz covariance and the CPT-symmetry are fundamental in the construction of any field theory describing elementary (or not elementary) particles. Both together with the local gauge symmetry are the cornerstones in the construction of the Standard Model and of others modern field theories. However, it is cogitate that as much the Lorentz covariance as the CPT-symmetry can be spontaneously broken at Planck energy scale (or in the very early Universe when energies are close to the Planck scale) due to quantum gravity effects. The possible residual effects of such spontaneous symmetry breaking are studied within the structure of the Standard Model Extension (SME). The U(1)-local gauge symmetry sector of the SME describes the effects produced in Maxwell s electrodynamics due to the Lorentz-covariance violation and the spontaneous symmetry breaking of the CPT-invariance. Here, we study the finite temperature properties of the CPT-even electrodynamics of SME, represented by the term (kF )ανρφFανFρφ. First, we construct a well-defined and gauge invariant partition function in the functional integration formalism for an arbitrary tensor (kF ). Then, we specialize for the leading-order-nonbirefringent coefficients of the tensor (kF ) and we study in separate the parityeven and the parity-odd sectors. Consequently, for both sectors, the partition function is exactly caculated by showing that it is a power of Maxwell s partition function. Such power is an explicit function of the respective parameters ruling the Lorentz-covariance violation. This way, Planck s radiation law retains its frequency dependence and the Stefan-Boltzmann law is maintained, except for a change in Stefan-Boltzmann s constant that is multiplied by a global factor containing all the LIV contributions. Nevertheless, in general, it is observed that the LIV coefficients induce an anisotropy in the angular distribution of the black body energy density.