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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
281

MECHANICAL PROPERTIES OF Sc₀․₁Ce₀․₀₁Zr₀․₈₉O₂ ELECTROLYTE MATERIAL FOR INTERMEDIATE TEMPERATURE SOLID OXIDE FUEL CELLS

Lim, Wendy 2009 December 1900 (has links)
Scandia doped zirconia has been considered a candidate for electrolyte material in intermediate temperature Solid Oxide Fuel Cells (SOFCs) due to its high ionic conductivity, chemical stability and good electrochemical performance. The aim of this study is to determine the mechanical properties of SCZ, ie. zirconia (ZrO₂) doped with Scandia (Sc₂O₃) and small amount of ceria (CeO₂) that are important for reliability and durability of the components manufactured from SCZ. The SCZ was prepared from powder by uniaxiall cold pressing at subsequent sintering at 1550 ºC for 4 hours. The density and porosity of the sintered samples was measured following the ASTM Standard C20-00 for alcohol immersion method. A pure cubic phase of SCZ sample was identified by X-ray diffraction (XRD) at room temperature. Quantitative compositional analyses for Zr, Sc, Ce, Hf and Ti were carried out on a Cameca SX50 electron microprobe with wavelength-dispersive spectroscopy (WDS) and energy-dispersive spectroscopy (EDS). Scanning Electron Microscopy (SEM) images were acquired using both secondary electron (SE) and back-scattered electron (BSE) detectors. WDS and EDS analysis also revealed that Zr, Sc, Ce, Hf and Ti are relatively homogeneously distributed in the structure. The average grain size of sintered SCZ samples was measured to be 4 μm. Thermal expansion at different temperatures for the SCZ ceramic was determined using Thermal Mechanical Analyzer, and the instantaneous Coefficient of Thermal Expansion (CTE) was found to be 8.726х10⁻⁶ 1/°C in the in 25-400 °C temperature range. CTE increases monotonically with temperature above 400 ºC to 1.16х10⁻⁵ at 890 °C, most likely as a result of thermo-chemical expansion due to an increase in oxygen vacancy concentration. Room temperature Vickers hardens of 12.5 GPa was measured at loads of 1000 g, while indentation fracture toughness was found to vary from 2.25 to 4.29 MPa m¹⁄², depending on the methodology that was used to calculate fracture toughness from the length of the median corner cracks. Elastic moduli, namely Young and shear moduli were determined using Resonance Ultrasound Spectroscopy (RUS). It was found that elastic moduli decreases with temperature in non-linear manner, with significant drop in the 300-600 °C temperature range, the same temperature range in which loss modulus determined by Dynamic Mechanical Analyzer exhibits frequency dependant peaks. The high loss modulus and significant drop in elastic moduli in that temperature regime is attributed to the relaxation of doping cation-oxygen vacancies clusters. The flexural strength in 4-point bending was measured at room temperature, 400 °C, 600 °C and 800 °C. and the results were analyzed using Weibull statistics. It was found that flexural strength changes with temperature in a sigmoidal way, with the minimum strength at around 600 °C. Non-linear decrease in strength with temperature can be traced back to the changes in elastic moduli that are caused predominately by relaxation of oxygen vacancies.
282

Characterisation of the ceria and yttria co-doped scandia zirconia, produced by an innovative sol-gel and combustion process

de Carvalho Tomás, Eduarda M. S. January 2010 (has links)
In the last decade new materials appeared that are candidates to be used as an electrolyte in a Solid Oxide Fuel Cell, SOFC. Some materials show high ionic conductivity but lack in important properties, such as mechanical stability or chemical compatibility with other materials in the fuel cell. Scandia Stabilised Zirconia, SSZ, became a possibility when the scandia price dropped with the opening of the Chinese and Russian markets. In the starting system Ce[subscript(x)]Y[subscript(0.2-x)]Sc₀.₆Zr₃.₂O[subscript(8-δ)], (0≤x≤0.2), scandia is introduced to improve conductivity and stabilise the cubic phase; yttria is introduced to fully stabilise the cubic phase and ceria to enhance conductivity lost with the introduction of yttria. The aim of this project is to develop a reliable new method to produce quality ceramics that are not strongly composition dependent, then to prepare a range of compositions and compare intrinsic properties without having to be concerned that poor sintering dominates conduction properties. This project can be divided in two sections, the first section the powder production method, the characteristics of the powders and its final products are in focus. In the second section the relation between electric characteristics and microstructure of the material is reported. In the first section, the effect of different compositions of the system Ce[subscript(x)]Y[subscript(0.2-x)]Sc₀.₆Zr₃.₂O[subscript(8-δ)], (0≤x≤0.2) is studied, in terms of structure, phase and microstructure. The nature, size and shape of the powders are discussed, and their effect on the final product. The sol-gel and combustion method gives the formation of hard agglomerates (shells), during the combustion, a wide range of grain sizes, between less than 1µm and 200 µm, and the formation of grains with non spherical shape. In this project, the sol-gel and combustion process and solid state method are also compared. In the second section of this project, AC Impedance measurements, as a function of temperature, oxygen partial pressure and time are discussed. The Arrhenius plot for all compositions shows two regions (high and low temperature) and the change of region occurs at 580 °C. At low temperatures there is a slight difference between compositions but this difference is less at high temperatures. The obtained ionic conductivity, at 350 °C, varies from 3.84×10⁻⁶ to 5.53×10⁻⁵ S/cm; at 700 °C, ionic conductivity from 0.013 to 0.044 S/cm. At low temperatures, the activation energy associated with bulk process is generally lower than grain boundary process; for example, the composition Ce₀.₁Y₀.₁Sc₀.₆Zr₃.₂O₇.₆₅ has an activation energy, for the bulk process, of 1.05 eV and an activation energy, for the grain boundary process, of 1.17 eV. For compositions with higher ceria content, activation energy, for bulk and grain boundary, have similar values. The AC impedance as function of oxygen partial pressure show that the amount of ceria introduced as an effect on the conductivity at low oxygen partial pressure. For the sample with no ceria in its composition, Y₀.₂Sc₀.₆Zr₃.₂O₇.₆₀, the conductivity does not vary significantly as the oxygen partial pressure is decreased; for oxygen partial of 0.21 atm, conductivity is 0.018 S/cm and when oxygen partial pressure is approximately 10⁻²⁴ atm conductivity is 0.018 S/cm. For the sample with a higher content of ceria, Ce₀.₁₂Y₀.₀₈Sc₀.₆Zr₃.₂O₇.₆₆, there is a decrease in conductivity while oxygen partial pressure decreases; and there is also the appearance of a semi-circle for lower oxygen partial pressures. For oxygen partial pressure approximately 0.21 atm, conductivity is 0.019 S/cm, but when oxygen partial pressure is decreased to 10⁻²⁴ atm conductivity decreases to 0.011 S/cm. AC impedance measurements as a function of annealing time at 600 °C were performed. Total conductivity is fairly stable, for all compositions, until 1800 hours but after this time, conductivity slowly decreases. Some compositions show a second semi-circle in the AC impedance spectra, either from the beginning, time equals 0 hours, or after some working hours. Here, the changes in conduction and conduction processes with time are discussed.
283

Development and characterisation of an A-site deficient perovskite as alternative anode material for solid oxide fuel cells

Aljaberi, Ahmed D. A. January 2013 (has links)
The research presented in this thesis is a collection of many different, yet connected, parts that stemmed from the development of a new alternative material intended to be utilised as anode material in solid oxide fuel cells. The main part is the research conducted in the development and characterisation of the novel A-site deficient La₀.2₂Sr₀.₇₋ₓCaₓTiO₃. Calcium introduction resulted in reducing this perovskite unit cell volume which, at the beginning, enhanced its electrical conductivity in reducing conditions. However, the ideal cubic symmetry coud not be maintained, as in the starting material LA₀.₂Sr₀.₇TiO₃, as a result of the increased A-site ionic radius mismatch and two lower symmetries were observed at room temperature. These were the tetragonal I4/mcm for 0.1 ≤ x ≤ 0.35 and orthorhombic Pbnm for 0.4 ≤ x ≤ 0.7. Higher temperature NPD data showed that the orthorhombic samples transformed into higher symmetries with Pbnm → I4/mcm → Pm3-m phase transitions. Detailed crystallographic analysis is discussed; where the different unit cells showed changes to the tilts of the BO₆ octahedra, along with distortions to these octahedra. DC conductivity measurements showed a high electrical conductivity of 27.5 S/cm for a pre-reduced composition La₀.₂Sr₀.₂₅Ca₀.₄₅TiO₃ at 900°C and pO₂ = 10⁻¹⁹ atm. This material showed very encouraging features; which makes it a very promising anode material for SOFCs. A study was also done which explores the best renewable energy options for the United Arab Emirates given its local climate and other aspects. The reliance on seawater desalination is argued to by unsustainable for different reasons. Thus, water security should be a main element in the planning process for adopting renewable energy technologies. A system that combines different technologies; with a focus on fuel cells technology; is outlined which is thought of to be a very promising basis for a broader system that will secure power and water in a very environment friendly way. Different compositions of the system La₀.₂Sr₀.₇₋ₓCaₓTiO₃ were also studied using AC impedance spectroscopy in order to establish whether or not this system can show a ferroelectric behaviour. Results showed a variation in the dielectric constant of different samples with temperature; however, no Curie point was observed. Nonetheless, the results did show that the different compositions were very homogeneous when fully oxygenated and there were some indications of possible symmetry changes at sub-ambient temperatures. The final part of this thesis outlined the work done towards the development of a new analytical instrument. An existing TGA instrument was altered in order to provide a simultaneous thermogravimetric analysis and DC conductivity measurement for solid solutions at controlled temperature and oxygen partial pressure. Results were obtained for different samples of the system La₀.₂Sr₀.₇₋ₓCaₓTiO₃ which showed a great dependence of the electrical conductivity on the oxygen stoichiometry in these oxides. Also, a direct method is possible with this instrument to estimate the oxygen chemical diffusion coefficient using the electrical conductivity relaxation method. This new setup will be very useful for different electrochemical and thermal studies which can broaden the understanding of the different mechanisms that affect the performance of different solid state materials.
284

Development of alternative cathodes for intermediate temperature solid oxide fuel cells

Kim, Junghyun 05 November 2009 (has links)
text
285

Termodynamická analýza článků s pevnými oxidy / Thermodynamic analysis of solid oxide cells

Vágner, Petr January 2019 (has links)
Thermodynamic analysis of solid oxide cells Petr Vágner The thesis deals with continuum thermodynamic modeling and analysis of phe- nomena in solid oxide electrochemical cells. A general description of the evo- lution of charged mixtures using partial mass densities, momentum density, entropy density, electric induction, magnetic field, polarization, and magnetiza- tion based on the GENERIC framework is formulated. The formulation is used to recover the Landau-Lifshitz magnetization relaxation model, the Single Re- laxation Time model for dielectrics, and the generalized Poisson-Nernst-Planck model. The latter model is consequently linked to the second part, where a novel double layer model of an yttria-stabilized zirconia interface is formulated within non-equilibrium thermodynamics. The model is solved for numerically in the time domain, and cyclic voltammetry of the system is analyzed. The last part of the thesis demonstrates the limits of Exergy Analysis on a simple solid oxide hydrogen fuel cell model with non-isothermal boundary. It is demon- strated that the minimization of entropy production does not necessarily lead to the maximization of the electric power for certain optimization scenarios. The thesis consists of a compilation of published and unpublished results of the author.
286

The Role of Bi/Material Interface in Integrity of Layered Metal/Ceramic / The Role of Bi/Material Interface in Integrity of Layered Metal/Ceramic

Masini, Alessia January 2019 (has links)
The present doctoral thesis summarises results of investigation focused on the characterisation of materials involved in Solid Oxide Cell technology. The main topic of investigation was the ceramic cell, also known as MEA. Particular attention was given to the role that bi-material interfaces, co-sintering effects and residual stresses play in the resulting mechanical response. The first main goal was to investigate the effects of the manufacturing process (i.e. layer by layer deposition) on the mechanical response; to enable this investigation, electrode layers were screen-printed one by one on the electrolyte support and experimental tests were performed after every layer deposition. The experimental activity started with the measurement of the elastic characteristics. Both elastic and shear moduli were measured via three different techniques at room and high temperature. Then, uniaxial and biaxial flexural strengths were determined via two loading configurations. The analysis of the elastic and fracture behaviours of the MEA revealed that the addition of layers to the electrolyte has a detrimental effect on the final mechanical response. Elastic characteristics and flexural strength of the electrolyte on the MEA level are sensibly reduced. The reasons behind the weakening effect can be ascribed to the presence and redistribution of residual stresses, changes in the crack initiation site, porosity of layers and pre-cracks formation in the electrode layers. Finally, the coefficients of thermal expansion were evaluated via dilatometry on bulk materials serving as inputs for finite elements analyses supporting experiments and results interpretation. The second most important goal was to assess the influence of operating conditions on the integrity of the MEA. Here interactions of ceramic–metal interfaces within the repetition unit operating at high temperatures and as well at both oxidative and reductive atmospheres were investigated. The elastic and fracture responses of MEA extracted from SOC stacks after several hours of service were analysed. Layer delamination and loss of mechanical strength were observed with increasing operational time. Moreover, SEM observations helped to detect significant microstructural changes of the electrodes (e.g. demixing, coarsening, elemental migration and depletion), which might be responsible for decreased electrochemical performances. All the materials presented in this work are part of SOC stacks produced and commercialised by Sunfire GmbH, which is one of the world leading companies in the field.
287

Performance, Temperature and Concentration Profiles in a Non-Isothermal Ammonia-Fueled Tubular SOFC

Jantakananuruk, Nattikarn 18 April 2019 (has links)
Ammonia has emerged as an attractive potential hydrogen carrier due to its extremely high energy density (hydrogen density), ease of storage and transportation as a liquid, and carbon-free nature. Direct utilization of ammonia in high-temperature solid oxide fuel cells (SOFCs) has been demonstrated over the past decade. Concurrence of in situ endothermic ammonia decomposition and exothermic electrochemical hydrogen oxidation permit efficient heat integration. In this study, the experimental analyses of axial temperature and concentration profiles along the tubular SOFC (t-SOFC) fed directly with ammonia are performed to investigate the coupled ammonia decomposition and hydrogen oxidation reactions as well as the effect of polarization. Fast ammonia decomposition over the Ni catalyst is evident at the inlet of t-SOFC and complete ammonia conversion is confirmed above 600ºC. It is found that direct ammonia-fueled t-SOFC and an equivalent hydrogen-nitrogen fueled t-SOFC provide identical performances. With 100 SCCM of ammonia fuel feed, a maximum power of 12.2 W and fuel utilization of 81% are obtained at 800ºC in a t-SOFC with active area of 32 cm2. The temperature and concentration profiles validate that the efficient heat integration inside ammonia-fueled t-SOFC is feasible if t-SOFC is operated at the temperature of 700ºC and below. The 23-hour performance test and SEM-EDS images of the fresh and used Ni-YSZ cermet surfaces confirm uniform performance and good durability of ammonia t-SOFC.
288

Síntese, processamento e caracterização de cátodo para aplicação em células a combustível de óxido sólido de temperatura intermediária / Synthesis, processing and characterization of cathode for application in intermediate temperature solid oxide fuel cells

Vargas, Reinaldo Azevedo 16 April 2012 (has links)
Os filmes micrométricos contendo óxido misto de lantânio, estrôncio, cobalto e ferro (La0,60Sr0,40)(Co0,20Fe0,80)O3-δ - LSCF, misturado com (Ce0,90Gd0,10)O1,95 - CGO, são relevantes para a utilização como camada funcional para o cátodo da Célula a Combustível de Óxido Sólido de Temperaturas Intermediárias. Estes filmes foram depositados no um substrato cerâmico e denso de CGO ou CGO sobre (ZrO2)0.92(Y2O3)0.08 - YSZ. O estudo deste cátodo é fundamental, pois é nele que ocorre a reação de redução do gás oxigênio, e o seu desempenho eletroquímico depende da interface destes dois materiais. Neste sentido, o presente trabalho contribui para a síntese dos particulados de LSCF para o processamento de filmes, utilizando a técnica de deposição com uso de aerógrafo e para sua conformação em camadas contendo porosidade com espessuras entre 30 e 50 μm. Inicialmente, os particulados de LSCF foram sintetizados pela técnica do citratos e de LSCFCGO obtidos por mistura mecânica, sendo caracterizados por DRX para a confirmação da formação da estrutura cristalina ortorrômbica para o LSCF e cúbica para CGO. Em seguida, foram preparadas suspensões orgânicas de LSCF, LSCFCGO e CGO que foram alimentadas por gravidade em um aerógrafo manual para deposição sobre substrato do eletrólito. Para a conformação dos substratos de CGO ou YSZ, utilizou-se prensa uniaxial e isostática, sinterização e retificação. Verificaram-se, pelas micrografias, que os substratos CGO e YSZ apresentaram densidades (> 92%) suficientes para serem utilizados como eletrólitos. Os filmes de LSCF e LSCFCGO apresentaram-se com porosidades adequadas (> 30%) e espessura total de aproximadamente 40 μm, com boa aderência ao eletrólito. A presença do cátodo compósito contendo eletrólito de CGO sobre YSZ possibilitou aumento de 25% no desempenho eletroquímico (2,50 Ω.cm2 para 650ºC) em decorrência da melhora na reação de redução do oxigênio na interface cátodo/eletrólito. / The study of micrometrics films of (La0.60Sr0.40)(Co0.20Fe0.80)O3-δ - LSCF mixture with (Ce0.90Gd0.10)O1.95 - CGO is relevant for use as functional cathode of Intermediate Temperature Solid Oxide Fuel Cells (ITSOFC). These films were deposited on the CGO or CGO and YSZ dense ceramic substrate, used as electrolyte, structural component of the module. The study of this cathode is fundamental, because is there that occurs oxygen reduction reaction, and the electrochemical performance depends on the interface of these two materials. In this sense, this work contributes for the synthesis of LSCF particulates, for processing films using the wet powder spraying technique, adopted for the conformation of the ceramic films for allowing the attainment porous layers with thicknesses between 30 and 50 μm. Initially, the LSCF particulates were synthesized by the citrate technique and the LSCFCGO produced by solid mixture were characterized by XRD to confirm the formation of LSCF orthorhombic structure and CGO cubic structure. In the stage of formation were prepared organic suspensions of LSCF, LSCFCGO and CGO fed by gravity in a manual airbrush for electrolyte substrate deposition, sintering and grinding for thickness reduction. The micrographs showed that the CGO and YSZ substrates were dense (> 92%) enough to be used as solid electrolyte. The LSCF and LSCFCGO films presented with adequate porosity (> 30%) and total thickness of approximately 40 μm, with good adhesion to electrolyte. The presence of the composite cathode containing CGO or YSZ electrolyte allowed the increase of 25% in the electrochemical performance (2.50 Ω.cm2 to 650ºC) due to improvement in the oxygen reduction reaction at the interface cathode/electrolyte.
289

Desenvolvimento de selantes vitrocerâmicos para uso em SOFC pertencentes ao sistema BAS (BaO-Al203-SiO2) modificados com B2O3 / Development of glass ceramic sealants for use in SOFC belonging to BAS (BaO-Al2O3-SiO2) system modified with B2O3

Silva, Maviael José da 25 September 2014 (has links)
O desenho planar para as células a Combustível de Óxido Sólido (SOFC) é melhor do que o tubular devido a sua maior densidade de corrente e menor custo de fabricação. No entanto, o projeto de SOFC planar requer selantes para evitar o vazamento de combustível e a mistura de gases em altas temperaturas. Os vidros e os vitrocerâmicos têm demonstrado serem os mais adequados por apresentarem boa compatibilidade com outros componentes da célula nas temperaturas de trabalho das SOFCs (700-1000°C). No presente estudo, uma série de composições pertencentes ao sistema BaO-Al2O3-SiO2 (BAS) com a adição de B2O3 foram sintetizados tomando as proporções apropriadas de cada óxido constituinte. Propôs-se melhorar este sistema utilizando-se formadores e teores relevantes de modificadores estruturais, de forma a compatibilizar tanto o desempenho térmico por meio do coeficiente de expansão térmica (CET) como a compatibilidade química com os demais componentes da célula. A originalidade deste estudo está na busca destas características em regiões de composições ainda não exploradas, localizadas dentro do triangulo de compatibilidade BS-B2S-BAS2 na região rica em bário do sistema ternário. Entre estes vidros sintetizados quatro composições (BAS-4, BAS-5, BAS-6 e BAS-7) foram escolhidas porque são as mais adequadas às solicitações termomecânicas exigidas para um material vítreo atuar como selante em SOFC. / The design for planar cells Fuel Solid Oxide (SOFC) is better than the tubular due to its higher current density and lower manufacturing cost. However, the design of planar SOFC requires sealant to prevent leakage of fuel and the mixture of gases at high temperatures. Glasses and glass-ceramics have proven to be the most suitable because they have good compatibility with the other components of the cell at working temperature (700-1000°C). In the present study, a series of compositions belonging to the BaO-Al2O3-SiO2 (BAS) system with the addition of B2O3 were synthesized having the appropriate proportions of each component oxide. It was proposed to improve this system using relevant levels of formers and structural modifiers oxides, in order to match both the thermal performance of thermal expansion coefficient (TEC) and chemical compatibility with other components of the cell. The originality of this study is to search for these characteristics in regions of compositions not yet explored, located inside the compatibility triangle BS-B2S-BAS2 at the barium rich part of the ternary diagram. Among the synthesized glasses four batch compositions (BAS-4, BAS-5, 6-BAS, BAS-7) were chosen because best matched the thermo-mechanical required for a glassy material to act as SOFCs sealant.
290

On governing equations and closure relations for the multiscale modeling of concentration polarization in solid-oxide fuel cells: mass transfer and concentration-induced voltage losses. / Sobre as equações de conservação e relações de fechamento para a modelagem multiescala da polarização por concentração em células a combustível de óxido-sólido: transferência de massa e perdas de tensão induzidas por concentração.

Teixeira Junior, Roberto Janny 29 March 2017 (has links)
The aim of this dissertation is to appraise and critically reflect on the physical pertinence of governing equations and closure relations often used for the modeling of gas-phase transport phenomena in high-temperature solid-oxide fuel cells (SOFCs). More precisely, this work conducts a critical literature review on the concentration-induced voltage losses (i.e., concentration polarization) resulting from mass transfer limitations. Thus, the overall object of this work was to stress awareness of the limits of mathematical models studied and developed in the SOFC literature to date, and which are specifically related to concentration polarization processes. To a great extent, the design of SOFC porous layers is likened to that of optimizing the transport of multicomponent gas mixtures in structured porous catalysts, for which diffusional and flow limitations are of cardinal importance. In both cases, severe inconsistencies in mass transport models cannot be simply ignored and the main uncertainties in utilizing such models should be clarified. It is hoped that the information herein will serve usefully to support future developments of more consistent theoretical frameworks, thereby improving the confidence on the results of numerical simulations. The critical literature review has been carried out so to identify a number of physical inconsistences, ill-defined approximations, and misleading mathematical derivations. Along the review, it is argued that the choice (or, more properly, the lack of conceptual refinement) of a particular mathematical model can significantly impair the \"prediction\" of transport processes relevant to concentration-induced power losses in SOFCs. One of the keystones of this work was therefore to re-interpret and thus to reassess the frequently contradictory literature related to certain classes of gas-phase transport models pertinent to the evaluation of concentration polarization. With this revisionary approach, it is expected that one could reduce confusion, clear up apparent contradictions, and improve the possibility of gaining new insights. / Esta dissertação tem o objetivo de avaliar e refletir criticamente sobre a pertinência física de equações de conservação e de relações de fechamento, frequentemente utilizadas na modelagem multiescala de fenômenos de transporte em células a combustível de óxido-sólido (SOFC). Dêu-se atenção especial ao escoamento em \"microescala\" de misturas gasosas multicomponentes, dentro de meios porosos quimicamente reativos. Em outras palavras, esta monografia busca ressaltar quais os limites para aplicação de certas classes de modelos matemáticos, os quais têm sido desenvolvidos e utilizados na literatura de SOFCs até o presente momento. O projeto de camadas porosas de SOFCs assemelha-se à tarefa de otimizar processos de transporte em catalisadores estruturados, para os quais a existência de limitações de transporte por difusão e por escoamento tem importância primordial. Por esta razão, inconsistências originadas em modelos de fenômenos de transporte não podem ser, simplesmente, negligenciadas e, portanto, as principais incertezas ao se utilizar tais modelos devem ser devidamente esclarecidas. Espera-se, com efeito, que as informações contidas neste trabalho sejam úteis para futuros desenvolvimentos teóricos mais consistentes, de forma a aumentar a confiabilidade no uso de resultados obtidos por simulações numéricas.

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