Solid oxide fuel cells with graded electrodes consisting of multiple composite layers yield generally lower polarization resistances than single layer composite electrodes. Optimization of the performance of solid oxide fuel cells with graded electrode composition and/or microstructure requires an evaluation of both the three phase boundary length per unit volume and the effective diffusion coefficient in order to provide insight into how these properties vary over the design space. A numerical methodology for studying the three phase boundary length and effective diffusivity in composite electrode layers with controlled properties is developed. A three dimensional solid model of a sintered composite electrode is generated for which the mean particle diameter, composition, and total porosity may be specified as independent variables. The total three phase boundary length for the modeled electrode is calculated and tomographic methods are used to estimate the fraction of this length over which the electrochemical reactions can theoretically occur. Furthermore, the open porosity of the modeled electrode is identified and the effective diffusion coefficient is extracted from the solution of the concentration of the diffusing species within the open porosity. Selected example electrode models are used to illustrate the application of the methods developed, and the resulting connected three phase boundary length and diffusion coefficients are compared. A significant result is the need for thickness-specific effective diffusivity to be determined, rather than the general volume averaged property, for electrodes with porosity between the upper and lower percolation thresholds. As the demand for current increases, more of the connected three phase boundaries become active, and therefore a greater fraction of the electrode layer is utilized for a given geometry, resulting in a higher apparent effective diffusivity compared to the same electrode geometry operating at a lower current. The methods developed in this work may be used within a macroscopic electrode performance model to investigate optimal designs for solid oxide fuel cell electrodes with stepwise graded composition and/or microstructure.

Solid oxide fuel cells with graded electrodes consisting of multiple composite layers yield generally lower polarization resistances than single layer composite electrodes. Optimization of the performance of solid oxide fuel cells with graded electrode composition and/or microstructure requires an evaluation of both the three phase boundary length per unit volume and the effective diffusion coefficient in order to provide insight into how these properties vary over the design space. A numerical methodology for studying the three phase boundary length and effective diffusivity in composite electrode layers with controlled properties is developed. A three dimensional solid model of a sintered composite electrode is generated for which the mean particle diameter, composition, and total porosity may be specified as independent variables. The total three phase boundary length for the modeled electrode is calculated and tomographic methods are used to estimate the fraction of this length over which the electrochemical reactions can theoretically occur. Furthermore, the open porosity of the modeled electrode is identified and the effective diffusion coefficient is extracted from the solution of the concentration of the diffusing species within the open porosity. Selected example electrode models are used to illustrate the application of the methods developed, and the resulting connected three phase boundary length and diffusion coefficients are compared. A significant result is the need for thickness-specific effective diffusivity to be determined, rather than the general volume averaged property, for electrodes with porosity between the upper and lower percolation thresholds. As the demand for current increases, more of the connected three phase boundaries become active, and therefore a greater fraction of the electrode layer is utilized for a given geometry, resulting in a higher apparent effective diffusivity compared to the same electrode geometry operating at a lower current. The methods developed in this work may be used within a macroscopic electrode performance model to investigate optimal designs for solid oxide fuel cell electrodes with stepwise graded composition and/or microstructure.

Solid oxide fuel cells with graded electrodes consisting of multiple composite layers yield generally lower polarization resistances than single layer composite electrodes. Optimization of the performance of solid oxide fuel cells with graded electrode composition and/or microstructure requires an evaluation of both the three phase boundary length per unit volume and the effective diffusion coefficient in order to provide insight into how these properties vary over the design space. A numerical methodology for studying the three phase boundary length and effective diffusivity in composite electrode layers with controlled properties is developed. A three dimensional solid model of a sintered composite electrode is generated for which the mean particle diameter, composition, and total porosity may be specified as independent variables. The total three phase boundary length for the modeled electrode is calculated and tomographic methods are used to estimate the fraction of this length over which the electrochemical reactions can theoretically occur. Furthermore, the open porosity of the modeled electrode is identified and the effective diffusion coefficient is extracted from the solution of the concentration of the diffusing species within the open porosity. Selected example electrode models are used to illustrate the application of the methods developed, and the resulting connected three phase boundary length and diffusion coefficients are compared. A significant result is the need for thickness-specific effective diffusivity to be determined, rather than the general volume averaged property, for electrodes with porosity between the upper and lower percolation thresholds. As the demand for current increases, more of the connected three phase boundaries become active, and therefore a greater fraction of the electrode layer is utilized for a given geometry, resulting in a higher apparent effective diffusivity compared to the same electrode geometry operating at a lower current. The methods developed in this work may be used within a macroscopic electrode performance model to investigate optimal designs for solid oxide fuel cell electrodes with stepwise graded composition and/or microstructure. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

No description available.

As the demand for green energy and fuel cells grows, more attention is drawn towards Solid Oxide Fuel Cells (SOFCs). Random and complex structure of composite electrodes and underlying electrochemical process has not been completely unveiled yet and further study is required to acquire more understanding. Modeling in this regard plays an important role as it pinpoints key parameters in optimum design of the cell without resorting to costly and uncertain experiments which might even lead to misinterpretations due to random nature of experimental data. The aim of this work is to develop a new rigorous model to study the structure performance relationship of (SOFC) composite electrodes. The work has been conducted in two phases, a two-dimensional continuous approach and three-dimensional discrete model. A new two-dimensional, geometrical model which captures the inhomogeneous nature of the location of electrochemical reactions based on random packing of electronic and ionic conducting particles has been developed. The results show that the concentration of oxygen inside the cathode in the two-dimensional model is not only a function of the electrode depth but also changes along the width of the electrode. Furthermore the effect of composition of the electrode on the length of three phase boundary (TPB) and total polarization resistance has been demonstrated. A parametric study of the effect of the conductivity of ionic conductor and diffusion coefficient on the performance of the electrode has been given. To make a more realistic analysis, a three-dimensional reconstruction of (SOFC) composite electrodes was developed to evaluate the performance and further investigate the effect of microstructure on the performance of electrodes. To enhance connectivity between particles and increase the length of TPB, sintering process is mimicked by enlarging particles to certain degree. Geometrical characteristics such as length of TBP and active contact area as well as porosity can easily be calculated using the current model. Electrochemical process is simulated using resistor-network model and complete Butler-Volmer equation is used to deal with charge-transfer process on TBP. The model shows that TPBs are not uniformly distributed across the electrode and location of TPBs as well as amount of electrochemical reaction is not homogeneous. Effects of particle size, electrode thickness, particle size ratio, electron and ion conductor conductivities and rate of electrochemical reaction on overall electrochemical performance of electrode are investigated. / Chemical Engineering

It is well established that the temperature gradients in the interiors of internally-heated mantle convection models are subadiabatic (e.g. Parmentier et al., 1994; Bunge et al., 1997, 2001). The subadiabatic gradients have been explained to arise due to a balance between vertical advection and internal heating, however, a detailed analysis of the energy balance in the subadiabatic regions has not been undertaken. In this research, I examine in detail the energy balance in a suite of two-dimensional convection calculations with mixed internal and basal heating, depth-dependent viscosity and continents. I find that there are three causes of subadiabatic gradients. One is the above-mentioned balance, which becomes significant when the ratio of internal heating to surface heat flux is large. The second mechanism involves the growth of the overshoot (maximum and minimum Temperatures along a geotherm) of the geotherm near the lower boundary where the dominant balance is between vertical and horizontal advection. The latter mechanism is significant even in relatively weakly internally heated calculations. For time-dependent calculations, I find that local secular cooling can be a dominant term in the energy equation and can lead to subadiabaticity. However, it does not show its signature on the shape of the time-averaged geotherm. I also compare the basal heat flux with parameterized calculations based on the temperature drop at the core-mantle boundary, calculated both with and without taking the subadiabatic gradient into account and I find a significantly improved fit with its inclusion.<p> I also explore a wide range of parameter space to investigate the dynamical interaction between effects due to surface boundary conditions representing continental and oceanic lithosphere and the endothermic phase boundary at 660 km-depth in two-dimensional Cartesian coordinate convection calculations. I find that phase boundary induced mantle layering is strongly affected by the wavelength of convective flows and mixed surface boundary conditions strongly increase the horizontal wavelength of convection. My study shows that for mixed cases the effects of the surface boundary conditions dominate the effects of the phase boundary. I show that the calculations with complete continental coverage have the most significantly decoupled lower and upper mantle flows and substantial thermal and mechanical layering. Unlike the free-slip case where the surface heat flux decreases substantially with increasing magnitude of the Clapeyron slope, surface heat flux is shown to be almost independent of the Clapeyron slope for mixed boundary condition cases. Although very different when not layered, models with free and mixed surfaces have very similar planforms with very large aspect ratio flows when run with large magnitudes of the Clapeyron slope. I also calculate the critical boundary layer Rayleigh number as a measure of the thermal resistance of the surface boundary layer. My results show that the thermal resistance in the oceanic and the continental regions of the mixed cases are similar to fully free and no-slip cases, respectively. I find that, even for purely basally heated models, the mantle becomes significantly subadiabatic in the presence of partial continental coverage. This is due to the significant horizontal advection of heat that occurs with very large aspect ratio convection cells.

It is well established that the temperature gradients in the interiors of internally-heated mantle convection models are subadiabatic (e.g. Parmentier et al., 1994; Bunge et al., 1997, 2001). The subadiabatic gradients have been explained to arise due to a balance between vertical advection and internal heating, however, a detailed analysis of the energy balance in the subadiabatic regions has not been undertaken. In this research, I examine in detail the energy balance in a suite of two-dimensional convection calculations with mixed internal and basal heating, depth-dependent viscosity and continents. I find that there are three causes of subadiabatic gradients. One is the above-mentioned balance, which becomes significant when the ratio of internal heating to surface heat flux is large. The second mechanism involves the growth of the overshoot (maximum and minimum Temperatures along a geotherm) of the geotherm near the lower boundary where the dominant balance is between vertical and horizontal advection. The latter mechanism is significant even in relatively weakly internally heated calculations. For time-dependent calculations, I find that local secular cooling can be a dominant term in the energy equation and can lead to subadiabaticity. However, it does not show its signature on the shape of the time-averaged geotherm. I also compare the basal heat flux with parameterized calculations based on the temperature drop at the core-mantle boundary, calculated both with and without taking the subadiabatic gradient into account and I find a significantly improved fit with its inclusion.<p> I also explore a wide range of parameter space to investigate the dynamical interaction between effects due to surface boundary conditions representing continental and oceanic lithosphere and the endothermic phase boundary at 660 km-depth in two-dimensional Cartesian coordinate convection calculations. I find that phase boundary induced mantle layering is strongly affected by the wavelength of convective flows and mixed surface boundary conditions strongly increase the horizontal wavelength of convection. My study shows that for mixed cases the effects of the surface boundary conditions dominate the effects of the phase boundary. I show that the calculations with complete continental coverage have the most significantly decoupled lower and upper mantle flows and substantial thermal and mechanical layering. Unlike the free-slip case where the surface heat flux decreases substantially with increasing magnitude of the Clapeyron slope, surface heat flux is shown to be almost independent of the Clapeyron slope for mixed boundary condition cases. Although very different when not layered, models with free and mixed surfaces have very similar planforms with very large aspect ratio flows when run with large magnitudes of the Clapeyron slope. I also calculate the critical boundary layer Rayleigh number as a measure of the thermal resistance of the surface boundary layer. My results show that the thermal resistance in the oceanic and the continental regions of the mixed cases are similar to fully free and no-slip cases, respectively. I find that, even for purely basally heated models, the mantle becomes significantly subadiabatic in the presence of partial continental coverage. This is due to the significant horizontal advection of heat that occurs with very large aspect ratio convection cells.

No description available.

The theory and computation of line defects are discussed in the context of both solids and liquid crystals. This dissertation includes four parts. The Generalized Disclination theory is discussed and applied to numerous interfacial and bulk line defect problems. An augmented Oseen-Frank energy as well as a novel 2D-model is proposed and demonstrated for disclination dynamics in liquid crystal. A model based on kinematics and thermodynamics is devised to predict tactoid dynamics during the process of the isotropic-nematic phase transition in LCLC. In the first part of the thesis, the utility of the notion of generalized disclinations in materials science is discussed within the physical context of modeling interfacial and bulk line defects. The Burgers vector of a disclination dipole in linear elasticity is derived, clearly demonstrating the equivalence of its stress field to that of an edge dislocation. An explicit formula for the displacement jump of a single localized composite defect line in terms of given g.disclination and dislocation strengths is deduced based on the Weingarten theorem for g.disclination theory at finite deformation. The Burgers vector of a g.disclination dipole at finite deformation is also derived. In the second part, a numerical method is developed to solve for the stress and distortion fields of g.disclination systems. Problems of small and finite deformation theory are considered. The fields of various line defects and grain/phase boundary problems are approximated. It is demonstrated that while the far-field topological identity of a dislocation of appropriate strength and a disclinationdipole plus a slip dislocation comprising a disconnection are the same, the latter microstructure is energetically favorable. This underscores the complementary importance of all of topology, geometry, and energetics (plus kinetics) in understanding defect mechanics. It is established that finite element approximations of fields of interfacial and bulk line defects can be achieved in a systematic and routine manner, thus contributing to the study of intricate defect microstructures in the scientific understanding and predictive design of materials. In the third part, nonsingular disclination dynamics in a uniaxial nematic liquid crystal is modeled within a mathematical framework where the kinematics is a direct extension of the classical way of identifying these line defects with singularities of a unit vector field representing the nematic director. We devise a natural augmentation of the Oseen-Frank energy to account for physical situations where infinite director gradients have zero associated energy cost, as would be necessary for modeling half-integer strength disclinations within the framework of the director theory. A novel 2D-model of disclination dynamics in nematics is proposed, which is based on the extended Oseen-Frank energy and takes into account thermodynamics and the kinematics of conservation of defect topological charge. We validate this model through computations of disclination equilibria, annihilation, repulsion, and splitting. In the fourth part, the isotropic-nematic phase transition in chromonic liquid crystals is studied. We simulate such tactoid equilibria and dynamics with a model using degree of order, a variable length director as state descriptors, and an interfacial descriptor. We introduce an augmented Oseen-Frank energy, with non-convexity in both interfacial energy and the dependence of the energy on the degree of order. A strategy is devised based on continuum kinematics and thermodynamics. The model is used to predict tactoid dynamics during the process of phase transition. We reproduce observed behaviors in experiments and perform an experimentally testable parametric study of the effect of bulk elastic and tactoid interfacial energy constants on the interaction of interfacial and bulk fields in the tactoids.

Phase field modeling and simulation is employed to study the underlying mechanism of enhancing electromechanical properties in single crystals and polycrystals of perovskite-type ferroelectrics around the morphotropic phase boundary (MPB). The findings include: (I) Coherent phase decomposition near MPB in PZT is investigated. It reveals characteristic multidomain microstructures, where nanoscale lamellar domains of tetragonal and rhombohedral phases coexist with well-defined crystallographic orientation relationships and produce coherent diffraction effects. (II) A bridging domain mechanism for explaining the phase coexistence observed around MPBs is presented. It shows that minor domains of metastable phase spontaneously coexist with and bridge major domains of stable phase to reduce total system free energy, which explains the enhanced piezoelectric response around MPBs. (III) We demonstrate a grain size- and composition-dependent behavior of phase coexistence around the MPBs in polycrystals of ferroelectric solid solutions. It shows that grain boundaries impose internal mechanical and electric boundary conditions, which give rise to the grain size effect of phase coexistence, that is, the width of phase coexistence composition range increases with decreasing grain sizes. (IV) The domain size effect is explained by the domain wall broadening mechanism. It shows that, under electric field applied along the nonpolar axis, without domain wall motion, the domain wall broadens and serves as embryo of field-induced new phase, producing large reversible strain free from hysteresis. (V) The control mechanisms of domain configurations and sizes in crystallographically engineered ferroelectric single crystals are investigated. It reveals that highest domain wall densities are obtained with intermediate magnitude of electric field applied along non-polar axis of ferroelectric crystals. (VI) The domain-dependent internal electric field associated with the short-range ordering of charged point defects is demonstrated to stabilize engineered domain microstructure. The internal electric field strength is estimated, which is in agreement with the magnitude evaluated from available experimental data. (VII) The poling-induced piezoelectric anisotropy in untextured ferroelectric ceramics is investigated. It is found that the maximum piezoelectric response in the poled ceramics is obtained along a macroscopic nonpolar direction; and extrinsic contributions from preferred domain wall motions play a dominant role in piezoelectric anisotropy and enhancement in macroscopic nonpolar direction. (VIII) Stress effects on domain microstructure are investigated for the MPB-based ferroelectric polycrystals. It shows that stress alone cannot pole the sample, but can be utilized to reduce the strength of poling electric field. (IX) The effects of compressions on hysteresis loops and domain microstructures of MPB-based ferroelectric polycrystals are investigated. It shows that longitudinal piezoelectric coefficient can be enhanced by compressions, with the best value found when compression is about to initiate the depolarization process. / Ph. D.