994 resultados para porous layers
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Thermal effects of the heat transfer at free surface (represented by Biot number) on the Rayleigh-Marangoni-Benard instability in a system of liquid-porous layers with top free surface are investigated numerically. The results indicate that this thermal effect can evidently lead to the mode transition of convection, which is overlooked in previous works. (C) 2010 Elsevier Ltd. All rights reserved.
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A mathematical model was developed in order to study the behavior of thermal stratification of liquid in a typical storage tank with porous medium. The model employs a transient stream function-vorticity formulation to predict the development of stream function and temperature fields in a charging process. Parameters analyzed include Biot, Darcy, Reynolds and Richardson numbers, position, and the thickness of the porous medium. The results show the influence of these physical parameters that should be considered for a good design of storage tanks with thermal stratification.
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An experimental setup was designed to visualize water percolation inside the porous transport layer, PTL, of proton exchange membrane, PEM, fuel cells and identify the relevant characterization parameters. In parallel with the observation of the water movement, the injection pressure (pressure required to transport water through the PTL) was measured. A new scaling for the drainage in porous media has been proposed based on the ratio between the input and the dissipated energies during percolation. A proportional dependency was obtained between the energy ratio and a non-dimensional time and this relationship is not dependent on the flow regime; stable displacement or capillary fingering. Experimental results show that for different PTL samples (from different manufacturers) the proportionality is different. The identification of this proportionality allows a unique characterization of PTLs with respect to water transport. This scaling has relevance in porous media flows ranging far beyond fuel cells. In parallel with the experimental analysis, a two-dimensional numerical model was developed in order to simulate the phenomena observed in the experiments. The stochastic nature of the pore size distribution, the role of the PTL wettability and morphology properties on the water transport were analyzed. The effect of a second porous layer placed between the porous transport layer and the catalyst layer called microporous layer, MPL, was also studied. It was found that the presence of the MPL significantly reduced the water content on the PTL by enhancing fingering formation. Moreover, the presence of small defects (cracks) within the MPL was shown to enhance water management. Finally, a corroboration of the numerical simulation was carried out. A threedimensional version of the network model was developed mimicking the experimental conditions. The morphology and wettability of the PTL are tuned to the experiment data by using the new energy scaling of drainage in porous media. Once the fit between numerical and experimental data is obtained, the computational PTL structure can be used in different types of simulations where the conditions are representative of the fuel cell operating conditions.
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Porous InP layers were formed electrochemically on (100) oriented n-InP substrates in various concentrations of aqueous KOH under dark conditions. In KOH concentrations from 2 mol dm-3 to 5 mol dm-3, a porous layer is obtained underneath a dense near-surface layer. The pores within the porous layer appear to propagate from holes through the near-surface layer. Transmission electron microscopy studies of the porous layers formed under both potentiodynamic and potentiostatic conditions show that both the thickness of the porous layer and the mean pore diameter decrease with increasing KOH concentration. The degree of porosity, estimated to be 65%, was found to remain relatively constant for all the porous layers studied.
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The Rolls-Royce Integrated-Planar Solid Oxide Fuel Cell (IP-SOFC) consists of ceramic modules which have electrochemical cells printed on the outer surfaces. The cathodes are the outermost layer of each cell and are supplied with oxygen from air flowing over the outside of the module. The anodes are in direct contact with the ceramic structure and are supplied with fuel from internal gas channels. Natural gas is reformed into hydrogen for use by the fuel cells in a separate reformer module of similar design except that the fuel cells are replaced by a reforming catalyst layer. The performance of the modules is intrinsically linked to the behaviour of the gas flows within their porous structures. Because the porous layers are very thin, a one-dimensional flow model provides a good representation of the flow property variations between fuel channel and fuel cell or reforming catalyst. The multi-component convective-diffusive flows are simulated using a new theory of flow in porous material, the Cylindrical Pore Interpolation Model. The effects of the catalysed methane reforming and water-gas shift chemical reactions are also considered using appropriate kinetic models. It is found that the shift reaction, which is catalysed by the anode material, has certain beneficial effects on the fuel cell module performance. In the reformer module it was found that the flow resistance of the porous support structure makes it difficult to sustain a high methane conversion rate. Although the analysis is based on IP-SOFC geometry, the modelling approach and general conclusions are applicable to other types of SOFC.
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Recasting process influence upon corrosion behavior of Co-Cr-Mo dental alloy in simulated physiological serum has been investigated using chemical and electrochemical techniques. Recast Co-Cr-Mo alloy by induction (IND) or by blowtorch (FLAME) has exhibited similar dendritic structures. Both IND and FLAME alloys have presented good corrosion resistance in physiological serum. Passivation process provides this corrosion resistance. Codissolution makes this process difficult. Passive films, formed on these alloys, have been analyzed as a dual layer consisting of an inner barrier and an outer porous layer. Passive film protective characteristics are higher in FLAME than in IND alloy. On this last alloy, the passive film is more porous due to a higher Codissolution. ©Carl Hanser Verlag, München.
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Die im Süden der Türkei gelegen, antiken Städte Aspendos und Patara, waren in der Römerzeit zwei bedeutende Handelszentren mit hoher Bevölkerungsdichte. Aquädukte versorgten beide Städte mit carbonathaltigem Wasser, wobei sich Kalksinter (Calciumcarbonat) in der Kanalrinne ablagerte. Dabei lagern sich im Wechsel eine hellere und dunklere Kalksinterlage ab, die als Sinterpaar bezeichnet wird. Um die Entstehung dieser Sinterpaare besser zu verstehen, und die beteiligten Prozesse mit saisonalen Veränderungen der Umwelt zu korrelieren, werden in der vorliegenden Arbeit laminierten Sinterablagerungen mit geochemischen und petrographischen Methoden untersucht.rnEntlang der Kanalrinne beider Aquädukte wurden an mehreren Stellen Proben entnommen. Es wurde untersucht in wieweit sich die Sinterstruktur aufgrund von Änderungen in der Neigung des Wasserkanals oder des Kanaltyps ändert. Um die Kristallform und die kristallografische Orientierung der Kristalle innerhalb der verschiedenen Sinterpaare zu untersuchen, wurden die entnommenen laminierten Kalksinterablagerungen mit Hilfe optischer Mikroskopie und EBSD (Electron Backscatter Diffraction) analysiert. Der Electron Probe Micro-Analyzer (EPMA) wurde verwendet, um saisonale Schwankungen der Hauptelementverteilung und den Anteil der stabilen Isotope im Wasser zu bestimmen. Die LA-ICP-MS (Laser Ablation-induktiv gekoppeltem Plasma-Massenspektrometrie) Spurenelementanalyse wurde durchgeführt, um kleinste Schwankungen der Spurenelemente zu finden. Basierend auf diesen Analysen wurde festgestellt, dass laminierten Kalksinterablagerungen laterale Änderungen in der Aquäduktstruktur und -neigung, jahreszeitliche Änderungen der Wasserchemie, der Temperatur sowie der Entgasungsrate während eines Jahres widerspiegeln. Die Kalksinterablagerungen zeigen eine deutliche Laminierung in Form von feinkörnig-porösen und grobkörnig-dichten Schichten, die trockene und nasse Jahreszeiten anzeigen. Feinkörnige Schichten zeigen eine hohe Epifluoreszenz aufgrund reichhaltiger organischer Inhalte, die vermutlich eine Folge der bakteriellen Aktivität während der warmen und trockenen Jahreszeit sind. Stabile Sauerstoff und Kohlenstoff-Isotop-Kurven entsprechen auch den jahreszeitlichen Schwankungen der verschiedenen Schichtenpaare. Vor allem δ 18O spiegelt jährliche Veränderungen in der Temperatur und jahreszeitliche Veränderungen des Abflusses wieder. Das wichtigste Ergebnis ist, dass die Periodizität von δ 18O durch Erwärmen des Wassers im Wasserkanal und nicht durch die Verdunstung oder der Brunnenwasser-Charakteristik verursacht wird. Die Periodizität von δ 13C ist komplexer Natur, vor allem zeigen δ 18O und δ 13C eine Antikorrelation entlang der Lamellenpaare. Dies wird wohl vor allem durch Entgasungsprozesse im Aquädukt verursacht. Die Ergebnisse der Spurenelemente sind meist inkonsistent und zeigen keine signifikanten Veränderungen in den verschiedenen Lamellenpaaren. Die Isotope Mg, Sr und Ba zeigen hingegen bei einigen Proben eine positive Korrelation und erreichen Höchstwerte innerhalb feinkörnig-poröser Schichten. Auch sind die Hauptelementwerte von Fe, K, Si und anderer detritischer Elemente innerhalb der feinkörnige-porösen Schichten maximal. Eine genaue Datierung der Kalksinterablagerungen ist wünschenswert, da der Zeitraum, in dem die Aquädukte aktiv waren, bereits archäologisch auf 200-300 Jahre festgelegt wurde. Paläomagnetische und 14C-Datierung geben keine brauchbare Ergebnisse. Die U/Th Isotopie wird durch eine hohe Anfangskonzentration von Th in den Proben behindert. Trotz dieser Schwierigkeiten war eine U/Th Datierung an einem Testbeispiel des Béziers Aquädukt erfolgreich. Mit Hilfe von analogen Untersuchungen an aktiven Wasserkanälen der heutigen Zeit, werden die Ablagerungsmechanismen und die geochemische Entwicklung der laminierten Sinterschichten besser verstanden. Ein weiteres laufendes Projekt dieser Doktorarbeit ist die Überwachung von Sinterabscheidungen und der saisonale Zusammensetzung des Wassers an einigen heute noch aktiven Aquädukten. Das Ziel ist die Untersuchung der jetzigen Calciumcarbonatabscheidungen in Aquäduktkanälen unter den heutigen Umgebungsbedingungen. Erste Ergebnisse zeigen, dass kleine regelmäßige jahreszeitliche Veränderungen in der Isotopenzusammensetzung des Wassers vorliegen, und dass die beobachtete Periodizität der stabilen Isotope aufgrund von Änderungen im eigentlichen Kanal entstanden ist. Die Untersuchung von Kalksinterablagerungen in römischen Aquädukten liefern vielversprechende Ergebnisse, für die Untersuchung des Paläöklimas, der Archaeoseismologie und anderer Umweltbedingungen in der Römerzeit. Diese Studie beschränkt sich auf zwei Aquädukte. Die Untersuchungen weiterer Aquädukte und einer Überwachung, der noch in Betrieb stehenden Aquädukte werden genauere Ergebnisse liefern.
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Los sistemas micro electro mecánicos (MEMS) han demostrado ser una exitosa familia de dispositivos que pueden usarse como plataforma para el desarrollo de dispositivos con aplicaciones en óptica, comunicaciones, procesado de señal y sensorización. Los dispositivos MEMS estándar suelen estar fabricados usando tecnología de silicio. Sin embargo, el rendimiento de estos MEMS se puede mejorar si se usan otros materiales. Por ejemplo, el diamante nanocristalino (NCD) ofrece unas excelentes propiedades mecánicas, transparencia y una superficie fácil de funcionalizar. Por otro lado, el sistema de materiales (In; Ga; Al)N, los materiales IIIN, se pueden usar para producir estructuras monocristalinas con alta sensibilidad mecánica y química. Además, el AlN se puede depositar por pulverización catódica reactiva sobre varios substratos, incluyendo NCD, para formar capas policristalinas orientadas con alta respuesta piezoeléctrica. Adicionalmente, tanto el NCD como los materiales III-N muestran una gran estabilidad térmica y química, lo que los hace una elección idónea para desarrollar dispositivos para aplicaciones para alta temperatura, ambientes agresivos e incluso para aplicaciones biocompatibles. En esta tesis se han usado estos materiales para el diseño y medición de demostradores tecnológicos. Se han perseguido tres objetivos principales: _ Desarrollo de unos procesos de fabricación apropiados. _ Medición de las propiedades mecánicas de los materiales y de los factores que limitan el rendimiento de los dispositivos. _ Usar los datos medidos para desarrollar dispositivos demostradores complejos. En la primera parte de esta tesis se han estudiado varias técnicas de fabricación. La estabilidad de estos materiales impide el ataque y dificulta la producción de estructuras suspendidas. Los primeros capítulos de esta disertación se dedican al desarrollo de unos procesos de transferencia de patrones por ataque seco y a la optimización del ataque húmedo sacrificial de varios substratos propuestos. Los resultados de los procedimientos de ataque se presentan y se describe la optimización de las técnicas para la fabricación de estructuras suspendidas de NCD y materiales III-N. En un capítulo posterior se estudia el crecimiento de AlN por pulverización catódica. Como se ha calculado en esta disertación para obtener una actuación eficiente de MEMS, las capas de AlN han de ser finas, típicamente d < 200 nm, lo que supone serias dificultades para la obtención de capas orientadas con respuesta piezoeléctrica. Las condiciones de depósito se han mapeado para identificar las fronteras que proporcionan el crecimiento de material orientado desde los primeros pasos del proceso. Además, durante la optimización de los procesos de ataque se estudió un procedimiento para fabricar películas de GaN nanoporoso. Estas capas porosas pueden servir como capas sacrificiales para la fabricación de estructuras suspendidas de GaN con baja tensión residual o como capas para mejorar la funcionalización superficial de sensores químicos o biológicos. El proceso de inducción de poros se discutirá y también se presentarán experimentos de ataque y funcionalización. En segundo lugar, se han determinado las propiedades mecánicas del NCD y de los materiales III-N. Se han fabricado varias estructuras suspendidas para la medición del módulo de Young y de la tensión residual. Además, las estructuras de NCD se midieron en resonancia para calcular el rendimiento de los dispositivos en términos de frecuencia y factor de calidad. Se identificaron los factores intrínsecos y extrínsecos que limitan ambas figuras de mérito y se han desarrollado modelos para considerar estas imperfecciones en las etapas de diseño de los dispositivos. Por otra parte, los materiales III-N normalmente presentan grandes gradientes de deformación residual que causan la deformación de las estructuras al ser liberadas. Se han medido y modelado estos efectos para los tres materiales binarios del sistema para proporcionar puntos de interpolación que permitan predecir las características de las aleaciones del sistema III-N. Por último, los datos recabados se han usado para desarrollar modelos analíticos y numéricos para el diseño de varios dispositivos. Se han estudiado las propiedades de transducción y se proporcionan topologías optimizadas. En el último capítulo de esta disertación se presentan diseños optimizados de los siguientes dispositivos: _ Traviesas y voladizos de AlN=NCD con actuación piezoeléctrica aplicados a nanoconmutadores de RF para señales de alta potencia. _ Membranas circulares de AlN=NCD con actuación piezoeléctrica aplicadas a lentes sintonizables. _ Filtros ópticos Fabry-Pérot basados en cavidades aéreas y membranas de GaN actuadas electrostáticamente. En resumen, se han desarrollado unos nuevos procedimientos optimizados para la fabricación de estructuras de NCD y materiales III-N. Estas técnicas se han usado para producir estructuras que llevaron a la determinación de las principales propiedades mecánicas y de los parámetros de los dispositivos necesarios para el diseño de MEMS. Finalmente, los datos obtenidos se han usado para el diseño optimizado de varios dispositivos demostradores. ABSTRACT Micro Electro Mechanical Systems (MEMS) have proven to be a successful family of devices that can be used as a platform for the development of devices with applications in optics, communications, signal processing and sensorics. Standard MEMS devices are usually fabricated using silicon based materials. However, the performance of these MEMS can be improved if other material systems are used. For instance, nanocrystalline diamond (NCD) offers excellent mechanical properties, optical transparency and ease of surface functionalization. On the other hand, the (In; Ga; Al)N material system, the III-N materials, can be used to produce single crystal structures with high mechanical and chemical sensitivity. Also, AlN can be deposited by reactive sputtering on various substrates, including NCD, to form oriented polycrystalline layers with high piezoelectric response. In addition, both NCD and III-N materials exhibit high thermal and chemical stability, which makes these material the perfect choice for the development of devices for high temperatures, harsh environments and even biocompatible applications. In this thesis these materials have been used for the design and measurement of technological demonstrators. Three main objectives have been pursued: _ Development of suitable fabrication processes. _ Measurement of the material mechanical properties and device performance limiting factors. _ Use the gathered data to design complex demonstrator devices. In a first part of the thesis several fabrication processes have been addressed. The stability of these materials hinders the etching of the layers and hampers the production of free standing structures. The first chapters of this dissertation are devoted to the development of a dry patterning etching process and to sacrificial etching optimization of several proposed substrates. The results of the etching processes are presented and the optimization of the technique for the manufacturing of NCD and III-N free standing structures is described. In a later chapter, sputtering growth of thin AlN layers is studied. As calculated in this dissertation, for efficient MEMS piezoelectric actuation the AlN layers have to be very thin, typically d < 200 nm, which poses serious difficulties to the production of c-axis oriented material with piezoelectric response. The deposition conditions have been mapped in order to identify the boundaries that give rise to the growth of c-axis oriented material from the first deposition stages. Additionally, during the etching optimization a procedure for fabricating nanoporous GaN layers was also studied. Such porous layers can serve as a sacrificial layer for the release of low stressed GaN devices or as a functionalization enhancement layer for chemical and biological sensors. The pore induction process will be discussed and etching and functionalization trials are presented. Secondly, the mechanical properties of NCD and III-N materials have been determined. Several free standing structures were fabricated for the measurement of the material Young’s modulus and residual stress. In addition, NCD structures were measured under resonance in order to calculate the device performance in terms of frequency and quality factor. Intrinsic and extrinsic limiting factors for both figures were identified and models have been developed in order to take into account these imperfections in the device design stages. On the other hand, III-N materials usually present large strain gradients that lead to device deformation after release. These effects have been measured and modeled for the three binary materials of the system in order to provide the interpolation points for predicting the behavior of the III-N alloys. Finally, the gathered data has been used for developing analytic and numeric models for the design of various devices. The transduction properties are studied and optimized topologies are provided. Optimized design of the following devices is presented at the last chapter of this dissertation: _ AlN=NCD piezoelectrically actuated beams applied to RF nanoswitches for large power signals. _ AlN=NCD piezoelectrically actuated circular membranes applied to tunable lenses. _ GaN based air gap tunable optical Fabry-Pérot filters with electrostatic actuation. On the whole, new optimized fabrication processes has been developed for the fabrication of NCD and III-N MEMS structures. These processing techniques was used to produce structures that led to the determination of the main mechanical properties and device parameters needed for MEMS design. Lastly, the gathered data was used for the design of various optimized demonstrator devices.
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Porous structures are being widely investigated for use in biomedical implants, aiming to mechanically integrate and functionally the implant inside the bone tissue. Moreover, this structure is also important for drugs that can be stored and can induce and accelerate the process of osseointegration. With the purpose to investigate this effect, Ti, Nb and Sn metal powders, were sintered by plasma using a hollow cathode discharge. Sintering was performed in argon plasma set at 4 mbar pressure and temperatures of 500 ° C, 600 ° C and 700 ° C. Samples were also sintered in the electrical resistance furnace at 1200 ° C in order to compare plasma sintering with the conventional method. It was observed that plasma samples sintered with the hollow cathode configuration showed a gradient in porosity, while the samples sintered in the resistive furnace did not. Furthermore, differences in the microstructure of the samples were found, were a surface with higher porosity and ales porous core were obtained at different temperatures. The percolation profile of distilled water and the chemical compositions of the porous layers of the plasma treated samples were the main results obtained. Based on these results, we can conclude that this structure is particularly important for application in the biomedical field such as scaffolds for drug delivery and implants
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Porous layers can be formed electrochemically on (100) oriented n-InP substrates in aqueous KOH. A nanoporous layer is obtained underneath a dense near-surface layer and the pores appear to propagate from holes through the near-surface layer. In the early stages of the anodization transmission electron microscopy (TEM) clearly shows individual porous domains that appear to have a square-based pyramidal shape. Each domain appears to develop from an individual surface pit which forms a channel through this near-surface layer. We suggest that the pyramidal structure arises as a result of preferential pore propagation along the <100> directions. AFM measurements show that the density of surface pits increases with time. Each of these pits acts as a source for a pyramidal porous domain. When the domains grow, the current density increases correspondingly. Eventually the domains meet, forming a continuous porous layer, the interface between the porous and bulk InP becomes relatively flat and its total effective surface area decreases resulting in a decrease in the current density. Current-time curves at constant potential exhibit a peak and porous layers are observed to form beneath the electrode surface. The density of pits formed on the surface increases with time and approaches a plateau value. Porous layers are also observed in highly doped InP but are not observed in wafers with doping densities below ~5 × 1017 cm-3. Numerical models of this process have been developed invoking a mechanism of directional selectivity of pore growth preferentially along the <100> lattice directions. Manipulation of the parameters controlling these curves shows that the fall-off in current is controlled by the rate of diffusion of electrolyte through the pore structure with the final decline in current being caused by the termination of growth at the pore tips through the formation of passivating films or some other irreversible modification of the pore tips.
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The anodic behavior of InP in 1 mol dm-3 KOH was investigated and compared with its behavior at higher concentrations of KOH. At concentrations of 2 mol dm-3 KOH or greater, selective etching of InP occurs leading to thick porous InP layers near the surface of the sustrate. In contrast, in 1 mol dm-3 KOH, no such porous layers are formed but a thin surface film is formed at potentials in the range 0.6 V to 1.3 V. The thickness of this film was determined by spectroscopic ellipsometry as a function of the upper potential and the measured film thickness corresponds to the charge passed up to a potential of 1.0 V. Anodization to potentials above 1.5 V in 1 mol dm- 3 KOH results in the growth of thick, porous oxide films (~ 1.2 µm). These films are observed to crack, ex-situ, due to shrinkage after drying in ambient air. Comparisons between the charge density and film thickness measurements indicate a porosity of approximately 77% for such films.
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To study the dissipation of heat generated due to the formation of pinholes that cause local hotspots in the catalyst layer of the Polymer Electrolyte Fuel Cell, a two-phase non-isothermal model has been developed by coupling Darcy’s law with heat transport. The domain under consideration is a section of the membrane electrode assembly with a half-channel and a half-rib. Five potential locations where a pinhole might form were analyzed: at the midplane of the channel, midway between the channel midplane and the channel wall, at the channel or rib wall, midway between the rib midplane and the channel wall, at the midplane of the rib. In the first part of this work, a preliminary thermal model was developed. The model was then refined to account for the two-phase effects. A sensitivity study was done to evaluate the effect of the following properties on the maximum temperature in the domain: Catalyst layer thermal conductivity, the Microporous layer thermal conductivity, the anisotropy factor of the Catalyst layer thermal conductivity, the Porous transport layer porosity, the liquid water distribution and the thickness of the membrane and porous layers. Accounting for the two-phase effects, a slight cooling effect was observed across all hotspot locations. The thermal properties of the catalyst layer were shown to have a limited impact on the maximum temperature in the catalyst layer of new fuel cells without pinhole. However, as hotspots start to appear, thermal properties play a more significant role in mitigating the thermal runaway.
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A solid state lithium metal battery based on a lithium garnet material was developed, constructed and tested. Specifically, a porous-dense-porous trilayer structure was fabricated by tape casting, a roll-to-roll technique conducive to high volume manufacturing. The high density and thin center layer (< 20 μm) effectively blocks dendrites even over hundreds of cycles. The microstructured porous layers, serving as electrode supports, are demonstrated to increase the interfacial surface area available to the electrodes and increase cathode loading. Reproducibility of flat, well sintered ceramics was achieved with consistent powderbed lattice parameter and ball milling of powderbed. Together, the resistance of the LLCZN trilayer was measured at an average of 7.6 ohm-cm2 in a symmetric lithium cell, significantly lower than any other reported literature results. Building on these results, a full cell with a lithium metal anode, LLCZN trilayer electrolyte, and LiCoO2 cathode was cycled 100 cycles without decay and an average ASR of 117 ohm-cm2. After cycling, the cell was held at open circuit for 24 hours without any voltage fade, demonstrating the absence of a dendrite or short-circuit of any type. Cost calculations guided the optimization of a trilayer structure predicted that resulting cells will be highly competitive in the marketplace as intrinsically safe lithium batteries with energy densities greater than 300 Wh/kg and 1000 Wh/L for under $100/kWh. Also in the pursuit of solid state batteries, an improved Na+ superionic conductor (NASICON) composition, Na3Zr2Si2PO12, was developed with a conductivity of 1.9x10-3 S/cm. New super-lithiated lithium garnet compositions, Li7.06La3Zr1.94Y0.06O12 and Li7.16La3Zr1.84Y0.16O12, were developed and studied revealing insights about the mechanisms of conductivity in lithium garnets.
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The nonsimilar non-Darcy mixed convection flow about a heated horizontal surface in a saturated porous medium has been studied when the surface temperature is a power function of distance (Tw = T∞ ± Axλ). The analysis is performed for the cases of parallel and stagnation flows with favourable induced pressure gradient. The partial differential equations governing the flow have been solved numerically using the Keller box method. The heat transfer is enhanced due to the buoyancy parameter and wall temperature, but the non-Darcy parameter reduces it. For non-Darcy flow, the similarity solution exists only for the case of parallel flow.