Sintering, a process of forming dense solid bodies from powder compacts remains the most important route for processing of ceramics. The process of sintering involves formation and growth of necks during initial stage, coarsening, relative particle rotation, filling of connected pores in intermediate stage, filling of isolated pores during final stage sintering and rapid grain growth towards the end of densification. The processes involve a combi-nation of grain boundary diffusion, surface diffusion, grain boundary migration and grain boundary sliding. Studies of interfacial processes during sintering are still of interest since modifying interface structure offers a means to tailor low and high temperature mechanical properties of ceramics. Many of the studies in literature on single phase systems are based on geometric changes during sintering. Sintering has been modelled as 1D or 2D array of spheres. The simplest of these consist of a contacting pair of spherical particles. Early models studied changes in size and shape of the necks during initial stage sintering and associated mass transport mechanisms. There have been studies on coarsening that report shrinkage rates of smaller particles is a system of two particles with different radii. In both the cases of neck growth and coarsening, thermodynamic variables as given by dihedral angle (relative grain boundary to surface energy of the system) and kinetic parameters of grain boundary surface diffusivity have been found to influence the size and shape evolution with time. Also, there have been studies comparing self similar geometries at different absolute length scales such as a system of micro and nano sized particles, which show different sintering behaviour depending on the absolute particle size. There have been studies on multi particle arrays both linear and closed. Early studies on linear arrays observed rearrangement of particles and relative rotation due to non spherical shape and bond angle of an array of three particles. Also there was a study that predicted rearrangement due to differential shrinkage in an assembly containing a combi-nation of large and small particles. Similar observations were also made on closed arrays of four or more particles both in 2D and 3D. Formation of high energy local configurations such as six grain boundaries (GBs) meeting at a line were found, followed by the topological transitions such as formation of new GBs or elimination of existing ones, leading to specific features in sintering behaviour. Geometrical evolution during final stage sintering is critical for forming dense final products. While most studies related the shrinkage behaviour to shape of the pore (convex or concave) and the number of grains surrounding a pore, later the absolute size of the pore was observed to be an important parameter. In 2D simulations and experiments large convex pores were found to shrink due to mass transport from surrounding GBs. In 3D simulations, pores with large coordination number as high as 32, pore shrinkage was observed followed by gradual reduction in coordination number and final elimination. Also studied are evolution of pore -GB configuration in case of small pores as separation of these from GB and entrapment into grains will freeze further shrinkage. In addition to the geometry related changes are also crystallography related microstructural changes. Crystallographic arrangement at the atomic scale leads to anisotropy of interfacial energies and diffusivities, that effect microstructural evolution. The presence of positive and negative ions in ionic solids can result in additional features such as charged and neutral planes Crystallography can affect the rotation of powder particles in initial stage sintering to subtle differences in microstructure evolution during grain growth in final stage sintering. Conversely crystallography has to be related to diffusion at interfaces. The rotation of spheres is governed by energetics. The final configuration corresponds to local energy minima in misorientations between the spheres and the single crystal plate. This technique is useful in finding a number of crystallography related aspects such as low energy GBs and equilibrium shapes of metal droplets. Rotation of unconstrained crystal related to neighbouring crystal has also been observed in thin films. Surface energy anisotropy has often been studied using topography of annealed sur-faces studied using atomic force microscopy (AFM). While low energy stable surfaces show perfectly flat surfaces, planes close to a stable plane form terrace and ledge structures whereas unstable planes form hill and valley structures. A method of “inverse Wulff shape” of pores trapped in single crystals has been used to find relative stability of sur-face planes using a combination of electron back scattered diffraction (EBSD) and AFM. Crystallography is very much related to the phenomenon of abnormal grain growth that occurs during later stages of sintering. Similarly, polycrystal assemblies have shown varying GB migration velocities for different crystallographic planes. Most recently, 3D EBSD has been used to study crystallography of GBs in sintered polycrystalline materials. In the present study, we address two specific issues. The first is related to the effect of microstructure of polycrystalline powder particles on initial stage sintering, where we compare sintering between particles with same particle size but different grain sizes. The second is related to the crystallographic aspects of interfaces in sintered materials with specific reference to yttria stabilized cubic zirconia. The present study is mostly confined to pressure less (free) sintering where the only driving force is the reduction in interfacial energy of the system. The effect of polycrystalline nature on initial stage sintering is investigated and com-pared with the behaviour of single crystal particles. We extend the model by Coble on single crystals to polycrystalline particles containing space filling tetrakaidecahedral grains with an identical grain size. The grain boundaries within particles are considered to be additional sources for mass to be plated at the neck and the flux equations are suitably modified. A model was developed to characterize the variation with time in the growth rate (x/R), where x and R are radii of the neck and particle respectively. The model indicated that the neck growth rate for polycrystalline spheres was faster compared to single crystals towards end of initial stage sintering (large value of x/R). There is large scope for extending the model further for complex geometries, diffusion distances and grain size distributions. Sintering experiments were conducted with annealed 2D random arrays of spheres of zirconia with two different grain sizes and a particle size of 40 m. Two different forms of zirconia (8YCZ and 3YTZ) were used as model systems for a few and a large number of grains in a particle respectively. The experimental results were limited, but broadly consistent with the new model. However necks were found to grow to a value f x=R = 0:12 and they did not grow further. In the second part of our study, grain boundaries in yttria stabilized cubic zirconia were studied in the context of macroscopic crystallographic parameters of misorientations of grains on either side of the grain boundary and crystallographic coordinates of grain boundary planes. Our aim was to study the evolution of misorientations and grain bound-ary planes during sintering process, starting from formation of necks during the initial stage to grain boundary migration during later stages. Orientation imaging microscopy based on an EBSD technique in an SEM was carried out on fully dense samples and also on porous samples obtained by interrupting sintering before attaining full density. The fraction of CSL misorientations on nearly dense cubic zirconia with grain sizes varying from submicrocrystalline 0.61 to 10 m was close to a random distribution. The number fraction of necks with CSLs formed in porous cubic zirconia with microcrysatlline particles was slightly higher than a random distribution. However, the present study covers only nearly dense-microcrystalline, nearly dense- submicrocrystalline, porous - microcrystalline regime , but misorientation information could not be obtained experimentally in a low density - submi-crocrystalline regime that is critical for sintering process. We also studied the distribution of grain boundary planes in fully dense 8YCZ with a grain size of 2.8 m by a stereological method using 2D OIM data. The overall distribution of grain boundary planes showed very weak anisotropy with slight maxima with 1.1 multiples of random distribution (MRD) at {100} planes, which is consistent with observations in literature on larger grain sizes. Interestingly, the planes that were abundant were not low energy surface planes (also mentioned in literature), in clear contrast with other ceramics studied in literature. The distribution of grain boundary planes was also plotted for specific misorientations, including those around low index axes of [100], [110], [111] and low misorientations. The grain boundary character distribution (GBCD) shows a high frequency of occurrence in position of pure twists about [100] and symmetric tilts at certain low misorientations . The highest frequency of occurrence was observed for coherent twin 3 on {111} plane and symmetric tilt (higher order twin) 11 on {113} plane, both corresponding to low energy GBs reported in literature in bicrystal experiments. With pure twists on {100} for rotations about [100] axis and pure tilts with {11w} or {1ww} planes for rotations about [110], both the criteria for specialness based on surface planes forming GB or symmetric tilts are found to be valid for specific cases. Notable is the frequency of occurrence of coherent twin 3 on {111} and 11 on {113}, that was 4.8 MRD for microcrystalline 8YCZ and as high as 7.8 MRD for submicrocrystalline 8YCZ samples, which is much higher than frequency of occurrence of any GB plane in any oxide studied in literature.

Afin de mieux appréhender la plasticité des alliages métalliques, il est important de pouvoir décrire à l'échelle atomique les interactions entre dislocations et solutés et d’en déduire l’effet sur la mobilité des dislocations. Au cours de cette thèse, nous nous sommes intéressés aux métaux de transition cubiques centrés (CC), et en particulier au fer, en présence de solutés interstitiels. A l’aide de calculs en Théorie de la Fonctionnelle de la Densité (DFT), la structure de cœur de la dislocation vis de vecteur de Burgers b=½<111> a été étudiée dans le fer en présence de solutés de bore, carbone, azote et oxygène et dans les métaux CC des groupes 5 (V, Nb et Ta) et 6 (Mo, W) en présence de carbone. Nous avons mis en évidence dans le fer et les métaux du groupe 6 une reconstruction du cœur de la dislocation en présence de solutés, associée à une très forte énergie d’attraction dislocation/soluté. Un comportement différent a été observé pour le groupe 5, la configuration la plus stable pour le carbone étant un site octaédrique proche de la dislocation, sans reconstruction de cœur. Cette tendance de groupe a été reliée à la structure des mono-carbures. Les conséquences des interactions fortement attractives dans le fer en présence de carbone ont ensuite été développées. D’une part la ségrégation d’équilibre du carbone proche du cœur de la dislocation a été étudiée à l’aide de modèles en champ moyen et de simulations Monte Carlo. D’autre part, la mobilité de la dislocation décorée a été étudiée en modélisant le mécanisme de double décrochement, en lien avec des observations expérimentales en microscopie électronique à transmission / In order to improve our understanding of alloy plasticity, it is important to describe at the atomic scale the dislocation-solute interactions and their effect on the dislocation mobility. This work focuses on the body-centered cubic (BCC) transition metals, in particular Fe, in presence of interstitial solute atoms. Using Density Functional Theory (DFT) calculations, the core structure of the screw dislocation of Burgers vector b=½<111> was investigated in iron in presence of boron, carbon, nitrogen and oxygen solute atoms, and in BCC metals from group 5 (V, Nb, Ta) and 6 (Mo, W) in presence of carbon solutes. A core reconstruction was evidenced in iron and group 6 metals, along with a strong attractive dislocation-solute interaction energy. A different behavior was observed in group 5 metals, for which the most stable configuration for the carbon atom is an octahedral site in the vicinity of the dislocation, without any core reconstruction. This group tendency was linked to the structure of mono-carbides. Consequences of the strongly attractive dislocation-solute interactions in Fe(C) were then investigated. First the equilibrium segregation close to the dislocation core was studied using a mean-field model and Monte Carlo simulations. Then, the mobility of the dislocation in presence of carbon atoms was investigated by modeling the double-kink mechanism with DFT, in relation with experimental data obtained with transmission electron microscopy

This thesis is dedicated to the coloring of cubic graphs. It summarizes the knowledge we have about so called Steiner coloring, which is an edge-coloring such that the colors incident with one vertex form a triple of some partial Steiner system. The main objects of interest are the projective and affine systems. Afterwards the sufficient condition for universality of the system is stated and it is observed, that all other transitive Steiner triple systems satisfy it. This thesis also contains methods of construction of the coloring for the Fano plane, for the affine system Z3 3 and for the universal system created as a product of the Fano plane and the trivial system (F7 S⊠ 3). Finally an algorithm usable for the rest of the systems and graphs with bounded treewidth is presented.

Depuis quelques années, nous assistons à une prise de conscience croissante des effets à long terme des polluants chimiques sur l'environnement et la santé humaine. Il est donc nécessaire d'étudier non seulement leurs propriétés écotoxicologiques mais également leurs propriétés physicochimiques tels que la tension de vapeur (ou volatilité) et leur solubilité dans l'eau. L'Europe, quant à elle, a introduit la réglementation REACH (Registration, Evaluation and Autorisation of CHemicals) qui est entrée en vigueur le 1 juin 2007 dont le principal objectif est une meilleure connaissance des propriétés environnementales et sanitaires des substances chimiques. De même dans l’industrie, la détermination de la tension de vapeur des corps purs est une donnée indispensable pour les opérations de purification et de séparation. Dans ce but nous avons amélioré un appareil à saturation de gaz inerte existant au laboratoire. Une fois le bon fonctionnement de l’appareil vérifié (par mesure de la tension de vapeur d’un composé de référence : le phénanthrène) nous avons étudié des n-alcanes compris entre le C30 et le C60 ainsi que 8 hydrocarbures aromatiques polycycliques dans un large domaine de température (20 à 320 °C) et de pression (10-1 Pa à 10-7 Pa). Les résultats obtenus ont été comparés avec la littérature lorsque celle-ci est disponible. La détermination des tensions de vapeur de composés inorganiques d’intérêt industriel : tétrachlorure de Zirconium (ZrCl4) et le tétrachlorure d’hafnium (HfCl4) a été également entreprise. Les résultats expérimentaux des hydrocarbures polyaromatiques nous ont permis l’amélioration d’une équation d’état cubique (dérivée de celle de Peng-Robinson) dont les paramètres sont estimés par une méthode de contribution de groupes développée par Rauzy-Coniglio. Les tensions de vapeur prédites par le modèle sont en bon accord avec les valeurs expérimentales / For a few years, we have attended an increasing importance of the long-term effects of the chemical pollutants on the environment and human health. It is thus necessary to study not only their ecotoxicological properties but also their physico-chemical properties such as the vapor pressure (or volatility) and aqueous solubility. In Addition, the introduction of the regulation REACH (Registration, Evaluation and Authorization of CHemicals) in June 2007 whose main objective is a better knowledge of the environmental and medical properties of chemical substances has increased the necessity of compound characterization. From an industrial point of view, the determination of the vapor pressure of the pure substances is an essential data in many unit operations such as purification and separation. Thus, we improved an apparatus with saturation of inert gas existing at the laboratory. Once the good performance of the apparatus checked (by measurement of the vapor pressure of a reference compound: phenanthrene) we studied N-alkanes ranging between C30 and C60 and 8 polycyclic aromatic hydrocarbons in a broad temperature range (20 to 320°C) and of pressure (10-1 Pa with 10-7 Pa). The obtained results were compared with the literature when available. In addition, determination of the vapor pressure of inorganic compounds of industrial interest : zirconium tetrachloride (ZrCl4) and the hafnium tetrachloride (HfCl4) was also undertaken. The experimental results of polyaromatic hydrocarbons have allowed us to improve a cubic equation of state (derivative of Peng-Robinson EOS) whose parameters are estimated by a method of contribution of groups developed by Rauzy-Coniglio. The predicted vapor pressures were in good agreement with the experimental values

La synthèse Fischer-Tropsch (FT) permet de convertir un mélange d'hydrogène et de monoxyde de carbone (gaz de synthèse) sélectivement en hydrocarbures avec une distribution large de longueur de chaine. Le gaz de synthèse peut être produit à partir de différentes ressources comme le gaz naturel, le charbon et la biomasse. A la lumière de la volonté de diversifier les sources d'énergies, la synthèse FT peut apporter une contribution cruciale pour la production de carburants liquides. Les catalyseurs à base de Cobalt supportés sur alumine sont utilisés pour produire des cires lourdes. L'activité et la sélectivité dépendent des propriétés structurales et texturales du catalyseur. Cette étude a pour but d'établir un lien entre les propriétés structurales des catalyseurs à base de Cobalt supportés sur alumine et des paramètres cinétiques spécifiques. Pour atteindre cet objectif, il a été mis en oeuvre une étude cinétique en régime permanent couplé à la technique « SSITKA » sur différents échantillons de Cobalt. En utilisant cette méthodologie, il a été trouvé que la conversion en CO sur 5 catalyseurs à base de Cobalt dépend uniquement du nombre de site initial sur la surface atomique de Cobalt réduit. Aucune influence de la taille de particule, de l'orientation de la phase cristalline ou du promoteur n'a pu être mis en évid ence. Les expériences SSTIKA réalisées sur une longue durée ont permis d'estimer le nombre de sites actifs dans les conditions de travail. Enfin, la modélisation cinétique a démontré que l'espèce la plus abondante sur la surface est le monoxyde de carbone adsorbé et que deux intermédiaires distincts de surface conduisent à la production de méthane et des hydrocarbures plus lourds / The Fischer-Tropsch synthesis (FTS) converts a mixture of hydrogen and carbon monoxide (syngas) selectively into hydrocarbons with a large chain length distribution. Syngas can be produce from different resources such as natural gas, coal and biomass. In the light of energy resource diversi fication, FTS can make a crucial contribution to the production of liquid fuels. Alumina supported cobalt catalysts are used to produce heavy waxes. The activity and selectivity depend on the structural and textural properties of the catalyst. This study aims at establishing a link between the structural properties of alumina supported cobalt catalysts and specific kinetic parameters. To this purpose, the steady-state and SSITKA kinetics over different cobalt samples have been carried out. By using this met hodology, it was found that the CO conversion over 5 cobalt catalysts only depends on the initial number of reduced cobalt surface atoms. No influence of the cobalt particle size, phase orientation or promotor could be identified. SSITKA experiments during long-term catalyst testing allowed estimating the number of active sites under working conditions. Further modelling showed that the most abundant surface species is adsorbed carbon monoxide and that two distinct surface intermediates lead to the production of methane and higher hydrocarbons

No description available.

There has been a rapid increase interest in computational number theory ever since the invention of public-key cryptography. Various attempts to solve the underlying hard problems behind public-key cryptosystems has led to interesting problems in computational number theory. One such problem, called the cubic sieve congruence problem, arises in the context of the cubic sieve method for solving the discrete logarithm problem in prime fields. The cubic sieve method requires a nontrivial solution to the Cubic Sieve Congruence (CSC)x3 y2z (mod p), where p is a given prime. A nontrivial solution must satisfy x3 y2z (mod p), x3 ≠ y2z, 1≤ x, y, z < pα , where α is a given real number ⅓ < α ≤ ½. The CSC problem is to find an efficient algorithm to obtain a nontrivial solution to CSC. This thesis is concerned with the CSC problem. Recently, the parametrization x y2z (mod p) and y υ3z (mod p) of CSC was introduced. We give a deterministic polynomial-time (O(ln3p) bit-operations) algorithm to determine, for a given υ, a nontrivial solution to CSC, if one exists. Previously it took Õ(pα) time to do this. We relate the CSC problem to the gap problem of fractional part sequences. We also show in the α = ½ case that for a certain class of primes the CSC problem can be solved deterministically Õ(p⅓) time compared to the previous best of Õ(p½). It is empirically observed that about one out of three primes are covered by this class, up to 109

The dependence of flow stress of body centered cubic metals on variables such as strain rate, temperature, strain and microstructural is a research area of continued interest. Recently, there has been renewed interest in deformation of fine grained BCC metals, which display characteristics that are different from their coarse-grained counterparts. Deformation mechanisms, strain-rate and temperature dependence, and strain hardening characteristics of fine-grained BCC metals are not well understood. The aim of this thesis is to understand the effect of strain-rate, temperature, strain and microstructure (i.e., grain size) on the mechanical response of poly¬crystalline tantalum. Among the topics addressed were constitutive modeling of flow stress, understanding the microstructural origins of strain hardening, and characterizing the effect of severe plastic deformation (SPD) on microstructure and mechanical properties. Rolling and equal-channel angular pressing (ECAP) were among the processing techniques employed. Mechanical testing was conducted over a range of temperatures and strain rates, and this was supported by a slew of microscopic characterization methods. It was found that the strain hardening response depends on microstructural evolution at different strain rates. Results indicate that the same thermally activated mechanisms operate in both as-received and processed material and this was found to be the overcoming of Peierls barriers via a double-kink mechanism. Lastly, it was found that the low strain rate sensitivity of SPD processed material was not due to fine grain size, but instead due to high internals stresses.

Given a complete graph K_n = (V,E) with non-negative edge costs c ∈ R^E, the problem multi-2EC_cost is that of finding a 2-edge connected spanning multi-subgraph of K_n with minimum cost. It is believed that there are no efficient ways to solve the problem exactly, as it is NP-hard. Methods such as approximation algorithms, which rely on lower bounds like the linear programming relaxation multi-2EC^LP of multi-2EC , thus become vital cost cost to obtain solutions guaranteed to be close to the optimal in a fast manner. In this thesis, we focus on the integrality gap αmulti-2EC of multi-2EC^LP , which is a measure of the quality of multi-2EC^LP as a lower bound. Although we currently only know cost that 6/5 ≤ αmulti-2EC_cost ≤ 3 , the integrality gap for multi-2EC_cost has been conjectured to be 6/5. We explore the idea of using the structure of solutions for αmulti-2EC_cost and the concept of convex combination to obtain improved bounds for αmulti-2EC_cost. We focus our efforts on a family J of half-integer solutions that appear to give the largest integrality gap for multi-2EC_cost. We successfully show that the conjecture αmulti-2EC_cost = 6/5 is true for any cost functions optimized by some x∗ ∈ J. We also study the related problem 2EC_size, which consists of finding the minimum size 2-edge connected spanning subgraph of a 2-edge connected graph. The problem is NP-hard even at its simplest, when restricted to cubic 3-edge connected graphs. We study that case in the hope of finding a more general method, and we show that every 3-edge connected cubic graph G = (V ′, E′), with n = |V ′| allows a 2EC_size solution for G of size at most 7n/6 This improves upon Boyd, Iwata and Takazawa’s guarantee of 6n/5 and extend Takazawa’s 7n/6 guarantee for bipartite cubic 3-edge connected graphs to all cubic 3-edge connected graphs.

The zero coupon yield curve is one of the most fundamental tools in finance and is essential in the pricing of various fixed-income securities. Zero coupon rates are not observable in the market for a range of maturities. Therefore, an estimation methodology is required to derive the zero coupon yield curves from observable data. If we deal with approximations of empirical data to create yield curves it is necessary to choose suitable mathematical functions. We discuss the following methods: the methods based on cubic spline functions, methods employing linear combination of the Fourier or exponential basis functions and the parametric model of Nelson and Siegel. The current mathematical apparatus employed for this kind of approximation is outlined. In order to find parameters of the models we employ the least squares minimization of computed and observed prices. The theoretical background is applied to an estimation of the zero-coupon yield curves derived from the Czech coupon bond market. Application of proper smoothing functions and weights of bonds is crucial if we want to select a method which performs best according to given criteria. The best performance is obtained for Bspline models with smoothing.