Viabilidad de la síntesis mecanoquímica para obtener La1-xSrxGaO3-δ con estructura perovskita

En este trabajo de fin de grado se ha llevado a cabo el estudio de la viabilidad de la síntesis mecanoquímica para obtener La1-xSrxGaO3-δ con estructura perovskita. Se han obtenido varias muestras del sistema La1-xSrxGaO3-δ (x=0, 0.1, 0.2, 0.3, 0.4 y 0.5) por molienda mecánica usando un molino planetario y las muestras fueron caracterizadas por difracción de rayos X (DRX) y microscopía electrónica de barrido (SEM). Las muestras en polvo obtenidas por molienda presentaban estructura perovskita y simetría pseudo-cúbica Pm-3m, formando una solución sólida La1-xSrxGaO3-δ hasta x=0.3. El resto de las muestras (x>0.3) estaban formadas por dos fases, además de la fase perovskita aparecía una fase secundaria de composición LaSrGa3O7. Después del tratamiento térmico a 800 ºC, la solución sólida del sistema La1-xSrxGaO3-δ solamente se mantenía hasta x=0.1, con estructura perovskita y simetría ortorrómbica Pbnm. Para x>0.1 aparece La1-xSrxGaO3-δ junto con LaSrGa3O7 y para x=0.5 aparece además LaSrGaO4. Al aumentar la temperatura del tratamiento térmico a 1100 ºC solamente la muestra con x=0 (LaGaO3) se mantenía monofásica. A medida que aumentaba el valor de x y la temperatura del tratamiento térmico aumentaba el porcentaje de las fases secundarias. El tratamiento térmico favoreció el crecimiento de los dominios cristalinos.Universidad de Sevilla. Grado en Ingeniería de Materiale

Algebraicity Criteria and Their Applications

We use generalizations of the Borel–Dwork criterion to prove variants of the Grothedieck–Katz p-curvature conjecture and the conjecture of Ogus for some classes of abelian varieties over number fields. The Grothendieck–Katz p-curvature conjecture predicts that an arithmetic differential equation whose reduction modulo p has vanishing p-curvatures for all but finitely many primes p, has finite monodromy. It is known that it suffices to prove the conjecture for differential equations on P^1 − {0, 1, ∞}. We prove a variant of this conjecture for P^1 − {0, 1, ∞}, which asserts that if the equation satisfies a certain convergence condition for all p, then its monodromy is trivial. For those p for which the p-curvature makes sense, its vanishing implies our condition. We deduce from this a description of the differential Galois group of the equation in terms of p-curvatures and certain local monodromy groups. We also prove similar variants of the p-curvature conjecture for a certain elliptic curve with j-invariant 1728 minus its identity and for P^1 − {±1, ±i, ∞}. Ogus defined a class of cycles in the de Rham cohomology of smooth proper varieties over number fields. This notion is a crystalline analogue of l-adic Tate cycles. In the case of abelian varieties, this class includes all the Hodge cycles by the work of Deligne, Ogus, and Blasius. Ogus predicted that such cycles coincide with Hodge cycles for abelian varieties. We confirm Ogus’ conjecture for some classes of abelian varieties, under the assumption that these cycles lie in the Betti cohomology with real coefficients. These classes include abelian varieties of prime dimension that have nontrivial endomorphism ring. The proof uses a crystalline analogue of Faltings’ isogeny theorem due to Bost and the known cases of the Mumford–Tate conjecture. We also discuss some strengthenings of the theorem of Bost.Mathematic

Development by Mechanochemistry of La0.8Sr0.2Ga0.8Mg0.2O2.8 Electrolyte for SOFCs

In this work, a mechanochemical process using high-energy milling conditions was employed to synthesize La0.8Sr0.2Ga0.8Mg0.2O3-δ (LSGM) powders from the corresponding stoichiometric amounts of La2O3, SrO, Ga2O3, and MgO in a short time. After 60 min of milling, the desired final product was obtained without the need for any subsequent annealing treatment. A half solid oxide fuel cell (SOFC) was then developed using LSGM as an electrolyte and La0.8Sr0.2MnO3 (LSM) as an electrode, both obtained by mechanochemistry. The characterization by X-ray diffraction of as-prepared powders showed that LSGM and LSM present a perovskite structure and pseudo-cubic symmetry. The thermal and chemical stability between the electrolyte (LSGM) and the electrode (LSM) were analyzed by dynamic X-ray diffraction as a function of temperature. The electrolyte (LSGM) is thermally stable up to 800 and from 900 °C, where the secondary phases of LaSrGa3O7 and LaSrGaO4 appear. The best sintering temperature for the electrolyte is 1400 °C, since at this temperature, LaSrGaO4 disappears and the percentage of LaSrGa3O7 is minimized. The electrolyte is chemically compatible with the electrode up to 800 °C. The powder sample of the electrolyte (LSGM) at 1400 °C observed by HRTEM indicates that the cubic symmetry Pm-3m is preserved. The SOFC was constructed using the brush-painting technique; the electrode-electrolyte interface characterized by SEM presented good adhesion at 800 °C. The electrical properties of the electrolyte and the half-cell were analyzed by complex impedance spectroscopy. It was found that LSGM is a good candidate to be used as an electrolyte in SOFC, with an Ea value of 0.9 eV, and the LSM sample is a good candidate to be used as cathode

Newton Polygons of Cyclic Covers of the Projective Line Branched at Three Points

We review the Shimura–Taniyama method for computing the Newton polygon of an abelian variety with complex multiplication. We apply this method to cyclic covers of the projective line branched at three points. As an application, we produce multiple new examples of Newton polygons that occur for Jacobians of smooth curves in characteristic p. Under certain congruence conditions on p, these include: the supersingular Newton polygon for each genus g with 4 ≤ g ≤ 11; nine non-supersingular Newton polygons with p-rank 0 with 4 ≤ g ≤ 11; and, for all g ≥ 5, the Newton polygon with p-rank g − 5 having slopes 1∕5 and 4∕5

Newton Polygons of Cyclic Covers of the Projective Line Branched at Three Points

We review the Shimura–Taniyama method for computing the Newton polygon of an abelian variety with complex multiplication. We apply this method to cyclic covers of the projective line branched at three points. As an application, we produce multiple new examples of Newton polygons that occur for Jacobians of smooth curves in characteristic p. Under certain congruence conditions on p, these include: the supersingular Newton polygon for each genus g with 4 ≤ g ≤ 11; nine non-supersingular Newton polygons with p-rank 0 with 4 ≤ g ≤ 11; and, for all g ≥ 5, the Newton polygon with p-rank g − 5 having slopes 1∕5 and 4∕5