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In the present paper we solve the time dependent Ginzburg–Landau (TDGL) equations by using the link variables technique for two shapes of circular geometry, a circular sector and a disc. The implemented algorithm is applied to a circular geometry surrounded by different kinds of material and immersed in an external magnetic field applied perpendicular to its plane. The properties of these materials are accounted for in the de Gennes boundary conditions with the de Gennes extrapolation length (the so called b parameter). We evaluate the magnetization, the superconducting electron density, the superconducting–normal magnetic field transition, and the applied magnetic field/b-parameter phase diagram. For the circular sector, our results point out that, under an appropriate choice of the b parameter, the third critical field Hc3 can be greatly increased. For the disc, we determine the b-limit for the occurrence of the Meissner, single and multi-vortex states in a type-II superconductor. In addition, we show that under an appropriate construction of the boundary, a type-II superconducting disc may behave like a type-I.

Abstract:In this work, a set of nanoparticles of Nb 2 O 5 nanoparticles were grown by both the Pechini and the sol-gel methods. The amorphous materials were calcined at 650 • C or at 750 • C. X-ray diffraction, scanning electron microscopy, luminescence and Raman spectroscopy were used in order to characterize the materials. From the study, it is possible to state that the method of production of nanoparticles, beyond the temperature of synthesis, has a great influence on whether the phase produced is hexagonal or orthorhombic. Additionally, compared to de Sol-gel method, the Pechini method produced samples with smaller particle sizes. The photoluminescence spectra of niobium pentoxide nanostructure materials show that the emission peaks are positioned between 334 to 809 nm and there is a change of intensity which varies depending on the synthesis route used. High pressure Raman spectra at room temperature were obtained from two samples grown by the sol-gel method. Up to 6 GPa, where it is possible to observe the Raman bands, no modification other than the increase of disorder was observed, and this can be associated with a change of phase.

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Raman spectra of ferroelectric Pb1−xLaxTiO3, in the tetragonal phase of the material and for different La concentrations, were studied for different temperatures and pressures. While temperature was varied from 8 K to transition temperature (Tc) at atmospheric pressure, applied hydrostatic pressure was increased from zero to transition pressure (Pc) at room temperature. Isobaric and isothermal mode-Grüneisen parameters were calculated from the measured Raman spectra, and previously reported coefficients of thermal expansion [Chen et al., J. Am. Ceram. Soc. 88, 1356 (2005)] and bulk moduli. Also the coefficient of intrinsic anharmonicity was calculated. Although the absolute value of Grüneisen parameters strongly depends on the Raman mode under study, all of them grow as La concentration increases.

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