A NaCeP2O7 compound was successfully synthesized by a high-temperature reaction with the solid-state method.
The NaCeP2O7 compound was successfully synthesized by a high-temperature reaction with the solid-state method. Analyzing the XRD pattern, of the studied compound, confirms the orthorhombic phase with the Pnma space group. The examination of SEM images reveals that the majority of grains are around 500 to 900 nm with a uniform distribution. As for the EDX analysis, all chemical elements were detected and found in their appropriate ratio. The curves of temperature-dependent imaginary modulus M" versus angular frequency reveal the presence of one peak at each temperature, proving that the dominant contribution is associated to the grains. The frequency dependence of the conductivity of alternating current is explained using Jonscher's law. The close values of the activation energies obtained from the jump frequency and extracted from the dielectric relaxation of the modulus spectra, as well from the continuous conductivity imply that the transport takes place by the Na+ ions hopping mechanism. The charge carrier concentration in the title compound has been evaluated and shown to be independent of temperature. The exponent s increases with the increase in temperature, this behavior proves that the non-overlapping small polaron tunneling (NSPT) is the appropriate conduction mechanism model.
The mechanical discrete or continuum structures are actually of great importance in the application field of contemporary modern industry. However, during their life time these structures are often subjected to considerable external stresses or to high amplitudes of vibrations which can cause them large deformations and internal stresses which can cause them internal cracking or even their total destruction. In order to avoid these types of problems, the concept of static and dynamic analysis of these structures is recommended, and due to the complexity of their shape and size, the finite element method is the most used. The latter is currently recognized as a very powerful technique for the static and dynamic analysis of discrete or continuous structures of complicated form applied in the field of mechanics, aeronautics, civil engineering, maritime or robotics. Consequently, the calculation and dimensioning of these mechanical systems by the finite element method plays an important role at the service of the industry for possible sizing and prediction of their lifetime. Our work consists of static and dynamic analysis of two-dimensional discrete and continuous mechanical systems using the finite element method based on the main elements of bars, beams and plates, under the effect of external excitations with different boundary conditions. The discrete structures considered are two-dimensional in metallic framework interconnected to the nodes by welding, riveting or bolted under various boundary conditions. Their elements are modeled comparatively by bar elements and beam elements, while for continuous structures the elements are rectangular thin plates with different boundary conditions. The excitation forces are based on periodic, random or impulsive forces and a numerical solution by development of a program to describe the behavior of these structures is realized. The mass and stiffness matrices of all the structures are determined respectively by assembling the bars, beam and plate elements based on the kinetic and deformation energy for each element. The displacements, the node reactions and the axial forces in all the elements as well as the transverse stresses and the eigenvalues of the structures under different boundary conditions were also calculated and good results were obtained compared to those obtained using other software already existing. In fact, analysis using the finite element method will allow the proper dimensioning and design of complex industrial mechanical structures according to different boundary conditions, their internal loading and their vibratory level.
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