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This study investigates the influence of samarium (Sm3+) doping on the structural, microstructural, mechanical, and dielectric properties of BaBi2Nb2O9 (BBN) ceramics. Using the solid-state reaction method, samples of BaBi2-xSmxNb2O9 with varying concentrations of Sm (x = 0.01; 0.02; 0.04; 0.06; 0.08; 0.1) were prepared. Thermal analysis, microstructure characterization via SEM and EDS, X-ray diffraction, mechanical testing, and dielectric measurements were conducted. The results revealed that increasing Sm3+ concentration led to the formation of single-phase materials with a tetragonal structure at room temperature. Mechanical properties, such as Young's modulus and stiffness, improved with Sm doping, indicating stronger atomic bonding. Dielectric properties showed that low concentrations of Sm3+ slightly increased electrical permittivity, while higher concentrations reduced it. The presence of Sm3⁺ also affected the relaxor properties, evidenced by changes in the freezing temperature and activation energy. Overall, the study concludes that samarium doping enhances the structural and functional properties of BBN ceramics, making them promising candidates for high-temperature piezoelectric and dielectric applications. The findings provide valuable insights into tailoring ceramic materials for advanced technological applications. [ABSTRACT FROM AUTHOR]

This investigation focuses on the impact of Sm3+ dopants on BaBi2Nb2O9 (BBN) ceramics. These ceramics were obtained using the traditional solid state reaction approach. Techniques like scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS) were employed to explore the structure and morphology of the ceramics. The results showed that the chemical composition of the ceramic samples matched well with the initial ceramic powder stoichiometry. Increasing the amount of samarium resulted in a slight reduction in the average ceramic grain size. The ceramics exhibited a tetragonal structure categorized under the space group I4/mmm. The electrical properties were analyzed using complex impedance spectroscopy (SI) across various temperatures and frequencies, revealing that both grains and intergranular boundaries are significant in the material's conductivity. [ABSTRACT FROM AUTHOR]

An analytical solution is presented for the interaction of an I-core coil with a metal tube of finite length. Using the Truncated Region Eigenfunction Expansion (TREE) method, the impedance variation of the I-core coil is expressed in a closed form. Notably, the 1D finite element method (1D FEM) is adopted to calculate the complex eigenvalues and eigenfunctions of the steel tube, by which the overflow issue of complex eigenfunctions has been surmounted. And the 1D FEM also simplifies the calculation in the ferrite core region immensely. A performant algorithm is obtained due to the matrix formalization and the high speed of the sparse eigenvalue solver. The tubes made of aluminum alloy and stainless steel are investigated by the proposed method and tested in the experiment. The high reliability and efficiency of the proposed method are proved, and the results are also validated by the comparison with simulation and measurement data. [ABSTRACT FROM AUTHOR]

In eddy current testing, probe-coils with the E-type pot core are commonly used for detecting defects in test objects. In this paper, an analytical mathematical model of such a probe placed above a two-layered conductive material with a surface hole has been presented. The final formulas in the closed form that make it possible to calculate the coil impedance were worked out using the truncated region eigenfunction expansion (TREE) method and implemented in Matlab. Changes in resistance and reactance were determined for both material without a hole and for space containing no conductor. The results were compared with those obtained for the air-cored coil and the I-cored coil. The correctness of the calculations was confirmed through experimental measurements and with the finite element method (FEM) in the COMSOL Multiphysics package

This work presents an axially symmetric mathematical model of an I-cored coil placed over a two-layered conductive material with a cylindrical surface hole. The problem was divided into regions for which the magnetic vector potential of a filamentary coil was established applying the truncated region eigenfunction expansion method. Then the final formula was developed to calculate impedance changes for a cylindrical coil with reference to both the air and to a material with no hole. The influence of a surface flaw in the conductive material on the components of coil impedance was examined. Calculations were made in Matlab for a hole with various radii and the results thereof were verified with the finite element method in COMSOL Multiphysics package. Very good consistency was achieved in all cases.

The paper presents a mathematical model of an ideal filamentary coil with a finite number of turns, derived by means of the method called truncated region eigenfunction expansion (TREE). The proposed solution allows quick computation of the filamentary coil impedance as well as of the impedance changes caused by the presence of a two-layered conductive material. The final formulas were presented in the closed form and implemented in Matlab. The results were verified using the finite element method in the COMSOL Multiphysics package as well as by means of other mathematical models. In all cases they show a very good agreement. The obtained values of coil impedance changes were compared in terms of the time of reaching the final results. In the case of the most significant calculations, which consisted of many iterations, the proposed solution turned out to be by far the fastest one. [ABSTRACT FROM AUTHOR]