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Ba (barium) and Ti (titanium) co-doped bismuth ferrite (Bi1−xBaxFe1−xTixO3 or BBFT) ceramics with x = 0.050, 0.075, 0.100, and 0.150 are synthesized by tartaric acid modified sol–gel technique. The Rietveld refinement of X-ray diffraction patterns confirms that no structural phase transition exists from rhombohedral to cubic phase by the co-doping of Ba and Ti up to 15%. The average crystallite size reduces from 26.62 nm to 14.30 nm and the lattice strain increases from 0.00379 to 0.00650 with the increase in co-doping concentration. The increase in dielectric constant whereas decrease in loss tangent was observed with an increase in co-doping concentration. The ac conductivity analysis employing Jonscher's universal power law suggests the existence of small polaron hopping (SPH) mechanism and overlapping large polaron tunneling (OLPT) for low and high co-doping concentration respectively. The Arrhenius plots of all samples show that for a particular value of frequency ~104 Hz, ac conductivity of all the samples increases with the increase in temperature. The activation energy is found to lies between 0.14 eV and 0.61 eV. The Nyquist plot represents the effect of grain and grain boundaries in terms of equivalent electrical circuits, which reveals a temperature-dependent relaxation process. The frequency-dependent real and imaginary part of the impedance spectra of sample shows that after a critical frequency ~ 104 Hz, all the curves merges because of increased hopping rate of charge carries, which indicates the existence of negative temperature coefficient of resistance (NTCR). These kinds of variation suggest the improved dielectric properties of BBFT ceramics. Highlights: No crystallographic phase transition was observed up to 15% of co-doping of Ba and Ti in BiFeO3. With increase in co-doping concentration, average crystallite sizes decrease whereas lattice strain increases. SPH and OLPT mechanism are appropriate for low and high co-doping concentrations respectively. Ba and Ti co-doped bismuth ferrite shows the enhanced dielectric properties. [ABSTRACT FROM AUTHOR]

A series of La and Ti co-doped bismuth ferrite ceramics have been synthesized using the modified sol–gel approach and their crystal structures were verified using X-ray diffraction. Complex impedance analysis has been used to examine the conduction mechanisms and microscopic dielectric relaxations in all of these materials. To examine the behaviour of the dielectric constant's dispersion, the modified Debye's function has been utilized. The dielectric characteristics of each sample have been described using the brick-layer model. In order to understand the conduction mechanism, relaxation period and activation energies, Arrhenius equation and Jonscher's power law were used. The dc conductivity (σDc) decreases significantly by increasing the co-doping percentage of La and Ti which indicates that the dielectric properties of the BFO is improved by the co-doping. The Jonscher's power law fitting parameters indicate that the correlated barrier hopping (CBH) conduction model is followed in all the co-doped samples. Moreover, Electric modulus spectroscopy and the observed values of activation energies suggests the localized and long-range relaxation processes, which are basically non-Debye type relaxation processes. The minimum value of dielectric loss factor was obtained for 10% of La and Ti co-doping. The observed trend in values of activation energies also suggests that the best dielectric properties are obtained for the 10% of La and Ti co-doping in BFO and it retain high dielectric constant up to higher temperature. [ABSTRACT FROM AUTHOR]

Bi0.85La0.15FeO3, a Lanthanum (La) modified form of bismuth ferrite (BFO) crystallizes to crystal structure which is free from any impurity, which improves the multiferroic properties of BFO. To achieve the enhanced multiferroic characteristics, the composition of Bi0.85La0.15FeO3 has been optimized with the Mn substitution which increases magnetization more effectively than those of magnetic cations. Therefore, Bi0.85La0.15Fe1−xMnxO3 polycrystalline samples were synthesized using a tartaric acid modified sol–gel technique for x = 0.000, 0.025, 0.050, and 0.100. The effects of substitution of Mn (non-magnetic in nature) at the Fe site on crystal structure, magnetic properties, and optical properties were then investigated. The formation of crystalline phases was checked by using X-ray diffraction. The structural transition from rhombohedral (R3c, space group) to orthorhombic (Pbnm, space group) is strongly supported by the Rietveld refinement of the XRD pattern as well as analysis of Raman spectra. As Mn substitution increases, the intensity of Raman peak at about 650 cm−1 increases as well, indicating an increase in the contribution of orthorhombic phase. Magnetic properties of Bi0.85La0.15Fe1−xMnxO3 polycrystalline samples were assessed at room temperature. In Bi0.85La0.15Fe1−xMnxO3, the Mn substitution at the Fe site produced the highest magnetic moment for x = 0.025. Magnetic hysteresis loops show a substantial change in the magnetization with the increase in Mn substitution. Using the Kubelka–Munk (K–M) function and Tauc plot, the band gap energies of all the samples were calculated from UV–Vis diffuse reflectance spectra and it was observed that the band gap energy decreases with the increase in Mn substitution in Bi0.85La0.15Fe1−xMnxO3. These findings provide better understanding for tuning of the multiferroic properties of Mn substituted Bi0.85La0.15FeO3 ceramics. [ABSTRACT FROM AUTHOR]

In this article, we undertake the problem of finding the first four trees on a fixed number of vertices with the maximum smallest positive eigenvalue. Let T n , d denote the class of trees on n vertices with diameter d. First, we obtain the bounds on the smallest positive eigenvalue of trees in T n , d for d = 2 , 3 , 4 and then upper bounds on the smallest positive eigenvalue of trees are obtained in general class of all trees on n vertices. Finally, the first four trees on n vertices with the maximum, second maximum, third maximum and fourth maximum smallest positive eigenvalue are characterized. [ABSTRACT FROM AUTHOR]

Bismuth ferrite (BiFeO3 or BFO), is an extremely promising multiferroic material having broad range of applications. In the present study, we investigated the optimization of annealing temperature for the preparation of pure phase bismuth ferrite using quantitative Rietveld analysis of XRD patterns. The rhombohedral structure was confirmed by X-ray diffraction with R3c space group as a primary phase (pure BFO) along with a cubic secondary phase (Bi25FeO40) having space group I23. The quantitative analysis of refine data shows the decrease in the values of fitting parameters in case of double refinement and hence convergence towards the best fitting. Also, with the increase in annealing temperature, very nominal decrease in phase percentage of secondary phase was observed. At annealing temperature of 780 °C, the intensity of (110) planes suddenly becomes more in comparison to (104) planes. The average crystallite size of samples was calculated using Scherrer formula, W–H plot method, and Rietveld method, and lattice strain was derived from the W–H plot method. Overall, the crystallite size increases with the increase in annealing temperature. It has been also observed that the strain, lattice parameters, unit cell volume, and effective bond lengths decrease with the increase in annealing temperature, but no significant change was observed in bond angles with the variation in annealing temperature. [ABSTRACT FROM AUTHOR]

The effect on the smallest positive eigenvalue of a bipartite graph is studied when the graph is perturbed by attaching a pendant vertex at one of its vertices. Let T ^ (v) be the graph obtained by attaching a pendant at vertex v of T. We characterize the vertices v such that the smallest positive eigenvalue of T ^ (v) is equal or greater than that of T. As an application, we obtain the pairs of nonisomorphic noncospectral trees having the same smallest positive eigenvalue. [ABSTRACT FROM AUTHOR]

In this article, we consider the class of tress on a fixed number of vertices. We consider the problem of finding trees with first four minimum smallest positive eigenvalues. First we obtain the upper and lower bounds on number of alternating paths in a tree. It is shown that the smallest positive eigenvalue of a tree is related to the number of alternating paths in it. With the help of combinatorial arguments, the trees with the maximum, second maximum and third maximum number of alternating paths are derived. Subsequently, the unique trees with the second minimum, third minimum and fourth minimum smallest positive eigenvalue are characterized. [ABSTRACT FROM AUTHOR]