We investigated double perovskite compounds of the form Sr$_2$XOsO$_6$ (X = Li, Na, Ca) using the fullpotential linearized augmented plane wave (FP-LAPW) method. For the exchange-correlation energy, Wu andCohen generalized gradient approximation (WC-GGA), Perdew, Burke and Ernzerhof GGA (PBE-GGA), Engel and Vosko GGA (EV-GGA), and GGA plus Hubbard U-parameter (GGA $+$ U) were used. The calculated structuralparameters are in good agreement with the existing experimental results. Calculation of different elastic constants and elastic moduli reveals that these compounds are elastically stable and possess ductile nature. The GGA $+$ Uapproach yields quite accurate results of the bandgap as compared with the simple GGA schemes. The density of states plot shows that Sr-4d, Os-5d and O-2p states predominantly contribute to the conduction and valence bands.Further, our results regarding to the magnetic properties of these compounds reveal their ferromagnetic nature. In addition, these compounds seem to possess half-metallic properties, making them useful candidates for applicationsin spintronics devices.

The structural parameters, elastic constants, electronic and optical properties of the bi-alkali antimonides (Na$_2$KSb, Na$_2$RbSb, Na$_2$CsSb, K$_2$RbSb, K$_2$CsSb and Rb$_2$CsSb) were calculated using state-of-the-art density functional theory. Different exchange-correlation potentials were adopted to predict the physical properties of these compounds. The calculated structural parameters are found in good agreement with the available experimental and theoretical results. All the compounds are mechanically stable. The compounds Na$_2$KSb, K$_2$RbSb, K$_2$CsSb and Rb$_2$CsSb have direct bandgaps, in which chemical bonding among the cations and anions is mainly ionic. Furthermore, the optical properties of these compounds are described in detail in terms of the dielectric function, refractive index, reflectivity, optical conductivity and absorption coefficient.

Y ions incorporation effect on structural, ferroelectric and ferromagnetic properties of Bi$_{1-x}$Dy$_x$FeO$_3$ (x = 0.00, 0.05, 0.10, 0.15 and 0.20) has been elaborated by solid-state reaction method. The beam of Y ions (500 keV) at a fluence of 3 ${\times}$ 10$^{12}$ ions cm$^{-2}$ was exposed in studied samples. The X-ray diffraction technique and Rietveld refinement indicate the rhombohedral polycrystalline structure. The FESEMx analysis show dense grains uniformly distributed on sample surface and decrease in grain size by decreasing the Dy concentration. The bonding nature and chemical composition have been studied by X-ray photoelectron spectroscopy. The coexistence of ferromagnetic and ferroelectric orderings has been observed at room temperature. The polarization (10.50 ${\mu}$C cm$^{-2}$) and ferromagnetism is maximum at 15% Dy concentration and decreases with further increase in Dy contents.