First-principle calculations have been performed to study Gd impurities doping effect on the physical propertiesof the Heusler half-metallic ferromagnet Co$_2$CrSi using the density functional theory in the local spin density approximationwith an additional Hubbard correlation term for the rare-earth 4f states. The results show that the gadolinium moment isaligned antiparallel to that of transition metal atoms for both Co$_{16}$Cr$_7$GdSi$_8$ and Co$_{15}GdCr$_8$Si$_8$. The analysis of the doped material band structures shows that the half-metallic properties are completely conserved if Gd substitutes Cr atoms, while the minority-spin gap is filled and half-metallicity is lost when Gd substitutes Co atoms.

In this work, the first-principles computational study on the structural, elastic, electronic and optical propertiesof Y$_x$Ga$_{1−x}$As as a function of yttrium concentration ($x$) is presented. The computations are performed using the fullpotential linearized augmented plane wave plus local orbital method designed within density functional theory. Firstly,we performed our calculations on the most stable phases, NaCl and zinc blende, then their transition pressure for eachconcentration is determined and analysed. Our computed results for the zero yttrium concentration are found consistentwith the available experimental measurements as well as with theoretical predictions. Moreover, the dependencies of theseparameters upon yttrium concentration ($x$) were found to be non-linear.We also report computed results on electronic-bandstructure, electronic energy band gap results and density of states. A systematic study on optical properties to analyse itsoptoelectronic character and elastic properties is presented.