\textbf{Structural, Electronic and Magnetic Properties of Ti}$_{\mathbf{1+x}}$\textbf{FeSb and TiFe}$_{\mathbf{0.75}}$\textbf{M}$_{\mathbf{0.25}}$\textbf{Sb ( M}$=$\textbf{ Ni, Mn) Heusler Alloys}

Density functional theory calculations based on full potential linearized augmented plane-wave (FPLAPW) plus local orbital method in the framework of GGA-PBE, as embodied in the WIEN2k code, is used to investigate the structural, electronic and magnetic properties of intermetallic Ti$_{1+x}$FeS Heusler compounds, where ($x=$\textit{i/4, i}$=$\textit{-3,-2,-1,0,1,2,3,4}) and the TiFe$_{0.75}$M$_{0.25}$Sb (M $=$ Ni, Mn) quaternary semi-Heusler compounds. Moreover, the modified Becke-Johnson exchange potential, as a semi-local method, was employed to predict the band-gap more precisely. We examined the site preference of the parent compound TiFeSb and varying the electron concentration by doping or removing a Ti atom. It is found that they play a crucial role in physical properties of these material systems. The lattice parameters and spin magnetic moment calculated were consistent with the previous experimental and theoretical data available. Moreover, alloys with x\textless 0 are found to exhibit a ferrimagnetic phase, and the alloy with x$=$0.25 exhibit a non-magnetic properties, whereas the rest have shown ferromagnetic phase. The band-structure analysis of Ti$_{1.75}$FeSb, Ti$_{2}$FeSb and TiFe$_{0.75}$Ni$_{0.25}$Sb alloys suggested that they could be a ferromagnetic half-metallic members with band-gaps 0.67, 0.41 and 0.54 eV, respectively.