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Structural stability and magnetic properties in X 2 Al X ′ (X= Fe , Co, Ni; X ′ = Ti , Cr) Heusler alloys from quantum mechanical calculations Employing the first-principles exact muffin-tin orbital method in combination with the coherent potential approximation, we calculated the total energy and local magnetic moments of paramagnetic Fe-Cr-M (M ¼ Cr, Mn, Fe, Co, Ni) alloys along the tetragonal distortion (Bain) path connecting the body centered cubic (bcc) and the face centered cubic (fcc) structures. The paramagnetic phase is modeled by the disordered local magnetic moment scheme. For all alloys, the local magnetic moments on Fe atoms decrease from the maximum value corresponding to the bcc phase toward the minimum value realized for the fcc phase. Cobalt atoms have non-vanishing local magnetic moments only for tetragonal lattices with c/a < 1.30, whereas the local magnetic moments of Mn show weak crystal structure dependence. We find that Cr stabilizes the bcc lattice and increases the energy barrier as going from the bcc toward the fcc phase. Both Co and Ni favor the fcc lattice and decrease the energy barrier relative to the bcc phase. On the other hand, the tetragonal distortion around the fcc phase is facilitated by Cr and to a somewhat lesser extent also by Ni, but strongly impeded by Co. Manganese has negligible effect on the structural energy difference as well as on the energy barrier along the Bain path. Our findings on the alloying induced softening or hardening of Fe-Cr based alloys against tetragonal distortions are important for understanding the interstitial driven martensitic transformations in alloy steels.