First-principles study of L$1_0$ Ti-Al and V-Al alloys

As a first step towards understanding the reduced embrittlement of L$1_0$ Ti-Al alloys which accompanies the introduction of small concentrations of V, we have determined from first principles, using full-potential linearized–augmented-plane-wave calculations, the equilibrium values of the structural parameters and the associated electronic structure for the stoichiometric (L$1_0$) Ti-Al (tetragonal) compound. Our calculated values of c/a and a are in good agreement with experiment. Using the same method of calculation, we have also studied the electronic structure associated with the (hypothetical) L$1_0$ V-Al alloy that would form when V is substituted for Ti. We find that (1) the electronic structures of these V-Al alloys are relatively insensitive to variations of c/a and a; (2) near the Ti-Al equilibrium geometry, the electronic structures of the V-Al and Ti-Al alloys are very similar; and (3) that a rigid-band model involving substitution of V for Ti can be used to gain a qualitative understanding of the reduction in c/a which accompanies the introduction of small concentrations of V. We relate the reduction in c/a to important changes in the bonding that accompany the occupation of bands immediately above the Fermi level of the stoichiometric Ti-Al compound.