Electronic structure, phase stability, and cohesive properties of ${\mathrm{Ti}}_{2}X\mathrm{Al}$ $(X=\mathrm{N}\mathrm{b},\mathrm{}\mathrm{V},\mathrm{}\mathrm{Zr})$

The self-consistent tight-binding linear muffin-tin orbital method was employed to calculate the electronic structure and the total energy of ${\mathrm{Ti}}_{2}X\mathrm{Al}$ $(X=\mathrm{N}\mathrm{b},\mathrm{}\mathrm{V},\mathrm{}\mathrm{Zr})$ in $B2,$ ${D0\mathrm{}}_{19},$ and O (orthorhombic) phases and the results were used to study the phase stability and cohesive properties of these intermetallic compounds. Our theoretical calculation shows that the $B2\mathrm{}$ phase is the most stable phase of ${\mathrm{Ti}}_2\mathrm{NbAl}$ as observed by experimentalists. However, the three phases are close in energy indicating the possibility of the presence of all these phases in equilibrium over a range of temperatures, which is in accordance with experimental observations. Our calculations predict that ${\mathrm{Ti}}_2\mathrm{VAl}$ is more stable in the $B2\mathrm{}$ phase whereas ${\mathrm{Ti}}_2\mathrm{ZrAl}$ is more stable in the ${D0\mathrm{}}_{19}$ phase. We also report the calculated equilibrium lattice parameters, cohesive energies, heats of formation, and bulk modulii of these systems, and a possible comparison of the calculated quantities with the available experimental data is made. From our studies we are made to conclude that the concept of pseudogaps which has been very much emphasized for binary intermetallics does not carry so much significance with respect to ternary systems.