First-Principles Study of the Jahn-Teller Distortion in the Ti$_{1-X}$V$_{X}$H$_{2}$ and Zr$_{1-X}$Nb$_{x}$H$_{2}$ Alloys

The transition metal dihydrides TiH$_{2}$ and ZrH$_{2}$ present the fluorite structure (CaF$_{2})$ at high temperature but undergoes a tetragonal distortion with c/a$<$1 at low temperature. Electronic band structure calculations have shown that TiH$_{2}$ and ZrH$_{2}$ in the cubic phase display a very flat band at the Fermi level. Thus the low temperature tetragonal distortion has been associated to a Jahn-Teller effect. In order to understand the role of band filling in controlling the structural instability of the transition metal dihydrides, we have performed a first-principles total energy study of the Ti$_{1-X}$V$_{x}$H$_{2}$ and Zr$_{1-x}$Nb$_{x}$H$_{2}$ alloys. The calculations were performed using FP-LAPW method within the (DFT) and we use the GGA for exchange correlation functional energy. The critical concentration for which the Jahn-Teller effect is suppressed, was determined from the evolution of the tetragonal-cubic energy barrier. We discuss the electronic mechanism of the structural-instability, in terms of the band filling. From the obtained results we conclude that the tetragonal distortion in TiH$_{2}$ and ZrH$_{2}$ is not produced only by a Jahn-Teller Effect. This research was supported by Consejo Nacional de Ciencia y Tecnolog\'{\i}a (Conacyt) under Grant No. 43830-F.