Band filling and structural stability of cubic trialuminides: ${\mathrm{YAl}}_3$, ${\mathrm{ZrAl}}_3$, and ${\mathrm{NbAl}}_3$

The electronic structure and the structural stability of the trialuminides ${\mathrm{YAl}}_3$, ${\mathrm{ZrAl}}_3$, and ${\mathrm{NbAl}}_3$ in the cubic L$1_2$ and tetragonal D$0_{22}$ structures were investigated by means of the total-energy all-electron self-consistent linear muffin-tin orbitals (LMTO) method. The variation of the stability across the constituent transition-metal series can be understood simply in terms of the band filling of the bonding states. And surprisingly, the simple rigid-band approximation appears adequate to describe the structural stability of these (p-d covalent) trialuminides.