Band filling and structural stability of cubic trialuminides:YAl3,ZrAl3

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.