Ab initiostudy of long-period superstructures in close-packedA3Bcompounds

Abstract

We have performed ab initio calculations of the stability of one-dimensional long-period superstructures in ${\mathrm{Cu}}_{3}$Pd, ${\mathrm{Cu}}_{3}$Al, and ${\mathrm{Ag}}_{3}$Mg by means of an interface Green's function technique based on the linear-muffin-tin-orbitals method within the tight-binding and atomic-sphere approximations. The energies of the superstructures relative to the L${1}_{2}$ structure are found by an expansion based on the calculated energy of a single (001) antiphase boundary and the calculated interaction energy between two and three antiphase boundaries of varying distance. The expansion agrees with standard band-structure calculations of the structural energy differences for the two short-period superstructures ${\mathit{DO}}_{22}$ and ${\mathit{DO}}_{23}$. We find that at zero temperature the ground states of ${\mathrm{Cu}}_{3}$Pd, ${\mathrm{Cu}}_{3}$Al, and ${\mathrm{Ag}}_{3}$Mg are one-dimensional superstructures with antiphase boundary separations of 2--5 unit cells of the underlying L${1}_{2}$ structure.