Figure 5.

(a) Formation energy of the $\delta$-AlNb₃ phase containing Al vacancies (circles) or Nb antisites (crosses) as a function of the Nb content. The black solid line shows the convex hull, while the shaded area denotes region for the chemically stable compounds. (b) The $\delta$-Al_0.19Nb_0.81 structural variant with ordered Nb antisites lying on the convex hull. The blue, green, and red spheres denote Al, Nb, and Nb antisite atoms, respectively. The phonon DOS of the defect-free $\delta$-AlNb₃ (c) compared to that of the $\delta$-Al_0.19Nb_0.81 with ordered Nb antisites (d). The grey shaded area represents the total phonon DOS, while the solid lines show the partial contribution from Al and Nb atoms.