Phase stability in the systems AeAl_2-xMg_x (Ae = Ca, Sr, Ba): Electron concentration and size controlled variations on the laves phase structural theme

The systems AeAl_2-xMg_x (Ae = Ca, Sr, Ba) display electron concentration induced Laves phase structural changes. However, the complete sequence MgCu₂ → MgNi₂ → MgZn ₂ with increasing x (decreasing electron count) is only observed for Ae = Ca. Compounds SrAl_2-xMg_x (0 < x ≤ 2) and BaAl_2-xMg_x (x = 0.85 and 2.0) were synthesized and structurally characterized by X-ray diffraction experiments. For the Sr system the structural sequence CeCu₂ → MgNi₂ → MgZn₂ occurs with increasing Mg content x. Thus, larger Sr does not allow the realization of the MgCu₂ structure at low x. For Ae = Ba a binary compound BaAl₂ does not exist, but more Ba-rich Ba ₇Al₁₃ forms. The reinvestigation of the crystal structure of Ba₇Al₁₃ by selected area and convergent beam electron diffraction in a transmission electron microscope revealed a superstructure, which subsequently could be refined from single X-ray diffraction data. The formula unit of the superstructure is Ba₂₁Al₄₀ (space group P31m, Z = 1, a = 10.568(1) Å, c = 17.205(6) Å). In Ba ₂₁Al₄₀ a size match problem between Ba and Al present in Ba₇Al₁₃ is resolved. The structure of Ba ₇Al₁₃ (Ba₂₁Al₄₀) can be considered as a Ba excess variant of the hexagonal MgNi₂ Laves phase type structure. An incommensurately modulated variant of the MgNi₂ structure is obtained for phases BaAl_2-xMg_x with x = 0.8-1. At even higher Mg concentrations a structural change to the proper MgZn₂ type structure takes place.