Ordered BaAl4‑Type Variants in the BaAuxSn4–x System: A Unified View on Their Phase Stabilities versus Valence Electron Counts

Three ordered structures of the tetragonal BaAl4 type were identified in the Ba–Au–Sn system, from which a unified view of the interplay between the valence electron counts (VECs) and phase stabilities of these three types of derivatives can be developed. The BaNiSn3 (I4mm), ThCr2Si2 (I4/mmm), and CaBe2Ge2 (P4/nmm) type BaAuxSn4–x phases occurred respectively at x = 0.78(1)–1, 1.38(1)–1.47(1), and 1.52(1)–2.17(1), consistent with theoretical atomic “coloring” analyses that reveal an optimal VEC of ∼14 for the ThCr2Si2 type but larger and smaller values respectively for the BaNiSn3- and CaBe2Ge2-type structures.