Interpenetrating polar and nonpolar sublattices in intermetallics: the NaCd(2) structure

In the 1960s, Samson solved the structures of some of the most complicated intermetallic phases known, including those of NaCd(2), Mg(2)Al(3), and Cu(3)Cd(4) (each with over 1000 atoms per unit cell). Following remarkable earlier constructions by Samson and by Andersson, we use quantum-mechanical calculations as a guide to describing and understanding these structures. Our electronic Aufbau begins with the relatively simple Mg(17)Al(12) structure and works up to Samson's NaCd(2) structure. In both structures, a division of the sites into electron-rich and electron-poor (with respect to an average electron count) reveals MgCu(2)-type fragments. Between the interiors and exteriors of these fragments, a change in bonding character takes place-the interiors are more polar, the interfaces relatively nonpolar. This electronic situation is traced to the geometry of the interface sites; they lie simultaneously on electron-rich and electron-poor networks. The resulting polar and nonpolar sites in NaCd(2) are separated by a minimal surface, the D surface. The driving force for assuming this structure is electronic: NaCd(2) features an interpenetration of polar and nonpolar bonding regions. This sort of thinking can be applied to other structures.