"Design" in solid-state chemistry based on phase homologies. The concept of structural evolution and the new megaseries A(m)[M(1+l)Se(2+l)]2m[M(2l+n)Se(2+3l+n)]

An attractive way to advance the design and prediction of new compositions and structures of solid-state compounds is to identify large homologies that are amenable to chemical control. Homologies allow the systematization of phases under a common conceptual umbrella and have the potential to capture the vast majority of existing and possible compounds. We have demonstrated this in the broad system A/M'/M''/Se (A = K, Rb, Cs, Sr, Ba; M' = Pb, Sn; M'' = Sb, Bi) by identifying the homologous "superseries" A(m)[M(1+l)Se(2+l)]2m[M(2l+n)Se(2+3l+n)]. This series generates a large variety of compounds with predictable composition and structure. All the compounds contain fundamental building units representing different fragments of the NaCl-type lattice. The three independent integers l, m, and n determine width, height, and shape of the building units and therefore cause structural evolution of the homologous series in three different dimensions. On the basis of this general formula one can design, in a modular fashion, new compounds that fit the structural evolution of the superseries, predicting simultaneously their structure and composition. Several new phases have been discovered with this approach. Here we give an overview of the character and predictive properties of the superseries and propose the classification of phases into homologies (when possible) which could serve as devices to predict new members.