Disentangling Structural Patterns in Quaternary Germanides with Materials Informatics and Exploratory Synthesis: <i>RE</i> ₄ IrInGe ₄ ( <i>RE</i> = Y, Ce–Nd, Sm, Gd, Ho–Er) Series

The structural diversity and applications of intermetallic germanides make them interesting candidates for exploration. Past the ages of binary and ternary compound explorations, quaternary structures have gained more attention. Counterintuitively, more components do not directly translate into more compounds in a given system. Often, quaternary phases are thermodynamic competitors, e.g., Tb₄RhInGe₄-type vs Ho₄Ni₂InGe₄-type, which prior to this work, were never observed in the same system. In this work, we expand the quaternary germanide series <i>RE</i>₄IrInGe₄ (<i>RE</i> = Y, Ce-Nd, Sm, Gd, Ho-Er) synthesized via arc-melting followed by annealing. To explore the bonding trends, electronic structure calculations were performed for Ce₄IrInGe₄ and Ce₄Ir₂InGe₄, which crystallize in Tb₄RhInGe₄- and Ho₄Ni₂InGe₄-types, respectively. Along with the obvious Ir-Ge bonding contribution, Ce-Ge bonding turned out to be one of the most important interactions that govern the structure formation and explain the <i>RE</i> series limits. To separate the Tb₄RhInGe₄-type from the closely related Ho₄Ni₂InGe₄-type, a structure map was developed by using the PLS-DA technique. In the PLS-DA loadings, the radii of the elements and valence electron counts made the top contributions to the classification of these two types. Further, to understand the structural evolution, we analyzed the germanides using materials informatics tools and proposed a mechanism using their coordination environments.