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Thomas Hammerschmidt, Alvin Noe Ladines, Jörg Koßmann, Ralf Drautz

• The moments of the electronic density-of-states provide a robust and transparent means for the characterization of crystal structures. Using \(\it d\)-valent canonical tight-binding, we compute the moments of the crystal structures of topologically close-packed (TCP) phases as obtained from density-functional theory (DFT) calculations. We apply the moments to establish a measure for the difference between two crystal structures and to characterize volume changes and internal relaxations. The second moment provides access to volume variations of the unit cell and of the atomic coordination polyhedra. Higher moments reveal changes in the longer-ranged coordination shells due to internal relaxations. Normalization of the higher moments leads to constant (A15,C15) or very similar (\(\chi\), C14, C36, \(\mu\), and \(\sigma\) higher moments of the DFT-relaxed TCP phases across the 4\(\it d\) and 5\(\it d\) transition-metal series. The identification and analysis of internal relaxations is demonstrated for atomic-size differences in the V-Ta system and for different magnetic orderings in the \(C14-Fe_{2}Nb\) Laves phase.