Chemical trends of the rattling phonon modes in alloyed germanium clathrates

Alloys based on Ge clathrates are promising thermoelectric materials because of their expected “rattling” properties. We have incorporated the elements of columns I and II into the cages of ${\mathrm{(Ge, Ga)}}_{\mathrm{46}}$ type-I clathrates as cation guests and have theoretically examined their “rattling” behavior using density functional theory. The potential energy curves of guest atoms in the cages are evaluated to understand the nature of the weak guest–framework interaction. Some atoms are unstable at the center of the cages, while others appear to be bonded by weak restoring forces. We calculate the phonon modes and the Raman spectra and find that heavy alkali-earth elements, such as Sr and Ba, induce low-frequency “rattling” phonon modes as predicted by Slack’s model, while heavy alkali metal atoms (K, Rb, and Cs) are less “rattler-like” since they interact less with the acoustic modes of the Ge-based clathrate framework.