A clathrate compound has a host structure with cavities containing guest atoms or molecules. The host and guest motions can have very different stiffnesses and characteristic frequencies. Cage-like germanium frameworks with metal guests provide examples with low-energy rattling modes.
A germanium cage compound with barium and sodium guests. Its low-temperature heat capacity supplies an example of a rattling mode in addition to the leading electronic and acoustic contributions.[ref]
Superconductivity in the Filled Cage Compounds Ba6Ge25 and Ba4Na2Ge25 by Friedrich Malte Grosche and others. Figure 3: calorimetric example
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