Mechanical Properties of Intermetallic Clathrates

The present work provides a comprehensive compilation and discussion covering hardness, experimentally determined elastic properties, thermal expan- sion, and Debye and Einstein temperatures for intermetallic clathrates. Comparing hardness values and elastic properties a major influence of the framework atoms is observed. Hardness and elastic moduli change linearly with the Si/Ge-ratio. Also a linear temperature dependence of the elastic properties is observed. In the case that vacancies are present in the clathrate framework, the hardness of different com- pounds decreases almost linearly with an increasing vacancy-content. As Debye and Einstein temperatures are of significance for the vibrational spectra and per- formance of thermoelectric materials, corresponding values extracted from various measurement techniques such as thermal expansion, sound velocity, specific heat, electrical resistivity or X-ray absorption and diffraction measurements are evalu- ated. The Debye temperatures correlate with the melting temperatures of the intermetallic clathrates, and the Einstein temperatures for similar guest atoms show a linear dependence on the cage size. Wherever available, experimental data are compared with those from DFT model simulations. In general the experi- mentally derived values match those theoretically calculated