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M. Falmbigl, G. Rogl, P. Rogl, M. Kriegisch, H. Müller, E. Bauer, M. Reinecker, W. Schranz:
"Thermal expansion of thermoelectric type-I-clathrates";
Journal of Applied Physics, 108 (2010), 043529; 1 - 9.

Thermal expansion was determined for two series of ternary compounds, Ba8MxGe46−x and Ba8MxSi46−x, with M = Cu, Zn, Pd, Ag, Cd, Pt, and Au and for several quaternary compounds for which we investigated the influence of substitution by Zn/Ni in Ba8ZnxGe46−x as well as the dependence of thermal expansion on the Si/Ge ratio in Ba8Cu5SixGe41−x. In the temperature range from 4.2 to 300 K the thermal expansion of all ternary compounds was measured with a capacitance dilatometer, whereas from 300 to 700 K for several selected samples a dynamic mechanical analyzer was employed. The low temperature data compare well with the lattice parameters of single crystals, gained from measurements at three different temperatures (100, 200, and 300 K). For a quantitative description of thermal expansion the semiclassical model of Mukherjee et al. [Phys. Rev. Lett. 76, 1876 (1996)] was used, which also provided reliable accurate values of the Debye and Einstein temperatures. Results in this respect show good agreement with the corresponding data derived from temperature dependent x-ray diffraction and specific heat measurements. Furthermore the present paper is a comprehensive collection and discussion of all thermal expansion data of intermetallic type-I-clathrate materials so far available in the literature including our results of thermal expansion measurements of the Ge- and Si-based type-I-clathrates listed above.

http://dx.doi.org/10.1063/1.3465637