Theoretical Evaluation of the Thermal Conductivity in Framework (Clathrate) Semiconductors
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Theoretical Evaluation of the Thermal Conductivity in Framework (Clathrate) Semiconductors Jianjun Dong1, Otto F. Sankey1, Charles W. Myles2, Ganesh K. Ramachandran3, Paul F. McMillan3, and Jan Gryko4 1 Department of Physics and Astronomy, Arizona State University, Tempe, AZ 85287, 2 Department of Physics, Texas Tech University, Lubbock, TX 79409, 3 Department of Chemistry, Arizona State University, Tempe, AZ 85287, 4 Department of Physical and Earth Sciences, Jacksonville State University, Jacksonville, AL 36265. ABSTRACT We have calculated the room temperature thermal conductivity in semiconductor germanium clathrates using statistical linear-response theory and an equilibrium molecular dynamics (MD) approach. A key step in our study is to compute a realistic heat-current J (t) and a corresponding auto-correlation function < J (t) J (0) >. To ensure convergence of our results and to minimize statistical fluctuations in our calculations, we have constructed large super-cell models (2944 atoms) and have performed several independent long time simulations (>1,500 ps in each simulation). Our results show an unexpected “oscillator” character in the heat-current correlation function of the guest-free Ge clathrate frameworks. This is absent in the denser diamond phase and other with simple structural frameworks. We seek to interpret these results using lattice dynamics information. A study of the effects of the so-called “rattling” guest atoms in the openframework clathrate materials is in progress.
INTRODUCTION Recent experiments reveal that certain crystalline forms of Ge-based clathrates (e.g. Sr8Ga16Ge30) have an abnormally low, glass-like thermal conductivity (κ) [1]. This makes these materials very promising for the design of high ZT thermoelectric materials. However, the mechanism of this reduction of κ is still not fully understood. Slack and coworkers have suggested [2] that the small guest atoms (e.g. Sr) located inside the open framework (e.g. clathrate) behave like loosely bound “rattlers”, and that their lowfrequency rattling phonon modes scatter the heat-carrying acoustic phonons of the framework. No quantitative theoretical calculation has yet been reported to support this conjecture. We have recently performed a detailed first-principles theoretical study of the lattice dynamics of alloyed Ge clathrates, which showed that interaction between the framework acoustic phonon branches and the Sr-related rattling modes is possible because of avoided crossing [3]. These results provide the lattice dynamics basis to interpret the Slack-proposed rattler scattering mechanism. It is, however, possible that the large reduction in κ is caused by multiple mechanisms. The novel open-framework of the clathrates may also be relevant. In a broader context, the conventional transport formalism in condensed matter physics has been developed based on our understanding of simple crystals, such as diamond. This
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