Structural Dynamics, Phonon Spectra and Thermal Transport in the Silicon Clathrates

The potential of thermoelectric power to reduce energy waste and mitigate climate change has led to renewed interest in "phonon-glass electron-crystal" materials, of which the inorganic clathrates are an archetypal example. In this work we present a detailed first-principles modelling study of the structural dynamics and thermal transport in bulk diamond Si and five framework structures, including the reported Si Clathrate I and II structures and the recently-synthesised oC24 phase, with a view to understanding the relationship between the structure, lattice dynamics, energetic stability and thermal transport. We predict the IR and Raman spectra, including ab initio linewidths, and identify spectral signatures that could be used to confirm the presence of the different phases in material samples. Comparison of the energetics, including the contribution of the phonons to the finite-temperature Helmholtz free energy, shows that the framework structures are metastable, with the energy differences to bulk Si dominated by differences in the lattice energy. Thermal-conductivity calculations within the single-mode relaxation-time approximation show that the framework structures have significantly lower κlatt than bulk Si, which we attribute quantitatively to differences in the phonon group velocities and lifetimes. The lifetimes vary considerably between systems, which can be largely accounted for by differences in the three-phonon interaction strengths. Notably, we predict a very low κlatt for the Clathrate-II structure, in line with previous experiments but contrary to other recent modelling studies, which motivates further exploration of this system.