First-Principles Analysis of Vibrational Properties of Type II SiGe Alloy Clathrates

We have mostly performed vibrational studies of Type-II silicon-germanium clathrate alloys, namely, Si_136-xGe_x (0 < x ≤ 128), using periodic density functional theory (DFT). Our computed lattice constant for various stoichiometric amount, namely, x, of Ge agrees to some extent with the observed X-ray diffraction (XRD) data, along with monotonically increasing dependence on x. According to our bandgap energy calculation via Vienna ab initio simulation package (VASP), Si₁₂₈Ge₈ has a "nearly-direct" bandgap of approximately 1.27 eV, which agrees well with the previously calculated result (~1.23 eV), which was obtained using the Cambridge sequential simulation total energy package (CASTEP). Most of our first-principles calculations focus on exploring the low-energy transverse acoustic (TA) phonons that contribute dominantly to the induction of negative thermal expansion (NTE) behavior. Moreover, our work has predicted that the Si₁₀₄Ge₃₂ framework exhibits NTE in the temperature range of 3-80 K, compared to the temperature regime (10-140 K) of NTE observed in such pure Si₁₃₆. It is posited that the increased number of Ge-Ge bonds may weaken the NTE effect substantially, as the composition, which is denoted as x, in Si_136-xGe_x is elevated from 32 (or 40) to 96 (or 104).