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-x)Ge(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), Si(128)Ge(8) 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 Si(104)Ge(32) 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 Si(136). 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-x)Ge(x) is elevated from 32 (or 40) to 96 (or 104).