Thermal properties ofSi136: Theoretical and experimental study of the type-II clathrate polymorph of Si

Abstract

The thermal properties of the metastable type-II clathrate phase $({\mathrm{Si}}_{136})$ and the equilibrium ground state diamond phase $(d\text{\ensuremath{-}}\mathrm{Si})$ of silicon have been studied using first-principles methods to calculate the static total energy and the harmonic lattice dynamics. The equilibrium temperature-pressure phase boundary between the two phases occurs in the negative pressure regime. The ${\mathrm{Si}}_{136}$ clathrate polymorph has higher static bonding energy, lower density and larger compressibility than the diamond-structured form of crystalline $d\text{\ensuremath{-}}\mathrm{Si}$. However, the two tetrahedrally-bonded polymorphs have similar lattice dynamic properties. Our theoretical results of phonon frequencies and mode Gr\"uneisen parameters are in good agreement with the Raman data. We further show that the two polymorphs have comparable thermal properties, including heat capacities and coefficients of thermal expansion. Our first-principles calculations of heat capacities are inconsistent with results of a previous calculation for clathrate phases based on empirical methods. Like diamond-structured $d\text{\ensuremath{-}}\mathrm{Si}$, we predict that ${\mathrm{Si}}_{136}$ has a region of negative thermal expansion between $T=10--240\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. This prediction is confirmed by our x-ray diffraction results at low temperature.