High-pressure phases, vibrational properties, and electronic structure ofNe(He)2andAr(He)2: A first-principles study

Abstract

We have carried out a comprehensive first-principles study of the energetic, structural, and electronic properties of solid rare-gas (RG)-helium binary compounds, in particular, $\text{Ne}{(\text{He})}_{2}$ and $\text{Ar}{(\text{He})}_{2}$, under pressure and at temperatures within the range of $0\ensuremath{\le}T\ensuremath{\le}2000\text{ }\text{K}$. Our approach is based on density-functional theory and the generalized gradient approximation for the exchange-correlation energy; we rely on total Helmholtz free-energy calculations performed within the quasiharmonic approximation for most of our analysis. In $\text{Ne}{(\text{He})}_{2}$, we find that at pressures of around 20 GPa the system stabilizes in the ${\text{MgZn}}_{2}$ Laves structure, in accordance to what was suggested in previous experimental investigations. In the same compound, we predict a solid-solid phase transition among structures of the Laves family of the type ${\text{MgZn}}_{2}\ensuremath{\rightarrow}{\text{MgCu}}_{2}$, at a pressure of ${P}_{t}=120(1)\text{ }\text{GPa}$. In $\text{Ar}{(\text{He})}_{2}$, we find that the system stabilizes in the ${\text{MgCu}}_{2}$ Laves phase at low pressures but it transitates toward the ${\text{AlB}}_{2}$-type structure by effect of compression at ${P}_{t}=13.8(4)\text{ }\text{GPa}$. The phonon spectra of the $\text{Ne}{(\text{He})}_{2}$ crystal in the ${\text{MgZn}}_{2}$ and ${\text{MgCu}}_{2}$ Laves structures, and that of $\text{Ar}{(\text{He})}_{2}$ in the ${\text{AlB}}_{2}$-type phase, are reported. We observe that the compressibility of RG-RG and He-He bond distances in $\text{RG}{(\text{He})}_{2}$ crystals is practically identical to that found in respective RG and He pure solids. This behavior emulates that of a system of noninteracting hard spheres in closed-packed configuration and comes to show the relevance of short-range interactions on this type of mixtures. Based on size-ratio arguments and empirical observations, we construct a generalized phase diagram for all $\text{RG}{(\text{He})}_{2}$ crystals up to a pressure of 200 GPa where we map out systematic structural trends. Excellent qualitative agreement between such generalized phase diagram and accurate ab initio calculations is proved. A similar construction is done for $\text{RG}{({\text{H}}_{2})}_{2}$ crystals; we find that the ${\text{MgCu}}_{2}$ Laves structure, which has been ignored in all ${\text{RG-H}}_{2}$ works so far, might turn out to be competitive with respect to the ${\text{MgZn}}_{2}$ and ${\text{AlB}}_{2}$-type structures. Furthermore, we explore the pressure evolution of the energy-band gap in $\text{RG}{(\text{He})}_{2}$ solids and elaborate an argument based on electronic-band theory which explains the observed trends.