Compression of sodium-filled and empty open-frameworkSi24under quasihydrostatic and nonhydrostatic conditions

Abstract

Isothermal equations of state were determined for the open-framework silicon allotrope ${\mathrm{Si}}_{24}$ and its sodium-filled precursor $({\mathrm{Na}}_{4}{\mathrm{Si}}_{24})$ using different pressure media including hydrogen and argon, and with no pressure medium. ${\mathrm{Si}}_{24}$ does not transform into diamond-cubic silicon under compression, and the low-density phase possesses a bulk modulus of 91(2) GPa. The sodium-filled precursor exhibits a comparable volumetric compressibility with different axial trends that are explained by the crystallographic structure. Above 11 GPa, ${\mathrm{Si}}_{24}$ transforms to the \ensuremath{\beta}-tin structure, followed by other high-pressure silicon allotropes similar to diamond-cubic silicon, driven by a large increase in density. Small molecules such as ${\mathrm{H}}_{2}$ do not enter the channels of ${\mathrm{Si}}_{24}$ during compression at room temperature, however, hydrostaticity strongly influences the transformation pressure and range of coexistence with other phases including \ensuremath{\beta}-Sn, $Imma$, and simple-hexagonal Si.