Abnormal negative thermal expansion of sodium: A first-principles discovery at high pressures

Abstract

Negative thermal expansion coefficients ($\ensuremath{\alpha}$) are found in the fcc and cI16 (a distorted bcc structure) phases of sodium at pressures above 90 GPa from first principles. At room temperature, the most significant negative $\ensuremath{\alpha}$ of about $\ensuremath{-}4.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\phantom{\rule{4pt}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ is predicted in fcc sodium at 120 GPa, which represents the first prediction of a robust negative $\ensuremath{\alpha}$ in a simple metal. Anharmonic lattice dynamics calculations were carried out to rationalize this intriguing behavior. We find that the negative thermal expansion of fcc sodium originates from the transverse acoustic modes with large negative Gr\uneisen parameters. Furthermore, full phonon spectra of fcc sodium at elevated temperatures are calculated from perturbation theory. The phonon-phonon couplings in fcc sodium are found to increase abnormally under high pressures.