Anisotropic elasticity drives negative thermal expansion in monocrystalline SnSe

Abstract

Negative thermal expansion (NTE) materials have been at the center of attention for the past few decades as thermal expansion compensators in the fields of engineering, photonics, electronics, and medicine. Numerous crystalline materials exhibit NTE, wherein a combination of positive and negative linear thermal expansion coefficients results from their highly anisotropic elasticity. In this study, we selected SnSe, an anisotropic uniaxial NTE material as a model system where theoretical studies have linked its NTE along the $c$ direction to transverse phonons and to positive Gr\"uneisen parameters along all crystallographic axes. However, the fundamental origin of NTE in SnSe have not been experimentally resolved. Here we performed temperature-dependent resonant ultrasound spectroscopy (between 295--773 K) on single-crystalline SnSe to experimentally measure all nine independent elastic constants (${C}_{11}, {C}_{22}, {C}_{33}, {C}_{44}, {C}_{55}, {C}_{66}, {C}_{12}, {C}_{13}, {C}_{23}$). Our data revealed a high degree of anisotropy in the temperature-dependent elastic constants with shear anisotropic factors show a contrasting pattern with increasing temperature. From this data we also deduced its material compressibility and negative Poisson's ratios in the major crystallographic directions that could explain its colossal linear thermal expansion coefficient along the $c$ direction, reaching $\ensuremath{\sim}--12\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ at 773 K as reported in this study. Furthermore, we confirmed positive Gr\"uneisen parameters along all the crystallographic axes and observe that SnSe behaves like a semicompressible parallelepiped with elastically coupled $a$ and $b$ axes, with the NTE being driven by the displacement of Sn atoms in the $c$ direction.