Phonon anharmonicity and negative thermal expansion in SnSe

The anharmonic phonon properties of SnSe in the Pnma phase were investigated\nwith a combination of experiments and first-principles simulations. Using\ninelastic neutron scattering (INS) and nuclear resonant inelastic X-ray\nscattering (NRIXS), we have measured the phonon dispersions and density of\nstates (DOS) and their temperature dependence, which revealed a strong,\ninhomogeneous shift and broadening of the spectrum on warming. First-principles\nsimulations were performed to rationalize these measurements, and to explain\nthe previously reported anisotropic thermal expansion, in particular the\nnegative thermal expansion within the Sn-Se bilayers. Including the anisotropic\nstrain dependence of the phonon free energy, in addition to the electronic\nground state energy, is essential to reproduce the negative thermal expansion.\nFrom the phonon DOS obtained with INS and additional calorimetry measurements,\nwe quantify the harmonic, dilational, and anharmonic components of the phonon\nentropy, heat capacity, and free energy. The origin of the anharmonic phonon\nthermodynamics is linked to the electronic structure.\n