Phonon anharmonicity and negative thermal expansion in SnSe

Abstract

The anharmonic phonon properties of SnSe in the Pnma phase were investigated with a combination of experiments and first-principles simulations. Using inelastic neutron scattering (INS) and nuclear resonant inelastic X-ray scattering (NRIXS), we have measured the phonon dispersions and density of states (DOS) and their temperature dependence, which revealed a strong, inhomogeneous shift and broadening of the spectrum on warming. First-principles simulations were performed to rationalize these measurements, and to explain the previously reported anisotropic thermal expansion, in particular the negative thermal expansion within the Sn-Se bilayers. Accurate treatment of the phonon free energy, in addition to the electronic ground state energy, is essential to reproduce the negative thermal expansion. From the phonon DOS obtained with INS and additional calorimetry measurements, we quantify the harmonic, dilational, and anharmonic components of the phonon entropy, heat capacity, and free energy. The origin of the anharmonic phonon thermodynamics is linked to the electronic structure.

Strong anharmonicity in the phonon spectra of PbTe and SnTe from first principles

“…The ferroelectric transition (imaginary TO phonon at zone center) is present when using the more expanded theoretical PBE volume while it disappears if the experimental volume is used. This again underlines the critical role of the volume used in the calculation of phonon spectra in ferroelectrics and thermoelectrics 34 . Finally, we also investigated the role of hole doping by using the virtual crystal approximation in appendix D In the rest of the paper we consider the PBE optimized lattice parameter at T = 0 K in all calculations.…”

Evidence for hard and soft substructures in thermoelectric SnSe

“…2(a) and is characterised by a linear increase beyond the Dulong-Petit value of 3R/atom, consistent with the high-temperature data in the literature. 7,9,19,23 A plot of C p /T versus T 2 reveals that there is no electronic contribution to the heat capacity at low-temperature, which is in keeping with the semiconducting nature of SnSe [ Fig. 2(b)].…”

“…The phonon calculations reveal that the modes in the lower band are more strongly associated with Sn displacements, with a pronounced peak associated with motions perpendicular to the rocksalt layers. 9 The higher energy band in the PDOS is more strongly associated with Se displacements. This is consistent with our link to the weak and strong bonds in the crystal structure, where the weaker bonds allow for lowenergy anharmonic Sn displacements, while Se is less strongly displaced.…”

“…[8][9][10] A lower band spanning 0-13 meV containing 3 acoustic and 9 optic modes and a higher energy band from 13 to 25 meV with the remaining 12 optic modes. The upper energies for these two bands correspond very closely to highest phonon frequency for the fitted Debye modes (k B h D1 ¼ 29.7(8) meV and k B h D2 ¼ 13.2(2) meV).…”

“…[7][8][9][10][11][12] The crystal structure can be understood as a highly distorted rock salt derivative. 13,14 At high-temperatures, adjacent two-atom thick rock salt layers are translated by a/2 so that Sn is coordinated by 5 Se atoms in the rocksalt layer and by 2 Se atoms in an adjacent layer.…”