Phonon Collapse and Second-Order Phase Transition in Thermoelectric SnSe

Abstract

Since 2014 the layered semiconductor SnSe in the high-temperature Cmcm phase is known to be the most efficient thermoelectric material. Making use of first-principles calculations we show that its vibrational and thermal transport properties are determined by huge non-perturbative anharmonic effects. We show that the transition from the Cmcm phase to the low-symmetry P nma is a second-order phase transition driven by the collapse of a zone border phonon, whose frequency vanishes at the transition temperature. Our calculations show that the spectral function of the in-plane vibrational modes are strongly anomalous with shoulders and double-peak structures. We calculate the lattice thermal conductivity obtaining good agreement with experiments only when non-perturbative anharmonic scattering is included. Our results suggest that the good thermoelectric efficiency of SnSe is strongly affected by the non-perturbative anharmonicity. We expect similar effects to occur in other thermoelectric materials.Thermoelectric materials can convert waste heat into useful electricity 1,2 . The thermoelectric efficiency of a material is measured by the dimensionless figure of merit ZT = S 2 σT /κ, where S is the Seebeck coefficient, σ the electrical conductivity, T the temperature, and κ = κ e + κ l the thermal conductivity, constituted by electronic κ e and lattice κ l contributions. The thermoelectric efficiency can be thus enhanced by decreasing the thermal conductivity while keeping a high power factor S 2 σ. Materials have been doped 3-5 or nanostructured 6,7 in order to get a high power factor combined with a low thermal conductivity, yielding, i.e., ZT 2.2 in PbTe 8 . In the proximity to a phase transition ZT may also soar, as in the case of Cu 2 Se 9 . Recently, however, Zhao et al. reported for SnSe 10 the highest thermoelectric figure of merit ever reached in a material without doping, material treatment or without being in the proximity to a phase transition: ZT 2.6 above 800 K.SnSe is a narrow gap semiconductor that crystallizes at room temperature in an orthorhombic P nma phase. At T 800 K 10-13 it transforms into a more symmetric base-centered orthorhombic Cmcm structure (see Fig. 1). The order of the transition is not clear: some works 10-12 claim it is a continuous second-order transition and others it has a first-order character 13 . A recent work 14 argues the transition occurs in two steps, where increasing temperature induces first a change in the lat-tice parameters that induces after a lattice instability. There is no inelastic scattering experiment so far for the high-temperature phase, which should show a prominent phonon collapse at the transition temperature if it belonged to the displacive second-order type 15-17 .The most interesting thermoelectric properties appear in the high-temperature Cmcm phase, where the reduction of the electronic band gap increases the number of carriers providing a higher power factor, while the thermal conductivity remains very low 10 . The value of the intrinsic κ l of SnSe r...

High‐Performance Thermoelectric SnSe: Aqueous Synthesis, Innovations, and Challenges

“…The eutectic point of L1 (Sn) + SnSe is very close to pure Sn, and this should be one of the reasons that occasionally Sn secondary phase is formed in aqueously synthesized SnSe. Besides, SnSe has two phases, namely α‐SnSe ( T < ≈800 K) with lattice parameters of a = 11.37 Å, b = 4.19 Å, and c = 4.44 Å and a space group of Pnma and β‐SnSe ( T > ≈800 K) with lattice parameters of a = 4.31 Å, b = 11.71 Å, and c = 4.32 Å and a space group of Cmcm 3,194. In this Review, we focus on α‐SnSe phase because it has a much stable performance than β‐SnSe.…”

“…For further reducing κ l , understanding the anharmonic bonding in SnSe becomes critical since it plays a significant role in determining low κ l with strong anisotropy. The anharmonic bonding can be described when an atom is forced to deviate from its equilibrium position during the phonon transportation, and the applied force is no longer proportional to its displacement, thus resulting in imbalanced phonon transport and in turn a strengthening of phonon scattering,220 which overall contributes to a low κ l 194,215,221–227. It should be noted that all bonds are anharmonic in most of the materials, but the degree of anharmonicity varies from different materials 228–233.…”

Lattice dynamics of Pnma Sn(S1–xSex) solid solutions: energetics, phonon spectra and thermal transport

“…Due to the record-breaking high-temperature ZT of SnS, the Te-free Sn(S, Se) alloys are of particular interest, and experimental studies have demonstrated a reduction in the thermal conductivity of mixed compositions [12,14].Thermoelectricity is unique in that all four of the terms in the figure of merit ZT are amenable to calculation using first-principles electronic-structure methods such as density-functional theory (DFT) [18]. There have been a number of theoretical studies on existing and potential new single-component bulk thermoelectrics [6,[19][20][21][22][23], and there have recently been efforts to use high-throughput modelling to screen large numbers of compounds in a bid to identify new candidate thermoelectrics [24,25].Studying multicomponent alloy systems with first-principles methods is challenging, however, as building a realistic model requires calculations on a large number of configurations that for complex systems with lowsymmetry unit cells can easily approach the cost of a screening study [26]. Ektarawong and Alling used a firstprinciples cluster expansion method to study the Pnma Sn(S 1-x Se x ) system and confirmed the stability of the mixed phases at finite temperature [27].…”

“…Thermoelectricity is unique in that all four of the terms in the figure of merit ZT are amenable to calculation using first-principles electronic-structure methods such as density-functional theory (DFT) [18]. There have been a number of theoretical studies on existing and potential new single-component bulk thermoelectrics [6,[19][20][21][22][23], and there have recently been efforts to use high-throughput modelling to screen large numbers of compounds in a bid to identify new candidate thermoelectrics [24,25].…”

Quantum effects in muon spin spectroscopy within the stochastic self-consistent harmonic approximation

“…The SSCHA is a quantum variational method that efficiently calculates anharmonic free energies and phonon frequencies in a non-perturbative way. This approach has been very successful for calculating phonon frequencies and superconducting properties in hydrogen-rich materials, as well as in systems undergoing charge density wave (CDW) transitions, ferroelectrics, and thermoelectrics [23,[27][28][29][30][31][32]. For the muon, the SS-CHA is variational in the muon (free) energy, with this energy evaluated stochastically from forces and energies calculated at a sufficient number of random muon configurations.…”