Intrinsic anharmonic localization in thermoelectric PbSe

Abstract

Lead chalcogenides have exceptional thermoelectric properties and intriguing anharmonic lattice dynamics underlying their low thermal conductivities. An ideal material for thermoelectric efficiency is the phonon glass-electron crystal, which drives research on strategies to scatter or localize phonons while minimally disrupting electronic-transport. Anharmonicity can potentially do both, even in perfect crystals, and simulations suggest that PbSe is anharmonic enough to support intrinsic localized modes that halt transport. Here, we experimentally observe high-temperature localization in PbSe using neutron scattering but find that localization is not limited to isolated modes - zero group velocity develops for a significant section of the transverse optic phonon on heating above a transition in the anharmonic dynamics. Arrest of the optic phonon propagation coincides with unusual sharpening of the longitudinal acoustic mode due to a loss of phase space for scattering. Our study shows how nonlinear physics beyond conventional anharmonic perturbations can fundamentally alter vibrational transport properties.

Fig. 1

Triple-axis thermal neutron scattering measurements of the phonons PbSe. a Summary of the temperature dependence of the measured phonon dispersion for the transverse acoustic (TA), longitudinal acoustic (LA), and transverse optic (TO) phonons folded into the first zone along phonon wavevector q = [h, h, 0]. The data points were determined by fitting Lorentzians to the data. The flattening of the TO phonon at 793 K indicates a phonon group velocity, v_g = dE/dq, that goes to zero (localization). b–d Temperature dependence of the spectral intensity distribution for the TO phonon measured in the (113) zone along scattering wavevector Q = [H, H, 3]. Data sets are offset for clarity. e, f Temperature dependence of the spectral intensity distribution for the LA and TA phonons. The TA appears despite the longitudinal geometry because of finite Q resolution effects. Surprisingly, the LA phonon is sharper at 793 K than at 643 K. Intensity bars are in counts. Error bars are statistical and represent one s.d.

Fig. 2

Time-of-flight cold neutron scattering measurements and ab initio simulations. These measurements resolve fine energy structure in the spectral distribution for comparison with the ab initio simulations. a, b Measurements of the TO and TA phonon spectral intensities along Q = [H, H, 3] at 294 and 760 K (out-of-plane direction integrated ±0.1 r.l.u.). c, d Ab initio molecular dynamics simulation predictions of the same phonon spectral intensities. Intensity bars are in arbitrary units. e Simulation at 1000 K

Fig. 3

Phonon sharpening measured using inelastic x-ray scattering. These measurements provide an essentially background free measure of the anomalous sharpening longitudinal acoustic (LA) phonon at high temperatures in Fig. 1e, f. a Spectrum at T = 294 and 770 K (circles) along with fits (lines) to the data. Error bars are statistical and represent one s.d. The transverse acoustic (TA) mode also appears but is weaker than with the triple axis measurements (Fig. 1e, f) because of a better out-of-plane Q resolution. b Resolution corrected energy linewidths for the LA phonon, Γ_LA, full width at half maximum (FWHM). c The LA phonon dispersion showing good agreement with the triple-axis neutron results

Fig. 4

Calculated phase space for three-phonon scattering processes in PbSe. This surface in the Brillouin zone represents the three-phonon scattering processes allowed by energy and momentum conservation for the transverse optic (TO) mode fixed at the zone center, ω₁ = TO(Γ), the longitudinal acoustic (LA) phonon, ω₂ = LA(q₂), and the TO phonon, ω₃ = TO(−q₁ −q₂). The surface represents allowed values for q₂ for a fixed q₁ (q₃ = −q₁ −q₂ is not shown). The resulting reduction in scattering phase space with increasing temperature provides an explanation for the observed decrease in LA phonon scattering rate and linewidth at high temperatures despite the increase in phonon population

Fig. 5

Thermal diffusivity anomaly absent a structural transition. a Thermal diffusivity measured using laser flash method on a piece of the same crystal used in the neutron scattering measurements. Lower panel shows a closeup view of a small negative kink in the data near 750 K (line is guide to the eye). b Single crystal diffraction pattern measured on the HYSPEC instrument above and below the temperature of the kink. The rings are aluminum powder rings from the crystal holder, which were used to calibrate the instrument when determining the PbSe lattice parameter. c Lattice parameter as a function of temperature determined by fitting the single crystal diffraction peaks. The refined lattice parameter of 6.124 ± 0.0005 Å at 300 K is in good agreement with the known value (the Al rings were used to calibrate the instrument assuming an Al lattice parameter of 4.046 Å at room temperature)