Strong anharmonic phonon scattering induced giant reduction of thermal conductivity in PbTe nanotwin boundary

Lead telluride (PbTe) is a renowned thermoelectric material with high energy conversion efficiency in medium to high temperature range. However, the performance of PbTe at room temperature is poor due to its relatively high lattice thermal conductivity, which is difficult to be engineered due to its intrinsic very short phonon mean-free path. By performing systematic first-principles and molecular-dynamics simulations, we report that the room-temperature lattice thermal conductivity of PbTe can be reduced by almost one order of magnitude (86%) using the recent experimentally observed nanotwin structure. The mechanism responsible for the dramatic decrease of thermal conductivity strongly depends on the type and mass of atoms at the twin boundary. For PbTe nanotwinned structures with Te at the twin boundary, phonon transport is dominated by the phonon confinement effect and phonon-twin boundary scattering, and the thermal conductivity converges to the bulk value when half of the periodic length is larger than the dominant phonon mean-free path. The same phenomenon is found in another comparison system of KCl nanotwinned structures. However, when Pb is present at the twin boundary, a scattering mechanism occurs: anharmonicity induced by the twin boundary. Due to the mass difference between Pb and Te, the thermal resistance for Pb residing at the twin boundary is found to be one order of magnitude larger than the case with Te at the twin boundary, which results in much stronger phonon-twin boundary scattering. Consequently, the lowest thermal conductivity of such PbTe nanotwinned structure is only 0.4 W/mK, which is reduced by about sevenfold compared to the bulk value of 2.85 W/mK; finally, the converged thermal conductivity cannot restore the bulk value even when half of the periodic length is much larger than the dominant mean-free path. These results offer useful guidance for the development of PbTe-based thermoelectrics and also suggest that nanotwins are excellent building blocks for enhancing the performance of existing thermoelectrics.

Figure 1

(a) Polycrystalline nanotwin PbTe structure. Charge density difference of (b) bulk PbTe, (c) PbTe nanotwinned structure with Pb at twin boundary.

Figure 2

Periodic length-dependent thermal conductivity of nanotwinned structures calculated by Green-Kubo equilibrium molecular-dynamics simulation for: (a) KCl, (b) PbTe with Te at twin boundary, and (c) PbTe with Pb at TB. The blue solid lines denote the thermal conductivity of bulk KCl and PbTe. Different shading color represents different regimes of phonon scattering.

Figure 3

(a) Comparison of thermal conductivity of PbTe and KCl nanotwinned structures calculated by first-principles equilibrium molecular dynamics coupled with TDNMA (without shaded pattern) and classical GK-EMD (with shaded pattern). (b) Scattering rate for PbTe nanotwinned structures (black and red circles are results for Pb and Te at the twin boundary, respectively). (c) Scattering rate for KCl nanotwinned structures (blue and green circles are results for Cl and K at the twin boundary, respectively). The periodic length for all cases is 2.3 nm. Only the columns with shaded pattern are calculated by classical MD [right panel in (a)]. All other results here are computed by first-principles equilibrium molecular-dynamics simulation coupled with TDNMA.

Figure 4

Temperature distribution and thermal boundary resistance for (a) KCl nanotwinned structure with K at the TB, (b) KCl nanotwinned structure with Cl at the twin boundary, (c) PbTe nanotwinned structure with Pb at the twin boundary, (d) PbTe nanotwinned structure with Pb at the twin boundary and the mass of Pb and Te is exchanged, (e) PbTe nanotwinned structure with Te at the twin boundary. The blue vertical line stands for the position of the twin boundary and the dashed red circle implies the temperature jump at the twin boundary due to the anharmonicity. (Inset) Detailed real temperature distribution across the PbTe twin boundary with red lines denoting the linear temperature distribution. The periodic length for all cases is 41 nm.

Figure 5

Phonon vibrational density of states and transmission coefficient at the twin boundary for (a) PbTe nanotwinned structures and (b) KCl nanotwinned structures. The periodic length for all cases is 41 nm.

Figure 6

Thermal conductivity of nanotwinned structures (solid lines) by only considering the phonon boundary scattering: (a) KCl nanotwin with K at the twin boundary, (b) KCl nanotwin with Cl at the twin boundary, (c) PbTe nanotwin with Te at the twin boundary, and (d) PbTe nanotwin with Pb at the twin boundary. The arrow indicates the increase of the strength of phonon boundary scattering. The filled squares are results from GK-EMD simulations.

Figure 7

Potential energy changes for displacement in the [111] direction for (a) KCl and (c) PbTe nanotwinned structure. The corresponding anharmonic energy for (b) KCl and (d) PbTe nanotwinned structure.