Nanoporous PbSe–SiO2 Thermoelectric Composites

Abstract Nanoporous architecture has long been predicted theoretically for its proficiency in suppressing thermal conduction, but less concerned as a practical approach for better thermoelectric materials hitherto probably due to its technical challenges. This article demonstrates a study on nanoporous PbSe–SiO2 composites fabricated by a facile method of mechanical alloying assisted by subsequent wet‐milling and then spark plasma sintering. Owing to the formation of random nanopores and additional interface scattering, the lattice thermal conductivity is limited to a value as low as 0.56 W m−1 K−1 at above 600 K, almost the same low level achieved by introducing nanoscale precipitates. Besides, the room‐temperature electrical transport is found to be dominated by the grain‐boundary potential barrier scattering, whose effect fades away with increasing temperatures. Consequently, a maximum ZT of 1.15 at 823 K is achieved in the PbSe + 0.7 vol% SiO2 composition with >20% increase in average ZT, indicating the great potential of nanoporous structuring toward high thermoelectric conversion efficiency.


VI. Electrical Transport Analyzation on Mobility at near RT
Apart from the composite effects from porous structures, the carrier mobility at RT was supposed to be dominated by multiple mechanisms: acoustic phonons, boundary barriers and nanoparticle/nanopore scattering (characterized by a cross-section of scattering), thus the total mobility can be written in the form of the Matthiessen-type relations: where is the total mobility for dense bulks derived from the MG theory, [1] the individual mobility dominated by acoustic phonons (AC), [2] the individual mobility from boundary-barrier scattering (BB), [3] and the nanoparticle scattering (NP) dominant mobility, [4] respectively.
First, the mobility under acoustic phonon domination is expressed as in the framework of SKB model: Assuming little change in the elastic parameters by the SiO 2 addition and setting the temperature a constant, such as 323K, this mobility component would remain nearly constant.
Secondly, the carrier mobility dominated by boundary barrier scattering adopts the following expression: = ( This barrier height was experimentally found quite relevant to the SiO 2 content, thus E b here was simply derived from Figure 3(b) and Figure S4 as a function of the SiO 2 volume fraction (but actually the barrier height should be some combined effects as stated in the text, including the porosity to some degree; here we use the following relation for simplicity): ≈ 3500 (S4) Figure S5. Energy barrier estimation on PbSe-SiO 2 composites.
Thirdly, the nanoparticle scattering (including nanopore scattering) is identified as: where V np is the average volume of an individual nanoparticle/nanopore. Taking v e =10 5 m/s, roughly assuming = 15.5 , and 20nm/15 nm for the average radius of nanopore/nanoparticle, respectively.
By subjecting these partitions to Equation S1, the total mobility (at 323K) could be roughly obtained as shown in Figure 3(c), where 323 = 500 cm 2 V −1 s −1 was reasonably suggested (this value is smaller than that predicted by Equation S2, as some underlying defects derived by MA processing also contribute the carrier scattering here, which is taken into the equivalent value of ). The resultant value of L, the effective distance of boundary barriers, was estimated to be 23(1+0.001/ ) nm, revealing a little smaller than the magnitude of grain sizes. However, it is perhaps reasonable sometime as the energy barriers are often related to the sub-grains or other crystal defects inside (especially in this work, the interface scattering from nanoparticles and nanopores), but not the real grain boundaries. The individual contribution from these scattering mechanisms can also be found in Figure 3(c), where both AC and BB mechanisms generated a majority of impacts on the total mobility, however, the nanoparticle/nanopore played a tiny role here probably due to their small amounts and overlarge dimensions.
VII. Estimation of the κ L reduction from diffuse scattering of nanopores Figure S6. Estimation for the diffuse scattering on κ L , where the left bar shows the accumulative κ L calculated by the Debye model and acoustic phonon scattering, and the right bar was cited from ref.5 by assuming the pore radius of 20 nm, 50 nm and 100 nm, with the porosity of 15%. Here κ meff refers to the modified κ L of the matrix due to diffuse scattering from nanopores and κ m the original κ L value of the material. The average size (diameter) is determined to be 100~200 nm from the TEM images, thus the contribution of the diffuse scattering is estimated as 5-8% of the total κ L (0.8W/mK), or 15-25% of the κ L reduction (0.24 W m -1 K -1 ) for the 0.7 vol % sample.