Heterogeneous Distribution of Sodium for High Thermoelectric Performance of p‐type Multiphase Lead‐Chalcogenides

Abstract

recovery. [ 1 ] The search for high performance materials has continued to improve the relatively low conversion effi ciency of thermoelectric materials. The effi ciency is defi ned by the dimensionless fi gure of merit, zT = S 2 Tσ /( κ E + κ L ), where, S , σ , T , κ L , and κ E are the Seebeck coeffi cient, electrical conductivity, absolute temperature, and the lattice and electronic components of the thermal conductivity, respectively. Pb chalcogenides have received considerable attention amongst existing thermoelectric materials due to the relatively high thermoelectric conversion effi ciencies for both n-type [ 2 ] and p-type [ 3,4 ] compounds.Intrinsic semiconducting lead chalcogenides (PbQ, Q = Te, Se, S) can be tuned to p-type through substitution of monovalent sodium on the lead sublattice. [ 5,6 ] Although, sodium has been the most viable dopant for lead chalcogenides, [ 3,7,8 ] its solubility limits to ≈2 at% in PbS, [ 9 ] ≈0.9 at% in PbSe, [ 9 ] and a maximum of ≈0.7 at% in PbTe. [ 10 ] The exceptionally high thermoelectric performance of ≈2 has been reported for a 2 at% Na-doped multiphase nanostructured PbTe, [ 4,11,12 ] ≈1.6 for 2 at% Na-doped nanostructured multiphase PbSe [ 13 ] and ≈1.2 for 2.5 at% Nadoped nanostructured multiphase PbS. [ 14 ] However, the mechanisms by which these high thermoelectric effi ciencies have been achieved in multiphase compounds with dopant concentrations above the solubility level of the matrix have not been studied systematically. Little attention has been given to the effect of the inhomogeneous distribution of sodium between the component phases on the thermoelectric properties of multiphase compounds. Here, we have explored the thermoelectric properties of multi phase nanostructured quaternary (PbTe) 0.65 (PbS) 0.25 (PbSe) 0.1 compounds at various Na-dopant concentrations.Strategies aiming to improve the power factor (S 2 σ) through tuning of the electronic band structure near the Fermi level, include resonant states, [ 15,16 ] multiple bands, [ 14,17 ] manipulating the band gap, [18][19][20] and/or modulation doping. [21][22][23] During the last decade, tremendous efforts have also been devoted to reducing the lattice thermal conductivity of bulk thermoelectric materials by nanostructuring. [ 4,8,24 ] Multiphase lead chalcogenides compounds invariably exhibit higher zT values than those of their constituent phases. This is attributed to the combined effects of: band engineering resulting from the effects of alloying; a reduction in the lattice thermal conductivity, which Despite the effectiveness of sodium as a p-type dopant for lead chalcogenides, its solubility is shown to be very limited in these hosts. Here, a high thermoelectric effi ciency of ≈2 over a wide temperature range is reported in multiphase quaternary (PbTe) 0.65 (PbS) 0.25 (PbSe) 0.1 compounds that are doped with sodium at concentrations greater than the solubility limits of the matrix. Although these compounds present room temperature thermoelectric effi ciencies similar to sodium doped PbT...

Elemental distributions within multiphase quaternary Pb chalcogenide thermoelectric materials determined through three-dimensional atom probe tomography

“…Given that the magnitude of non--equilibrium segregation is known to increase with temperature [28], it seems reasonable to assume that this applies in the case of sodium. It would help explain the increase in Hall carrier concentration observed for the heavily--doped sample at temperatures above 600 K [5] (See Supporting Information). A sudden increase in Hall carrier concentration as a function of temperature is the result of a combination of the thermodynamically driven process of sodium segregation to the interfaces and the kinetically driven diffusion-controlled migration of sodium atoms.…”

“…Non--equilibrium segregation of sodium in multiphase Pb chalcogenides has attracted considerable attention due to the significant improvement achieved in thermoelectric performance of sodium--doped multiphase compounds at concentrations higher than the solubility limit of the matrix [2,5,11,14,33] and the low diffusion coefficient of Na in the PbTe matrix below 600 K [15,34].…”

“…We have attributed the high thermoelectric performance (zT ~ 2) observed in heavily doped p--type quaternary Pb chalcogenides to heterogeneous distribution of sodium between the matrix and precipitates, with an enhanced contribution from modulation doping at elevated temperatures [5]. Dopant partitioning between PbTe--rich matrix and PbS--rich precipitates was identified in heavily--doped multiphase Pb--chalcogenides by energy dispersive X--ray spectroscopy analysis (EDS) in the transmission electron microscope (TEM) [5,15,16]. However, due to its limited sensitivity, this technique is unable to provide compositional information about dopant distribution in lightly--doped compounds.…”

“…Sodium is the most viable p--type dopant [1,2,10,11] for Pb chalcogenides, though its solubility has been shown to be limited [12,13]. Sodium doping results in considerably higher thermoelectric performance of p--type multiphase compounds when the alloys are doped at concentrations greater than the solubility limit of the matrix [2,5,11,14]. We have attributed the high thermoelectric performance (zT ~ 2) observed in heavily doped p--type quaternary Pb chalcogenides to heterogeneous distribution of sodium between the matrix and precipitates, with an enhanced contribution from modulation doping at elevated temperatures [5].…”

“…Sodium doping results in considerably higher thermoelectric performance of p--type multiphase compounds when the alloys are doped at concentrations greater than the solubility limit of the matrix [2,5,11,14]. We have attributed the high thermoelectric performance (zT ~ 2) observed in heavily doped p--type quaternary Pb chalcogenides to heterogeneous distribution of sodium between the matrix and precipitates, with an enhanced contribution from modulation doping at elevated temperatures [5]. Dopant partitioning between PbTe--rich matrix and PbS--rich precipitates was identified in heavily--doped multiphase Pb--chalcogenides by energy dispersive X--ray spectroscopy analysis (EDS) in the transmission electron microscope (TEM) [5,15,16].…”