Entropy Engineering of SnTe: Multi‐Principal‐Element Alloying Leading to Ultralow Lattice Thermal Conductivity and State‐of‐the‐Art Thermoelectric Performance

Abstract

TE material research has attracted intense interest over the past few decades. [1] The TE performance of a material is measured by zT = σS 2 T/κ, where T, σ, S, and κ are the absolute temperature, electrical conductivity, Seebeck coefficient, and total thermal conductivity, respectively. Typically, κ = κ el + κ ph , where the κ el and κ ph are the carrier and lattice thermal conductivity, respectively. Since σ, S, and κ el are adversely interrelated whereas the κ ph is relatively independent of σ, S, and κ el , the stride toward high zT is in line with a two-pronged strategy, coined by Slack as "electron-crystal phonon-glass" (ECPG): [2] i) decoupling σ, S, and κ el through band structure engineering toward a high power factor (PF) = σS 2 ; [3,4] and ii) suppressing the κ ph via all-scale hierarchical microstructures. [5][6][7] Rooted in the core effects of high entropy alloys (HEAs), entropy engineering enables a synergy of band structure engineering and multiscale hierarchical microstructures through high entropy alloying. HEAs typically refer to the solid solutions in which more than five principal elements each in 5-35% molar ratio compete for the same crystallographic site, yielding high entropy of mixing and a wider variety of exciting properties. [8] HEA is a subset of multielement-doped materials. Neither the doping process nor the resulting composition would differentiate aThe core effects of high entropy alloys distinguish high entropy alloying from ordinary multielement doping, allowing for a synergy of band structure and microstructure engineering. Here, a systematic synthesis, structural, theoretical, and thermoelectric study of multi-principal-element-alloyed SnTe is reported. Toward high thermoelectric performance, the entropy of mixing needs to be high enough to make good use of the core effects, yet low enough to minimize the degradation of carrier mobility. It is demonstrated that high entropy of mixing extends the solubility limit of Mn while retaining the lattice symmetry, the enhanced Mn content elicits multiscale microstructures. The resulting ultralow lattice thermal conductivity of ≈0.32 W m −1 K −1 at 900 K in (Sn 0.7 Ge 0.2 Pb 0.1 ) 0.75 Mn 0.275 Te is not only lower than the amorphous limit of SnTe but also comparable to those thermoelectric materials with complex crystal structures and strong anharmonicity. Co-alloying of (Sn,Ge,Pb,Mn) also enhances band convergence and band effective mass, yielding good power factors. Further tuning of the Sn excess yields a state-of-the-art zT ≈1.42 at 900 K in (Sn 0.74 Ge 0.2 Pb 0.1 ) 0.75 Mn 0.275 Te. In view of the simple face-centeredcubic structure of SnTe-based alloys, these results attest to the efficacy of entropy engineering toward a new paradigm of high entropy thermoelecrics.

Multi-Principal-Element Approach to High-Performance Thermoelectric Materials

“…Interestingly, alloying GeSe with Ag or Sb alone didn't stabilize this rhombohedral phase. The alloying-induced new Fermi surface topology and Ge vacancies led to a desired high carrier concentration, close to the optimal one, and a promising ZT ~ 0.86 in GeAg0.2Sb0.2Se1.4 at 710 K. Through alloying SnTe with Ge, Pb, Mn and Te vacancies, Hu et al (2018) reported (i) an extended solubility limit of Mn in (Ge, Pb)-doped SnTe compared to that in pristine SnTe; (ii) a systematic crossover in the carrier scattering mechanism with increasing number of alloying elements, i.e., from electron-phonon scattering to alloy scattering; (iii) the degraded carrier mobility was compensated by increased carrier concentration, heavier effective mass, and band convergence towards a good ZT; and (iv) rich multi-scale microstructures including line defects, strain clusters and dislocation arrays along with point defects led to low lattice thermal conductivity. Fine tuning carrier concentration by Sn excess further boost the peak ZT value to 1.42 at 900 K in (Sn 0.74 Ge 0.2 Pb 0.1 ) 0.75 Mn 0.275 Te.…”

“…The references are listed in Table 3. (Hu 2018) distortion. Doping with a trace amount of Ag effectively enhanced the Seebeck coefficient and further reduced the lattice thermal conductivity.…”

Atomic‐Scale Visualization and Quantification of Configurational Entropy in Relation to Thermal Conductivity: A Proof‐of‐Principle Study int‐GeSb2Te4

“…The configurational entropy (CE) gauges the level of site occupational disorder and thus governs the lattice thermal conductivity L . [3][4][5][6] In diverse research and application regimes of structural and functional materials, there has been a long pressing need for direct visualization of site disorder and quantification of CE in relation to the material's lattice thermal conductvitiy. However, from site disorder and configurational entropy to lattice thermal conductivity, it spans statics and dynamics of crystal lattice as well as the kinetics of thermal transport over orders of magnitude in spatial and temporal domain.…”

Nanostructured high-entropy materials

“…In the NC-Ti 2 NiCoSnSb system (grain size ;12 nm), a secondary phase of TiC is obtained after long ball-milling times, facilitating more Ni 3 Sn 4 formation and leading to higher electrical and thermal conductivities, but undermining the thermoelectric performance [103]. By contrast, Mn-rich nanoscale precipitates (20-30 nm in size) in SnTe-MnTe (medium-entropy) and Sn 0.555 Ge 0.15 Pb 0.075 Mn 0.275 Te (high-entropy) systems promote the formation of nano line-defects, nanoscale strain clusters, and microscale interfaces, which scatter phonons and, therefore, reduce thermal conductivity, leading to excellent thermoelectric properties [106,107]. The results from these studies showing the synergetic effect between nanostructure and lattice distortion are shown in Fig.…”