Influence of Subvalent Twin-Rattler for High <i>n</i>-Type Thermoelectric Performance in Bi₁₃S₁₈Br₂ Chalcohalide

Metal chalcohalides, owing to their higher stability over halides and greater tunability of electronic features over chalcogenides, open new avenues for investigating properties of materials. Complex metal chalcohalides can be a good choice for thermoelectric studies for their halide-like low thermal conductivity and chalcogenide-like high electrical conductivity. Here, we have investigated the thermoelectric properties of <i>n</i>-type Bi₁₃S₁₈Br₂ and utilized the concept of Fajans' polarization to describe the formation of a dimer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mi>Bi</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:math> and explained how it can help achieve high thermoelectric figure of merit (zT) of ∼1.0 at 748 K. This zT value is so far the highest-reported value for pristine metal chalcohalides. The existence of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mi>Bi</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:math> subunit in Bi₁₃S₁₈Br₂ is experimentally verified by synchrotron X-ray pair distribution function (X-PDF) analysis. The complex structure of Bi₁₃S₁₈Br₂ having a large unit cell exhibits simultaneous dimer-cation rattler (i.e., "twin-rattler"), which decreases the lattice thermal conductivity drastically. We observed evidence of such low-energy rattling vibrations from DFT-calculated eigen mode visualizations of the phonon dispersion. The subvalent nature of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mi>Bi</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:math>accommodates an extra electron in <i>Bi</i>(<i>6p</i>_<i>z</i>) orbital, which helps form a weakly dispersed donor band just below the Fermi energy (<i>E</i>_F), leading to a significant reduction in band gap (0.77 eV), which is favorable for high thermoelectric performance. Consequently, we obtained a semiconducting nature of <i>n</i>-type Bi₁₃S₁₈Br₂ with moderate electrical conductivity, as well as a high Seebeck coefficient. Our investigation presents the importance of fundamental chemistry in thermoelectrics and demonstrates the influence of subvalent twin-rattler in triggering high thermoelectric performance in metal chalcohalides.