Role of Nb vacancies and Sn substitution in modulating the thermoelectric properties of NbCoSb

The half-Heusler (HH) alloy ($\mathrm{N}{\mathrm{b}}_{1\ensuremath{-}z}\mathrm{CoSb}$) with a defective 19 valence electron configuration exhibits a short-range ordering of vacancies within its crystal structure, giving low electrical resistivity and thermal conductivity. In this paper, we investigate the thermoelectric properties of the Sn-substituted $\mathrm{N}{\mathrm{b}}_{0.83}\mathrm{CoSb}$ across a temperature range of 300--1123 K. The samples of $\mathrm{N}{\mathrm{b}}_{0.83}\mathrm{CoS}{\mathrm{b}}_{1\ensuremath{-}x}\mathrm{S}{\mathrm{n}}_{x}$ ($x=0$, 0.01, 0.03, and 0.05) are synthesized by vacuum arc melting followed by vacuum hot press. The x-ray diffraction analysis identified the main phase as the HH phase. The electron probe microanalyzer revealed a deficiency of Nb content from 0.83 to 0.80. The Sn substitution reduces the number of valence electrons, resulting in an increase in the Seebeck coefficient. Also, density functional theory calculations indicate the Nb vacancy displaces the Co atom from the original tetrahedral position toward Sb, which generates additional scattering channels near Brillouin zone edges, arising from the lifting of degeneracy. Additionally, Sn substitution in the Nb vacancy system restores the Co atom to its original position, effectively eliminating these scattering channels and enhancing the transport properties. The high power factor (PF) of $1.79\phantom{\rule{0.16em}{0ex}}\mathrm{mW}/(\mathrm{m}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{2})$ at 1126 K is achieved by the $x=0.03$ sample, surpassing the $x=0$ sample PF $[1.53\phantom{\rule{0.16em}{0ex}}\mathrm{mW}/(\mathrm{m}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{2})\phantom{\rule{0.16em}{0ex}}\mathrm{at}\phantom{\rule{0.16em}{0ex}}1126\phantom{\rule{0.16em}{0ex}}\mathrm{K}]$ attributed to the optimized carrier concentration and elimination of scattering channels after Sn substitution. The Debye-Callaway model, applied to lattice thermal conductivity data, identifies Umklapp and point defect scattering as significant phonon scattering mechanisms. Furthermore, our bonding analysis also reveals the presence of a bonding hierarchy, which reduces the lattice thermal conductivity, contributing to improved thermoelectric performance. Due to this low $\ensuremath{\kappa}$ and high PF, the $x=0.03$ sample achieves a $\mathit{zT}$ of 0.92 at 1126 K.