  High lattice thermal conductivity in half-Heusler alloys has been the major
bottleneck in thermoelectric applications. Disordered half-Heusler alloys could
be a plausible alternative to this predicament. In this paper, utilizing
first-principles simulations, we have demonstrated the low lattice thermal
conductivity in two such phases, NbFe$_{0.5}$Ni$_{0.5}$Sn and
TaFe$_{0.5}$Ni$_{0.5}$Sn, in comparison to well-known half-Heusler alloy
TiCoSb. We trace the low thermal conductivity to their short phonon lifetime,
originating from the interaction among acoustic and low-lying optical phonons.
We recommend nanostructuring as an effective route in further diminishing the
lattice thermal conductivity. We further predict that these alloys can be best
used in the temperature range 400-600~K and carrier concentration of less than
10$^{21}$ carriers cm$^{-3}$. We found $\sim$35\% and $\sim$17\% enhancement in
$ZT$ for NbFe$_{0.5}$Ni$_{0.5}$Sn and TaFe$_{0.5}$Ni$_{0.5}$Sn, respectively,
as compared to TiCoSb. We are optimistic of the findings and believe these
materials would attract experimental investigations.
