According to theoretical predictions [Phys. Rev. Lett. 114, 136601 (2015)], Sb substitution in $\mathrm{F}{\mathrm{e}}_{2}\mathrm{TiSn}$ full-Heusler compounds is thought to enhance the $n$-type thermoelectric power factors. We prepare $\mathrm{F}{\mathrm{e}}_{2}\mathrm{TiSn}$ samples with 0%, 10%, and 20% Sb substitution on the Sn site and study the effects of the heat treatment protocol and of Sb substitution by structural characterization, electrical, thermoelectrical, and thermal transport measurements from room temperature down to 10 K, and by comparison with ab initio calculations. For the undoped $\mathrm{F}{\mathrm{e}}_{2}\mathrm{TiSn}$ phase, we find a bad metallic gapless transport behavior in the as-cast sample and a small gap semiconducting behavior for the annealed samples. These observations, together with the $p$-type character emerging from the Hall effect and Seebeck effect, are explained by ab initio calculations, provided that antisite disorder and vacancy defects are included. In these undoped $\mathrm{F}{\mathrm{e}}_{2}\mathrm{TiSn}$ samples, we find that increasing thermal annealing temperature up to 800 \ifmmode^\circ\else\textdegree\fi{}C slightly decreases the carrier concentration, enhances the Seebeck coefficient in the low-temperature regime (below 100--200 K), induces magnetic ordering at low temperature $(l150\phantom{\rule{0.16em}{0ex}}\mathrm{K})$, and improves the thermoelectric figure of merit and power factor in the low-temperature regime (below \ensuremath{\sim}200 K). As for Sb substitution, we find that 10% substitution increases hole carrier concentration and induces a weakly metallic behavior as compared to the semiconducting behavior of the corresponding undoped annealed samples. On the other hand, 20% substitution lowers the carrier density and increases the resistivity by a factor \ensuremath{\sim}50, with semiconducting behavior measured in the whole temperature range. We interpret the observed effect of Sb doping as a complement to disorder. Indeed, using first-principles techniques we unearth the experimental signature related to density of states features induced by native impurities in the realized samples. The Seebeck coefficient exhibits a maximum at around 200--250 K for the undoped and 20%-doped samples, as typical of semiconducting compounds, while it increases monotonically with temperature for the metallic 10%-doped sample. The latter behavior, joined with the good electrical properties of the 10% sample, determines the room-temperature power factor of $\ensuremath{\sim}1.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\phantom{\rule{0.16em}{0ex}}\mathrm{W}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}2}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}1}$ in the 10% Sb-doped sample, more than twice as much as to the value of the undoped sample.
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