Optimization of the thermoelectric properties in self-substituted Fe2VAl

Thermoelectric properties were determined in self-substituted ${\mathrm{Fe}}_{2}\mathrm{VAl}$ Heusler alloys $({\mathrm{Fe}}_{2}{\mathrm{V}}_{1+x}{\mathrm{Al}}_{1\ensuremath{-}x}$, $\ensuremath{-}0.1<x<0.1)$, pursuing the goal of their optimization. A parabolic band model fitted to experimental plots of Seebeck coefficient versus charge carrier concentration at 220 K yielded values of the density of states (DOS) effective mass, ${m}_{v}^{*}=3.2{m}_{e}$ and ${m}_{c}^{*}=13.7{m}_{e}$ for the holes and electrons, respectively (${m}_{e}$ is the bare electron mass). The measured Sommerfeld coefficient of the electronic specific heat is consistently smaller in $p$-type ${\mathrm{Fe}}_{2}{\mathrm{V}}_{0.92}{\mathrm{Al}}_{1.08}$ $({\ensuremath{\gamma}}_{p}=7.8\phantom{\rule{0.16em}{0ex}}\mathrm{mJ}\phantom{\rule{0.16em}{0ex}}\mathrm{mo}{\mathrm{l}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}2})$ than in $n$-type ${\mathrm{Fe}}_{2}{\mathrm{V}}_{1.07}{\mathrm{Al}}_{0.93}$ $({\ensuremath{\gamma}}_{n}=11.5\phantom{\rule{0.16em}{0ex}}\mathrm{mJ}\phantom{\rule{0.16em}{0ex}}\mathrm{mo}{\mathrm{l}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}2})$. First-principles calculations of the DOS lead to the theoretical values ${m}_{v}^{*}=2.4{m}_{e}$, ${m}_{c}^{*}=13.0{m}_{e}$, and $\frac{{\ensuremath{\gamma}}_{n}}{{\ensuremath{\gamma}}_{p}}=1.9$, in good agreement with the experimental values. These direct comparisons of calculations with experiments unambiguously show that the heavy electrons arise from flat Fe ${e}_{g}$ conduction bands. Calculations of the optimum thermoelectric power factor $(PF)$ show that it is nearly reached experimentally in $n$-type ${\mathrm{Fe}}_{2}{\mathrm{V}}_{1.03}{\mathrm{Al}}_{0.97}$ ($PF=6.6\phantom{\rule{0.16em}{0ex}}\mathrm{mW}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}2}$ for $n=1.4\ifmmode\times\else\texttimes\fi{}{10}^{21}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}3}$) whereas $p$-type ${\mathrm{Fe}}_{2}{\mathrm{V}}_{0.985}{\mathrm{Al}}_{1.015}$ ($PF=2.7\phantom{\rule{0.16em}{0ex}}\mathrm{mW}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}2}$ at $p=6.7\ifmmode\times\else\texttimes\fi{}{10}^{20}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}3}$) is not yet optimum. The easier optimization of the thermoelectric properties in $n$-type self-substituted ${\mathrm{Fe}}_{2}\mathrm{VAl}$ can be traced back to the larger effective DOS mass of its electrons.