Stoichiometric and off-stoichiometric full Heusler ${\mathrm{Fe}}_2{\mathrm{V}}_{1-x}{\mathrm{W}}_x\mathrm{Al}$ thermoelectric systems

A series of full Heusler alloys, ${\text{Fe}}_2{\text{V}}_{1-x}{\text{W}}_x\text{Al}$, $0\le x\le 0.2$, was prepared and characterized, and relevant physical properties to account for the thermoelectric performance were studied in a wide temperature range. Additionally, off-stoichiometric samples with similar compositions have been included, and a 10% improvement of the thermoelectric figure of merit was obtained. The V/W substitution causes (i) a change of the main carrier type, from holes to electrons as evidenced from Seebeck and Hall measurements, and (ii) a substantial reduction of the lattice thermal conductivity due to a creation of lattice disorder by means of a distinct different mass and metallic radius upon the V/W substitution. Moreover $ZT$ values above 0.2 have been obtained. A microscopic understanding of the experimental data observed is revealed from ab initio calculations of the electronic and phononic structure. This series of alloys constitutes the basis for thin film systems, which have recently been found to exhibit $ZT$ values beyond those reported so far in the literature.

Figure 1

Upper panel: X-ray diffraction pattern for ${\mathrm{FeV}}_{0.9}{\mathrm{W}}_{0.1}\mathrm{Al}$ (filled circles), together with results from a Rietveld refinement (solid line), the difference between experimental and model data (lower part of the figure), and respective Bragg positions. Lower panel: Concentration dependence of the lattice parameter $a$ of ${\text{FeV}}_{1-x}{\text{W}}_x\text{Al}$ taken at room temperature. The inset is a sketch of the crystal structure of ${\mathrm{Fe}}_2\mathrm{VAl}$.

Figure 2

Atom-like and total electronic density of states $N\left(E\right)$ near Fermi energy $E_F$. Upper panel: ${\mathrm{Fe}}_2\mathrm{VAl}$; central panel: ${\mathrm{Fe}}_2{\mathrm{V}}_{0.875}{\mathrm{W}}_{0.125}\mathrm{Al}$; lower panel: ${\mathrm{Fe}}_2{\mathrm{V}}_{0.75}{\mathrm{W}}_{0.25}\mathrm{Al}$. Results for W-doped compounds are derived from 32-atom supercell calculations at equilibrium volumes. Al-like DOS is zero around $E_F$ and very small otherwise.

Figure 3

Field dependent Hall resistivity ${\rho }_{xy}$ of ${\text{Fe}}_2{\text{V}}_{1-x}{\text{W}}_x\text{Al}$ for $x=0$ (left panel) and $x=0.2$ (right panel) for various temperatures.

Figure 4

(a) Temperature dependent absolute charge carrier density $n$ (left axis) and absolute mobility $\mu$ (right axis) of ${\text{Fe}}_2{\text{V}}_{1-x}{\text{W}}_x\text{Al}$ for $x=0$ and $x=0.2$. (b) Charge carrier density $n$ (left axis) and absolute mobility $\mu$ of ${\text{Fe}}_2{\text{V}}_{1-x}{\text{W}}_x\text{Al}$ for various concentrations of $x$, derived at room temperature.

Figure 5

Temperature dependent electrical resistivity $\rho$ of ${\mathrm{Fe}}_2{\mathrm{V}}_{1-x}{\mathrm{W}}_x\mathrm{Al}$ for various concentrations $x$. The solid lines are least squares fits (see the text).

Figure 6

Temperature dependent thermopower $S$ for various concentrations $x$ of ${\text{Fe}}_2{\text{V}}_{1-x}{\text{W}}_x\text{Al}$.

Figure 7

Calculated $\vec{q}$ dependent phonon dispersion at DFT equilibrium volumes weighted according to local atomic contributions (Fe, red; V, green; Al, blue; W, black; mixed colors indicate mixed contributions). Upper panel: ${\mathrm{Fe}}_2\mathrm{VAl}$; middle panel: ${\mathrm{Fe}}_2{\mathrm{V}}_{0.875}{\mathrm{W}}_{0.125}\mathrm{Al}$; lower panel: ${\mathrm{Fe}}_2{\mathrm{V}}_{0.75}{\mathrm{W}}_{0.25}\mathrm{Al}$.

Figure 8

Temperature dependent thermal conductivity $\lambda$ for various concentrations $x$ of ${\text{Fe}}_2{\text{V}}_{1-x}{\text{W}}_x\text{Al}$. The solid and dashed lines are least squares fits as explained in the text.

Figure 9

Concentration dependent point defect scattering parameter $A$ of ${\text{Fe}}_2{\text{V}}_{1-x}{\text{W}}_x\text{Al}$ [compare Eq. (7)] (left axis) and lattice thermal conductivity ${\lambda }_{ph}$ taken at room temperature.

Figure 10

Concentration dependent disorder parameter of ${\text{Fe}}_2{\text{V}}_{1-x}{\text{W}}_x\text{Al}$ derived experimentally (${\mathrm{\Gamma }}_{\exp }$) and theoretically ($\mathrm{\Gamma }$); the latter consists of a mass (${\mathrm{\Gamma }}_M$) and volume related contribution (${\mathrm{\Gamma }}_S$).

Figure 11

Left panel: Temperature dependent Seebeck coefficient $S$ (left axis) and temperature dependent electrical resistivity $\rho$ of ${\left[{\mathrm{Fe}}_{2/3}{\left({\mathrm{V}}_{0.9}{\mathrm{W}}_{0.1}\right)}_{1/3}\right]}_{0.76}{\mathrm{Al}}_{0.24}$. Right panel: Temperature dependent thermal conductivity $\lambda$ of ${\left[{\mathrm{Fe}}_{2/3}{\left({\mathrm{V}}_{0.9}{\mathrm{W}}_{0.1}\right)}_{1/3}\right]}_{0.76}{\mathrm{Al}}_{0.24}$. The electronic and lattice thermal conductivity are added together with least squares fits according to Eqs. (4) and (5).

Figure 12

Temperature dependent power factor $p_f$ (left axis) and figure of merit $ZT$ (right axis) of ${\left[{\mathrm{Fe}}_{2/3}{\left({\mathrm{V}}_{0.9}{\mathrm{W}}_{0.1}\right)}_{1/3}\right]}_{0.76}{\mathrm{Al}}_{0.24}$.