Effect of vacancies on the thermoelectric properties of Mg${}_2$Si${}_{1-x}$Sb${}_x$ (0 $⩽x⩽$ 0.1)

Mg${}_2$Si${}_{1-x}$Sb${}_x$ compositions with $x$ ranging from 0 to 0.1 were prepared by induction melting and compacted by hot uniaxial pressing. The lattice parameter and the positional occupancy at the Mg site as a function of Sb substitution were calculated from Rietveld refinement. A monotonic increase in the $a$lattice constant value was observed with increasing Sb substitution. Also, a decrease in the Mg site occupancy was observed with increasing Sb substitution and was confirmed by energy dispersive analysis of x-ray measurements. Room temperature carrier concentration ($n$) measurements show an increase from $1.4\times {10}^{18}$ cm${}^{-3}$ for $x=0$ to $1.4\times {10}^{20}$ cm${}^{-3}$ for $x=0.025$ followed by a nearly constant $n$, indicating the influence of vacancy formation. Electrical conductivity ($\sigma$), Seebeck coefficient ($S$), and thermal conductivity ($\kappa$) values were measured from 300 to 773 K. The observed trends in the absolute values of $\sigma$ and $S$ can be explained based on the vacancy formation at the Mg site which counteracts the doping influence of Sb. The $\kappa$${}_L$ (phonon component of the thermal conductivity) values show a significant decrease with increasing Sb substitution. Calculation of the thermoelectric figure of merit ($\mathit{ZT}$) shows a maximum $\mathit{ZT}$ of 0.55 for $x=0.10$ compared to a $\mathit{ZT}$ of $~$0.05 for $x=0.0$.

Figure 1

(a) XRD patterns for the different Sb-substituted compositions. The encircled peaks show the systematic changes in the relative peak intensities. (Inset) Change of the $a$ lattice parameter with increasing Sb substitution. (b) The effect of Sb substitution and Mg vacancies on the relative peak intensities of the indexed peaks in (a) (theoretically calculated). The two encircled peaks in (a), corresponding to the (200) and (511) planes, show a decrease and increase in the relative peak intensities with increasing Sb and vacancy formation.

Figure 2

Temperature dependence of the (a) electrical conductivity and (b) Seebeck coefficient for the different compositions.

Figure 3

Abundance distribution of the room temperature $S$ values for the different compositions measured by PSM. Full widths at half maximum for the different compositions are given.

Figure 4

Temperature dependence of power factor for the different compositions.

Figure 5

Temperature dependence of (a) total ($\kappa$) and (b) lattice component ($\kappa$${}_L$) of the thermal conductivity for the different compositions.

Figure 6

Variation of $\kappa$${}_L$ with Sb substitution ($x$) at room temperature (both experimental and calculated values). The inset shows the inverse temperature dependence of the experimental $\kappa$${}_L$ values for the different compositions.

Figure 7

Temperature dependence of the dimensionless figure of merit ($\mathit{ZT}$) for the different compositions.