Estimation of the band gap of a series of new thermoelectric materials

The band gap $E_{g}$ of a number of new thermoelectric materials, such as skutterudites, clathrates, Heusler phases, [(Ge,Sn,Pb)(Te,Se)]$_{m}$[(Bi,Sb)$_{2}$(Te,Se)$_{3}$]$_{n}$ ($m,n$ = 0, 1, 2 $\dots$) ternary alloys, and others is estimated. Estimations are performed using Goldsmid–Sharp's formula $E_{g}=2e|\alpha_{\operatorname{max}}|T_{\operatorname{max}}$, Vegard’s rule $E_{g}=(mE_{g}^{\operatorname{A}}+nE_{g}^{\operatorname{B}})/(m+n)$, and the empirical dependence $T_{\operatorname{max}}=f(E_{g})$ (A and B denote the corresponding binary alloys, $T_{\operatorname{max}}$ is the temperature corresponding to the thermoelectric-power maximum $|\alpha_{\operatorname{max}}|$ or the thermoelectric figure of merit $(ZT)_{\operatorname{max}}$, and $e$ is the elementary charge). It is shown that the empirical dependence $E_{g}=f(T_{\operatorname{max}})$ gives the most accurate estimates of $E_{g}$ for difference classes of thermoelectric materials.