Revisiting Mott's model for the thermopower of ${\mathrm{Pd}}_x{\mathrm{Ag}}_{1-x}$ alloys with support of density functional theory

Electronic properties of palladium-silver alloys have been studied for almost a century as a prototype of a transition-metal alloy with entangled $s$ and $d$ bands. We review the literature starting from Mott's model of 1935 and discuss from a quantitative point of view a series of common assumptions stemming from that seminal paper. We also show that spectral functions obtained by unfolding the band structures of a sample of supercells can be used for the ab initio computation of the thermopower of such systems within a Boltzmann transport equation approach.

Figure 1

Band structure with orbital characters of pure Pd, and total density of states.

Figure 2

Fermi surface of ${\mathrm{Pd}}_x{\mathrm{Ag}}_{1-x}$ in the virtual crystal approximation at 0 K.

Figure 3

Spectral functions of ${\mathrm{Pd}}_{0.6}{\mathrm{Ag}}_{0.4}$ (left) and of Pd (right) at 1000 K, along the $\mathrm{\Gamma }$-X-W-K-$\mathrm{\Gamma }$-L path and with energy bins of 10 meV. The Fermi level is indicated by a white dashed line.

Figure 4

Carrier lifetimes on the Fermi surfaces of ${\mathrm{Pd}}_x{\mathrm{Ag}}_{1-x}$ due to electron-phonon scattering at 1000 K for the pure compounds and only to alloy scattering in other cases.

Figure 5

Thermopower of $\mathrm{Pd}{}_x{\mathrm{Ag}}_{1-x}$ at 1000 K as computed using the virtual crystal and constant relaxation-time approximations (green dots), with a scattering rate proportional to the DOS (blue crosses), and using energies and lifetimes extracted from the spectral functions (black triangles). We also show reference experimental values from Ref. [33] (red line).