Disordered electronic systems. III. Thermoelectric power in alloys with phase separation

Applying effective medium theory and the Boltzmann transport equation, a formula is derived for calculation of the Seebeck coefficient α (thermoelectric power) of alloys with phase separation (composite) under especial consideration of the electrochemical potential μ and its change with temperature T,0.2em0exdμ∕dT. dμ∕dT is essentially determined by the electronic structure, carrier densities, and electron-electron-interaction in the phases. For metal-metal composites and metal-insulator composites, α can be calculated approximately by ${{∑}}ᵢ{{υ}}ᵢ({{σ}}ᵢ∕{{α}}ᵢ{-}{σ}∕{α})∕({{σ}}ᵢ∕{{α}}ᵢ+2{σ}∕{α}){}0$ and ${α}{}{{α}}A$, respectively, where ${σ}$ is the specific electrical conductivity of the composite. ${{σ}}ᵢ$, ${{α}}ᵢ$, and ${{υ}}ᵢ$ are the specific electrical conductivity, the Seebeck coefficient, and the volume fraction, respectively, of the phase $i{{0.3em}{0ex}}(i=A,B)$. Both ${{σ}}ᵢ$ and ${{α}}ᵢ$ depend on concentration caused by the condition of a common electrochemical potential in the composite. The ${α}$ formulas derived can also be applied to composites with strong scattering. ${α}$ vs $x$ is calculated for $a{{-}}{Cr}_{1{-}x}{Si}ₓ$ alloys and compared with experimental data.