Electron transfer in solids. Temperature dependence of dielectric relaxation and conductivity in mixed-valence potassium manganate–permanganate

Abstract

The site-transfer conductivity expression σ=ne²a²ν/6 kT has been further tested for K₃(MnO₄)₂ by observations of the d.c. conductivity, σ, and of the electron-transfer frequency, ν, from dielectric relaxometry, over a temperature range, providing good agreement both individually and in activation energies E: ν/ν₀= exp [–(6080 K)/T] and σ/σ₀= exp [–(5908 K)/T] with ν₀= 4.8 × 10¹² Hz and σ₀= 84.7 Ω^–1 cm^–1. The Marcus–Hush semi-classical formulation for E as a sum of E_in= 3 k₁k₂Δr²/(k₁+k₂) and E_out=¼e²(½r^–1₁+½r^–1₁–r^–1₁₂)(n^–2_r–ε^–1_s) together with summary adoption of ν₀=kT/h in the site-transfer expression, gives a complete theoretical formulation for the conductivity as σ=(ne²a²/6h) exp [–(E_in+E_out)/kT] or numerically (204 Ω^–1 cm^–1)× exp [–(5300 K)/T], acceptably according with experiment. KMnO₄ and K₂MnO₄ have lower conductivities; dielectric relaxometry on KMnO₄ does not show the Cole–Cole behaviour which we associate with simple electron transfer in such materials, and K₂MnO₄ is not amenable to dielectric relaxometry.