Electron transfer in solids. Temperature dependence of dielectric relaxation and conductivity in mixed-valence potassium manganate–permanganate
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 Ein= 3 k1k2Δr2/(k1+k2) and Eout=¼e2(½r–11+½r–11–r–112)(n–2r–Îµ–1s) 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 [–(Ein+Eout)/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.