Ion conduction in proton- and related defect (super) ionic conductors: Mechanical, electronic and structure parameters

We find the relationships among optical dielectric constant ε∞, activation energy Eac, averaged atomic mass per a formula unit, ∑jmj / N, volume V and transition temperature Tc for various type ion conductors with forms of Eac = α / (ε∞ − β), Eac = A0 + δ / [(∑jmj / N) − d], Eac = Av / V2/3, and ln(Tc) = g − hln(∑jmj), where α, β, δ, A0, d, Av, g and h are constants depending on the kinds of conduction elements. We derive those proportional forms from a simple equation of motion under the assumption of ion hopping assisted by enhanced vibration displacement of host lattice. The enhancement is induced from the large fourth-order term of the host lattice potential originating from the electronic shielding effect of Coulomb force, heavy atomic mass of constituent ion, and volume expansion under the long-range periodicity of crystal structure. This mechanism is ascertained from characteristic phenomena of various kinds of conduction elements. For impurity-type H+-ion or defect conductor, the proportional form is shifted from that of superionic conductor because of weakened effect of host lattice vibration mode on H+-ion or O-ion defect. Photo-induced spectra of mobile ion in AgCl are understood, and a small quantum effect of H+ -ion is suggested.