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

Abstract

We find the relationships among optical dielectric constant ε ∞ , activation energy E ac , averaged atomic mass per a formula unit, ∑ j m j / N , volume V and transition temperature T c for various type ion conductors with forms of E ac = α / ( ε ∞ − β ), E ac = A 0 + δ / [(∑ j m j / N ) − d ], E ac = A v / V 2/3 , and ln( T c ) = g − h ln(∑ j m j ), where α , β , δ , A 0 , d , A v , 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.