Relaxation Modes of Classical Hopping Protons in Perovskite Structures I

Abstract

The relaxations by proton hopping in a perovskite lattice are theoretically investigated: the 24 sites available for protons in the primitive unit cell give rise to the 24 relaxation branches composed of 1 diffusive ( ε =1) and 23 nondiffusive bands ( ε =2–24). It turns out that two lowest nondiffusive modes ε =2,3, being degenerate at q =0, can work for a radio-frequency dielectric function. On the other hand, the cell including a dopant results in impurity modes when proton has a deep potential energy as a trapping state. The impurity modes consist of five radio frequency modes, two- and three-degenerate modes. It is discussed how these relaxation modes and impurity modes get involved in proton diffusions or two-peaks mechanism of the dielectric loss, experimentally observed.