Origin of the low-energy mode in superionic conductors

The energy of phonon modes in the beta phase of AgI is estimated from the phonon modes of the gamma phase since the Brillouin zone (B zone) of the former phase can be obtained by folding that of the latter. The idea of folding the Brillouin zone is extended to other binary and ternary superionic conductors (SIC's). Then the low-energy mode, which is observed for many SIC's at the center of the B zone, is assigned to an optical phonon at the lowest frequency (LEO phonon), originating from a transverse-zone-edge acoustic phonon. The proportionality of mode frequency with the inverse square root of mobile ion mass, the pressure and temperature dependencies of the mode frequency, and the close relationship of the LEO phonon to the low transition temperature are understood from the result of folding the B zone with respect to the specific crystal structure of the SIC's.