Cooperative excitations within the superionic phase of PbF2

Links between dynamical Frenkel defects and collective diffusion of
fluorides in beta-PbF2 are  explored using Born-Oppenheimer
molecular dynamics. The calculated self diffusion coefficient and ionic
conductivity are 3.2 x 10-5 cm2s-1 and 2.4 Omega-1 
cm-1  at 1000 K in excellent agreement with results from pulsed
field gradient and conductivity measurements: DPFG = 4 x 10-5 cm2 s-1
and  sigmad.c. sim 3 Omega-1cm-1. The calculated ratio of tracer
diffusion to conductivity diffusion is slightly less than unity (about
0.85), which in previous work has been interpreted as providing little
evidence for collective diffusion. In contrast, our molecular dynamics
simulations show that diffusion of fluorides is highly correlated and a
range of mechanisms play important roles. These include, for example,
direct collinear ``knock out'' chains - where a fluoride enter
an occupied tetrahedral hole/cavity and pushes the resident fluorine out
of its cavity - and `loops'' which  generate no net
charge transport. Jumps into an occupied cavity leaves behind a vacancy,
thereby forming dynamic Frenkel defects which trigger a chain of migrating
fluorides assisted by local relaxations of the leads. The calculated
lifetime of the Frenkel defects and the collective chains are around
similar to 1 ps in good agreement with that found from  neutron
diffraction.