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.

Methods
The datafile .xml is output file from atomistic ab intio molecular dynamics calculations of PbF2 using the VASP software [ https://www.vasp.at/]. The .xml file contains all input parameters along with the  ionic positions dumped along the trajectories (raw outputfiles). The trajectories can be analysed and visualised using programs such as e.g. VMD and VESTA. See also details of the paper.