Cooperative excitations in superionic PbF 2

Abstract

Links between dynamical Frenkel defects and collective diffusion of fluorides in β -PbF 2 are explored using Born–Oppenheimer molecular dynamics. The calculated self-diffusion coefficient and ionic conductivity are 3.2 × 10 −5  cm 2  s −1 and 2.4 Ω −1  cm −1 at 1000 K in excellent agreement with pulsed field gradient and conductivity measurements. The calculated ratio of the tracer-diffusion coefficient and the conductivity-diffusion coefficient (the Haven ratio) is slightly less than unity (about 0.85), which in previous work has been interpreted as providing evidence against collective ‘multi-ion’ diffusion. By contrast, our molecular dynamics simulations show that fluoride diffusion is highly collective. Analysis of different mechanisms shows a preference for direct collinear ‘kick-out’ chains where a fluoride enters an occupied tetrahedral hole/cavity and pushes the resident fluoride out of its cavity. Jumps into an occupied cavity leave behind a vacancy, thereby forming dynamic Frenkel defects which trigger a chain of migrating fluorides assisted by local relaxations of the lead ions to accommodate these chains. The calculated lifetime of the Frenkel defects and the collective chains is approximately 1 ps in good agreement with that found from neutron diffraction. This article is part of the Theo Murphy meeting issue ‘Understanding fast-ion conduction in solid electrolytes’.