Cooperative excitations in superionic PbF₂

Links between dynamical Frenkel defects and collective
diffusion of fluorides in β-PbF₂ are explored using
Born-Oppenheimer molecular dynamics. The calculated
self diffusion coefficient and ionic conductivity are
3.2 × 10⁻⁵ cm² s⁻¹and 2.4 Ω⁻¹ cm⁻¹
at 1000 K in excellent agreement with results from pulsed
field gradient and conductivity measurements. The
calculated ratio of the tracer diffusion coefficient
and the conductivity diffusion coefficient (the Haven
ration), is slightly less than unity (about 0.85), which
in previous work has been interpreted as providing
little evidence for collective “multi-ion” diffusion. In
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 around ∼ 1 ps in good
agreement with that found from neutron diffraction.