Molecular dynamics study of cage decay, near constant loss, and crossover to cooperative ion hopping in lithium metasilicate

Abstract

Molecular dynamics (MD) simulations of lithium metasilicate [formula presented] in the glassy and supercooled liquid states have been performed to illustrate the decay with time of the cages that confine individual [formula presented] ions before they hop out to diffuse cooperatively with each other. The self-part of the van Hove function of [formula presented] ions, [formula presented] is used as an indicator of the cage decay. At 700 K, in the early time regime [formula presented] when the cage decays very slowly, the mean square displacement [formula presented] of [formula presented] ions also increases very slowly with time approximately as [formula presented] and has weak temperature dependence. Such [formula presented] can be identified with the near constant loss (NCL) observed in the dielectric response of ionic conductors. At longer times, when the cage decays more rapidly as indicated by the increasing buildup of the intensity of [formula presented] at the distance between [formula presented] ion sites, [formula presented] broadly crosses over from the NCL regime to another power law [formula presented] with [formula presented] and eventually it becomes [formula presented] corresponding to long-range diffusion. Both [formula presented] and [formula presented] terms have strong temperature dependence and they are the analogs of the ac conductivity [formula presented] and dc conductivity of hopping ions. The MD results in conjunction with the coupling model support the following proposed interpretation for conductivity relaxation of ionic conductors: (1) the NCL originates from very slow initial decay of the cage with time caused by few independent hops of the ions because [formula presented] where [formula presented] is the independent hop relaxation time; (2) the broad crossover from the NCL to the cooperative ion hopping conductivity [formula presented] occurs when the cage decays more rapidly starting at [formula presented] (3) [formula presented] is fully established at a time [formula presented] comparable to [formula presented] when the cage has decayed to such an extent that thereafter all ions participate in the slowed dynamics of cooperative jump motion; and (4) finally, at long times σ(ω) becomes frequency independent, i.e., the dc conductivity. MD simulations show the non-Gaussian parameter peaks at approximately [formula presented] and the motion of the [formula presented] ions is dynamically heterogeneous. Roughly divided into two categories of slow (A) and fast (B) moving ions, their mean square displacements [formula presented] and [formula presented] are about the same for [formula presented] but [formula presented] of the fast ions increases much more rapidly for [formula presented] The self-part of the van Hove function of [formula presented] reveals that first jumps for some [formula presented] ions, which are apparently independent free jumps, have taken place before [formula presented] While after [formula presented] the angle between the first jump and the next is affected by the other ions, again indicating cooperative jump motion. The dynamic properties are analogous to those found in supercooled colloidal particle suspension by confocal microscopy. © 2002 The American Physical Society.