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

Molecular dynamics ~MD! simulations of lithium metasilicate (Li2SiO3) in the glassy and supercooledliquid states have been performed to illustrate the decay with time of the cages that confine individual Li1 ionsbefore they hop out to diffuse cooperatively with each other. The self-part of the van Hove function of Li1ions, Gs(r,t), is used as an indicator of the cage decay. At 700 K, in the early time regime t,tx1 , when thecage decays very slowly, the mean square displacement ^r2& of Li1 ions also increases very slowly with timeapproximately as t0.1 and has weak temperature dependence. Such ^r2& can be identified with the near constantloss ~NCL! observed in the dielectric response of ionic conductors. At longer times, when the cage decays morerapidly as indicated by the increasing buildup of the intensity of Gs(r,t) at the distance between Li1 ion sites,^r2& broadly crosses over from the NCL regime to another power law tb with b'0.64 and eventually itbecomes t1.0, corresponding to long-range diffusion. Both tb and t1.0 terms have strong temperature dependenceand they are the analogs of the ac conductivity @s(v)}v12b # and dc conductivity of hopping ions. TheMD results in conjunction with the coupling model support the following proposed interpretation for conductivityrelaxation of ionic conductors: ~1! the NCL originates from very slow initial decay of the cage with timecaused by few independent hops of the ions because tx1!t o , where t o is the independent hop relaxation time;~2! the broad crossover from the NCL to the cooperative ion hopping conductivity s(v)}v12b occurs whenthe cage decays more rapidly starting at tx1 ; ~3! s(v)}v12b is fully established at a time tx2 comparable tot o when the cage has decayed to such an extent that thereafter all ions participate in the slowed dynamics ofcooperative jump motion; and ~4! finally, at long times s~v! becomes frequency independent, i.e., the dcconductivity. MD simulations show the non-Gaussian parameter peaks at approximately tx2 and the motion ofthe Li1 ions is dynamically heterogeneous. Roughly divided into two categories of slow ~A! and fast ~B!moving ions, their mean square displacements ^rA 2 & and ^rB 2 & are about the same for t,tx2 , but ^rB 2 & of the fastions increases much more rapidly for t.tx2 . The self-part of the van Hove function of Li1 reveals that firstjumps for some Li1 ions, which are apparently independent free jumps, have taken place before tx2 . Whileafter tx2 the angle between the first jump and the next is affected by the other ions, again indicating cooperativejump motion. The dynamic properties are analogous to those found in supercooled colloidal particle suspensionby confocal microscopy