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 supercooled liquid states have been performed to illustrate the decay with time of the cages that confine individual Li+ ions before they hop out to diffuse cooperatively with each other. The self-part of the van Hove function of Li+ ions, G(s)(r,t), is used as an indicator of the cage decay. At 700 K, in the early time regime t<t(x1), when the cage decays very slowly, the mean square displacement <r(2)> of Li+ ions also increases very slowly with time approximately as t(0.1) and has weak temperature dependence. Such <r(2)> 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 G(s)(r,t) at the distance between Li+ ion sites, <r(2)> broadly crosses over from the NCL regime to another power law t(beta) with betaapproximate to0.64 and eventually it becomes t(1.0), corresponding to long-range diffusion. Both t(beta) and t(1.0) terms have strong temperature dependence and they are the analogs of the ac conductivity [sigma(omega)proportional toomega(1-beta)] 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 t(x1)<tau(o), where tau(o) is the independent hop relaxation time; (2) the broad crossover from the NCL to the cooperative ion hopping conductivity sigma(omega)proportional toomega(1-beta) occurs when the cage decays more rapidly starting at t(x1); (3) sigma(omega)proportional toomega(1-beta) is fully established at a time t(x2) comparable to tau(o) 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 sigma(omega) becomes frequency independent, i.e., the dc conductivity. MD simulations show the non-Gaussian parameter peaks at approximately t(x2) and the motion of the Li+ ions is dynamically heterogeneous. Roughly divided into two categories of slow (A) and fast (B) moving ions, their mean square displacements <r(A)(2)> and <r(B)(2)> are about the same for t<t(x2), but <r(B)(2)> of the fast ions increases much more rapidly for t>t(x2). The self-part of the van Hove function of Li+ reveals that first jumps for some Li+ ions, which are apparently independent free jumps, have taken place before t(x2). While after t(x2) 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.