Molecular-dynamicssimulations have been carried out on a "soft-sphere" model for binary alloys quenched into supercooled and amorphous states. The main emphasis of the work is on the static and dynamic characterization of the glass transition. A comparison between moleculardynamics data and the results of a self-consistent integral equation shows that the equation of state bifurcates into "glass" and "fluid" branches below a glass transition temperature Tg. The static pair structures differ significantly along the two branches. The structurally relaxed "fluid" branch leads to a phase separation at very low temperatures.Close to the glass transition, the atomic mean-square displacements of the two species go over more and more slowly to the asymptotic diffusive regime, due to the emergence of an intermediate time scale linked to the slowing down of structural relaxation. The diffusion constants of the two species follow closely a scaling law, as predicted by mode-coupling theory, except in the immediate vicinity of the glass transition where activated processes lead to residual diffusion.

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Three very long runs of constant temperature molecular dynamics (MD) simulations, extending over typically 2×105 time steps, have been carried out for a state just above the glass transition of equimolar soft-sphere mixtures, with 500 atoms interacting through vαβ(r) =ε(σαβ /r)12, where σαβ =(σα +σβ )/2, and α,β (species indices)=1, 2. The ratio of diameters σ2/σ1 was chosen to be 1.2. Jump-type atomic motions are clearly found to occur in the glassy states. A coordinated (strongly correlated) jump motion was observed, where a cluster of several atoms dynamically linked at nearest-neighbor distances jump at successive close times. These simulations demonstrate that the characteristic time scale of structural relaxation becomes very long near the glass transition, and calculated mean square displacements exhibit complicated behaviors. Thermodynamic quantities, however, such as the mean pressure, energy, and pair distribution functions, appear to behave normaly, with no significant observable relaxations for increasing time, so that their averages are well defined.

1.0 , corresponding to long-range diffusion. Both t ␤ and t 1.0 terms have strong temperature dependence and they are the analogs of the ac conductivity ͓()ϰ 1Ϫ␤ ͔ 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: ͑1͒ the NCL originates from very slow initial decay of the cage with time caused by few independent hops of the ions because t x1 Ӷ o , where o is the independent hop relaxation time; ͑2͒ the broad crossover from the NCL to the cooperative ion hopping conductivity ()ϰ 1Ϫ␤ occurs when the cage decays more rapidly starting at t x1 ; ͑3͒ ()ϰ 1Ϫ␤ is fully established at a time t x2 comparable to o when the cage has decayed to such an extent that thereafter all ions participate in the slowed dynamics of cooperative jump motion; and ͑4͒ finally, at long times ͑͒ 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 ϩ ions is dynamically heterogeneous. Roughly divided into two categories of slow ͑A͒ and fast ͑B͒ moving ions, their mean square displacements ͗r A 2 ͘ and ͗r B 2 ͘ are about the same for tϽt x2 , but ͗r B 2 ͘ of the fast ions increases much more rapidly for tϾt x2 . The self-part of the van Hove function of Li ϩ reveals that first jumps for some Li ϩ 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. I. BACKGROUNDThe most commonly used experimental technique to probe the ions is electrical conductivity relaxation that measures the macroscopic dielectric response of a sample as a function of frequency. The conductance and capacitance of the sample are usually measured and from the results the complex dielectric susceptibility *() and complex conductivity *() are obtained ͓1-10͔, or directly the complex electric modulus M *() is obtained ͓11,12͔. The frequency dependence of data in the complex conductivity representation usually is well described by using Jonscher's expression ͓7͔where 0 is the dc conductivity, p a characteristic relaxation frequency, and n J a fractional exponent. On the other hand, the same data in the electric modulus representation are also well described by the one-sided Fourier transform,of the Kohlrausch stretched exponential function ͓1-5,13͔⌽͑t ͒ϭexp͓Ϫ͑ t/ ͒ 1Ϫn ͔. ͑3͒The Ј() obtained from Eqs. ͑2͒ and ͑3͒ is similar to the Jonscher's expression in having the dc conductivity at low frequencies and increases as a power law () n at high frequencies.

We have examined the relaxation behavior of alkali metal ions in lithium metasilicate glasses by means of molecular dynamics simulation. We have observed a change of slope of the mean squared displacement at ϳ300 ps. In shorter time regions, localized motion of lithium ions within neighboring sites is observed, which is caused by the small fracton dimension ͑fracton excitation͒. On the other hand, an accelerated motion of particles due to cooperative jumps is found, which characterizes the diffusion and conduction mechanisms of the alkali metal ions in longer time regions. The dynamics of accelerated motion is discussed in relation to Lévy flight dynamics. ͓S0163-1829͑97͒03510-8͔