Heterogeneous diffusion, viscosity, and the Stokes-Einstein relation in binary liquids.

We investigate the origin of the breakdown of the Stokes-Einstein relation (SER) between diffusivity and viscosity in undercooled melts. A binary Lennard-Jones system, as a model for a metallic melt, is studied by molecular dynamics. A weak breakdown at high temperatures can be understood from the collectivization of motion, seen in the isotope effect. The strong breakdown at lower temperatures is connected to an increase in dynamic heterogeneity. On relevant time scales some particles diffuse much faster than the average or than predicted by the SER. The van Hove self-correlation function allows one to unambiguously identify slow particles. Their diffusivity is even less than predicted by the SER. The time span of these particles being slow particles, before their first conversion to be a fast one, is larger than the decay time of the stress correlation. The contribution of the slow particles to the viscosity rises rapidly upon cooling. Not only the diffusion but also the viscosity shows a dynamically heterogeneous scenario. We can define a "slow" viscosity. The SER is recovered as the relation between slow diffusivity and slow viscosity.

High temperature breakdown of the Stokes-Einstein relation in a computer simulated Cu-Zr melt.

Transport properties and the Stokes-Einstein (SE) relation in liquid Cu8Zr3 are studied by molecular dynamics simulation with a modified embedded atom potential. The critical temperature Tc of mode coupling theory (MCT) is derived as 930 K from the self-diffusion coefficient D and viscosity η. The SE relation breaks down around TSE = 1900 K, which is far above Tc. At temperatures below TSE, the product of D and η fluctuates around a constant value, similar to the prediction of MCT near Tc. The influence of the microscopic atomic motion on macroscopic properties is investigated by analyzing the time dependent liquid structure and the self-hole filling process. The self-holes for the two components are preferentially filled by atoms of the same component. The self-hole filling dynamics explains the different breakdown behaviors of the SE relation in Zr-rich liquid CuZr2 compared to Cu-rich Cu8Zr3. At TSE, a kink is found in the temperature dependence of both partial and total coordination numbers for the three atomic pair combinations and of the typical time of self-hole filling. This indicates a strong correlation between liquid structure, atomic dynamics, and the breakdown of SE relation. The previously suggested usefulness of the parameter d(D1/D2)/dT to predict TSE is confirmed. Additionally we propose a viscosity criterion to predict TSE in the absence of diffusion data.

Velocity autocorrelation function in supercooled liquids: Long-time tails and anomalous shear-wave propagation.

Molecular dynamic simulations are performed to reveal the long-time behavior of the velocity autocorrelation function (VAF) by utilizing the finite-size effect in a Lennard-Jones binary mixture. Whereas in normal liquids the classical positive t^{-3/2} long-time tail is observed, we find in supercooled liquids a negative tail. It is strongly influenced by the transfer of the transverse current wave across the period boundary. The t^{-5/2} decay of the negative long-time tail is confirmed in the spectrum of VAF. Modeling the long-time transverse current within a generalized Maxwell model, we reproduce the negative long-time tail of the VAF, but with a slower algebraic t^{-2} decay.

Pressure dependence of diffusion in simple glasses and supercooled liquids.

Using molecular dynamics simulation, we have calculated the pressure dependence of the diffusion coefficient in a binary Lennard-Jones glass. We observe four temperature regimes. The apparent activation volume drops from high values in the hot liquid to a plateau value. Near the critical temperature of the mode coupling theory it rises steeply, but in the glassy state we find again small values, similar to the ones in the liquid. The peak of the activation volume at the critical temperature is in agreement with the prediction of mode coupling theory.