Experimental evidence for the long-time decay of the velocity-autocorrelation in liquid sodium

Abstract

Incoherent inelastic neutron-scattering experiments on liquid sodium at high temperature revealed that atomic motions in simple liquids are governed by hydrodynamic shear modes leading to measurable deviations from Fick's law of diffusion. The experiments for the first time verify earlier predictions of a "long-time tail" behavior of the velocity-autocorrelation function of liquid particles as derived from computer-simulation data and theory. A proper analysis of the experimental data demonstrates the existence of a corresponding low-frequency cusp in the velocity-autocorrelation spectrum.There is a long-standing interest in single-particle behavior in simple liquids since a distinct coupling effect between a single moving particle and its liquid environment has been first observed in computer simulations, 1 ' 2 where it was found that the velocity-autocorrelation function (VAF) of the liquid particles varies as t ~3 /2 for /-* oo. This effect was explained within a simple hydrodynamic picture taking long-living diffusive shear excitations in the liquid into account. Shear modes generated by the moving particle in its surroundings act back on the particle itself at a later time, thus leading to a slower decay of the velocity-autocorrelation function (v/(0) • v/(/)>. This feature of single-particle motion is well described by mode-coupling theory developed in the last years. 3-6 This hydrodynamically founded theory has been supposed to be valid only at very low momentum transfers h Q (Q < 0.1 A " l ). 4 But it will be shown here that hydrodynamic behavior of single-particle motion in liquid sodium at high temperatures extends up to Q values of the order of 1 A ~l.As a consequence we restrict ourselves in this Letter to the hydrodynamic low-g region (Q < 1 A -1 ) which in addition requires high energy resolution (AE < 0.05 meV), whereas in earlier attempts much larger Q values and poorer energy resolutions have been used. 7 Further, this study of mode-coupling effects in a simple liquid was performed at high temperature (7" = 803 K) and not as in previous experiments 7 near the triple point, where these effects are very small, as will become clearer below.A convenient experimental technique for the study of atomic motions on the time and space range of interest is neutron scattering. A neutron-scattering experiment determines the scattering law S(Q,co), the Fourier transform of the space-and time-dependent density correlation function. Incoherent scattering projects out Ss (Q, (o), the self-part of this function, which is well characterized by reduced half-width y(Q) and peak height 8 Z(Q) defined as y(Q)=a) l/2 (Q)/DQ\( 1) where cox/iiQ) is the measured half-width of Ss(Q,co) at constant Q, D is the self-diffusion coefficient of the liquid, and L(Q)-xDQ 2 S s (Q,0).Both quantities are normalized to ordinary diffusion (Fick's law), for which Ss(q,co) is a simple Lorentzian of half-width (0\/ 2 (Q) = DQ 2 and peak height SS(Q,0) = (KDQ 2 )-\

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