A new high-frequency and short-wavelength collective mode specific to binary liquid mixtures with large mass difference is observed in a computer simulation of Lio.8Pbo.2 and discussed within the framework of the Mori-Zwanzig formalism. The mode shows linear dispersion in a wave-number regime 0.1 A "* < ^ < 0.6 A~^ but its propagation velocity is higher than the ordinary sound velocity by more than a factor of 3. Its attenuation is only weakly q dependent in contrast to the damping of ordinary sound. In Lio.8Pbo.2 "fast sound" entails motion of the lighter atoms only.PACS numbers: 61.25.MvWe report the existence of an additional propagating collective mode in binary liquid mixtures, confined to high frequencies and large wave numbers well beyond the hydrodynamic regime. It can be observed in inelastic neutron-scattering experiments or in computer simulation studies of two-component systems with large atomic-mass difference. Some of these systems may respond to a high-frequency short-wavelength perturbation with a density wave, which is supported by the light particles alone, essentially, without the heavy particles participating in the collective motion. Since the dispersion law of this excitation mode is much steeper in the linear region than that of the Brillouin peak of ordinary sound, we call the new mode "fast sound." We have observed fast sound in a computer simulation study ^ of a liquid alloy system of 250 particles in a periodic cell modeling Lio.gPbo.i^ at temperature r=1085 K and total number density w =0.045 58 A ~l Results for the partial dynamic structure factorsSss '(q\(o)

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A binary mixture of hard spheres is investigated within mode-coupling theory under conditions that ensure that the large particles form an amorphous solid. The localization length of small spheres grows continuously with decreasing diameter ratio S, diverging at a critical value £ c -0.15. Close to the localization-delocalization transition both the Lamb-Mossbauer and the Debye-Waller factors of the small particles show striking deviations from their commonly assumed wave-number dependence. Implications for quasielastic neutron scattering on hydrogen in (amorphous) metals are discussed.PACS numbers: 64.60. Cn, 61.40.+b In this Letter we apply the recent mode-coupling theory of the liquid-glass transition 1 to a binary mixture of hard spheres with the aim of studying the localization-delocalization transition of a system of interacting small particles in a glassy matrix executing thermal vibrations. Having in mind the description of dynamical properties of systems such as high loads of hydrogen in metals 2 or liquids in porous media, 3 it is obvious that our model overcomes several limitations inherent in the Lorentz-gas model studied extensively in the past. 4,5 For the numerical evaluation we choose numbers N\=N 2 of hard spheres with diameter ratio S = CJ\/(q,t) ss , of partial-density relaxation functions defined with variables N s (q)/^/S^(q) normalized by partial structure factors. These two quantities coincide in an harmonic solid and they show merely quantitative differences in a glass 1 as a result of anharmonicities. They will, however, differ from each other qualitatively in an assembly of small particles in a glassy matrix. For /-• °°, the generalized oscillator equation of motion for <& s (q,t) with relaxation kernel K s {q,t) reduces to the exact equation 7 q 2 fs(q) + K s (q,)[f s (q)-\]=0.(3)Applying a mode-coupling approximation to the friction kernel we find (s = 1,2; s '^s) KAq^)=(\/V)^k(k'q/q) 2 f s (\q-k\){c ss (k) 2 f(k) ss S ss (k) + 2c 5 ,Uk^)/U)^[S^ (4)The direct correlation functions c ss Xk) entering Eq. (4) represent the only external input required. We use results of the Percus-Yevick approximation 8 known to be reliable for hard spheres and available in analytical form for all values of the system parameters 77, 5, and c =N\/(N\ + N 2 ). Figure 1(a) shows representative examples of the partial static structure factors S ss .(q)-V-c(q)]->.

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