The isotope effect E °D a ͞D b 2 1 ¢ ͑͞ p m b ͞m a 2 1͒ of cobalt diffusion in the deeply supercooled melt of the metallic alloy Zr 46.7 Ti 8.3 Cu 7.5 Ni 10 Be 27.5 has been measured employing the radiotracers 57 Co and 60 Co. The isotope effect is very small, E 0.09 6 0.03, and exhibits no significant temperature dependence in a range up to 120 K above the calorimetric glass transition temperature T g , encompassing almost 3 orders of magnitude in the diffusivity. This result suggests that long-range diffusion in the deeply supercooled melt is not mediated by viscous flow but rather proceeds by collective hopping processes involving about ten atoms. [S0031-9007(98)06275-9] PACS numbers: 66.10. Cb, 66.30.Fq, 64.70.Dv Atomic transport in liquids and glasses has been the subject of many theoretical and experimental investigations, particularly in connection with the glass transition [1,2]. Diffusion in ordinary liquids at high temperatures is well understood. In this hydrodynamic regime all atoms contribute continuously to the mean square atomic displacement, and diffusion takes place via viscous flow, as described by the Stokes-Einstein relation [3]. Microscopically, transport in the hydrodynamic regime is governed by uncorrelated binary collisions of atoms. Kinetic theories for a simple liquid [3,4] predict the following mass and temperature dependence of the diffusivity D:where m is the atomic mass and n is close to 2 according to molecular dynamics simulations [1] and experiments [5]. Upon supercooling a liquid or melt the viscosity increases markedly because, due to the increase in density, atoms are more and more trapped in their nearest-neighbor "cages" for times much longer than the vibration time.According to the mode coupling theory [6] this cage effect causes viscous flow to freeze in at a critical temperature T c . Below T c , which is typically some 20% above the caloric glass transition temperature T g [7], long-range diffusion in the supercooled liquid is expected to occur only via thermally activated hopping processes. Molecular dynamics simulations have shown the transition from viscous flow at high temperatures to hopping in the glassy state [8][9][10]. The coexistence of both processes was observed in a certain temperature range in the supercooled liquid state. Moreover, computer simulations as well as neutron scattering [11] have confirmed the existence of a critical temperature above T g , where the decay of density correlations slows down drastically. Whereas generally hopping in crystalline solids is a single-atom jump process [12], recent extensions of the mode coupling theory to the glassy state envision hop-ping in glasses as a highly cooperative medium-assisted process [13]. Highly collective hopping processes have indeed been observed in molecular dynamics simulations [10,14,15]. These simulations reveal chainlike displacements involving some ten atoms, which are suggested to be closely related to the well known low frequency excitations in glasses [14]. While, depending on the alloy ...

The isotope effect E = d ln(D)/d In ( l / f i ) of CO diffusion in structurally relaxed CoS6Zrl4 and CoslZrlg glasses has been measured by means of a radiotracer technique. Within experimental accuracy no isotope effect was detected ( E < 0.04). This suggests a highly cooperative diffusion mechanism. The connection between diffusion and collective low-frequency relaxations in glasses is discussed.have been shown to be in conflict with a defect mechanism (see, e.g., [SI).Recently, we have succeeded in measuring the pressure dependence and the isotope effect

Amorphous metallic alloys, also called metallic glasses, are of considerable technological importance. The metastability of these systems, which gives rise to various rearrangement processes at elevated temperatures, calls for an understanding of their diffusional behavior. From the fundamental point of view, these metallic glasses are the paradigm of dense random packing. Since the recent discovery of bulk metallic glasses it has become possible to measure atomic diffusion in the supercooled liquid state and to study the dynamics of the liquid-to-glass transition in metallic systems. In the present article the authors review experimental results and computer simulations on diffusion in metallic glasses and supercooled melts. They consider in detail the experimental techniques, the temperature dependence of diffusion, effects of structural relaxation, the atom-size dependence, the pressure dependence, the isotope effect, diffusion under irradiation, and molecular-dynamics simulations. It is shown that diffusion in metallic glasses is significantly different from diffusion in crystalline metals and involves thermally activated, highly collective atomic processes. These processes appear to be closely related to low-frequency excitations. Similar thermally activated collective processes were also found to mediate diffusion in the supercooled liquid state well above the caloric glass transition temperature. This strongly supports the mode-coupling scenario of the glass transition, which predicts an arrest of liquidlike flow already at a critical temperature well above the caloric glass transition temperature. CONTENTS

Using a radiotracer technique, we have measured the isotope effect E = dln(D)/dln(m(1/2)) of Co diffusion in CoxZr1-x glasses for 0. 31

No abstract