We show that a vibrational instability of the spectrum of weakly interacting quasi-local harmonic modes creates the maximum in the inelastic scattering intensity in glasses, the Boson peak. The instability, limited by anharmonicity, causes a complete reconstruction of the vibrational density of states (DOS) below some frequency ωc, proportional to the strength of interaction. The DOS of the new harmonic modes is independent of the actual value of the anharmonicity. It is a universal function of frequency depending on a single parameter -the Boson peak frequency, ω b which is a function of interaction strength. The excess of the DOS over the Debye value is ∝ ω 4 at low frequencies and linear in ω in the interval ω b ≪ ω ≪ ωc. Our results are in an excellent agreement with recent experimental studies.

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

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We examine the vibrational spectrum of a glass of soft spheres produced by quenching an equilibrated liquid (produced via constant-energy molecular-dynamics simulation) to zero temperature. Normalmode analysis shows clearly the existence of (quasi)localized modes at the low-frequency end of the vibrational spectrum. The modes are found to be localized around atoms whose neighborhood structure diA'ers signficantly from the average glass environment.The eAective masses of these modes range upwards from 10 atomic masses.

We show that the same physical mechanism is fundamental for two seemingly different phenomena such as the formation of two-level systems in glasses and the boson peak in the reduced density of low-frequency vibrational states g͑͒ / 2 . This mechanism is the vibrational instability of weakly interacting harmonic modes. Below some frequency c Ӷ 0 ͑where 0 is of the order of Debye frequency͒, the instability, controlled by the anharmonicity, creates a new stable universal spectrum of harmonic vibrations with a boson peak feature as well as double-well potentials with a wide distribution of barrier heights. Both are determined by the strength of the interaction I ϰ c between the oscillators. Our theory predicts in a natural way a small value for the important dimensionless parameter C = P ␥ 2 / v 2 Ϸ 10 −4 for two-level systems in glasses. We show that C Ϸ͑W / ប c ͒ 3 ϰ I −3 and decreases with increasing interaction strength I. The energy W is an important characteristic energy in glasses and is of the order of a few Kelvin. This formula relates the two-level system's parameter C with the width of the vibration instability region c , which is typically larger or of the order of the boson peak frequency b . Since ប c տប b ӷ W, the typical value of C and, therefore, the number of active two-level systems is very small, less than 1 per 1 ϫ 10 7 of oscillators, in good agreement with experiment. Within the unified approach developed in the present paper, the density of the tunneling states and the density of vibrational states at the boson peak frequency are interrelated.