Basic characteristics of the liquid-glass transition are reviewed, emphasizing its universality and briefly summarizing the most popular phenomenological models. Discussion is focused on a number of alternative models which one way or the other connect the fast and slow degrees of freedom of viscous liquids. It is shown that all these ``elastic'' models are equivalent in the simplest approximation.

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Colloquium : The glass transition and elastic models of glass-forming liquids

This review covers a wide range of experimental and theoretical studies of two-level or tunnelling states in glasses. Emphasis is on fundamental physics rather than a detailed comparison of experiment and theory. Sections cover the static and dynamic properties of tunnelling states, their contribution to thermal properties and their response to weak and strong electric and acoustic fields, both steady state and pulsed. A section on metallic glasses focuses on the importance of electron tunnelling-state interactions, and a final section illustrates approaches to a microscopic description by means of selected examples.

https://iopscience.iop.org/article/10.1088/0034-4885/50/12/003/pdf

Two-level states in glasses

Although liquids normally crystallize on cooling, there are members of all liquid types (including molecular, ionic and metallic) that supercool and then solidify at their glass transition temperature, Tg. This continuous solidification process exhibits great diversity within each class of liquid-both in the steepness of the viscosity-temperature profile, and in the rate at which the excess entropy of the liquid over the crystalline phase changes as Tg is approached. However, the source of the diversity is unknown. The viscosity and associated relaxation time behaviour have been classified between 'strong' and 'fragile' extremes, using Tg as a scaling parameter, but attempts to correlate such kinetic properties with the thermodynamic behaviour have been controversial. Here we show that the kinetic fragility can be correlated with a scaled quantity representing excess entropy, using data over the entire fragility range and embracing liquids of all classes. The excess entropy used in our correlation contains both configurational and vibration-related contributions. In order to reconcile our correlation with existing theory and simulations, we propose that variations in the fragility of liquids originate in differences between their vibrational heat capacities, harmonic and anharmonic, which we interpret in terms of an energy landscape. The differences evidently relate to behaviour of low-energy modes near and below the boson peak.

A thermodynamic connection to the fragility of glass-forming liquids

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.

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Diffusion in Metallic Glasses and Supercooled Melts

We take familiar inorganic oxide glasses and non-oxide glasses and the liquids from which they derive to review the current understanding of their atomic structure, ranging from the local environments of individual atoms to the long-range order which can cover many interatomic distances. The structural characteristics of important glasses and melts, like silicates, borates, alumino-silicates, halides and chalcogenides, are drawn from the results of recent spectroscopy and scattering experiments. The techniques include Nuclear Magnetic Resonance (NMR) and X-ray Absorption Fine Structure (XAFS), Neutron Scattering (NS) and Small- and Wide-angle X-ray Scattering measurements (SAXS/WAXS), and are often combined with computer simulation experiments in order to obtain detailed images of structure and diffusion in the glassy as well as in the molten state. We then review the current understanding of relaxation in glasses, liquids and polyamorphic states. This includes phenomenological models and theories of rela...

Inorganic glasses, glass-forming liquids and amorphizing solids

Measurements of the elastic and inelastic neutron scattering from vitreous silica in the frequency range 0.3 to 4 THz and with scattering vectors in the range 0.2 to 5.3 A${\r{}}^{\mathrm{\ensuremath{-}}1}$ are analyzed in conjunction with heat-capacity measurements on the same samples to provide a microscopic description of low-frequency vibrational modes. The results show that additional harmonic excitations coexist with sound waves below 1 THz, and that these excitations correspond to relative rotation of ${\mathrm{SiO}}_{4}$ tetrahedra.

Low-frequency modes in vitreous silica

Structural relaxation in vitreous silica.

Inelastic-neutron-scattering studies of glassy, liquid, and polycrystalline selenium have been performed at temperatures between 100 and 600 K. A self-consistent data evaluation, taking careful account of multiple and multiphonon scattering, shows that a complete interpretation is possible in terms of a temperature-dependent density of vibrational states, together with diffusion broadening of the elastic line. This density of states is used to calculate thermodynamic properties and to show that about one-third of the additional entropy of the liquid is vibrational. The results raise a number of questions concerning current theories of the glass transition.

Dynamics of glassy and liquid selenium.

Absolute values of the far-infrared (FIR) absorption of Pb, Pb{sub 09}Bi{sub 01}, Pb{sub 08}Bi{sub 02}, and Au{sub 09}Cu{sub 01} have been obtained at 42 K using a calorimetric technique Measurements were made at discrete frequencies over the range 20--150 cm{sup {minus}1} (06--45 THz or 500--70 {mu}m) using an optically pumped FIR laser as the source of radiation, and with a typical absolute error in the absorptivity of approximately 01% The absorption in pure Pb and Pb-Bi alloys increases sharply at the superconducting energy gap and shows structure at frequencies that can be associated with peaks in the phonon density of states, and which is ascribed to the Holstein photon-phonon-electron process However, it appears from both the magnitude and the enhanced structure of the absorption in the alloys that the process is enhanced in the presence of impurity scattering, suggesting that existing theories are incomplete

W. A. Phillips

Papers

Low-frequency modes in vitreous silica

Structural relaxation in vitreous silica.

Dynamics of glassy and liquid selenium.

Far-infrared absorptivity of superconducting Pb-Bi alloys