skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Dynamics and thermodynamics of the glass transition

Abstract

The principal theme of this paper is that anomalously slow, super-Arrhenius relaxations in glassy materials may be activated processes involving chains of molecular displacements. As pointed out in a preceding paper with Lemaitre, the entropy of critically long excitation chains can enable them to grow without bound, thus activating stable thermal fluctuations in the local density or molecular coordination of the material. I argue here that the intrinsic molecular-scale disorder in a glass plays an essential role in determining the activation rate for such chains, and show that a simple disorder-related correction to the earlier theory recovers the Vogel-Fulcher law in three dimensions. A key feature of this theory is that the spatial extent of critically long excitation chains diverges at the Vogel-Fulcher temperature. I speculate that this diverging length scale implies that, as the temperature decreases, increasingly large regions of the system become frozen and do not contribute to the configurational entropy, and thus ergodicity is partially broken in the super-Arrhenius region above the Kauzmann temperature T{sub K}. This partially broken ergodicity seems to explain the vanishing entropy at T{sub K} and other observed relations between dynamics and thermodynamics at the glass transition.

Authors:
 [1]
+ Show Author Affiliations
  1. Department of Physics, University of California, Santa Barbara, California 93106-9530 (United States)
Publication Date:
OSTI Identifier:
20779238
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 73; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevE.73.041504; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DENSITY; ENTROPY; EXCITATION; FLUCTUATIONS; GLASS; MOLECULAR STRUCTURE; PHASE TRANSFORMATIONS; RELAXATION; THERMODYNAMICS

Citation Formats

Langer, J.S. Dynamics and thermodynamics of the glass transition. United States: N. p., 2006. Web. doi:10.1103/PHYSREVE.73.0.
Copy to clipboard
Langer, J.S. Dynamics and thermodynamics of the glass transition. United States. doi:10.1103/PHYSREVE.73.0.
Copy to clipboard
Langer, J.S. Sat . "Dynamics and thermodynamics of the glass transition". United States. doi:10.1103/PHYSREVE.73.0.
Copy to clipboard
@article{osti_20779238,
title = {Dynamics and thermodynamics of the glass transition},
author = {Langer, J.S.},
abstractNote = {The principal theme of this paper is that anomalously slow, super-Arrhenius relaxations in glassy materials may be activated processes involving chains of molecular displacements. As pointed out in a preceding paper with Lemaitre, the entropy of critically long excitation chains can enable them to grow without bound, thus activating stable thermal fluctuations in the local density or molecular coordination of the material. I argue here that the intrinsic molecular-scale disorder in a glass plays an essential role in determining the activation rate for such chains, and show that a simple disorder-related correction to the earlier theory recovers the Vogel-Fulcher law in three dimensions. A key feature of this theory is that the spatial extent of critically long excitation chains diverges at the Vogel-Fulcher temperature. I speculate that this diverging length scale implies that, as the temperature decreases, increasingly large regions of the system become frozen and do not contribute to the configurational entropy, and thus ergodicity is partially broken in the super-Arrhenius region above the Kauzmann temperature T{sub K}. This partially broken ergodicity seems to explain the vanishing entropy at T{sub K} and other observed relations between dynamics and thermodynamics at the glass transition.},
doi = {10.1103/PHYSREVE.73.0},
journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},
number = 4,
volume = 73,
place = {United States},
year = {Sat Apr 15 00:00:00 EDT 2006},
month = {Sat Apr 15 00:00:00 EDT 2006}
}
Copy to clipboard
Journal Article:
DOI:  10.1103/PHYSREVE.73.0
Other availability
Find in Google Scholar Find in Google Scholar
Search WorldCat Search WorldCat to find libraries that may hold this journal
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

  • ; ; - Journal of Applied Physics
    Differential scanning calorimetry (DSC) was used to determine the thermodynamic functions of the undercooled liquid and the amorphous phase with respect to the crystalline state of the Zr{sub 41.2}Ti{sub 13.8}Cu{sub 12.5}Ni{sub 10.0}Be{sub 22.5 }bulk metallic glass forming alloy. The specific heat capacities of this alloy in the undercooled liquid, the amorphous state and the crystal were determined. The differences in enthalpy, {Delta}{ital H}, entropy, {Delta}{ital S}, and Gibbs free energy, {Delta}{ital G}, between crystal and the undercooled liquid were calculated using the measured specific heat capacity data as well as the heat of fusion. The results indicate that the Gibbsmore » free energy difference between metastable undercooled liquid and crystalline solid, {Delta}{ital G}, stays small compared to conventional metallic glass forming alloys even for large undercoolings. Furthermore, the Kauzmann temperature, {ital T}{sub {ital K}}, where the entropy of the undercooled liquid equals to that of the crystal, was determined to be 560 K. The Kauzmann temperature is compared with the experimentally observed rate-dependent glass transition temperature, {ital T}{sub {ital g}}. Both onset and end temperatures of the glass transition depend linearly on the logarithm of the heating rate based on the DSC experiments. Those characteristic temperatures for the kinetically observed glass transition become equal close to the Kauzmann temperature in this alloy, which suggests an underlying thermodynamic glass transition as a lower bound for the kinetically observed freezing process.« less

  • ; ; ; ... - Journal of Chemical Physics
    A generic phenomenological theory of the glass transition is developed in the framework of a quasilinear formulation of the thermodynamics of irreversible processes. Starting from one of the basic principles of this science in its approximate form given by de Donder's equation, after a change of variables the temperature dependence of the structural parameter {xi}(T), the thermodynamic potentials {delta}G(tilde sign)(T), the thermodynamic functions and the time of molecular relaxation {tau} of vitrifying systems is constructed. In doing so, a new effect in the {delta}G(tilde sign)(T) course is observed. The analysis of the higher derivatives of the thermodynamic potential, and especiallymore » the nullification of the second derivative of the configurational specific heats {delta}C(tilde sign){sub p}(T) of the vitrifying liquid defines glass transition temperature T(tilde sign){sub g} and leads directly to the basic dependence of glass transition kinetics: the Frenkel-Kobeko-Reiner equation. The conditions guaranteeing the fulfillment of this equation specify the temperature dependence of the activation energy U(T,{xi}(tilde sign)) for viscous flow and give a natural differentiation of glass formers into fragile and strong liquids. The effect of thermal prehistory on the temperature dependence of both thermodynamic functions and kinetic coefficients is established by an appropriate separation of de Donder's equation. (c) 2000 American Institute of Physics.« less

  • ; ; - Proceedings of the Nation Academy of Sciences
    We consider the probability distribution for the fluctuations in the dynamical action of glass forming materials. We argue that the so-called glass transition is a manifestation of low action tails in these distributions where the entropy of trajectory space is sub-extensive in time. These low action tails are a consequence of dynamic heterogeneity and an indication of phase coexistence in trajectory space. The glass transition, where the system falls out of equilibrium, is then an order-disorder phenomenon in space-time occurring at a temperature T{sub g} which is a weak function of measurement time. We illustrate our perspective ideas with facilitatedmore » lattice models, and note how these ideas apply more generally.« less

  • ; ; ; ... - Physical Review, B: Condensed Matter
    carolyn BRODIN, B{umlt O}RJESSON, ENGBERG, TORELL, AND SOKOLOV RELAXATIONAL AND VIBRATIONAL DYNAMICS IN... The structural relaxation behavior of a strong glass former B{sub 2}O{sub 3} has been investigated over broad temperature (300{endash}1275 K) and frequency (0.5 GHz{endash}10 THz) ranges using depolarized light scattering. The spectra clearly show nonmonotonic temperature behavior with some dynamical crossover at about {ital T}{sub {ital c}}{approx_equal}800{endash}900 K. Above {ital T}{sub {ital c}} the spectra develop qualitatively according to the general scenario predicted by the mode-coupling theory (MCT), including a fast {beta} process and a much slower {alpha} process in addition to a vibrational contribution. However, theremore » is disagreement between the observed functional form of the fast relaxational dynamics and that predicted by MCT. The disagreement seems to be related to the influence of low-lying vibrational contributions, the so-called boson peak, which generally seems to be more pronounced in strong glass formers. Below {ital T}{sub {ital c}} the spectra do not follow MCT predictions, not even qualitatively; the main signature is a decrease of the level of the fast relaxation spectrum. Analysis in terms of an alternative phenomenological approach, in which the fast relaxation contribution is related to the damping of the vibrational modes (giving rise to the boson peak), reveals some crossover of the damping rate at about the same temperature {ital T}{sub {ital c}} as the crossover of the fast relaxation dynamics itself, and with similar temperature dependence as that recently reported for the Brillouin linewidth. We suggest that these variations are related to the temperature dependence of the relative strength of the fast relaxation. (Abstract Truncated)« less

  • ; ; ; ... - Journal of Applied Physics
    We study serrated flow dynamics during brittle-to-ductile transition induced by tuning the sample aspect ratio in a Zr-based metallic glass. The statistical analysis reveals that the serrated flow dynamics transforms from a chaotic state characterized by Gaussian-distribution serrations corresponding to stick-slip motion of randomly generated and uncorrelated single shear band and brittle behavior, into a self-organized critical state featured by intermittent scale-free distribution of shear avalanches corresponding to a collective motion of multiple shear bands and ductile behavior. The correlation found between serrated flow dynamics and plastic deformation might shed light on the plastic deformation dynamic and mechanism in metallicmore » glasses.« less