U. Buchenau

Neutron scattering study of the vibrations in vitreous silica and germania.

The incoherent approximation for the determination of the vibrational density of states of glasses from inelastic neutron or x-ray scattering data is extended to treat the coherent scattering. The method is applied to new room temperature measurements of vitreous silica and germania on the thermal time-of-flight spectrometer IN4 at the High Flux Reactor in Grenoble. The inelastic dynamic structure factor at the boson peak turns out to agree reasonably well with simulation results, but the long-wavelength fraction exceeds the expectation of the Debye model, in particular, in germania.

Neutron scattering evidence on the nature of the boson peak

Literature and unpublished neutron spectra of seven classical glass formers in the boson peak region are evaluated in terms of eigenvalue densities. The boson peak translates into a true maximum of the eigenvalue density, lying about a factor of two higher than the boson peak eigenvalue and followed by a slow decrease towards higher eigenvalues. We interpret the data in terms of a crossover from sound waves at low eigenvalues to a more or less constant eigenvalue density at high eigenvalues. The Ioffe–Regel limit of strong sound wave damping lies at the crossover eigenvalue λc, slightly higher than the boson peak. A four-parameter fit form based on the soft-potential model provides reasonable fits up to and including the beginning of the slow decrease. The parameters from the neutron data agree within their error bars with those determined from the low-temperature anomalies in the heat capacity and in the thermal conductivity. The results indicate that the strong scattering of sound waves in glasses is due to the interaction with the excess vibrational modes.

A new interpretation of dielectric data in molecular glass formers

Literature dielectric data of glycerol, propylene carbonate, and ortho-terphenyl show that the measured dielectric relaxation is a decade faster than the Debye expectation but still a decade slower than the breakdown of the shear modulus. From a comparison of time scales, the dielectric relaxation seems to be due to a process which relaxes not only the molecular orientation but also the entropy, the short range order, and the density. On the basis of this finding, we propose an alternative to the Gemant-DiMarzio-Bishop extension of the Debye picture.

An atomic mechanism for the boson peak in metallic glasses

The boson peak in metallic glasses is modelled in terms of local structural shear rearrangements. Using Eshelbys solution of the corresponding elasticity theory problem, one can calculate the saddle point energy of such a structural rearrangement. The neighborhood of the saddle point gives rise to soft resonant vibrational modes. One can calculate their density, their kinetic energy, their fourth-order potential term and their coupling to longitudinal and transverse sound waves.

The breakdown of the shear modulus at the glass transition

The glass transition is described in terms of thermally activated local structural rearrangements, the secondary relaxations of the glass phase. The interaction between these secondary relaxations leads to a much faster and much more dramatic breakdown of the shear modulus than without interaction, thus creating the impression of a separate primary process which in reality does not exist. The model gives a new view on the fragility and the stretching, two puzzling features of the glass transition.

Structural relaxation and highly viscous flow

The highly viscous flow is due to thermally activated Eshelby transitions which transform a region of the undercooled liquid to a different structure with a different elastic misfit to the viscoelastic surroundings. A self-consistent determination of the viscosity in this picture explains why the average structural relaxation time is a factor of eight longer than the Maxwell time. The physical reason for the short Maxwell time is the very large contribution of strongly strained inherent states to the fluidity (the inverse viscosity). At the Maxwell time, the viscous no-return processes coexist with the back-and-forth jumping retardation processes.

An Eshelby model for highly viscous flow

The shear flow and the dielectric alpha-process in molecular glass formers is modeled in terms of local structural rearrangements which reverse a strong local shear. Using Eshelbys solution of the corresponding elasticity theory problem (J. D. Eshelby, Proc. Roy. Soc. A241, 376 (1957)), one can calculate the recoverable compliance and estimate the lifetime of the symmetric double-well potential characterizing such a structural rearrangement. A full modeling of the shear relaxation spectra requires an additional parametrization of the barrier density of these structural rearrangements. The dielectric relaxation spectrum can be described as a folding of these relaxations with the Debye process.

Eshelby description of highly viscous flow—Half model, half theory

A recent description of the highly viscous flow ascribes it to irreversible thermally activated Eshelby transitions, which transform a region of the undercooled liquid to a different structure with a different elastic misfit to the viscoelastic surroundings. The description is extended to include reversible Eshelby transitions, with the Kohlrausch exponent β as a free parameter. The model answers several open questions in the field.

Dielectric and thermal relaxation in the energy landscape

We derive an energy landscape interpretation of dielectric relaxation times in undercooled liquids, comparing it to the traditional Debye and Gemant–DiMarzio–Bishop pictures. The interaction between different local structural rearrangements in the energy landscape explains qualitatively the recently observed splitting of the flow process into an initial and a final stage. The initial mechanical relaxation stage is attributed to hopping processes, the final thermal or structural relaxation stage to the decay of the local double-well potentials. The energy landscape concept provides an explanation for the equality of thermal and dielectric relaxation times. The equality itself is once more demonstrated on the basis of literature data for salol.

Relaxations in the glass phase of silica and of poly(methyl methacrylate)

Abstract Literature mechanical relaxation data of two glasses, vitreous silica and poly(methyl methacrylate) (PMMA), an amorphous polymer, are interpreted in terms of the Gilroy-Phillips model. For freauencies up to 1 GHz, one finds a temperature-independent barrier density function f(V) at all temperatures in the glass phase. If one looks at still higher freauencies, with the picosecond optical techniaue or with Brillouin, Raman and neutron scattering, one can sample the same barriers at a higher temperature. As long as the high-freauency measurements are made at Iow temperatures, up to about one fifth of the glass temperature, one finds again the same barrier density function. For higher temperatures, the barrier density function of the high-frequency data exceeds that determined at lower freauencies. This holds for the silica neutron data from the literature as well as for new neutron data on PMMA reported here. The finding supports earlier Raman results from other glasses in the literature. The deviation from the simplest form of the Gilroy-Phillips model is not a strong effect (at least not as long as one stays in the glass phase), but clearly measurable. Possible reasons for the deviation are discussed.