Observation of large momentum phononlike modes in glasses

Investigation of anisotropy in the collective dynamics and thermal diffusivity in the phenyl pyrimidine liquid crystal

Liquid crystals (LCs) are unique heat transfer media that exhibit large anisotropy in thermal properties depending on the direction of the director (n) of the LC state. This phenomenon is the basis of thermal conduction in ordered soft materials, and has been extensively studied to understand thermal conduction in soft materials. In this study, we used inelastic x-ray scattering (IXS) to investigate the anisotropic thermal diffusivity and collective dynamics in the terahertz region of a pyrimidine-type LC (PYP8O8). The dispersion relations at several frequencies corresponding to the LC state were analyzed in the directions parallel and perpendicular to n. The results showed that there was a significant difference between the anisotropy of the sound velocity and that of the attenuation coefficient (Γ) estimated from the shape parameter of the IXS spectrum. The results for the linewidth of inelastic excitation show Q^{2} dependence that is far beyond the viscoelastic relaxation of the system, and the anisotropy in the collective dynamics predicted by Forster et al. [Phys. Rev. Lett. 26, 1016 (1971)10.1103/PhysRevLett.26.1016] in the hydrodynamic region can be extensively applied to the more localized collective motion of LC systems.

Practical measurement of the energy resolution for meV-resolved inelastic X-ray scattering

Several different ways of measuring the energy resolution for meV-resolved inelastic X-ray scattering (IXS) are compared: using scattering from poly(methyl methacrylate), PMMA, using scattering from borosilicate glass (Tempax), and using powder diffraction from aluminium. All of these methods provide a reasonable first approximation to the energy resolution, but, also, in all cases, inelastic contributions appear over some range of energy transfers. Over a range of ±15 meV energy transfer there is good agreement between the measurements of PMMA and Tempax at low temperature, and room-temperature powder diffraction from aluminium, so we consider this to be a good indication of the true resolution of our ∼1.3 meV spectrometer. The resolution over a wider energy range is self-consistently determined using the temperature, momentum and sample dependence of the measured response. The inelastic contributions from the PMMA and Tempax, and their dependence on momentum transfer and temperature, are then quantitatively investigated. The resulting data allow us to determine the resolution of our multi-analyzer array efficiently using a single scan. The importance of this procedure is demonstrated by showing that the results of the analysis of a spectrum from a glass are changed by using the properly deconvolved resolution function. The impact of radiation damage on the scattering from PMMA and Tempax is also discussed.

Sound damping in soft particle packings: the interplay between configurational disorder and inelasticity

We numerically investigate sound damping in disordered two-dimensional soft particle packings. We simulate evolution of standing waves of particle displacements and analyze time correlation functions of particle velocities and power spectra. We control the strength of inelastic interactions between the particles in contact to show how the inelasticity affects anomalous sound characteristics of disordered systems: Increasing the strength of inelastic interactions, we find that (i) sound softening vanishes and (ii) attenuation coefficients exhibit a transition from the Rayleigh law to quadratic growth. We also report (iii) how the Ioffe-Regel limit frequencies depend on the strength of inelasticity as useful information for experiments and applications of the sound in disordered media. Our findings suggest that sound damping in soft particle packings is determined by the interplay between elastic heterogeneities and inelasticity.

Heat transport in model jammed solids

We calculate numerically the normal modes of vibrations in three-dimensional jammed packings of soft spheres as a function of the packing fraction and obtain the energy diffusivity, a spectral measure of transport that controls sound propagation and thermal conductivity. The crossover frequency between weak and strong phonon scattering is controlled by the coordination and shifts to zero as the system is decompressed toward the critical packing fraction at which rigidity is lost. We present a scaling analysis that relates the packing fraction dependence of the crossover frequency to the anomalous scaling of the shear modulus with compression. Below the crossover, the diffusivity displays a power-law divergence with inverse frequency consistent with Rayleigh law, which suggests that the vibrational modes are primarily transverse waves, weakly scattered by disorder. Above it, a large number of modes appear whose diffusivity plateaus at a nearly constant value before dropping to zero above the localization frequency. The thermal conductivity of a marginally jammed solid just above the rigidity threshold is calculated and related to the one measured experimentally at room temperature for most glasses.

Hydration structures near finite-sized nanoscopic objects reconstructed using inelastic x-ray scattering measurements

Recent work has shown that it is possible to use high resolution dynamical structure factor S(q,ω) data measured with inelastic x-ray scattering to reconstruct the Green's function of water, which describes its dynamical density response to a point charge. Here, we generalize this approach and describe a strategy for reconstructing hydration behavior near simple charge distributions with excluded volumes, with the long term goal of engaging hydration processes in complex molecular systems. We use this Green's function based imaging of dynamics method to generate hydration structures and show that they are consistent with those of well-studied model systems.

Evidence for a crossover in the frequency dependence of the acoustic attenuation in vitreous silica

We report measurements of the sound attenuation coefficient in vitreous silica, for sound waves of wavelength between 50 and 80 nm, performed with the new inelastic UV light scattering technique. These data indicate that in silica glass a crossover between a temperature-dependent (at low frequency) and a temperature-independent (at high frequency) acoustic attenuation mechanism occurs at Q approximately equal to 0.15 nm(-1). The absence of any signature in the static structure factor at this Q value suggests that the observed crossover should be associated with local elastic constant fluctuations.

Dynamical susceptibility of glass formers: contrasting the predictions of theoretical scenarios

We compute analytically and numerically the four-point correlation function that characterizes nontrivial cooperative dynamics in glassy systems within several models of glasses: elastoplastic deformations, mode-coupling theory (MCT), collectively rearranging regions (CRR's), diffusing defects, and kinetically constrained models (KCM's). Some features of the four-point susceptibility chi(4) (t) are expected to be universal: at short times we expect a power-law increase in time as t(4) due to ballistic motion (t(2) if the dynamics is Brownian) followed by an elastic regime (most relevant deep in the glass phase) characterized by a t or sqrt[t] growth, depending on whether phonons are propagative or diffusive. We find in both the beta and early alpha regime that chi(4) approximately t(mu), where mu is directly related to the mechanism responsible for relaxation. This regime ends when a maximum of chi(4) is reached at a time t= t(*) of the order of the relaxation time of the system. This maximum is followed by a fast decay to zero at large times. The height of the maximum also follows a power law chi(4) (t(*)) approximately t(*lambda). The value of the exponents mu and lambda allows one to distinguish between different mechanisms. For example, freely diffusing defects in d=3 lead to mu=2 and lambda=1 , whereas the CRR scenario rather predicts either mu=1 or a logarithmic behavior depending on the nature of the nucleation events and a logarithmic behavior of chi(4) (t(*)) . MCT leads to mu=b and lambda=1/gamma , where b and gamma are the standard MCT exponents. We compare our theoretical results with numerical simulations on a Lennard-Jones and a soft-sphere system. Within the limited time scales accessible to numerical simulations, we find that the exponent mu is rather small, mu<1 , with a value in reasonable agreement with the MCT predictions, but not with the prediction of simple diffusive defect models, KCM's with noncooperative defects, and CRR's. Experimental and numerical determination of chi(4) (t) for longer time scales and lower temperatures would yield highly valuable information on the glass formation mechanism.

High frequency dynamics in a monatomic glass

The high frequency dynamics of glassy selenium has been studied by inelastic x-ray scattering at beam line BL35XU (SPring-8). The high quality of the data allows one to pinpoint the existence of a dispersing acoustic mode for wave vectors (Q) of 1.5<Q<12.5 nm(-1), helping to clarify a previ-ous contradiction between experimental and numerical results. The sound velocity shows a positive dispersion, exceeding the hydrodynamic value by approximately 10% at Q<3.5 nm(-1). The Q2 dependence of the sound attenuation Gamma(Q), reported for other glasses, is found to be the low-Q limit of a more general Gamma(Q) proportional, variant Omega(Q)(2) law, which applies also to the higher Q region, where Omega(Q) proportional, variant Q no longer holds.

Jamming at zero temperature and zero applied stress: the epitome of disorder

We have studied how two- and three-dimensional systems made up of particles interacting with finite range, repulsive potentials jam (i.e., develop a yield stress in a disordered state) at zero temperature and zero applied stress. At low packing fractions phi, the system is not jammed and each particle can move without impediment from its neighbors. For each configuration, there is a unique jamming threshold phi(c) at which particles can no longer avoid each other, and the bulk and shear moduli simultaneously become nonzero. The distribution of phi(c) values becomes narrower as the system size increases, so that essentially all configurations jam at the same packing fraction in the thermodynamic limit. This packing fraction corresponds to the previously measured value for random close packing. In fact, our results provide a well-defined meaning for "random close packing" in terms of the fraction of all phase space with inherent structures that jam. The jamming threshold, point J, occurring at zero temperature and applied stress and at the random-close-packing density, has properties reminiscent of an ordinary critical point. As point J is approached from higher packing fractions, power-law scaling is found for the divergence of the first peak in the pair correlation function and in the vanishing of the pressure, shear modulus, and excess number of overlapping neighbors. Moreover, near point J, certain quantities no longer self-average, suggesting the existence of a length scale that diverges at J. However, point J also differs from an ordinary critical point: the scaling exponents do not depend on dimension but do depend on the interparticle potential. Finally, as point J is approached from high packing fractions, the density of vibrational states develops a large excess of low-frequency modes. Indeed, at point J, the density of states is a constant all the way down to zero frequency. All of these results suggest that point J is a point of maximal disorder and may control behavior in its vicinity-perhaps even at the glass transition.

Phonon interpretation of the 'boson peak' in supercooled liquids

Glasses are amorphous solids, in the sense that they display elastic behaviour. In crystalline solids, elasticity is associated with phonons, which are quantized vibrational excitations. Phonon-like excitations also exist in glasses at very high (terahertz; 10(12) Hz) frequencies; surprisingly, these persist in the supercooled liquids. A universal feature of such amorphous systems is the boson peak: the vibrational density of states has an excess compared to the Debye squared-frequency law. Here we investigate the origin of this feature by studying the spectra of inherent structures (local minima of the potential energy) in a realistic glass model. We claim that the peak is the signature of a phase transition in the space of the stationary points of the energy, from a minima-dominated phase (with phonons) at low energy to a saddle-point-dominated phase (without phonons). The boson peak moves to lower frequencies on approaching the phonon-saddle transition, and its height diverges at the critical point. Our numerical results agree with the predictions of euclidean random matrix theory on the existence of a sharp phase transition between an amorphous elastic phase and a phonon-free one.

Low frequency dynamics of disordered XY spin chains and pinned density waves: from localized spin waves to soliton tunneling

A long-standing problem of the low-energy dynamics of a disordered XY spin chain is reexamined. The case of a rigid chain is studied, where the quantum effects can be treated quasiclassically. It is shown that, as the frequency decreases, the relevant excitations change from localized spin waves to two-level systems to soliton-antisoliton pairs. The linear-response correlation functions are calculated. The results apply to other periodic glassy systems such as pinned density waves, planar vortex lattices, stripes, and disordered Luttinger liquids.

Microscopic dynamics of molecular liquids and glasses: role of orientations and translation-rotation coupling

We investigate the dynamics of a fluid of dipolar hard spheres in its liquid and glassy phases, with emphasis on the microscopic time or frequency regime. This system shows rather different glass transition scenarios related to its rich equilibrium behavior, which ranges from a simple hard sphere fluid to long range ferroelectric orientational order. In the liquid phase close to the ideal glass transition line and in the glassy regime a medium range orientational order occurs leading to a softening of an orientational mode. To investigate the role of this mode we use the molecular mode-coupling equations to calculate the spectra straight phi"lm(q,omega) and chi"lm(q,omega). In the center of mass spectra straight phi"00(q,omega) and chi"00(q,omega) we found, besides a high frequency peak at omega(hf), a peak at omega(op), about one decade below omega(hf) x omega(op) has almost no q dependence and exhibits an "isotope" effect omega(op) proportional to I(-1/2), with I the moment of inertia. We give evidence that the existence of this peak is related to the occurrence of medium range orientational order. It is shown that some of these features also exist for schematic mode coupling models.

Vibrational spectrum of topologically disordered systems

The topological nature of the disorder of glasses and supercooled liquids strongly affects their high-frequency dynamics. In order to understand its main features, we analytically studied a simple topologically disordered model, where the particles oscillate around randomly distributed centers, interacting through a generic pair potential. We present results of a resummation of the perturbative expansion in the inverse particle density for the dynamic structure factor and density of states. This gives accurate results for the range of densities found in real systems.

Nature of the short wavelength excitations in vitreous silica: An X-Ray brillouin scattering study

The dynamical structure factor [ S(Q,E)] of vitreous silica has been measured by inelastic x-ray scattering varying the exchanged wave vector ( Q) at fixed exchanged energy ( E)-an experimental procedure that, contrary to the usual one at constant Q, provides spectra with much better identified inelastic features. This allows us to obtain the first direct evidence of Brillouin peaks in the S(Q,E) of SiO2 at energies above the boson peak (BP) energy, a finding that excludes the possibility that the BP marks the transition from propagating to localized dynamics in glasses.

Experimental evidence of the acousticlike character of the high frequency excitations in glasses

The dynamic structure factor S(Q,E) of glassy glycerol has been measured by inelastic x-ray scattering as a function of momentum transfer Q and at constant energy transfer E. This allows one to establish independently from specific models of S(Q,E) the following: (i) Propagating collective excitations exist in glasses at high Q. (ii) Their dispersion up to E higher than E(BP) (the boson peak energy) confirms that E(BP) is not the onset of modes localization. (iii) The observation of an almost Q independent plateau on the high Q side of the Brillouin peak supports numerical simulations on glasses, describing the vibrational eigenvectors in terms of acousticlike and "random" components.

Dynamical structure factor in disordered systems

We study the spectral width as a function of the external momentum for the dynamical structure factor of a disordered harmonic solid, considered as a toy model for supercooled liquids and glasses. In the contexts of both the single-link coherent potential approximation and a single-defect approximation, two different regimes are clearly identified: if the density of states at zero energy is zero, the usual p(4) law is recovered for small momentum. On the contrary, if the disorder induces a nonvanishing density of states at zero energy, a linear behavior is obtained. The dynamical structure factor is numerically calculated in lattices as large as 96(3) and satisfactorily agrees with the analytical computations.

Evolution of vibrational excitations in glassy systems

The equations of the mode-coupling theory (MCT) for ideal liquid-glass transitions are used for a discussion of the evolution of the density-fluctuation spectra of glass-forming systems for frequencies within the dynamical window between the band of high-frequency motion and the band of low-frequency-structural-relaxation processes. It is shown that the strong interaction between density fluctuations with microscopic wavelength and the arrested glass structure causes an anomalous-oscillation peak, which exhibits the properties of the so-called boson peak. It produces an elastic modulus which governs the hybridization of density fluctuations of mesoscopic wavelength with the boson-peak oscillations. This leads to the existence of high-frequency sound with properties as found by x-ray-scattering spectroscopy of glasses and glassy liquids. The results of the theory are demonstrated for a model of the hard-sphere system. It is also derived that certain schematic MCT models, whose spectra for the stiff-glass states can be expressed by elementary formulas, provide reasonable approximations for the solutions of the general MCT equations.