Regel Crossover Research Articles

Universal Vibrational Properties of Disordered Systems in Terms of the Theory of Random Correlated Matrices

It has been shown that a correlated Wishart ensemble can be used to study the general vibrational properties of stable amorphous solids, where the energy is translationally invariant. The vibrational density of states and the dynamic structure factor of the system have been determined using the random matrix theory. The results indicate the existence of the Ioffe–Regel crossover between low-frequency propagating phonons and diffusons at higher frequencies. The presented vibrational density of states demonstrates the boson peak at the frequency close to the Ioffe—Regel crossover.

Enhancement and anticipation of the Ioffe-Regel crossover in amorphous/nanocrystalline composites.

Nanocomposites made of crystalline nanoinclusions embedded in an amorphous matrix are at the forefront of current research for energy harvesting applications. However, the microscopic mechanisms leading alternatively to an effectively reduced or enhanced thermal transport still escape understanding. In this work, we present a molecular dynamics simulation study of model systems, where for the first time we combine a microscopic investigation of phonon dynamics with the macroscopic thermal conductivity calculation, to shed light on thermal transport in these materials. We clearly show that crystalline nanoinclusions represent a novel scattering source for vibrational waves, modifying the nature of low energy vibrations and significantly anticipating the propagative-to-diffusive crossover (Ioffe-Regel), usually located at energies of few THz in amorphous materials. Moreover, this crossover position can be tuned by changing the elastic contrast between nanoinclusions and the matrix, and anticipated by a factor as large as 10 for a harder inclusion. While the propagative contribution to thermal transport is drastically reduced, the calculated thermal conductivity is not significantly affected in the chosen system, as the diffusive contribution dominates heat transport when all phonons are thermally populated. These findings allow finally to understand the panoply of contradictory results reported on thermal transport in nanocomposites and give clear indications to the characteristics that the parent phases should have for efficiently reducing heat transport in a nanocomposite.

Magnetic relaxation in Zn(PO3)2·Er(PO3)3 glass

The results of experimental studies of alternating (ac) magnetic susceptibility and specific heat of Zn(PO3)2·Er(PO3)3 glass are reported. Despite a high concentration of magnetic Er(III) ions the analysis of ac susceptibility ruled out the formation of a spin glass state in the used range of temperatures. Two relaxation processes were identified. The first one is thermally activated with a crossover in its temperature dependence observed at nominally 7K. The relaxation at lower temperatures seems to be governed by a direct process with pronounced effect of phonon bottleneck. Striking deceleration of spin dynamics with increasing temperature found above 7K is tentatively attributed to overcoming Ioffe – Regel crossover and strong scattering of acoustic phonons on local modes. Simplified prediction derived from a soft-mode-dynamics model confirms the presence of the boson peak observed in specific heat data and reasonably predicts the temperature of the crossover. The second process is consistent with a cross – tunneling relaxation. The obtained results suggest that magnetic doping of glasses and studying magnetic relaxation may represent an alternative tool for the investigation of lattice modes in glasses.

Origin of boson peak in glasses: Role of Ioffe–Regel crossover and atomic soft modes

A theoretical ‘ complete soft-mode-dynamics’ model of the origin and properties of the boson peak accompanied by a high-frequency sound, observed in glasses of a certain type, is described. The origin is determined by interaction of non-acoustic vibrations with acoustic phonons and a Ioffe–Regel crossover for their inelastic scattering. The non-acoustic excitations are associated with vibrations of atomic soft-mode ‘defects’. Two types of boson peak can be predicted in agreement with experiments.

Vibrational behavior of a realistic amorphous-silicon model

The vibrational properties of a high-quality realistic model of amorphous silicon are examined. The longitudinal and transverse dynamical structure factors are calculated, and fitted to a damped harmonic oscillator (DHO) function. The width Γ of the best-fit DHO to the longitudinal dynamical structure factor scales approximately as k 2 for wavevectors k ≲ 0.55 Å −1, which is above the Ioffe–Regel crossover frequency separating the propagating and diffusing regimes, occurring at k = 0.38 ± 0.03 Å −1. Using the DHO function as a fitting function for the transverse dynamical structure factor (without theoretical justification), gives a dependence of Γ ∝ k α with α ∼ 2.5 for wavevectors k ≲ 0.7 Å −1. There was no evidence for Γ ∝ k 4 behavior for either polarization.

Acoustic damping in Li2O–2B2O3 glass observed by inelastic X-ray and optical Brillouin scattering

The dynamic structure factor of lithium-diborate glass has been measured at several values of the momentum transfer Q using high resolution inelastic X-ray scattering. Much attention has been devoted to the low-Q-range, below the observed Ioffe–Regel crossover qIR≃2.1nm−1. We find that below qIR, the linewidth of longitudinal acoustic waves increases with a high power of either Q, or of the frequency Ω, up to the crossover frequency ΩIR≃9meV that nearly coincides with the center of the boson peak. This new finding strongly supports the view that resonance and hybridization of acoustic waves with a distribution of rather local low frequency modes forming the boson peak is responsible for the end of acoustic branches in strong covalent glasses. Further, we present high resolution Brillouin light-scattering data obtained at much lower frequencies on the same sample. These clearly rule out a simple Ω2-dependence of the acoustic damping over the entire frequency range.

Theory of resonant absorption of THz frequency waves by boson peak excitations in glasses

A resonant mechanism is predicted for the absorption of ultrasonic and electromagnetic waves of THz frequencies in glasses exhibiting both a boson peak and ‘high frequency sound’. The absorption is due to resonant transitions for harmonic excitations related to soft modes, determining the THz frequency dynamics of such glasses. The frequency dependence of the absorption coefficient exhibits a broad peak similar to the boson peak, related to a Ioffe–Regel crossover. For sufficiently low temperatures (still above a few K), the predicted qualitative behavior of the absorption coefficient can be observed in experiment. Furthermore, the as yet unknown frequency dependence of the large width of ill-defined excitations, in the Ioffe–Regel crossover, could be found by comparing the theoretical expression for the predicted absorption coefficient with experimental results.

THz frequency dynamics related to soft atomic modes in glasses

The soft-mode-dynamics theory is presented for the vibrational THz frequency dynamics and excitations for glasses exhibiting both the boson peak and ‘high frequency sound’ in scattering spectra. The spectrum of well-defined excitations for the dynamics is found to consist of two branches separated by a narrow ‘gap’. The eigenvalue density-of-states and the reduced density-of-states of the excitations are presented and shown to exhibit features similar to those of the boson peak and ‘high frequency sound’. The properties are due to a Ioffe–Regel crossover and related ill-defined excitations.

Calculations of the generalized dynamic structure factor for amorphous silicon

In an extension of our previous studies, a normal mode analysis is performed for a 4096 atom structural model, of cubic cell size L=44 Å, of amorphous silicon within the Stillinger Weber potential. The peaks in dynamic structure factor quantities S L ( Q, ω) and S T ( Q, ω), where L and T refer to projections of eigenvectors onto vectors parallel and perpendicular to Q , are studied. An attempt is made to estimate Ioffe–Regel crossover frequencies. In agreement with a previous estimate for the commencement of diffusons a frequency corresponding to 17 meV is found for the transverse-like Ioffe–Regel crossover. S L for fixed Q, is found to be reasonably Lorentzian up to Q=3 (2π/ L). S L functions which have peak-height frequencies above the transverse acoustic maximum frequency ω T,max are strongly skewed towards higher frequencies. The Lorentzian breadths below and above ω T,max are roughly of the forms Q 2 and Q 4, respectively. Finally, a small positive dispersion describes the peak positions of S L , in qualitative agreement with related studies on other model glassy systems.

Soft-mode dynamics model of boson peak and high frequency sound in glasses: “inelastic” Ioffe–Regel crossover and strong hybridization of excitations

A theoretical model of the vibrational “high frequency dynamics”, including both the boson peak (BP) and high frequency sound (HFS), is proposed for a glass. The model is an elastic continuum containing acoustic vibrations interacting with soft-mode vibrational excitations. The interaction gives rise to an “inelastic” Ioffe–Regel crossover (IRC) and related strong hybridization of the two types of excitations. The spectrum of the renormalized excitations looks as if the acoustic branch is broken into two parts separated by a narrow pseudogap related to the IRC states. For these excitations, the density of states is approximately calculated in accord with the definition of the IRC, which may exhibit features similar to those of the BP and HFS.

Density of states of interacting quasilocal harmonic modes in glasses

We have established for the first time that as a result of a bilinear coupling between quasilocal harmonic modes and phonons in glasses there should be always a correlation between the position of the boson peak and the Ioffe–Regel crossover frequency for phonons. Above this frequency, phonons (i.e. usual plane waves) cease to exist. At the same frequency the density of states of the quasilocal harmonic modes, as a result of their interaction (and strong level repulsion), transforms into a universal linear function of the frequency. As a result the new harmonic modes become completely delocalized and have a diffusive nature. We show that existing experimental data are in excellent agreement with these predictions.

Vibrations in disordered systems

Vibrational excitations in disordered systems have been investigated by numerical simulation by molecular dynamics of realistic models of glasses, and by analytical study using the coherent potential approximation of force-constant-disordered lattices. It is found that the boson peak arises from disorder-induced, level-repelling effects. Its frequency is associated with the Ioffe–Regel crossover between weak- and strong-scattering regimes, and not with vibrational localization, which occurs only at the extremities of vibrational bands (except at the bottom of the acoustic band). A zero-energy singularity in the energy density of states is found in an instantaneous normal-mode analysis of molecular-dynamics models in the liquid state, as well as in mechanically unstable disordered lattices.

The vibrational modes of glasses

Our recent experimental observations on the harmonic vibrational modes of glasses are presented. Emphasis is placed on normal and densified silica. These results are discussed within the broader current knowledge, including thermal properties and other spectroscopic data that are critically assessed. We find that propagating acoustic modes enter a regime of strong scattering as their wavelength is reduced, and that this leads to an Ioffe–Regel crossover at frequencies of the order of the terahertz, corresponding to wavelengths of several nanometers. At similar frequencies, an excess in the density of states of optical modes, generally called the Boson peak, is observed. Hyper-Raman spectroscopy on these modes clearly shows that in silica they are due to the rocking of small groups of tetrahedra. These findings provide unique and unexpected information on the structure of glasses at the extended length scale, about which so little is known otherwise. The strong elastic inhomogeneity found at this scale might be decisive in determining glass properties, and even stability, and this will justify further studies.