Vibrational Anomalies Research Articles

Quasi-localized vibrational modes, boson peak and sound attenuation in model mass-spring networks

We introduce an algorithm that constructs disordered mass-spring networks whose elastic properties mimic that of glasses by tuning the fluctuations of the local elastic properties, keeping fixed connectivity and controlling the prestress. In two dimensions, the algorithm reproduces the dependence of glasses’ vibrational properties, such as quasi-localised vibrational modes and Boson peak, on the degree of stability. The sound attenuation displays Rayleigh scattering and disorder-broadening regimes at different frequencies, and the attenuation rate decreases with increased stability. Our results establish a strong connection between the vibrational features of disordered solids and the fluctuations of the local elastic properties and provide a new approach to investigating glasses’ vibrational anomalies.

Experimental and theoretical revelation of a unique band topology in Sb[formula omitted]Te[formula omitted] topological insulator by substitution of Cu—A high pressure study

TI Sb1.9Cu0.1Te3 is an ideal platform for investigating such semiconducting to metal transition under extreme conditions. The unusual softening of two newly M1, M2 phonon modes combined with the sudden collapse in bond length, angle of succession, intralayer distance and the direct observation of band gap closure from theoretical density functional theory calculation validates a unique metal transition. To the best of our knowledge, the metallic transition pressure in the present observation is the lowest amongst the A2B3 TI family of compounds. This distinctive transition is stimulated by the p-d hybridization which is the concomitant effect of Cu and applied pressure. We also establish structural and vibrational anomalies from pressure induced angle dispersive synchrotron x-ray diffraction and Raman spectra of the bulk that signify changes in electronic topology of the Fermi surface. Our experimental observations on bulk corroborates an ETT (∼2.5 GPa) and 3 structural transitions in the present system.

Ab initio investigation of H-bond disordering in δ-AlOOH

\ensuremath{\delta}-AlOOH (\ensuremath{\delta}) is a high-pressure hydrous phase that participates in the deep geological water cycle. At 0 GPa, \ensuremath{\delta} has asymmetric hydrogen bonds (H bonds). Under pressure, it exhibits H-bond disordering, tunneling, and finally, H-bond symmetrization at \ensuremath{\sim}18 GPa. This study investigates these 300 K pressure-induced state changes in \ensuremath{\delta} with ab initio calculations. H-bond disordering in \ensuremath{\delta} was modeled using supercell multiconfiguration quasiharmonic calculations. We examine (a) energy barriers for proton jumps, (b) the pressure dependence of phonon frequencies, (c) 300 K compressibility, (d) neutron diffraction pattern anomalies, and (e) compare ab initio bond lengths with measured ones. Such thorough and systematic comparisons indicate that (a) proton ``disorder'' has a restricted meaning when applied to \ensuremath{\delta}. Nevertheless, H bonds are disordered between 0 and 8 GPa, and a gradual change in H-bond configuration results in enhanced compressibility. (b) Several structural and vibrational anomalies at \ensuremath{\sim}8 GPa are consistent with the disappearance of a particular (HOC-12) H-bond configuration and its change into another one (HOC-11*). (c) Between 8 and 11 GPa, H-bond configuration (HOC-11*) is generally ordered, at least in short- to midrange scale. (d) Between 11.5 and 18 GPa, H-bond lengths approach a critical value that impedes compression, resulting in decreased compressibility. In this pressure range, especially approaching H-bond symmetrization at \ensuremath{\sim}18 GPa, anharmonicity and tunneling should play an essential role in the proton dynamics. Further simulations accounting for these effects are desirable to clarify the protons' state in this pressure range.

Random quench predicts universal properties of amorphous solids

Amorphous solids display numerous universal features in their mechanics, structure, and response. Current models assume heterogeneity in mesoscale elastic properties, but require fine-tuning in order to quantitatively explain vibrational properties. A complete model should derive the magnitude and character of elastic heterogeneity from an initially structureless medium, through a model of the quenching process during which the temperature is rapidly lowered and the solid is formed. Here we propose a field-theoretic model of a quench, and compute structural, mechanical, and vibrational observables in arbitrary dimension d. This allows us to relate the properties of the amorphous solid to those of the initial medium, and to those of the quench. We show that previous mean-field results are subsumed by our analysis and unify spatial fluctuations of elastic moduli, long-range correlations of inherent state stress, universal vibrational anomalies, and localized modes into one picture.

Correlation between vibrational anomalies and emergent anharmonicity of the local potential energy landscape in metallic glasses

The boson peak (BP) is a universal feature in the Raman and inelastic scattering spectra of both disordered and crystalline materials. The current paradigm presents the boson peak as the result of a Ioffe-Regel crossover between ballistic (phonon) and diffusive-type excitations, where the loss of coherence of phonons is described as a purely harmonic process due to structural disorder. This "harmonic disorder" paradigm for the BP has never been challenged or tested at the atomistic level. Here, through a set of atomistically-resolved characterizations of amorphous metallic alloys, we uncover a robust inverse proportionality between the intensity of boson peak and the activation energy of excitations in the potential energy landscape (PEL). Larger boson peak is linked with shallower basins and lower activation barriers and, consequently, with strongly anharmonic sectors of the PEL. Numerical evidence from atomistic simulations indicates that THz atomic vibrations contributing the most to the BP in atomic glasses are strongly anharmonic, as evidenced through very large values of the atomic- and mode-resolved Gr\"{u}neisen parameter found for the atomic vibrations that constitute the BP. These results provide a direct bridge between the vibrational spectrum and the topology of the PEL in solids, and point towards a new "giant anharmonicity" paradigm for both generic disordered materials and for the phonon-glass problem in emerging materials for energy applications. In this sense, disorder and anharmonicity emerge as the two sides of the same coin.

Carbon nanowires under compression and their vibrational anomalies

Anomalous pressure dependence of Raman frequencies of carbon nanowires encapsulated in carbon nanotubes has been recently reported. Two hypotheses have been proposed to explain this phenomenon in linear carbon chains: softening of a carbon bond with pressure or charge transfer to the chain. However, carbon chains bend easily under stress, although stable structures under these conditions have yet to be discovered. In this study, we model linear and bent carbon nanowires under compression, including both stable and metastable structures. The structures, electronic properties, and vibrational frequencies are obtained through first-principles calculations within density functional theory. We find that polyyne, the dimerized linear ground-state structure of carbon chains at zero strain, is not stable under compression for an infinite carbon chain. Instead, the chain transforms into two possible configurations, a previously unknown three-dimensional helical shape or a two-dimensional sinusoidal shape. These structures can be modeled using an analytical atomistic force-constant model or with a continuum approach. In the continuum approach, an eigenvalue wave equation describes the energy and geometry of the chain. Moreover, this equation produces excited (metastable) structural states and can be applied to other one-dimensional systems. The wave equation formulation indicates that the much-pursued concept of Young's modulus in one-dimensional chains is ill-defined. Finally, the Raman anomaly under compression is not observed within the atomistic force-constant model contrary to assumptions in the literature. Instead, this anomaly can be understood using a model in which charge transfer between the nanotube and the nanowire occurs upon contact.

Distinction of charge transfer and Frenkel excitons in pentacene tracedviainfrared spectroscopy

The vibrational anomalies of pentacene molecules have been investigated in conjunction with the high-energy excitonic features. Self-trapped excitons have been distinguished from the others.

Unifying Description of the Vibrational Anomalies of Amorphous Materials.

The vibrational density of states D(ω) of solids controls their thermal and transport properties. In crystals, the low-frequency modes are extended phonons distributed in frequency according to Debye's law, D(ω)∝ω^{2}. In amorphous solids, phonons are damped, and at low frequency D(ω) comprises extended modes in excess over Debye's prediction, leading to the so-called boson peak in D(ω)/ω^{2} at ω_{bp}, and quasilocalized ones. Here we show that boson peak and phonon attenuation in the Rayleigh scattering regime are related, as suggested by correlated fluctuating elasticity theory, and that amorphous materials can be described as homogeneous isotropic elastic media punctuated by quasilocalized modes acting as elastic heterogeneities. Our numerical results resolve the conflict between theoretical approaches attributing amorphous solids' vibrational anomalies to elastic disorder and localized defects.

Comment on "Universal Origin of Boson Peak Vibrational Anomalies in Ordered Crystals and in Amorphous Materials".

In a recent article M. Baggioli and A. Zaccone (Phys. Rev. Lett. {\bf 112}, 145501 (2019)) claimed that an anharmonic damping, leading to a sound attenuation proportional to $\omega^2$ (Akhiezer-type damping) would imply a boson peak, i.e.\ a maximum in the vibrational density of states, divided by the frequency squared (reduced density of states). This would apply both to glasses and crystals.Here we show that this is not the case. In a mathematically correct treatment of the model the reduced density of states monotonously decreases, i.e.\ there is no boson peak. We further show that the formula for the would-be boson peak, presented by the authors, corresponds to a very short one-dimensional damped oscillator system. The peaks they show correspond to resonances, which vanish in the thermodynamic limit.

Disorder-induced vibrational anomalies from crystalline to amorphous solids

The origin of boson peak -- an excess of density of states over Debye's model in glassy solids -- is still under intense debate, among which some theories and experiments suggest that boson peak is related to van-Hove singularity. Here we show that boson peak and van-Hove singularity are well separated identities, by measuring the vibrational density of states of a two-dimensional granular system, where packings are tuned gradually from a crystalline, to polycrystals, and to an amorphous material. We observe a coexistence of well separated boson peak and van-Hove singularities in polycrystals, in which the van-Hove singularities gradually shift to higher frequency values while broadening their shapes and eventually disappear completely when the structural disorder $\eta$ becomes sufficiently high. By analyzing firstly the strongly disordered system ($\eta=1$) and the disordered granular crystals ($\eta=0$), and then systems of intermediate disorder with $\eta$ in between, we find that boson peak is associated with spatially uncorrelated random flucutations of shear modulus $\delta G/\langle G \rangle$ whereas the smearing of van-Hove singularities is associated with spatially correlated fluctuations of shear modulus $\delta G/\langle G \rangle$.

Machine-learning integrated glassy defect from an intricate configurational-thermodynamic-dynamic space

Optimizing materials' properties and functions by controlling defects in the crystalline phase has been a cornerstone of materials science and condensed matter physics. However, this paradigm has yet to be established in the broadly defined amorphous materials, which implies the identification of very subtle structural features in an otherwise uniformly disordered medium. Here we propose and define a new integrated glassy defect (IGD), based on machine learning strategy informed by atomistic physics, and also by an extremely wide configurational, thermodynamic, and dynamic variables space of the disordered state. The IGD simultaneously includes positional topology and vibrational features, as well as the local morphology of the potential energy landscape. This unprecedented combination gives rise to a much more comprehensive and more effective definition of the ``glassy defect,'' much beyond the conventional, purely structural input. IGD can be used not only as an efficient predictor of athermal plasticity but is also transferable to detect both short-time vibrational anomalies (the boson peak), and long-time relaxation and diffusion dynamics in glasses. The integrated strategy is instrumental to build the long-sought structure-property relationship in complex media.

A structural approach to vibrational properties ranging from crystals to disordered systems.

Many scientists generally attribute the vibrational anomalies of disordered solids to the structural disorder, which, however, is still under intense debate. Here we conduct simulations on two-dimensional packings with a finite temperature, whose structure is tuned from a crystalline configuration to an amorphous one, then the amorphous from very dense state to a relatively loose state. By measuring the vibrational density of states and the reduced density of states, we clearly observe the evolution of the boson peak with the change of the disorder and volume fractions. Meanwhile, to understand the structural origin of this anomaly, we identify the soft regimes of all systems with a novel machine-learning method, where the "softness", a local structural quantity, is defined. Interestingly, we find a strong monotonic relationship between the shape of the boson peak and the softness as well as its spatial heterogeneity, suggesting that the softness of a system may be a new structural approach to the anomalous vibrational properties of amorphous solids.

Universal Origin of Boson Peak Vibrational Anomalies in Ordered Crystals and in Amorphous Materials.

The vibrational spectra of solids, both ordered and amorphous, in the low-energy regime, control the thermal and transport properties of materials, from heat capacity to heat conduction, electron-phonon couplings, conventional superconductivity, etc. The old Debye model of vibrational spectra at low energy gives the vibrational density of states (VDOS) as proportional to the frequency squared, but in many materials the spectrum departs from this law which results in a peak upon normalizing the VDOS by frequency squared, which is known as the "boson peak." A description of the VDOS of solids (both crystals and glasses) is presented starting from first principles. Without using any assumptions whatsoever of disorder in the material, it is shown that the boson peak in the VDOS of both ordered crystals and glasses arises naturally from the competition between elastic mode propagation and diffusive damping. The theory explains the recent experimental observations of boson peak in perfectly ordered crystals, which cannot be explained based on previous theoretical frameworks. The theory also explains, for the first time, how the vibrational spectrum changes with the atomic density of the solid, and explains recent experimental observations of this effect.

Probing lattice dynamics and electron-phonon coupling in the topological nodal-line semimetal ZrSiS

Topological materials provide an exclusive platform to study the dynamics of relativistic particles in table-top experiments and offer the possibility of wide-scale technological applications. ZrSiS is a newly discovered topological nodal-line semimetal and has drawn enormous interests. In this report, we have investigated the lattice dynamics and electron-phonon interaction in single crystalline ZrSiS using Raman spectroscopy. Polarization and angle resolved measurements have been performed and the results have been analyzed using crystal symmetries and theoretically calculated atomic vibrational patterns along with phonon dispersion spectra. Wavelength and temperature dependent measurements show the complex interplay of electron and phonon degrees of freedom, resulting in resonant phonon and quasielastic electron scatterings through inter-band transitions. Our high-pressure Raman studies reveal vibrational anomalies, which were further investigated from the high-pressure synchrotron x-ray diffraction (HPXRD) spectra. From HPXRD, we have clearly identified pressure-induced structural transitions and coexistence of multiple phases, which also indicate possible electronic topological transitions in ZrSiS. The present study not only provides the fundamental information on the phonon subsystem, but also sheds some light in understanding the topological nodal-line phase in ZrSiS and other iso-structural systems.

Low-temperature anomalies of a vapor deposited glass

We investigate the low temperature properties of two-dimensional Lennard-Jones glass films, prepared in silico both by liquid cooling and by physical vapor deposition. We identify deep in the solid phase a crossover temperature $T^*$, at which slow dynamics and enhanced heterogeneity emerge. Around $T^*$, localized defects become visible, leading to vibrational anomalies as compared to standard solids. We find that on average, $T^*$ decreases in samples with lower inherent structure energy, suggesting that such anomalies will be suppressed in ultra-stable glass films, prepared both by very slow liquid cooling and vapor deposition.

Theory of heterogeneous viscoelasticity

We review a new theory of viscoelasticity of a glass-forming viscous liquid near and below the glass transition. In our model, we assume that each point in the material has a specific viscosity, which varies randomly in space according to a fluctuating activation free energy. We include a Maxwellian elastic term, and assume that the corresponding shear modulus fluctuates as well with the same distribution as that of the activation barriers. The model is solved in coherent potential approximation, for which a derivation is given. The theory predicts an Arrhenius-type temperature dependence of the viscosity in the vanishing frequency limit, independent of the distribution of the activation barriers. The theory implies that this activation energy is generally different from that of a diffusing particle with the same barrier height distribution. If the distribution of activation barriers is assumed to have the Gaussian form, the finite-frequency version of the theory describes well the typical low-temperature alpha relaxation peak of glasses. Beta relaxation can be included by adding another Gaussian with centre at much lower energies than that is responsible for the alpha relaxation. At high frequencies, our theory reduces to the description of an elastic medium with spatially fluctuating elastic moduli (heterogeneous elasticity theory), which explains the occurrence of the boson peak-related vibrational anomalies of glasses.

Heterogeneous Viscoelasticity: A Combined Theory of Dynamic and Elastic Heterogeneity.

We present a heterogeneous version of Maxwell's theory of viscoelasticity based on the assumption of spatially fluctuating local viscoelastic coefficients. The model is solved in coherent-potential approximation. The theory predicts an Arrhenius-type temperature dependence of the viscosity in the vanishing-frequency limit, independent of the distribution of the activation energies. It is shown that this activation energy is generally different from that of a diffusing particle with the same barrier-height distribution, which explains the violation of the Stokes-Einstein relation observed frequently in glasses. At finite but low frequencies, the theory describes low-temperature asymmetric alpha relaxation. As examples, we report the good agreement obtained for selected inorganic, metallic, and organic glasses. At high frequencies, the theory reduces to heterogeneous elasticity theory, which explains the occurrence of the boson peak and related vibrational anomalies.

A general anomaly detection approach applied to rolling element bearings via reduced-dimensionality transition matrix analysis

Rolling element bearings are vital components in most rotating machines. Bearings often operate in harsh environments where manufacturing imperfections, misalignments, and fatigue can result in reduced component lifespan. These failures are often preceded by changes in the normal vibration of the system. Modeling and detecting these vibrational anomalies is common practice in predicting machine failure. This paper develops and implements a novel approach to detecting bearing vibration anomalies in the time–frequency domain. The performance of the new approach is quantified using both simulated and experimental bearing vibration data. In these ground-truth experiments, the proposed time–frequency method successfully detects anomalies (>98% true positive) using short time spans (<0.1 s) with low false alarm rates (<1% false positive). Using experimental data, this time–frequency approach is shown to outperform one-dimensional time series analysis techniques.

Low-Frequency Vibrational Modes Anomalies and Rigidity: A Key to Understanding the Glass and the Electronic Properties of Flexible Materials from a Topological Perspective

Using rigidity (constraint) theory of glasses, the effects of low frequency vibrational modes anomalies in the glass transition are studied. It is discussed how the possibility of tailoring by chemical doping the number of low frequency modes gives clues about how to determine the glass transition temperature and glass formation ability. In particular, we present the effects of floppy modes in the specific heat, entropy , internal energy below glass transition, as well as a discussion of the thermodynamical effects above the glass transition. All the previous results can be extended to include the Boson peak, since it can also be understood from a rigidity point of view as a dilution of bonds in an over-constrained network. Finally, we discuss how a new subject is emerging: floppy modes effects in the electronic properties of flexible systems. Such relationship provides a natural connection with topological insulators and two dimensional materials like graphene.

Theory of vibrational anomalies in glasses

The theory of elasticity with spatially fluctuating elastic constants (heterogeneous-elasticity theory) is reviewed. It is shown that the vibrational anomalies associated with the boson peak can be qualitatively and quantitatively explained in terms of this theory. Two versions of a mean-field theory for solving the stochastic equation of motion are presented: the coherent-potential approximation (CPA) and the self-consistent Born approximation (SCBA). It is shown that the latter is included in the former in the Gaussian and weak-disorder limit. We are able to discuss and explain cases in which the change of the vibrational spectrum by varying an external parameter can be accounted for by changing the Debye frequency (elastic transformation) and cases in which this is not possible. In the latter case a change in the distribution of the elastic moduli has occurred.