Vibrational Instabilities Research Articles

Vibrational instabilities in multilayer graphene and graphite: Effects of strain and number of layers

We study the rippling instabilities of multilayer graphene and graphite as a function of strain and number of layers using density-functional theory and density-functional perturbation theory calculations. We find that, for multilayer graphene, a small but finite compressive strain is needed to induce a rippling instability, signaled by the onset of imaginary frequencies near the center of the Brillouin zone. For monolayer graphene, this critical strain is zero within numerical uncertainty. Using insights from continuum elasticity theory, we fit the phonon dispersion of the ZA mode near the zone center to a function ${\ensuremath{\omega}}^{2}(q)={C}_{2}{q}^{2}+{C}_{4}{q}^{4}$ and determine the ${C}_{2}$ and ${C}_{4}$ coefficients as a function of strain and number of layers. In particular, the ${C}_{2}$ coefficient is positive for multilayers in the absence of strain and shows a linear dependence with strain. It assumes negative values for compressive strains beyond a critical value and it is responsible for the appearance of imaginary frequencies in the ZA mode. We discuss these results in light of both continuum and atomistic approaches. Critical parameters vary smoothly with the number of layers from monolayer graphene (two-dimensional) to graphite (three-dimensional).

Anharmonic Lattice Dynamics in Sodium Ion Conductors.

We employ terahertz-range temperature-dependent Raman spectroscopy and first-principles lattice dynamical calculations to show that the undoped sodium ion conductors Na3PS4 and isostructural Na3PSe4 both exhibit anharmonic lattice dynamics. The anharmonic effects in the compounds involve coupled host lattice–Na+ ion dynamics that drive the tetragonal-to-cubic phase transition in both cases, but with a qualitative difference in the anharmonic character of the transition. Na3PSe4 shows an almost purely displacive character with the soft modes disappearing in the cubic phase as the change in symmetry shifts these modes to the Raman-inactive Brillouin zone boundary. Na3PS4 instead shows an order–disorder character in the cubic phase, with the soft modes persisting through the phase transition and remaining Raman active in the cubic phase, violating Raman selection rules for that phase. Our findings highlight the important role of coupled host lattice–mobile ion dynamics in vibrational instabilities that are coincident with the exceptional conductivity of these Na+ ion conductors.

A large field-of-view high-resolution hard x-ray microscope using polymer optics.

We present an effective approach using a matched pair of polymer-based condenser-objective lenses to build a compact full-field x-ray microscope with a high spatial resolution. A unique condenser comprising arrays of high-aspect-ratio prisms with equilateral cross section is used for uniformly illuminating samples over a large field of view (FOV) from all angles, which match the acceptance of an objective made of interdigitated orthogonal rows of one-dimensional lenses. State-of-the-art Talbot grating interferometry used to characterize these lenses for the first time revealed excellent focusing properties and minimal wavefront distortions. Using a specific lens pair designed for 20 keV x rays, short-exposure times, and image registration with a cross-correlation technique, we circumvent vibrational instabilities to obtain distortion-free images with a uniform resolution of 240 nm (smallest resolvable line pair) over a large FOV, 80 × 80 µm2 in extent. The results were contrasted with those collected using commercial two-dimensional parabolic lenses with a smaller FOV. This approach implemented on a diffractometer would enable diffraction-contrast or dark-field microscopy for fast observations of "mesoscopic" phenomena in real space complementing reciprocal-space studies using diffraction on the same instrument.

Connection between vibrational instabilities of molecules in surface-enhanced Raman spectroscopy and Raman lasing

To observe a vibrational instability in a molecule or Raman lasing, the molecules should be placed in a resonator and illuminated by a laser. Both these phenomena are self-oscillations of either photons in a resonator or nuclei in molecules. We show that, thanks to the coupling of the forced oscillations of electrons in a molecule with its nucleus vibrations, these two effects are manifestations of the same phenomenon. When the ratio of damping rates of the molecule and the resonator is large, the number of coherent photons is also large, causing Raman lasing. In this case, the number of quanta of the coherent molecular vibrations is negligible. In the opposite case, the number of coherent vibration quanta is large, causing vibrational instability. This leads to the nonlinear response in Raman scattering, which was recently observed in a surface-enhanced Raman spectroscopy (SERS) experiment [A. Lombardi et al., Phys. Rev. X 8, 011016 (2018)].

Hierarchical quantum master equation approach to electronic-vibrational coupling in nonequilibrium transport through nanosystems: Reservoir formulation and application to vibrational instabilities

We present a novel hierarchical quantum master equation (HQME) approach which provides a numerically exact description of nonequilibrium charge transport in nanosystems with electronic-vibrational coupling. In contrast to previous work [Phys. Rev. B $\bf{94}$, 201407 (2016)], the active vibrational degrees of freedom are treated in the reservoir subspace and are integrated out. This facilitates applications to systems with very high excitation levels, for example due to current-induced heating, while properties of the vibrational degrees of freedom, such as the excitation level and other moments of the vibrational distribution function, are still accessible. The method is applied to a generic model of a nanosystem, which comprises a single electronic level that is coupled to fermionic leads and a vibrational degree of freedom. Converged results are obtained in a broad spectrum of parameters, ranging from the nonadiabatic to the adiabatic transport regime. We specifically investigate the phenomenon of vibrational instability, that is, the increase of current-induced vibrational excitation for decreasing electronic-vibrational coupling. The novel HQME approach allows us to analyze the influence of level broadening due to both molecule-lead coupling and thermal effects. Results obtained for the first two moments suggest that the vibrational excitation is always described by a geometric distribution in the weak electronic-vibrational coupling limit.

Origin of Vibrational Instabilities in Molecular Wires with Separated Electronic States.

Current-induced heating in molecular junctions stems from the interaction between tunneling electrons and localized molecular vibrations. If the electronic excitation of a given vibrational mode exceeds heat dissipation, a situation known as vibrational instability is established, which can seriously compromise the integrity of the junction. Using out of equilibrium first-principles calculations, we demonstrate that vibrational instabilities can take place in the general case of molecular wires with separated unoccupied electronic states. From the ab initio results, we derive a model to characterize unstable vibrational modes and construct a diagram that maps mode stability. These results generalize previous theoretical work and predict vibrational instabilities in a new regime.

Pulsed Molecular Optomechanics in Plasmonic Nanocavities: From Nonlinear Vibrational Instabilities to Bond-Breaking

New experiments on molecules trapped in an ultrasmall optical cavity reveal details of how molecular bonds interact with light and how this can eventually lead to their ultimate breaking, potentially providing access to new regimes of optical chemistry.

Spontaneous Octahedral Tilting in the Cubic Inorganic Cesium Halide Perovskites CsSnX3 and CsPbX3 (X = F, Cl, Br, I).

The local crystal structures of many perovskite-structured materials deviate from the average space-group symmetry. We demonstrate, from lattice-dynamics calculations based on quantum chemical force constants, that all of the cesium-lead and cesium-tin halide perovskites exhibit vibrational instabilities associated with octahedral titling in their high-temperature cubic phase. Anharmonic double-well potentials are found for zone-boundary phonon modes in all compounds with barriers ranging from 108 to 512 meV. The well depth is correlated with the tolerance factor and the chemistry of the composition, but is not proportional to the imaginary harmonic phonon frequency. We provide quantitative insights into the thermodynamic driving forces and distinguish between dynamic and static disorder based on the potential-energy landscape. A positive band gap deformation (spectral blue shift) accompanies the structural distortion, with implications for understanding the performance of these materials in applications areas including solar cells and light-emitting diodes.

The interaction of thermocapillary and vibrational instabilities in a two-layer system subjected to the tangential vibrations

The paper deals with the investigation of interaction of thermocapillary, parametric and frozen wave instability mechanisms in a two-layer system of immiscible incompressible viscous fluids of different densities (more dense fluid is located below). External boundaries are rigid. They are maintained at constant different temperatures. The system is subjected to the gravity force and horizontal vibrations of finite frequency and amplitude. The study is performed taking into account the interface deformations. The thermal expansion of fluids is neglected. It is found that vibrations make strong destabilizing effect on the longwave instability mode related to the interface deformations and stabilizing effect on Pearson instability mode.

Thermal conductivity of Glycerol's liquid, glass, and crystal states, glass-liquid-glass transition, and crystallization at high pressures.

To investigate the effects of local density fluctuations on phonon propagation in a hydrogen bonded structure, we studied the thermal conductivity κ of the crystal, liquid, and glassy states of pure glycerol as a function of the temperature, T, and the pressure, p. We find that the following: (i) κcrystal is 3.6-times the κliquid value at 140 K at 0.1 MPa and 2.2-times at 290 K, and it varies with T according to 138 × T(-0.95); (ii) the ratio κliquid (p)/κliquid (0.1 MPa) is 1.45 GPa(-1) at 280 K, which, unexpectedly, is about the same as κcrystal (p)/κcrystal (0.1 MPa) of 1.42 GPa(-1) at 298 K; (iii) κglass is relatively insensitive to T but sensitive to the applied p (1.38 GPa(-1) at 150 K); (iv) κglass-T plots show an enhanced, pressure-dependent peak-like feature, which is due to the glass to liquid transition on heating; (v) continuous heating cold-crystallizes ultraviscous glycerol under pressure, at a higher T when p is high; and (vi) glycerol formed by cooling at a high p and then measured at a low p has a significantly higher κ than the glass formed by cooling at a low p. On heating at a fixed low p, its κ decreases before its glass-liquid transition range at that p is reached. We attribute this effect to thermally assisted loss of the configurational and vibrational instabilities of a glass formed at high p and recovered at low p, which is different from the usual glass-aging effect. While the heat capacity, entropy, and volume of glycerol crystal are less than those for its glass and liquid, κcrystal of glycerol, like its elastic modulus and refractive index, is higher. We discuss these findings in terms of the role of fluctuations in local density and structure, and the relations between κ and the thermodynamic quantities.

Current-induced runaway vibrations in dehydrogenated graphene nanoribbons.

We employ a semi-classical Langevin approach to study current-induced atomic dynamics in a partially dehydrogenated armchair graphene nanoribbon. All parameters are obtained from density functional theory. The dehydrogenated carbon dimers behave as effective impurities, whose motion decouples from the rest of carbon atoms. The electrical current can couple the dimer motion in a coherent fashion. The coupling, which is mediated by nonconservative and pseudo-magnetic current-induced forces, change the atomic dynamics, and thereby show their signature in this simple system. We study the atomic dynamics and current-induced vibrational instabilities using a simplified eigen-mode analysis. Our study illustrates how armchair nanoribbons can serve as a possible testbed for probing the current-induced forces.

Elastic properties and stress-temperature phase diagrams of high-temperature phases with low-temperature lattice instabilities

The crystal structures of many technologically important high-temperature phases are predicted to have lattice instabilities at low temperature, making their thermodynamic and mechanical properties inaccessible to standard first principles approaches that rely on the (quasi) harmonic approximation. Here, we use the recently developed anharmonic potential cluster expansion within Monte Carlo simulations to predict the effect of temperature and anisotropic stress on the elastic properties of ${\mathrm{ZrH}}_{2}$, a material that undergoes diffusionless transitions among cubic, tetragonal, and orthorhombic phases. Our analysis shows that the mechanical properties of high-temperature phases with low-temperature vibrational instabilities are very sensitive to temperature and stress state. These findings have important implications for materials characterization and multi-scale simulations and suggest opportunities for enhanced strain engineering of high-temperature phases exhibiting soft-mode instabilities.

Rayleigh and parametric thermo-vibrational instabilities in supercritical fluids under weightlessness

Under the absence of gravity forces, the interaction of vibration with a thermal boundary layer (TBL) can lead to a rich variety of dynamics in a supercritical fluid (SCF). When subjected to vibration, a SCF can display different kinds of instabilities for different relative directions of the TBL and vibration. Rayleigh vibrational instability is formed when the vibration direction is tangential to the TBL. When the direction of vibration is perpendicular to the TBL, instabilities of parametric nature can develop. Two-dimensional finite volume numerical analysis of supercritical H2 filled in a square cell under vibration is carried out. The vibrational amplitudes range from 0.05 to 5 times the side of the cell and frequencies vary between 2.78 Hz and 25 Hz. Three different thermal boundary conditions (isothermal walls, adiabatic vertical/isothermal horizontal walls, and adiabatic horizontal/isothermal vertical walls) have been considered with various temperature proximities to the critical point (10 mK, 100 mK, and 1 K). The results evidence Rayleigh vibrational and parametric instabilities in a thermal field. It is for the first time that the latter type of instability is observed in the thermal field under such conditions. Additionally, the role of the cell corners is highlighted (a “corner” instability is observed). These instabilities are analyzed and quantified. In particular, the stability domains have been plotted.

An evaluation of iced bridge hanger vibrations through wind tunnel testing and quasi-steady theory

Bridge hanger vibrations have been reported under icy conditions. In this paper, the results from a series of static and dynamic wind tunnel tests on a circular cylinder representing a bridge hanger with simulated thin ice accretions are presented. The experiments focus on ice accretions produced for wind perpendicular to the cylinder at velocities below 30 m/s and for temperatures between and . Aerodynamic drag, lift and moment coefficients are obtained from the static tests, whilst mean and fluctuating responses are obtained from the dynamic tests. The influence of varying surface roughness is also examined. The static force coefficients are used to predict parameter regions where aerodynamic instability of the iced bridge hanger might be expected to occur, through use of an adapted theoretical 3-DOF quasi-steady galloping instability model, which accounts for sectional axial rotation. A comparison between the 3-DOF model and the instabilities found through two degree-of-freedom (2-DOF) dynamic tests is presented. It is shown that, although there is good agreement between the instabilities found through use of the quasi-steady theory and the dynamic tests, discrepancies exist-indicating the possible inability of quasi-steady theory to fully predict these vibrational instabilities.

Lattice dynamics, thermodynamics and elastic properties of monoclinic Li2CO3 from density functional theory

Monoclinic Li2CO3 has been identified as a critical component of the solid electrolyte interphase (SEI), a passivating film that forms on Li-ion battery anode surfaces. Here, lattice dynamics, finite temperature thermodynamics and the elastic properties of monoclinic Li2CO3 are examined with density functional theory (DFT) and various exchange–correlation functionals. To account for LO-TO splittings in phonon dispersion relations of Li2CO3, which is a polar compound, a mixed-space phonon approach is employed. Bond strengths between atoms are quantitatively explored with phonon force constants. Temperature variations of the entropy, enthalpy, isobaric heat capacity and linear (average) thermal expansion are computed using the quasiharmonic approach. The single-crystal elasticity tensor components along with polycrystalline bulk, shear and Young’s moduli are computed with a least-squares approach based upon the stress tensor computed from DFT. Computed thermodynamic properties as well as structural and elastic properties of the monoclinic Li2CO3 are in close accord with available theoretical and experimental data. In contrast to a recent DFT study, however, computed vibrational spectra suggest that neither the monoclinic Li2CO3 nor its high-temperature hexagonal phase exhibits either elastic or vibrational instabilities.

Current-induced dynamics in carbon atomic contacts.

Background: The effect of electric current on the motion of atoms still poses many questions, and several mechanisms are at play. Recently there has been focus on the importance of the current-induced nonconservative forces (NC) and Berry-phase derived forces (BP) with respect to the stability of molecular-scale contacts. Systems based on molecules bridging electrically gated graphene electrodes may offer an interesting test-bed for these effects.Results: We employ a semi-classical Langevin approach in combination with DFT calculations to study the current-induced vibrational dynamics of an atomic carbon chain connecting electrically gated graphene electrodes. This illustrates how the device stability can be predicted solely from the modes obtained from the Langevin equation, including the current-induced forces. We point out that the gate offers control of the current, independent of the bias voltage, which can be used to explore current-induced vibrational instabilities due the NC/BP forces. Furthermore, using tight-binding and the Brenner potential we illustrate how Langevin-type molecular-dynamics calculations including the Joule heating effect for the carbon-chain systems can be performed. Molecular dynamics including current-induced forces enables an energy redistribution mechanism among the modes, mediated by anharmonic interactions, which is found to be vital in the description of the electrical heating.Conclusion: We have developed a semiclassical Langevin equation approach that can be used to explore current-induced dynamics and instabilities. We find instabilities at experimentally relevant bias and gate voltages for the carbon-chain system.

Vibrational instabilities in resonant electron transport through single-molecule junctions

We analyze various limits of vibrationally coupled resonant electron transport in single-molecule junctions. Based on a master equation approach, we discuss analytic and numerical results for junctions under a high bias voltage or weak electronic-vibrational coupling. It is shown that in these limits the vibrational excitation of the molecular bridge increases indefinitely, i.e. the junction exhibits a vibrational instability. Moreover, our analysis provides analytic results for the vibrational distribution function and reveals that these vibrational instabilities are related to electron-hole pair creation processes.

Vibrational Modes and Instabilities of a Dust-Particle Pair in a Complex Plasma

Vibrational modes and instabilities of a dust particle pair in a terrestrial laboratory complex plasma are investigated employing an analytical method whereby the plasma wakefield induced by an external electric field is modeled using an image charge method. It is found that for both horizontally and vertically aligned dust particle pairs in equilibrium, four normal modes exist. Variations of the confinement parameters cause a single type of instability in the horizontal pair and two types of instabilities in the vertical pair.

Cutting process dynamics by nonlinear time series and wavelet analysis

We have modeled the dynamics of a cutting process by a two-degree-of-freedom mass-spring system with dry friction. Using nonlinear time series and wavelet analysis, we have investigated the vibrational instabilities of the system for different values of the cutting force. By constructing the phase portraits and calculating the Lyapunov exponents we have delineated the conditions for which a periodic or chaotic motion can occur. The results are verified by means of a time-scale representation of the wavelet power spectrum.

Solid–liquid transitions of sodium chloride at high pressures

We investigate solid-liquid transitions in NaCl at high pressures using molecular dynamics simulations, including the melting curve and superheating/supercooling as well as solid-solid and liquid-liquid transitions. The first-order B1-B2 (NaCl-CsCl type) transition in solid is observed at high pressures besides continuous liquid structure transitions, which are largely analogous to the B1-B2 transition in solid. The equilibrium melting temperatures (T(m)) up to megabar pressure are obtained from the solid-liquid coexistence technique and the superheating-supercooling hysteresis method. Lindemann's vibrational and Born's mechanical instabilities are found upon melting. The Lindemann frequency is calculated from the vibrational density of states. The Lindemann parameter (fractional root-mean-squared displacement) increases with pressure and approaches a constant asymptotically, similar to the Lennard-Jones system. However, the Lindemann melting relation holds for both B1 and B2 phases to high accuracy as for the Lennard-Jonesium. The B1 and B2 NaCl solids can be superheated by 0.18T(m) and 0.24T(m), and the NaCl liquid, supercooled by 0.22T(m) and 0.32T(m), respectively, at heating or cooling rates of 1 K/s and 1 K/ps. The amount of maximum superheating or supercooling and its weak pressure dependence observed for NaCl are in accord with experiments on alkali halides and with simulations on the Lennard-Jones system and Al.