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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Mode-Selective Vibrational Energy Transfer Dynamics in 1,3,5-Trinitroperhydro-1,3,5-triazine (RDX) Thin Films

The coupling of inter- and intramolecular vibrations plays a critical role in initiating chemistry during the shock-to-detonation transition in energetic materials. In this work, we report on the subpicosecond to subnanosecond vibrational energy transfer (VET) dynamics of the solid energetic material 1,3,5-trinitroperhydro-1,3,5-triazine (RDX) by using broadband, ultrafast infrared transient absorption spectroscopy. Experiments reveal VET occurring on three distinct time scales: subpicosecond, 5 ps, and 200 ps. The ultrafast appearance of signal at all probed modes in the mid-infrared suggests strong anharmonic coupling of all vibrations in the solid, whereas the long-lived evolution demonstrates that VET is incomplete, and thus thermal equilibrium is not attained, even on the 100 ps time scale. Density functional theory and classical molecular dynamics simulations provide valuable insights into the experimental observations, revealing compression-insensitive time scales for the initial VET dynamics of high-frequency vibrations and drastically extended relaxation times for low-frequency phonon modes under lattice compression. Mode selectivity of the longest dynamics suggests coupling of the N–N and axial NO2 stretching modes with the long-lived, excited phonon bath.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Measurements and kinetic modeling of O 2 vibrational kinetics in O 2 –Ar mixtures partially dissociated by a Ns pulse discharge

Vibrational kinetics of O 2 is studied during the O atom recombination in an O 2 –Ar mixture, partially dissociated by a burst of ns discharge pulses in a heated plasma flow reactor. The time-resolved temperature in the discharge afterglow is determined by Rayleigh scattering. Time-resolved O atom number density is measured by ps Two-Photon absorption Laser Induced Fluorescence, calibrated in xenon. Time-resolved vibrational level populations of molecular oxygen, O 2 (v= 8–20), are measured by ps Laser Induced Fluorescence (LIF), with the absolute calibration by NO LIF. Time-resolved ozone number density is monitored by broadband UV absorption. The results are compared with the predictions of a state-specific kinetic model. The experimental data indicate a rapid initial decay of O 2 (v) populations generated by electron impact in the discharge, due to the vibration-translation (V–T) relaxation by O atoms. This is followed by a slower population reduction, on the time scale much longer compared to that for V–T relaxation or vibration-vibration (V–V) exchange. Both O atoms and the O 2 (v) populations decay on the same time scale, indicating that chemical reactions initiated by the O atom recombination result in the generation of vibrationally excited O 2 molecules. These trends are reproduced by the kinetic model, which shows that the reaction of O atoms with ozone is the dominant pathway of O 2 (v) generation at the present conditions. The predicted relative O 2 (v) populations are close to the experimental results, but absolute number densities differ from the experimental data. This is likely due to uncertainties in the absolute calibration of LIF measurements and in the spectroscopic model used in the data reduction. The present work demonstrates the capability for the absolute, time-resolved measurements of vibrationally excited O 2 in recombining gas flows, to quantify the energy partition in the recombination reactions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Strong Relativistic Effects in Lanthanide-Based Single-Molecule Magnets

Lanthanide-based single-molecule magnets (SMMs) are promising building blocks for quantum memory and spintronic devices. Designing lanthanide-based SMMs with long spin relaxation time requires a detailed understanding of their electronic structure, including the crucial role of the spin-orbit coupling (SOC). While traditional calculations of SOC using the perturbation theory applied to a solution of the non-relativistic Schrödinger equation are valid for light atoms, this approach is questionable for systems containing heavy elements such as lanthanides. We investigate the accuracy of the perturbation estimates of SOC by variationally solving the Dirac equation for the [DyO] + molecule, a prototype of a lanthanide-based SMM. We show that the energy splittings between the M J states involved in spin relaxation depend on the interplay between strong SOC and dynamic electron correlations. Here, we demonstrate that this interplay affects the resonances between the spin and vibrational transitions, and, therefore, the spin relaxation time.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Role of Electron Correlation beyond the Active Space in Achieving Quantitative Predictions of Spin-Phonon Relaxation

Single-molecule magnets (SMMs) are promising candidates for molecular-scale data storage and processing due to their strong magnetic anisotropy and long spin relaxation times. However, as temperature rises, interactions between electronic states and lattice vibrations accelerate spin relaxation, significantly limiting their practical applications. Recently, ab initio simulations have made it possible to advance our understanding of phonon-induced magnetic relaxation, but significant deviations from experiments have often been observed. The description of molecules’ electronic structure has been mostly based on complete active space self-consistent field (CASSCF) calculations, and the impact of electron correlation beyond the active space remains largely unexplored. In this study, we provide the first systematic investigation of spin-phonon relaxation in SMMs with post-CASSCF multiconfigurational methods, specifically CAS followed by second-order perturbation theory and multiconfiguration pair-density functional theory. Taking Co(II)- and Dy(III)-based SMMs as case studies, we analyze how electron correlation influences spin-phonon relaxation rates across a range of temperatures, comparing theoretical predictions with experimental observations. Our findings demonstrate that post-CASSCF treatments make it possible to achieve quantitative predictions for Co(II)-based SMMs. For Dy(III)-based systems, however, accurate predictions require consideration of additional effects, underscoring the urgent necessity of further advancing the study of the effects of electronic correlation in these complex systems.

Energy↗
DOE OSTI2025

Control of Energy Transport and Transduction in Photosynthetic Down-Conversion (Final Technical Report)

The research conducted under this contract focused on three areas related to control of energy transport and transduction in natural and synthetic light harvesting systems: (1) experimental and theoretical studies exploring the use of ultrafast laser pulse shaping to manipulate the initially excited states of multi-chromophore biological light harvesting networks and influence the early time energy transfer and electronic and vibrational relaxation pathways, (2) fundamental theoretical developments aimed at computing and analyzing the dynamics of excitations of complex heterogeneous environments and nano structures, and (3) joint experimental and theoretical design studies of artificial light harvesting materials exploring the influence of incorporating different types of organic layers in low dimensional lead halide perovskite materials on their hot carrier relaxation dynamics, and theoretical studies of the design of nano structured light harvesting antenna systems. These research projects supported the training of three theoretical and computational graduate students, one experimental graduate student, and one experimental post-doctoral researcher. The research has been published in seven peer reviewed papers and presented at several international meetings and workshops.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Stabilizing Ru-Formyl CO 2 Reduction Intermediates by Formation of Lewis Acid–Base Adducts: A Combined 2DIR and NMR Study

This work demonstrates how the stability of a Ru(II) formyl complex (cis-[Ru(bpy) 2 (CO)(CHO)][PF 6 ]), which is known to decarbonylate to form the metal hydride complex, is greatly enhanced by the addition of a Lewis acidic cation (Li + or Mg 2+ ). Multinuclear NMR is used to measure equilibrium constants of adduct formation, and then ultrafast 2DIR spectroscopy is applied to determine how the electronic structure and local molecular dynamics change upon complexation of the formyl ligand with the Lewis acid. We attribute the stabilization of the complex to the formation of a carbene-like structure where the bond strength between the Ru and the formyl group increases. The change in electronic structure is evidenced by steady-state NMR spectroscopy and DFT calculations. 2DIR measurements further confirm both the complexation of the formyl ligand with the Lewis acid and the change in electronic structure, where changes in vibrational frequency, relaxation kinetics, and a slowdown in the time scale of rotation about the metal-formyl bond are observed in the presence of Lewis acids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Direct observation of coherence transfer and rotational-to-vibrational energy exchange in optically centrifuged CO2 super-rotors

Abstract Optical centrifuges are laser-based molecular traps that can rotationally accelerate molecules to energies rivalling or exceeding molecular bond energies. Here we report time and frequency-resolved ultrafast coherent Raman measurements of optically centrifuged CO 2 at 380 Torr spun to energies beyond its bond dissociation energy of 5.5 eV ( J max = 364, E rot = 6.14 eV, E rot / k B = 71, 200 K). The entire rotational ladder from J = 24 to J = 364 was resolved simultaneously which enabled a more accurate measurement of the centrifugal distortion constants for CO 2 . Remarkably, coherence transfer was directly observed, and time-resolved, during the field-free relaxation of the trap as rotational energy flowed into bending-mode vibrational excitation. Vibrationally excited CO 2 ( ν 2 > 3) was observed in the time-resolved spectra to populate after 3 mean collision times as a result of rotational-to-vibrational (R-V) energy transfer. Trajectory simulations show an optimal range of J for R-V energy transfer. Dephasing rates for molecules rotating up to 5.5 times during one collision were quantified. Very slow decays of the vibrational hot band rotational coherences suggest that they are sustained by coherence transfer and line mixing.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

MD Simulation of Water Using a Rigid Body Description Requires a Small Time Step to Ensure Equipartition

In simulations of aqueous systems, it is common to freeze the bond vibration and angle bending modes in water to allow for a longer time step δt for integrating the equations of motion. Thus, δt = 2 fs is often used in simulating rigid models of water. We simulate the SPC/E model of water using δt from 0.5 to 3.0 fs and up to 4 fs using hydrogen mass repartitioning. In these simulations, we find that for all but δt = 0.5 fs, equipartition is not obtained between translational and rotational modes, with the rotational modes exhibiting a lower temperature than the translation modes. To probe the reasons for the lack of equipartition, we study the autocorrelation of the translational velocity of the center of mass and the angular velocity of the rigid water molecule, respectively. Here, we find that the rotational relaxation occurs on a timescale comparable to vibrational periods, calling into question the original motivations for freezing the vibrations. Furthermore, a time step with δt ≥ 1 fs is not able to capture accurately the fast rotational relaxation, which reveals its impact as an effective slowing-down of rotational relaxation. The fluctuation–dissipation relation then leads to the conclusion that the rotational temperature should be cooler for δt greater than the reference value of 0.5 fs. Consideration of fluctuation–dissipation in equilibrium molecular dynamics simulations also emphasizes the need to capture the temporal evolution of fluctuations with fidelity and the role of δt in this regard. The time step also influences the solution thermodynamic properties: both the mean system potential energies and the excess entropy of hydration of a soft repulsive cavity are sensitive to δt.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Mode-specific pressure effects on the relaxation of an excited nitromethane molecule in an argon bath

The vibrational and rotational mode-specific relaxations of CH 3 NO 2 with 50 kcal/mol of initial internal energy in an argon bath is computed at 300 K at pressures of 10-400 atm. This work uses archived information from our previously published [J. Chem. Phys. 142, 014303 (2015)] molecular dynamics simulations and employs our previous published [J. Chem. Phys. 151, 034303 (2019)] method for projecting time-dependent Cartesian velocities onto normal mode eigenvectors. The computed relaxations cover three types of energies: vibrational, rotational, and Coriolis. In general, rotational and Coriolis relaxations in all modes are initially fast followed by an orders of magnitude slower relaxation. For all modes, that slower relaxation rate is approximately comparable to the vibrational relaxation rate. For all three types of energies, there are small-scale mode-to-mode variations. Of particular prominence is the exceptionally fast relaxation shared in common by the external rotation about the C-N axis, the internal hindered rotation of the CH 3 group relative to the NO 2 group, and the symmetric stretch of the CH 3 group.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Reversible structural transformations in supercooled liquid water from 135 to 245 K

Water has many anomalous properties compared to “simple” liquids, and these anomalies are typically enhanced in supercooled water.1-3 While numerous models have been proposed, including the liquid-liquid critical point,4,5 the singularity-free scenario,6 and the stability limit conjecture,1 a molecular-level understanding remains elusive. The main difficulty in determining which, if any, of these models is correct is the limited amount of data in the relevant temperature and pressure ranges. For water at ambient pressures, which is the focus of this work, data is largely missing from 160 – 232 K (“No Man’s Land”) due to rapid crystallization.2,3 Whether rapid crystallization is just an experimental obstacle, or a fundamental problem signaling the inability of water to thermally equilibrate prior to crystallization is also a major unanswered question.5,7 Here, we investigate the structural transformations of transiently-heated, supercooled water with nanosecond time resolution using infrared vibrational spectroscopy. The experiments demonstrate three key results. First, water’s structure relaxes from its initial configuration to a “steady-state” configuration prior to the onset of crystallization over a wide temperature range. Second, water’s steady-state structure can be reproduced by a linear combination of two, temperature-independent structures that correspond to a “high-temperature liquid” and a “low-temperature liquid.” Third, the observed structural changes are reversible over the full temperature range. Taken together, these results show that supercooled water can equilibrate prior to crystallization for temperatures from the homogeneous nucleation temperature, TH ~232 K,3 down to the glass transition temperature (Tg ~ 136 K). Second, the results provide support for the hypothesis that supercooled water can be described as a mixture of two, structurally-distinct, interconvertible liquids from 135 K to 245 K.5,8-18

Kringle, Loni M.↗
DOE OSTI2021

Complex Formation and Dissociation Dynamics on Amorphous Silica Surfaces

Benzene complex formation and dissociation dynamics with silanols on the amorphous silica surfaces of nanoporous SiO 2 , from a benzene/carbon tetrachloride solution, were measured by the growth of off-diagonal peaks in the two dimensional infrared (2D IR) chemical exchange spectrum of the isolated Si-OD stretch. The presence of two types of isolated silanols, referred to as type I and II, was revealed, with dissociation time constants of 82 ps and 4.0 ps for type I and II complexes, respectively. The type I silanols are associated with the main IR absorption feature in the Si-OD stretching region, while the type II silanols give rise to a broader shoulder to lower frequency. Polarization selective pump-probe (PSPP) measurements provided the vibrational lifetimes and orientational relaxation rates of the two silanols in the CCl 4 (free) and benzene (complex) environments. The type II silanols constitute roughly 30% of the isolated silanol population and exhibit a substantially faster rate of vibrational relaxation, making the type I dynamics the dominant contribution to the PSPP and 2D IR signals. From the measured dissociation times, the enthalpies of formation for the two surface complexes were obtained; the formation of the type I complex being significantly more exothermic. Furthermore, as the type II site is preferentially removed from the amorphous silica surface with increasing activation temperature, the results provide a reasonable explanation for the increased exothermicity of benzene adsorption on silica with increasing activation temperature in previous calorimetry experiments.

14 SOLAR ENERGY↗
DOE OSTI2020

Ultrafast vibrational dynamics of a trigonal planar anionic probe in ionic liquids (ILs): A two-dimensional infrared (2DIR) spectroscopic investigation

A major impediment limiting the widespread application of ionic liquids (ILs) is their high shear viscosity. Incorporation of a tricyanomethanide (TCM - ) anion in ILs leads to low shear viscosity and improvement of several characteristics suitable for large scale applications. However, properties including interactions of TCM - with the local environment and dynamics of TCM - have not been thoroughly investigated. Herein, we have studied the ultrafast dynamics of TCM - in several imidazolium ILs using linear IR and two-dimensional infrared spectroscopy techniques. The spectral diffusion dynamics of the CN stretching modes of TCM - in all ILs exhibit a nonexponential behavior with a short time component of ~2 ps and a long time component spanning ~9 ps to 14 ps. The TCM - vibrational probe reports a significantly faster relaxation of ILs compared to those observed previously using linear vibrational probes, such as thiocyanate and selenocyanate. Our results indicate a rapid relaxation of the local ion-cage structure embedding the vibrational probe in the ILs. The faster relaxation suggests that the lifetime of the local ion-cage structure decreases in the presence of TCM - in the ILs. Linear IR spectroscopic results show that the hydrogen-bonding interaction between TCM - and imidazolium cations in ILs is much weaker. Shorter ion-cage lifetimes together with weaker hydrogen-bonding interactions account for the low shear viscosity of TCM - based ILs compared to commonly used ILs. In addition, this work demonstrates that TCM - can be used as a potential vibrational reporter to study the structure and dynamics of ILs and other molecular systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Experimental Quantification of Spin–Phonon Coupling in Molecular Qubits Using Inelastic Neutron Scattering

Electronic spin superposition states enable nanoscale sensing through their sensitivity to the local environment, yet their sensitivity to vibrational motion also limits their coherence times. In molecular spin systems, chemical tunability and atomicscale resolution are accompanied by a dense, thermally accessible phonon spectrum that introduces efficient spin relaxation pathways. Despite extensive theoretical work, there is little experimental consensus on which vibrational energies dominate spin relaxation or how molecular structure controls spin−phonon coupling (SPC). We present a fully experimental method to quantify SPC coefficients by combining temperature-dependent vibrational spectra from inelastic neutron scattering with spin relaxation rates measured by electron paramagnetic resonance. We apply this framework to two model S = 1/2 systems, copper(II) phthalocyanine (CuPc) and copper(II) octaethylporphyrin (CuOEP). Two distinct relaxation regimes emerge: below 40 K, weakly coupled lattice modes below 50 cm −1 dominate, whereas above 40 K, optical phonons above ∼185 cm −1 become thermally populated and drive relaxation with SPC coefficients nearly 3 orders of magnitude larger. Structural distortions in CuOEP that break planar symmetry soften the crystal lattice and enhance anharmonic scattering but also raise the energy of stretching modes at the molecular core where the spins reside. This redistributes vibrational energy toward the molecular periphery and out of plane, ultimately reducing SPC relative to CuPc and enabling room-temperature spin coherence in CuOEP. Although our method does not provide mode-specific SPC coefficients, it quantifies contributions from distinct spectral regions and establishes a broadly applicable, fully experimental link between crystal structure, lattice dynamics, and spin relaxation.

Lohaus, Stefan H. [California Institute of Technol↗
DOE OSTI2021

Slow spin relaxation in single endohedral fullerene molecules

Well-protected magnetization, tunable quantum states, and long spin-relaxation time are desired for the use of magnetic molecules in spintronics and quantum information technologies. In this work, endohedral fullerene molecules M@C 28 with different transition-metal cores were explored through systematic first-principles calculations and spin dynamics analyses. Many of them have bias-tunable structure, stable magnetization, and sizable magnetic anisotropy energy. Furthermore, some of them may have spin-relaxation time up to several milliseconds for their quantum spin states at high temperature (~10 K) after full consideration of spin-vibration couplings. In conclusion, our results suggest that these M@C 28 provide a rich pool of single-molecule magnets for diverse applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Abnormal Slow Phonon Dynamics Toward Prolonging Excited States Dynamics Enabled by Crystalline‐Assembling Donor–Acceptor Molecules

Phonon dynamics are a critical factor to control the optical properties of excited states in light-emitting materials. Here, we report an extremely slow relaxation of photoexcited lattice vibrations enabled by assembling the donor-acceptor (D–A) molecules [2-(9,9-dimethylacridin-10(9H)-yl)-9,9-dimethyl-9H-thioxanthene 10,10-dioxide], namely AC molecules, into dipolar crystal. By using photoexcitation-modulated Raman spectroscopy, we find that the crystalline-lattice vibrations monitored by Raman-scattering laser beam of 785 nm demonstrate an un-usual slow relaxation in the time scale of seconds after ceasing photoexcitation beam of 343 nm in such dipolar crystal. This presents extremely slow phonon dynamics enabled by crystalline-assembling the D–A molecules into a dipolar crystal. Simultaneously, the photoluminescence (PL) exhibits a prolonged behavior, lasting 10 ms after ceasing photoexcitation in dipolar AC crystal. This phenomenon provides an experimental hypothesis that the slow phonon dynamics function as an important mechanism to unusually prolong excited states dynamics upon crystalline-assembling the D–A molecules into dipolar crystal. Here, this hypothesis can be verified by directly suppressing the phonon dynamics through freezing D–A molecular liquid into dipolar crystalline solid at 77 K to largely prolong the PL to 1 s- after removing photoexcitation. Clearly, crystalline-assembling D–A molecules provide the necessary conditions to enable slow phonon dynamics toward prolonging excited states dynamics.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A Theory of Ultrafast Charge Transfer Relaxation with Non-Innocent Solvent Molecules

In this work we revisit the photodynamics of tetracyanoethylene-hexamethylbenzene (TCNE- HMB), the molecular complex studied by Hochstrasser et al. [J. Chem. Phys. 100, 4797–4810, 1994] that has long challenged the applicability of Marcus’s theory of elec- tron transfer for predicting photochemical reactions. Using a novel black-box electronic structure algorithm (time-dependent density functional theory with one double, TD- DFT-1D) to efficiently run molecular dynamics that can treat charge recombination, we run ab initio surface hopping molecular dynamics and confirm that, for a polar solvent, charge recombination rates can be incredibly fast (indeed faster than the sol- vent relaxation time); for non-polar solvents, the rate is much slower. We demonstrate that, although Marcus theory cannot be directly applied, these nonequilibrium (and sometimes incredibly fast) photoexcited dynamics can be effectively explained within a two-state model without any evidence of a transition through a conical intersection. Most importantly, for this paradigmatic model system, we are able to identify two nuclear coordinates of interest (rather than the single coordinate predicted by Marcus or a full set of internal quantum modes studied by Bixon and Jortner): the solvent relaxation in the first shell (that strongly modulates the energies of the charge trans- fer state and differentiates time scales for relaxation) and a nuclear displacement in the TCNE-HMB complex arising from a handful of vibrations that induces non-Born Oppenheimer motion and eventually facilitates an abrupt electronic transition to the ground state. Altogether, these findings suggest a tractable generalization of Marcus theory for future simulations of photochemistry with non-innocent solvent environ- ments in the spirit of a Hamiltonian suggested by Stuchebrukhov (J. Chem. Phys. 107, 3821, 1997).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Interplay of structural fluctuations and charge carrier dynamics is key for high performance of hybrid lead halide perovskites

The ability of methylammonium lead triiodide (MAPbI 3 ) to achieve photoelectric conversion efficiency that is on par with crystalline silicon has led to a surge of interest in perovskite photovoltaics. However, an in-depth understanding of how the ubiquitous coupling between the fast rovibrational movements of the organic cations and the phonon vibrations of the inorganic framework affects the relaxation and recombination of hot carriers remains largely elusive. Access to such knowledge is critical to guide design and increase efficiency of new classes of perovskite solar cells. In this report, we report a time-domain ab initio investigation of temperature dependent excited state dynamics in MAPbI 3 , with particular emphasis on nuclear anharmonic effects. The observed strong anharmonicity is attributed to softness of the material and unusual dynamical coupling between the organic and inorganic components. At an elevated temperature, the hydrogen bonding between MA and iodines is weakened, enhancing rotation of MA cations, which become more dynamically disordered. As a result, thermal vibrations of the inorganic Pb–I sublattice are suppressed, and the lattice anharmonicity is decreased. Thermal fluctuations of the electronic energy levels are found to follow the trend of anharmonic motions of Pb and I atoms, with holes relaxing faster to the band edges than electrons, due to higher density of the hole states. While elevated temperature accelerates intraband carrier cooling, it slows nonradiative carrier recombination. The latter result is important for performance, since solar cells and other devices heat up during operation. The reported signatures of coupled structural dynamics of the organic cations and inorganic framework unravel the interplay between anomalous structural fluctuations and charge carrier dynamics, which is of particular importance for fundamental understanding of the structure–property relationships in hybrid metal halide perovskites.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Reversible motions and disordered structure of soft particles in amorphous solids

In amorphous solids, soft vibrational modes derived from normal mode analysis can be utilized to identify the soft particles that are prone to irreversible rearrangements. However, the normal mode analysis approach cannot explain why the spatial distributions of clustered soft particles do not change over time. We define a softness parameter based on the vibrational density of states calculated directly from molecular dynamics simulations with both the harmonic vibrations and anharmonic relaxations being properly captured at finite temperatures. This parameter spontaneously correlates with the real space atomic motions and the dynamics heterogeneity. Using the softness parameter, we show that the softest particles are confined within rigid cages. These particles keep rearranging reversibly without long-range diffusion. The moderately soft particles rearrange irreversibly, and the hard particles mainly participate in vibrations without rearrangement. Here, we also show that the soft particles form locally disordered structures, while the hard particles present strong ordering. These findings confirm the defective nature of soft particles, and provide insights on the nature of softness as the ability to rearrange, but not necessarily irreversibly.

36 MATERIALS SCIENCE↗