Soft Vibrational Modes Research Articles

The local atomic distribution in tetragonal PZT.

Expanding on the comprehensive research conducted by previous scholars, herein, we aim to elucidate the intrinsic piezoelectricity of tetragonal Pb(Zr1-xTix)O3 (PZT), by focusing on the local atomic distribution which was neglected for a long time, through the supercell approach based on colour symmetry. Density functional theory (DFT) was employed to perform first-principles calculations on the electronic, phononic structures and piezoelectricity of various tetragonal PZT supercells. Building upon the evaluation of the piezoelectric properties of 22 distinct distributions, classical Monte Carlo methods were utilized to explore the statistical macroscopic properties at the morphotropic phase boundary (MPB). The results reveal that at x = 0.5 and x = 0.55, the d33 reached 957 pm V-1 and 893 pm V-1, respectively. The analysis of phonon vibration modes exposed significant disparity between different colour symmetries. The supercells of lower symmetry contain B-site atoms in asymmetric positions, and they exhibit softer vibrational frequencies in the phonon spectrum. These soft phonon vibration modes resulting from colour symmetry breaking were previously unknown. The weakening and reorientation of the covalent bonds between the O 2p and d orbitals were found in electronic structures. The free energy flattening in the polarization rotation path is the origin of the high piezoelectricity of this type of supercell. The analysis of the electronic structure is consistent with the experimental observations. Finally, colour symmetry proved to be an effective and accurate way to describe the local atomic distribution in supercells. It will also bring new perspectives to understanding the structure of domain walls, phase boundaries, etc.

Soft Vibrational Modes in the Wishart Ensemble with Unstable Bonds

Soft Vibrational Modes in the Wishart Ensemble with Unstable Bonds

Stress-dependent activation entropy in thermally activated cross-slip of dislocations

Cross-slip of screw dislocations in crystalline solids is a stress-driven thermally activated process essential to many phenomena during plastic deformation, including dislocation pattern formation, strain hardening, and dynamic recovery. Molecular dynamics (MD) simulation has played an important role in determining the microscopic mechanisms of cross-slip. However, due to its limited timescale, MD can only predict cross-slip rates in high-stress or high-temperature conditions. The transition state theory can predict the cross-slip rate over a broad range of stress and temperature conditions, but its predictions have been found to be several orders of magnitude too low in comparison to MD results. This discrepancy can be expressed as an anomalously large activation entropy whose physical origin remains unclear. Here, we resolve this discrepancy by showing that the large activation entropy results from anharmonic effects, including thermal softening, thermal expansion, and soft vibrational modes of the dislocation. We expect these anharmonic effects to be significant in a wide range of stress-driven thermally activated processes in solids.

Nucleation and quantum confinement of nano-platelet Bi2–Bi2Se3

The nucleation, nano-platelet growth, and optical properties under quantum confinement are investigated in the topological semimetal superlattice Bi2–Bi2Se3 as a function of thickness and Ar + ion pressure in sputtered growths. Quantum confinement and evolution of the band structure with a series of reduced dimensionality and surface terminations are studied by density functional theory corroborating the observed optical properties. An initial Volmer–Weber growth mode of nano-platelets is observed until a pressure-dependent critical thickness, where a transition to Frank–van der Merwe growth occurs. Nucleation statistics characterized using atomic force microscopy find the nearest-neighbor ordering of nano-platelets. Optical properties using ultraviolet to visible light spectroscopy measurements in transmission mode reveal a marked increase in optical bandgap below a nano-platelet critical volume reaching a maximum of 2.21 eV. Raman vibrational spectroscopy is performed, revealing softening of vibrational modes as the nano-platelet volume decreases.

High Dielectric Constants in BaTiO3 Due to Phonon Mode Softening Induced by Lattice Strains: First Principles Calculations

AbstractHigh‐dielectric‐constant materials attract much attention due to their broad applications in modern electronics. Barium titanate (BTO) is an established material possessing an ultrahigh dielectric constant; however, a complete understanding of the responsible underlying physical mechanism remains elusive. Here a set of density‐functional‐theory calculations for the static dielectric tensors of barium titanate under strain has been performed. The dielectric constant increases to ≈7300 under strain. The analysis of the computed vibrational modes shows that transverse vibrational mode softening (the appearance of low‐frequency modes) is responsible for this significant increase as driven by the relationship between lattice contribution for the static dielectric constant (k) and vibrational frequency (ω), i.e., . The relevant vibrational mode indicates a large counter‐displacement of Ti ions and O anions, which greatly enhances electrical dipoles to screen the electric field. The calculations not only interpreted experimental data on the high dielectric constants of BTO, where the lattice deformation due to the strains from the grain nanostructure plays an important role, but also pointed to exploring high‐throughput calculations to facilitate the discovery of the advanced dielectric materials. Moreover, the calculations can prove useful for doped BTO, for which local strains fields can be achieved using defect engineering.

Achieving glass-like lattice thermal conductivity in PbTe by AgBiTe2 alloying

Here, we report the thermal transport properties of lead telluride (PbTe)1−x(AgBiTe2)x (x = 0.05 and 0.15) alloys. It is found that the prominent peak in lattice thermal conductivity at 15 K for PbTe disappears after forming solid solution with AgBiTe2, exhibiting a typical glass-like thermal transport behavior. The high energy phonons are scattered by the point defects induced by cationic disorder, while the appearance of soft vibrational modes arises from Ag atoms acting like Einstein oscillators (ΘE1 = 5.4 K, ΘE2 = 67.3 K), which substantially affects the lattice thermal conductivity. Further with nanostructuring, the mid-frequency phonons are scattered by the high-density disc-like Ag2Te precipitates. As a result, an ultralow lattice thermal conductivity (≤1.0 W m−1 K−1) for (PbTe)0.85(AgBiTe2)0.15 is obtained, which is the lowest value ever reported to date for the PbTe-based TE materials. Our work highlights a synthetic route to achieve glass-like lattice thermal conductivity in PbTe over the entire temperature range.

Localized Soft Vibrational Modes and Coherent Structural Phase Transformations in Rutile TiO2 Nanoparticles under Negative Pressure.

We study the effect of size on the vibrational modes and frequencies of nanoparticles, by applying a newly developed, robust, and efficient first-principles-based method that we present in outline. We focus on rutile TiO2, a technologically important material whose bulk exhibits a softening of a transverse acoustic mode close to , which becomes unstable with the application of negative pressure. We demonstrate that, under these conditions, nanoparticles above a critical size exhibit unstable localized modes and we calculate their characteristic localization length and decomposition with respect to bulk phonons. We propose that such localized soft modes could initiate coherent structural phase transformations in small nanoparticles above a critical size.

Localized soft vibrational modes and coherent structural phase transformations in rutile TiO2 nanoparticles under negative pressure

Localized soft vibrational modes and coherent structural phase transformations in rutile TiO2 nanoparticles under negative pressure

Localized soft vibrational modes and coherent structural phase transformations in rutile TiO2 nanoparticles under negative pressure

Localized soft vibrational modes and coherent structural phase transformations in rutile TiO2 nanoparticles under negative pressure

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. 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.

Tetrahedral [Sb(AuMe)4 ]3- Occurring in Multimetallic Cluster Syntheses: About the Structure-Directing Role of Methyl Groups.

The anion of [K(crypt‐222)]3[Sb(AuMe)4]⋅py (1; crypt‐222=4,7,13,16,21,24‐hexaoxa‐1,10‐diazabicyclo[8.8.8]hexacosane; py=pyridine) represents a rare example of a homoleptic heavy p‐block metal atom being surrounded by four free‐standing transition metal complex fragments, and the third example for a corresponding Sb compound. In contrast to all reported complexes of this type, the transition metal atoms possess twofold coordination only, hence the complex as a whole does not exhibit significant steric shielding or further linkage of the metal atoms. This is reflected in a high flexibility, as confirmed by slight deviations from a tetrahedral coordination of the Sb atom in the crystal and soft vibrational modes. An alternative pyramidal conformer, observed for a related arsenic compound with terminal phosphine ligands, is apparently disfavored owing to electron correlation effects. The compound is formed in a reaction that in another solvent or at other reactant concentrations yields salts of ternary cluster anions. By a combined experimental and theoretical study of different reaction conditions and previously unidentified side‐products, we provide insight into multimetallic cluster synthesis reactions.

Tetrahedral [Sb(AuMe)4]3−Occurring in Multimetallic Cluster Syntheses: About the Structure‐Directing Role of Methyl Groups

AbstractThe anion of [K(crypt‐222)]3[Sb(AuMe)4]⋅py (1; crypt‐222=4,7,13,16,21,24‐hexaoxa‐1,10‐diazabicyclo[8.8.8]hexacosane; py=pyridine) represents a rare example of a homoleptic heavy p‐block metal atom being surrounded by four free‐standing transition metal complex fragments, and the third example for a corresponding Sb compound. In contrast to all reported complexes of this type, the transition metal atoms possess twofold coordination only, hence the complex as a whole does not exhibit significant steric shielding or further linkage of the metal atoms. This is reflected in a high flexibility, as confirmed by slight deviations from a tetrahedral coordination of the Sb atom in the crystal and soft vibrational modes. An alternative pyramidal conformer, observed for a related arsenic compound with terminal phosphine ligands, is apparently disfavored owing to electron correlation effects. The compound is formed in a reaction that in another solvent or at other reactant concentrations yields salts of ternary cluster anions. By a combined experimental and theoretical study of different reaction conditions and previously unidentified side‐products, we provide insight into multimetallic cluster synthesis reactions.

Anomalous thermoelectricity at the two-dimensional structural transition of SnSe monolayers

SnSe monolayers experience a temperature induced two-dimensional Pnm2$_1 \to$ P4/nmm structural transformation precipitated by the softening of vibrational modes. The standard theoretical treatment of thermoelectricity---which relies on a zero temperature phonon dispersion and on a zero temperature electronic structure---is incapable of describing thermoelectric phenomena induced by structural transformations. Relying on structural data obtained from {\em ab initio} molecular dynamics calculations that is utilized in a non-standard way to inform of electronic and vibrational transport coefficients, the present work establishes a general route to understand thermoelectricity across phase transitions. Similar to recent experimental observations pointing to an overestimated thermoelectric figure of merit $ZT$ past the transition temperature, our work indicates a smaller $ZT$ when compared to its value predicted by the standard paradigm. Its decrease is related to the dramatic changes in the electrical conductivity and lattice thermal conductivity as the structural transformation ensues. Though exemplified on a SnSe monolayer, the method does not have any built-in assumptions concerning dimensionality, and thus applicable to arbitrary thermoelectric materials in one, two, and three dimensions.

Effect of Ligand Functionalization on the Rate of Charge Carrier Recombination in Metal-Organic Frameworks: A Case Study of MIL-125.

Ligand functionalization is a powerful approach for modifying the electronic structure of metal-organic frameworks when targeting the optimal electronic properties for photocatalysis and photovoltaics. However, its effect on the charge carrier lifetimes and recombination pathways remains unexplored. In this work, first-principles simulations, including nonadiabatic molecular dynamics, are performed for the representative TiO2-based metal-organic framework systems MIL-125-X to unravel the impact of ligand functionalization on the nonradiative electron-hole recombination process, decoherence rates, and phonon modes giving the largest contribution to the nonradiative decay. Nonradiative recombination rates, simulated using the PBE0 density functional, are in excellent agreement with experiment. The ligand functionalization in MIL-125-X influences the recombination rates, unraveling the trend opposite to the evolution of the band gap and affecting the nonadiabatic coupling coefficients. Ligand modification impacts the phonon modes, which contribute most to the recombination process, altering the distribution between soft phonon modes and vibrational modes associated with specific structural motifs.

Moduli and modes in the Mikado model.

We determine how low frequency vibrational modes control the elastic shear modulus of Mikado networks, a minimal mechanical model for semi-flexible fiber networks. From prior work it is known that when the fiber bending modulus is sufficiently small, (i) the shear modulus of 2D Mikado networks scales as a power law in the fiber line density, G ∼ ρα+1, and (ii) the networks also possess an anomalous abundance of soft (low-frequency) vibrational modes with a characteristic frequency ωκ ∼ ρβ/2. While it has been suggested that α and β are identical, the preponderance of evidence indicates that α is larger than theoretical predictions for β. We resolve this inconsistency by measuring the vibrational density of states in Mikado networks for the first time. Supported by these results, we then demonstrate analytically that α = β + 1. In so doing, we uncover new insights into the coupling between soft modes and shear, as well as the origin of the crossover from bending- to stretching-dominated response.

Thermoelectric Effect in Janus Monolayer InSSe

Thermoelectric effect in Janus monolayer InSSe is investigated by non-equilibrium Green's function and density functional theory. Janus monolayer InSSe is an indirect gap semiconductor with a bandgap of 1.24 eV. The value of the thermoelectric figure of merit is up to 4.39 at the temperature of 500 K and 1.38 at room temperature. We found a remarkably low and anisotropic phononic thermal conductance about 0.05987 WK–1m–1, which is originated from the soft lattice vibration modes. This low thermal conductance is responsible for the high value of the figure of merit. All the results indicate that Janus monolayer InSSe is a more suitable low dimensional thermoelectric material.

High-pressure elastic anisotropy and superconductivity of hafnium: A first-principles calculation* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11874247 and U1530258), the National Key R&D Program of China (Grant No. 2017YFA0304500), the 111 Plan of China (Grant No. D18001), the Hundred Talent Program of the Shanxi Province (2018), and the Program of State Key Laboratory of

The elastic anisotropy and superconductivity upon hydrostatic compression of α, ω, and β Hf are investigated using first-principle methods. The results of elastic anisotropies show that they increase with increasing pressure for α and ω phases, while decrease upon compression for β phase. The calculated superconducting transition temperatures are in excellent agreement with experiments. Electron–phonon coupling constants (λ) are increasing with pressure for α and ω phases, while decreasing for β phase. For β phase, the large values of λ are mainly due to the obvious TA1 soft mode. Under further compression, the TA1 soft vibrational mode will disappear gradually.

Sharp Negative Differential Resistance from Vibrational Mode Softening in Molecular Junctions.

We unravel the critical role of vibrational mode softening in single-molecule electronic devices at high bias. Our theoretical analysis is carried out with a minimal model for molecular junctions, with mode softening arising due to quadratic electron-vibration couplings, and by developing a mean-field approach. We discover that the negative sign of the quadratic electron-vibration coupling coefficient can realize, at high voltage, a sharp negative differential resistance (NDR) effect with a large peak-to-valley ratio. Calculated current-voltage characteristics, obtained based on physical parameters for a nitro-substituted oligo(phenylene ethynylene) junction, agree very well with the measurements. Our results establish that vibrational mode softening is a crucial effect at high voltage, underlying NDR, a substantial diode effect, and the breakdown of current-carrying molecular junctions.

Bulk intrinsic heterogeneity of metallic glasses probed by Meissner effect

Structural heterogeneity has been proposed as a key intrinsic feature and mechanism underline unique properties and dynamic behavior of metallic glasses; however, it is still challenging in precisely describing and effectively characterizing the atomic-scale heterogeneity in metallic glasses. In this work, we employed the Meissner effect of superconductivity in magnetic susceptibility measurements as a sensitive bulk probe and successfully revealed the three-dimensional structural heterogeneity and its two-way evolution tuned by structural aging or rejuvenation in a La-based metallic glass. Compared with the resistivity measurements which only signal the most superconductive loop in inhomogeneous materials, the diamagnetic susceptibility signal of the Meissner effect maps the volumetric distribution of all superconductive regions and the corresponding structural heterogeneity in metallic glasses with high sensitivity. The experimental results reported in this article can be well interpreted based on a structural model of tunable “soft liquid-like” regions with soft vibration modes mixed with “hard solid-like” regions, validating the heterogeneity models of metallic glasses with new experimental data and approach.

Negative-to-Positive Thermal Conductivity Temperature Coefficient Transition Induced by Dynamic Fluctuations of the Alkyl Chains in the Layered Complex (C4 H9 NH3 )2 CuCl4.

A negative-to-positive transition of the temperature coefficients of thermal conductivity was found in the two-dimensional organic-inorganic layered complex (C4 H9 NH3 )2 CuCl4 (C4CuCl4) over the three structural phase transitions in the range 176-218 K. The coefficients of the low-temperature phases (85-200 K, α and β phases) were negative, as is typical for insulating crystals, whereas those of the high-temperature phases (200-300 K, γ and δ phases) were positive, as is typical for glasses and liquids. Single-crystal X-ray structure analyses revealed that the tilted C4 H9 NH3 + chains in the α and β phases were fully outstretched in the δ phase, and the interlayer distances between the CuCl4 2- planes increased significantly. The γ phase was an intermediate phase that crystallized with an incommensurate structure, in which the CuCl4 2- sheets formed wave-like structures consisting of connected alternating regions of β-like and δ-like moieties. In the γ and δ phases, thermal fluctuations of the C4 H9 NH3 + chains were found in the electron density maps; however, powder X-ray diffraction (PXRD) data indicated that the thermal expansion of the C4 H9 NH3 + layers was restricted by the rigid CuCl4 2- layers. This situation was considered to induce glass-like thermal conducting properties in the material, such as a positive temperature coefficient. The mean free path of the phonons estimated by using the thermal conductivities and heat capacities was a function of T-1 in the range 85-200 K, as would be expected for crystals, whereas it was approximately constant in the range 200-300 K, which is typical of glasses. In addition, the existence of soft vibration modes in the two-dimensional perovskite CuCl4 2- sheets was revealed by analysis of the incommensurate crystal structure of the γ phase. These low-energy vibration modes were believed to induce the cooperative phase transitions, along with the thermal fluctuations and van der Waals interactions in the C4 H9 NH3 + layers.