Anharmonic Components Research Articles

Relationship between physical, mechanical and thermal properties of flexible chain polymers

The results of the study on the relationship between the physical, mechanical and thermal properties of linear flexible polymers due to the harmonic and anharmonic components of the interatomic and intermolecular interaction force are presented. Using the example of polyvinyl chloride (PVC), polyvinyl butyral (PVB), polystyrene (PS), it is shown that in the region of 300 K < = T < = 400 K, the relaxation state of the system is realized due to the mobility of the structural elements, which makes it possible to apply the terms of thermodynamics and statistics of small systems to the properties of the material, and to treat the polymeric state as a special form of condensation of matter. The quantitative relationship between the properties of systems has been established, which is of interest for creating scientific foundations for predicting, obtaining and operating materials under the action of external fields of various nature.

Anharmonicity in grain boundary energy for Al: Thermodynamic integration with artificial-neural-network potential

Anharmonicity in grain boundary (GB) energies for Al is elucidated by employing a thermodynamic integration method with a high-accuracy artificial-neural-network potential. Symmetric tilt GBs with the [001] and [11¯0] rotational axes are examined. It is found that anharmonic components tend to be small at low temperatures and increasingly contribute to reduction of GB free energies at elevated temperatures. The magnitude of anharmonicity is roughly correlated with excess volume at GBs. This is presumably because GB atoms tend to have longer bond lengths than the bulk atom, and hence the inclination of the potential energy surface at GBs is more moderate than in the bulk. On the other hand, the Σ13(510) GB takes non-negligible values of the anharmonic component even at intermediate temperatures. This GB contains a distinct atom around which the potential-energy curve significantly deviates from that of the harmonic approximation. Similar trends are also observed for other [001] GBs.

Spectral and quantum mechanical investigation of calcium apatites isomorphically substituted in the anionic sublattice

The evolution of the valence band, the charge states of atoms, and the optical and vibrational spectra in Ca10(PO4)x(VO4)y(AsO4)z(OH)2 (x + y + z = 6) compound with three different types of oxygen tetrahedra have been studied by XPS, IR, and optical spectroscopy with the use of quantum mechanical calculation methods in the DFT approximation. It is shown that the occupied part of the valence band of compounds with three different types of tetrahedra has a pronounced band character with varying lengths of individual subbands. Two structural regions separated by energy are observed: the valence band's upper part and the valence band's lower part (subvalent states). The structure of the valence band's middle part, the region of valence states with energies from ∼ 13.0–19.0 eV, is weakly expressed. The sublattice of oxygen tetrahedra is decisive in forming the shape and the main features of the total density of electronic states of the compounds under study. The vibrations anharmonicity in the crystal lattice of such compounds can vary depending on the concentration of tetrahedra of a specific type. Such changes are local, and with the help of directed substitutions, it is possible to create the required spatial distribution of the anharmonic component over the crystal.The design of the calcium apatites structure by the method of isomorphic substitutions of (XO4) tetrahedra with tetrahedra of various types and with different ratios makes it possible to control the energy band gap width.

Components of the Shear Modulus and Their Dependence on Temperature and Plastic Deformation of a Metallic Glass

High-precision measurements of the temperature dependences of the high-frequency shear modulus G performed on as-cast, preannealed and predeformed Zr46Cu45Al7Ti2 bulk metallic glass allowed us to determine, for the first time, the harmonic, anharmonic, electronic and relaxation components of G. The dependence of anharmonic, electronic and relaxation components on temperature and preliminary inhomogeneous (localized) plastic deformation was investigated. It is found that plastic deformation results in a significant change in these components. We showed that the increase in the integral relaxation contribution to the shear modulus with an increase in plastic deformation can be quantitatively described within the framework of the interstitialcy theory. It is also found that plastic deformation simultaneously leads to an increase in the anharmonic and decrease in the electronic components of the shear modulus.

Partial coherence and amplified internal energy when thermal radiation is sourced within matter

Photons excited into ground state modes at finite temperature display partitioning among photon phases, lifetimes and distances travelled since creation. These distributions set the distance from an interface a created photon has some chance of emission. Excited photons have phase velocity set by their mode’s propagation index n which sets mode density then internal energy contribution. All photons that strike an interface obliquely if emitted are refracted, and their exit intensities are irreversible except when weak internal attenuation occurs. Attenuation index k near zero degrees is small, so reversibility is approximate. As temperature rises refraction of exiting photons varies. Total emission remains reversible after transitioning through a nonequilibrium state with no other heat inputs. In equilibrium the densities of excitations that create and annihilate photons are in balance with photon densities, and emissivity dependent on n, k, temperature, and internal incident direction. Exit intensities from pure water and crystalline silica are modelled. They contain strong resonant intensities, and match data accurately. Intrinsic resonances formed within liquids and compounds are due to photon modes hybridising with localized excitations, including molecular oscillations and the anharmonic component of lattice distortions. They explain the many resonant spectral intensities seen in remote sensing. Each hybrid oscillator is a photonic virtual bound state whose energy fluctuates between levels separated by hf. Other features addressed are radiance when solid angle changes at exit, anomalous refraction, thermal recycling of internally reflected photons, fluxes within multilayers, and enhanced internal heat flux from phonon drag by photon density gradients under an external temperature gradient.

Machine learned interatomic potentials for modeling interfacial heat transport in Ge/GaAs

Molecular dynamics simulations provide a versatile framework to study interfacial heat transport, but their accuracy remains limited by the accuracy of available interatomic potentials. Past researchers relied on simple analytic potentials and the use of mixing rules to model interface systems, but with minimal justification for their use. Contemporary researchers have access to highly flexible machine learned interatomic potentials (MLIPs), yet these remain understudied within this problem domain. In either case, efforts are needed to rigorously assess and validate interatomic potentials prior to their use in MD simulations of interfacial heat transport. Here, we pursue these efforts while developing interatomic potentials for a model Ge/GaAs system. We first assess the quality of ab initio harmonic force constants (IFC2s) obtained from the interface structure that is used to generate fitting data for MLIPs. We show that these force constants can converge to near bulk-like values within 1 nm away from the interface while also exhibiting a complex relationship across the interface, which likely precludes any successful application of mixing rules. Subsequently, we develop two different MLIPs to model Ge/GaAs using the linear spectral neighborhood analysis potential (SNAP) functional form: one standard SNAP fit to total forces, and another hybrid SNAP fit to anharmonic force components and combined with a harmonic Taylor expansion potential. Each potential is evaluated with respect to bulk thermal properties, interface IFC2s, and stability considerations, providing a valuable comparative analysis that can guide future work.

Revisiting the thermal conductivity of Si, Ge and diamond from first principles: roles of atomic mass and interatomic potential

The thermal conductivity (κ) of nonmetals is determined by the constituent atoms, the crystal structure and interatomic potentials. Although the group-IV elemental solids Si, Ge and diamond have been studied extensively, a detailed understanding of the connection between the fundamental features of their energy landscapes and their thermal transport properties is still lacking. Here, starting from first principles, we analyze those factors, including the atomic mass (m) and the second- (harmonic) and third-order (anharmonic) interatomic force constants (IFCs). Both the second- and third-order IFCs of Si and Ge are very similar, and thus Si and Ge represent ideal systems to understand how the atomic mass alone affects κ. Although the group velocity (v) decreases with increasing atomic mass (), the phonon lifetime (τ) follows the opposite trend (). Since the contribution to κ from each phonon mode is approximately proportional v 2 τ, κ is lower for the heavier element, namely Ge. Although the extremely high thermal conductivity of diamond is often attributed to weak anharmonic scattering, the anharmonic component of the interatomic potential is not much weaker than those of Si and Ge, which seems to be overlooked in the literature. In fact, the absolute magnitude of the third-order IFCs is much larger in diamond, and the ratios of the third-order IFCs with respect to the second-order ones are comparable to those of Si and Ge. We also explain the experimentally measured κ of high-quality diamonds (Inyushikin et al 2018 Phys. Rev. B 97 144305) by introducing boundary scattering into the picture, and obtain good agreement between calculations and measurements.

The “Generalized Skettrup Model” and Lattice Thermal Capacity of Graphene, h-BN, MoS2, and WS2 Flakes

Temperature dependencies of both harmonic (including contributions from the “flexural” modes) and anharmonic components of the isobaric lattice thermal capacity of square flakes of graphene, hexagonal boron nitride (h-BN) as well as of those of disulphides of molybdenum (MoS2) and tungsten (WS2) are simulated based on the many-body formalism denoted formerly as the “Generalized Skettrup Model” (GSM). This formalism (initially developed for the “first-principles” simulations on the essential features of electronic and optical bandtails of 3-dimensional (3D) polycrystalline and spatially non-homogeneous amorphous semi-conductors and insulators) had been refined herein for appropriate evaluations on the lattice thermal capacity of two-dimensional (2D) semiconductors. Obtained 2D GSM simulation results are discussed comparison with predictions of some other simulation approaches and results of appropriate experiments.

Harmonic phase transition in solids under high pressures

The binding energy of atoms in substances exceeds the energy of the harmonic vibrator owing to the anharmonicity (Fig. 1). Experiments show reduction of the anharmonic component of binding energy in solids under high pressures. These data allow us to determine values of pressures when the coefficients of thermal expansions become equal to zero, i.e. when the harmonic phase transition occurs.

Colloidal crystallites under external oscillation.

We study the two-dimensional assemblies of interacting colloidal particles in a loosely focussed optical trap. As the optical confinement is increased, the system becomes ordered and we investigate how these crystallites maintain their order under externally imposed oscillation. For small amplitudes, the crystalline order remains intact and the system behaves like a rigid body as predicted by numerical simulations. However, the rigidity breaks at large amplitudes, which we infer to be caused by the anharmonic component of the confinement potential. These studies are general enough to be applied to other physical systems comprising ordered finite-sized assemblies under external dynamic perturbation.

An Efficient Timer and Sizer of Biomacromolecular Motions

Life ticks as fast as how proteins move. Computationally expensive molecular dynamics simulation has been the only theoretical tool to gauge the time and sizes of these motions, though barely to their slowest ends. Here, we convert a computationally cheap elastic network model (ENM) into a molecular timer and sizer to gauge the slowest functional motions of structured biomolecules. Quasi-harmonic analysis, fluctuation profile matching, and the Wiener-Khintchine theorem are used to define the "time periods," t, for anharmonic principal components (PCs), which are validated by nuclear magnetic resonance (NMR) order parameters. The PCs with their respective "time periods" are mapped to the eigenvalues (λENM) of the corresponding ENM modes. Thus, the power laws t(ns)= 56.1λENM-1.6 and σ2(Å2)= 32.7λENM-3.0 can be established allowing the characterization of the timescales of NMR-resolved conformers, crystallographic anisotropic displacement parameters, and important ribosomal motions, as well as motional sizes of the latter.

Особенности релаксации сдвиговой упругости металлических стекол

Работа направлена на установление закономерностей изменения сдвиговой упругости, возникающих при структурной релаксации металлических стекол на основе Pd и Zr. Измерения модуля сдвига выполнялись на частотах около 500 кГц. Несмотря на отличия в физических свойствах исследованных металлических стекол (химический состав, стеклообразующая способность, температуры стеклования и др.), наблюдаются определенные общие закономерности релаксации их сдвиговой упругости при термообработке.
 
 ИСТОЧНИК ФИНАНСИРОВАНИЯ
 Работа поддержана грантом Минобрнауки РФ № 3.1310.2017/4.6.
 
 БЛАГОДАРНОСТИ
 Автор выражает благодарность проф. В.А. Хонику за обсуждение статьи
 
 
 ЛИТЕРАТУРА
 
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СЛАБОУСТОЙЧИВОЕ СОСТОЯНИЕ КРИСТАЛЛИЧЕСКОЙ РЕШЕТКИ МЕТАЛЛОВ И СПЛАВОВ

The state of the crystalline medium under the conditions of thermal fluctuations and mechanical stresses called weakly stable is determined by the displacement of atoms at a relative distance of 0.15 – 0.20 from the equilibrium positions. Such a displacement of the atoms follows the Lindemann criteria of the crystals melting, and the state of atomic ensemble can be described as delocalized one. The state of delocalization means the transition of the atom through the maximum of interaction force and is characterized by a strong anharmonic component of oscillations and softening of elastic modules. It is the state of delocalization of the atomic ensemble that is the weakly stable state of the crystal lattice. Weakly stable state of metal materials is manifested in a wide range of phenomena. These include abnormal reduction of elastic modules in thermoelastic martensitic transformations, second-order structural-phase transitions with the formation of long-period structures, abrupt plastic deformation, most clearly manifested in aluminium and its alloys, increasing the rate of deformation during creep in the ultrasonic field under static load. This paper presents the results of the analysis of the weakly stable state of the crystalline medium, especially in plastic deformation, that is, in the processes caused by the displacement of atoms from the equilibrium position. In these processes, the weakly stable state of the system can occur in the field of mechanical stresses and thermal fluctuations when the acoustic field of standing waves is applied, formed by primary acoustic emission signals, the combined action of which allows to overcome the potential barrier. In this state, the oscillatory displacement of the acoustic standing wave acts as a factor of self-organization, that is, it may be sufficient to activate the correlated dislocation slip, in fact, the athermal above-barrier slip in the weakly stable state of the crystal lattice.

Fundamentals of travelling wave ion mobility revisited: I. Smoothly moving waves

We give a generalised and simplified theoretical treatment of travelling wave ion mobility (TWIM), and demonstrate that it is equivalent to previously published results in the special case of symmetric waveforms. Using this result, we derive exact expressions for the trajectory and transit time of ions in a smoothly moving sinusoidal TWIM device, opening up the possibility of direct (i.e. uncalibrated) CCS measurement in such a device. We then show that two effects that would need to be considered in a realistic device, namely anharmonic components of the waveform and velocity relaxation, can be included perturbatively in our approach. We consider the effect of velocity relaxation on calibrated CCS measurement and examine the importance of including a realistic treatment of diffusion.

Finite Temperature Properties of NiTi from First Principles Simulations: Structure, Mechanics, and Thermodynamics.

We present a procedure to determine temperature-dependent thermodynamic properties of crystalline materials from density functional theory molecular dynamics (DFT-MD). Finite temperature properties (structural, thermal, and mechanical properties) of the phases (ground state monoclinic B33, martensitic B19', and austenitic B2) of the shape memory alloy NiTi are investigated. Fluctuation formulas and numerical derivatives are used to evaluate mechanical and thermal properties. A modified version of thermodynamic upsampling is used to enable simulations with lower DFT convergence thresholds. In addition, a thermodynamic integration expression is developed to compute free energies from isobaric DFT-MD simulations that accounts for volume changes. Structural parameters, elastic constants, volume expansion, and specific heats as a function of temperature are evaluated. Phase transitions between B2 and B19' and between B19' and B33 are characterized according to their thermal energy, entropy, and free energy differences as well as their latent heats. Anharmonic effects are shown to play a large role in both stabilizing the austenite B2 phase as well as suppressing the martensitic phase transition. The quasiharmonic approximation to the free energy results in large errors in estimating the martensitic transition temperature by neglecting these large anharmonic components.

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving.

We present a cooling method for a cold Fermi gas by parametrically driving atomic motions in a crossed-beam optical dipole trap (ODT). Our method employs the anharmonicity of the ODT, in which the hotter atoms at the edge of the trap feel the anharmonic components of the trapping potential, while the colder atoms in the center of the trap feel the harmonic one. By modulating the trap depth with frequencies that are resonant with the anharmonic components, we selectively excite the hotter atoms out of the trap while keeping the colder atoms in the trap, generating parametric cooling. This experimental protocol starts with a magneto-optical trap (MOT) that is loaded by a Zeeman slower. The precooled atoms in the MOT are then transferred to an ODT, and a bias magnetic field is applied to create an interacting Fermi gas. We then lower the trapping potential to prepare a cold Fermi gas near the degenerate temperature. After that, we sweep the magnetic field to the noninteracting regime of the Fermi gas, in which the parametric cooling can be manifested by modulating the intensity of the optical trapping beams. We find that the parametric cooling effect strongly depends on the modulation frequencies and amplitudes. With the optimized frequency and amplitude, we measure the dependence of the cloud energy on the modulation time. We observe that the cloud energy is changed in an anisotropic way, where the energy of the axial direction is significantly reduced by parametric driving. The cooling effect is limited to the axial direction because the dominant anharmonicity of the crossed-beam ODT is along the axial direction. Finally, we propose to extend this protocol for the trapping potentials of large anharmonicity in all directions, which provides a promising scheme for cooling quantum gases using external driving.

Structural Stability and Anharmonicity of Pr2Ti2O7: Raman Spectroscopic and XRD Studies.

Herein we report results of pressure- and temperature-dependent Raman scattering studies on Pr2Ti2O7. Pressure-dependent studies performed up to 23 GPa suggest a reversible phase transition above 15 GPa with subtle changes. Temperature-dependent investigations performed in the range of 77-1073 K showed anomalous temperature dependence of some of the Raman modes. Temperature-dependent X-ray diffraction data indicated no structural transition but nonlinear expansion of unit-cell parameters with increasing temperature. With increasing temperature, the structure dilates anisotropically, and volume of coordination polyhedra around all the atoms expands. Also with increasing temperature the distortions in coordination polyhedra around all the atoms decrease, and appreciable decrease is observed in Pr(1)O10 and Pr(3)O9 units. The pressure evolution of Raman-mode frequencies was analyzed for both ambient as well as high-pressure phases, and mode Grüneisen parameters for ambient pressure phase were obtained. The temperature evolution of Raman-mode frequencies was analyzed to obtain the explicit and implicit anharmonic components, and it was found that some of the modes attributable to TiO6 octahedra and PrOn polyhedra have dominating explicit anharmonic component. Comparison of the structural data with the temperature dependence of Raman modes suggests that the anomalous behavior in Raman modes is due to phonon-phonon interaction.

Phonon anharmonicity and negative thermal expansion in SnSe

The anharmonic phonon properties of SnSe in the Pnma phase were investigated with a combination of experiments and first-principles simulations. Using inelastic neutron scattering (INS) and nuclear resonant inelastic X-ray scattering (NRIXS), we have measured the phonon dispersions and density of states (DOS) and their temperature dependence, which revealed a strong, inhomogeneous shift and broadening of the spectrum on warming. First-principles simulations were performed to rationalize these measurements, and to explain the previously reported anisotropic thermal expansion, in particular the negative thermal expansion within the Sn-Se bilayers. Including the anisotropic strain dependence of the phonon free energy, in addition to the electronic ground state energy, is essential to reproduce the negative thermal expansion. From the phonon DOS obtained with INS and additional calorimetry measurements, we quantify the harmonic, dilational, and anharmonic components of the phonon entropy, heat capacity, and free energy. The origin of the anharmonic phonon thermodynamics is linked to the electronic structure.

Spontaneous ‐Symmetry Breaking in Nonlinearly Coupled van der Pol Oscillators

Parity‐time () symmetry, initially proposed in the context of Quantum Mechanics and Quantum Field Theory, has recently been studied and demonstrated in optical and electronic systems where laboratory demonstrations are possible. The model considered here consists of two nonlinearly coupled van der Pol (VDP) oscillators, originally studied in [1]. This dimer serves as an experimental realization of a class of nonlinear systems, where the anharmonic component has gain for one oscillator and loss of equal strength for the other, so that Hermiticity is broken while symmetry is preserved. The existence of spontaneous symmetry breaking at some critical value of the gain/loss parameter is proven by use of modulation theory in the weakly nonlinear regime, and by use of asymptotic methods to demonstrate relaxed oscillations for a strongly nonlinear coupling. We then prove similar phenomena in an infinite chain composed of such VDP dimers in the long‐wave limit. Finally, we perform initial studies of asymmetric transport properties in the VDP arrays.

Compositional behavior of Raman-active phonons inPb(Zr1−xTix)O3ceramics

A systematic study of the Raman spectra of Pb(Zr1-xTix)O-3 (PZT) ceramics has been performed in a broad temperature interval (10-600 K) and a broad Ti/Zr concentration range around the morphotropic phase boundary (x = 0.25-0.70). The number of the spectral components was estimated by a standard fitting procedure with damped harmonic oscillators as well as by counting the number of peaks and shoulders with the help of a purposely designed mathematical analysis based on frequency derivatives of the Raman spectra. This last method proves to be very useful to study Raman spectra of disordered materials. For the case of PZT, the comparison with the Raman modes of PbTiO3 allows us to assign the phonon bands on both sides of the morphotropic phase boundary, and the crossover from the tetragonal to rhombohedral phase spectra is clearly visible. However, there are no indications of a systematic splitting of the E-symmetry modes into monoclinic A'-A '' doublets in the morphotropic samples. Detailed adjusting of the response function to the spectrum requires to assume additional Raman-active modes, but this holds for a much broader concentration range than that of the anticipated monoclinic phase. In particular, the lowest frequency transverse optic mode of E-symmetry (soft mode of the ferroelectric phase transition) is split into two components, a THz frequency anharmonic (central modelike) component and a resonant component (at omega similar to 80 cm(-1)), both related to the same normal coordinate. The additional Raman band appearing in this frequency range (omega similar to 65 cm(-1)) at low temperatures is rather associated with the antiphase tilt vibrations of the oxygen octahedra.