Thermal Vibration Amplitude Research Articles

The role of thermal vibrations in transformation of structure transition for sodium nitrate in a restricted geometry

The temperature evolution of the crystal structure and dielectric response of a nanocomposite based on porous glasses with an average pore diameter of 7 nm and embedded sodium nitrate in the temperature range of 300–600 K have been studied on heating. The temperature dependences of the amplitudes of thermal vibrations of ions in sodium nitrate nanoparticles are obtained, and the activation energies of sodium hopping conductivity in these nanocomposite materials are determined. The results obtained allow us to state that it is the sharp increase in thermal vibrations that leads to the appearance of the previously observed crossover in the temperature dependence of the order parameter of the structural transition in sodium nitrate nanoparticles at T* ∼455 K and to a decrease in the activation energy of sodium ions hopping conductivity on heating above T*.

Quantifying Molecular Disorder in Tri-Isopropyl Silane (TIPS) Pentacene Using Variable Coherence Transmission Electron Microscopy.

Structural disorder in molecular crystals is a fundamental limitation for achieving high charge carrier mobilities. Quantifying and uncovering the mechanistic origins of disorder are, however, extremely challenging. Here we use variable coherence transmission electron microscopy to analyze disorder in tri-isopropyl silane pentacene films, utilizing diffuse scattering that is present both as linear streaks and as a slowly varying, isotropic background. The former is due to thermal vibration of the pentacene molecules along their long axis, while the latter is due to static defects kinetically frozen during film deposition. The thermal vibrational amplitude is ∼0.4 Å, while the static displacement parameter in our simplified analysis is much larger (1.0 Å), because it represents the cumulative scattering of all defect configurations that are frozen in the film. Thin film fabrication therefore has an important effect on crystallinity; our technique can be readily used to compare samples prepared under different conditions.

Metallic bonds and thermal vibration in brass.

Nature of the metallic bond and thermal vibration in brass alloy is investigated from the local structural and thermodynamical points of view by the temperature-dependent Cu and Zn K-edge extended X-ray absorption fine structure spectroscopy and the path-integral effective classical potential theoretical simulation. It is unexpectedly found that the thermal vibrational amplitude around Zn is a little but meaningfully smaller than that around Cu, although it is usually believed that Zn is a much softer metal than Cu in terms of various thermodynamical physical quantities of elemental metals. Moreover, it is found that the nearest neighbor distance around Zn is almost equivalent to that around Cu (only ∼0.01 Å difference), although the metallic radius of Zn commonly used is considerably larger than that of Cu (∼0.06-0.09 Å difference). These peculiar findings can be interpreted as a result of confinement of Zn atoms in a smaller space than usual and a significantly larger repulsive potential of Zn than Cu.

Dependences of the Interatomic Quasielastic Force Coefficient and the Root-Mean-Square Amplitude of Thermal Vibrations of Atoms on the Configuration of Valence Electrons

The interatomic quasielastic force coefficient f and the root-mean-square amplitude of thermal vibrations √︀u2 of atoms in s-, d-, and p-elements located in various groups of Mendeleev’s Periodic Table are calculated. It is found that, with an increase in the atomic number of elements in the groups, the quasielastic force coefficient f and the amplitudes √︀u2 of thermal vibrations of atoms in the s-, d-, and p-elements change according to different patterns depending on the atomic number of the element in a group. The discovered regularities can be explained by the configurational model of the electronic structure of matter.

Experimental X-ray Charge-Density Studies─A Suitable Probe for Superconductivity? A Case Study on MgB2.

Case studies of 1T-TiSe2 and YBa2Cu3O7-δ have demonstrated that X-ray diffraction (XRD) studies can be used to trace even subtle structural phase transitions which are inherently connected with the onset of superconductivity in these benchmark systems. However, the utility of XRD in the investigation of superconductors like MgB2 lacking an additional symmetry-breaking structural phase transition is not immediately evident. Nevertheless, high-resolution powder XRD experiments on MgB2 in combination with maximum entropy method analyses hinted at differences between the electron density distributions at room temperature and 15 K, that is, below the Tc of approx. 39 K. The high-resolution single-crystal XRD experiments in combination with multipolar refinements presented here can reproduce these results but show that the observed temperature-dependent density changes are almost entirely due to a decrease of atomic displacement parameters as a natural consequence of a reduced thermal vibration amplitude with decreasing temperature. Our investigations also shed new light on the presence or absence of magnesium vacancies in MgB2 samples─a defect type claimed to control the superconducting properties of the compound. We propose that previous reports on the tendency of MgB2 to form non-stoichiometric Mg1-xB2 phases (1 - x ∼ 0.95) during high-temperature (HT) synthesis might result from the interpretation of XRD data of insufficient resolution and/or usage of inflexible refinement models. Indeed, advanced refinements based on an Extended Hansen-Coppens multipolar model and high-resolution X-ray data, which consider explicitly the contraction of core and valence shells of the magnesium cations, do not provide any significant evidence for the formation of non-stoichiometric Mg1-xB2 phases during HT synthesis.

Elucidation of local structure deformation in κ−(BEDT−TTF)2Cu[N(CN)2]Br by x-ray fluorescence holography

$\ensuremath{\kappa}\text{\ensuremath{-}}{(\mathrm{BEDT}\text{\ensuremath{-}}\mathrm{TTF})}_{2}\mathrm{Cu}[\mathrm{N}{(\mathrm{CN})}_{2}]\mathrm{Br} (\ensuremath{\kappa}\text{\ensuremath{-}}\mathrm{Br})$ is an organic superconductor that changes to an Anderson-type insulator due to the random defects introduced by x-ray irradiation. In this study, we directly investigated the effects of irradiation on the local structures in the anion layer of $\ensuremath{\kappa}\text{\ensuremath{-}}\mathrm{Br}$ using x-ray fluorescence holography. The local structures around the Cu atoms in the anion layer were directly reconstructed from holograms. Prior to radiation damage, the reconstruction clearly shows the atomic images of the Br and N atoms that are directly coordinated to Cu. In the irradiated samples, the N images in the reconstructions were strongly suppressed as a result of the positional fluctuations of N introduced by the defects induced by irradiation. Using the previously proposed ``bond-shifted'' model and the thermal vibration amplitudes calculated from molecular dynamics simulations, we simulated the holograms and the atomic reconstructions of the anion layer. The simulations show that the ``bond-shifted'' model, along with thermal vibrations at 100 K, suppresses the N atomic images, as was observed in the experimental reconstructions.

Effect of temperature on the electrical conduction and dielectric behavior of solder

Solder is widely used as an electrical conductor in electronics. This paper reports the effect of heating up to 70 °C on the conduction and dielectric behavior of solder (Sn–4Ag lead-free eutectic solder). The effect of temperature on the electric permittivity is reported for the first time for metals in general. The electrical resistivity increases linearly with the temperature, with the temperature coefficient of resistivity equaling 3.59 × 10–3/°C. The relative permittivity is 3.24 × 106 (100 kHz) and does not change with the temperature. This suggests that the increase in the amplitude of thermal vibration as the temperature increases impacts the conduction behavior more than the dielectric behavior, which hinges on the electron–atom interaction. The increase in the thermal vibration amplitude apparently enhances the electron scattering without affecting the electron–atom interaction, which occurs primarily at defects such as the interfaces in the solder microstructure. The absence of change of the permittivity with the increase in temperature is attractive for the practical use of solder as electrical conductors in electronics.

О среднеквадратичной амплитуде нулевых колебаний атомов в кристалле

It is shown that the values of the energy and amplitude of zero-point vibrations of atoms in a crystal, due to the uncertainty principle, depend on the dynamic characteristics of atoms in the crystal. It was found that the root-mean-square amplitude of thermal and zero-point vibrations of atoms, like other properties, has a periodic dependence on the ordinal number of elements in the Mendeleev's Periodic Table. It is shown that the value of the root-mean-square amplitude of thermal vibrations of atoms in a lattice of elements with a high value of the Debye temperature at room temperature does not differ much from the value of the amplitude of zero-point vibrations of atoms (at T = 0 K). This is explained by the small number of excited vibrations with the maximum frequency in these crystals at room temperature, since the room temperature is much lower than their Debye temperature, at which the entire spectrum of thermal vibrations of atoms in the crystal is excited. The results can be used in materials science and technology to assess the strength and thermo physical characteristics of materials at cryogenic temperatures, without resorting to measuring them directly at absolute zero.

ОСОБЕННОСТИ ЭВОЛЮЦИИ НАНОМАСШТАБНЫХ ХАРАКТЕРИСТИК МЕТАЛЛА ПРИ НАГРУЖЕНИИ ТЕРМИЧЕСКИМИ ЦИКЛАМИ

Актуальность исследования обусловлена отсутствием экспериментальных данных, устанавливающих связь между субмикроскопическими свойствами (свойствами III рода) и макроскопическими свойствами I рода. Такая взаимосвязанность, являющаяся фактором влиянияна отношение «микроструктура–прочность», может способствовать дальнейшим успехам в решении вопросов ресурса. Цель исследования заключается в установлении влияния циклических термических нагрузок на среднеквадратичные смещения атомов как показатель прочности межатомных связей и микроповрежденности металла пароперегревательных труб. Объектом исследования являются образцы из околошовных зон однородного сварного шва, выполненного из жаропрочной перлитной стали 12Х1МФ. Методы: физическое моделирование условий эксплуатации путем воздействия на образцы циклами термической нагрузки в электропечи МИМП-10УЭ, рентгенометрия образцов, оценка внутренних структурных напряжений на рентгеновских дифрактометрах ДРОН, морфология поверхности с помощью портативного электронного микроскопа типа PENSCKOPE. Результаты.Установлено влияние циклических термических нагрузок на среднеквадратичные смещения атомов. Показано, что в результате термического влияния прочность межатомных связей увеличивается. Проиллюстрирована корреляция между субмикро- и макроскопическими характеристиками прочности, и показано, что амплитуда тепловых колебаний атомов, являясь характеристикой прочности межатомных связей, может быть диагностическим признаком накопления и развития повреждаемости металла. Уменьшение амплитуды среднеквадратичных смещений атомов при термоциклировании объяснено на основе гипотезы о возникновении твердых растворов замещения в результате процесса азотирования поверхности молекулярным азотом атмосферного воздуха. В рамках этой гипотезы показано, что одним из механизмов осцилляции внутренних напряжений I рода при термоциклировании может быть процесс азотирования поверхности, приводящий к организации в многокомпонентных легированных сталях сложных связей «металл–неметалл», направленных на поддержание устойчивости системы твердых растворов.

The origin of heavy element doping to relieve the lattice thermal vibration of layered materials for high energy density Li ion cathodes

We report an effective strategy to inhibit the phase transition of LiCoO2 from hexagonal layered to cubic spinel during delithiation. The small thermal vibration amplitude of the Sn dopant helps pin the lattice vibration, stabilizing CoO6 octahedra during charge/discharge.

Mechanical feedback cooling assisted by optical cavity cooling of the thermal vibration of a microcantilever

This study describes a new two-step process to cool the thermal vibration of microcantilevers. The process combines active mechanical feedback cooling and optical cavity cooling. A micro-Fabry–Perot interferometer, built in-house, is set atop a microcantilever to measure the vibration amplitude, the high optical power density of which induces cavity cooling in the optical cavity. Using a two-step cooling procedure, the equivalent temperature of the thermal vibration of a microcantilever is lowered from room temperature to the theoretical cooling limit of 0.063 K, a much lower temperature than that achieved via simple cavity cooling (18 K), and then by mechanical feedback cooling (0.135 K) obtained for the same type of microcantilevers in previous studies. This experimental demonstration showcases a new type of cooling process of the amplitude of thermal vibration for micro-mechanical resonators to a lower temperature and does not need additional cooling using a conventional cryogenic refrigerator.

Evaluation of lattice displacement and electrical property of Zn-ion implanted GaN by Rutherford backscattering spectrometry

The lattice displacement in Zn-ion implanted GaN single crystal wafer is evaluated by Rutherford backscattering spectrometry using proton beam and Photoluminescence measurements. Zn-ion implantation into GaN single crystal wafer is performed with energies of 300 KeV (ion fluence: 2.32 × 1014cm-2), 500 KeV (3.02 × 1014cm-2) and 700 KeV (4.65 × 1014cm-2) at room temperature. The displacement concentration of Ga and N atoms evaluated from minimum yields along <0 0 0 1> direction are 4.8 × 1021 cm−3 and 3.6 × 1021 cm−3 respectively, for as-implanted GaN and decrease to 2.3 × 1021 cm−3 and 4.7 × 1020 cm−3 by annealing in N2 ambient at 700 °C. The lattice displacement of Ga atoms for as-implanted GaN evaluated from the half-value angle of the channeling dip is 0.094 Å for Zn-implanted GaN and recovers to a value of the thermal vibrational amplitude by annealing. The intensity of Yellow Luminescence (YL) observed at around 530 nm for as-implanted GaN increases significantly compared to un-implanted ones, suggesting that gallium vacancy acceptor and nitrogen vacancy donor as origins of YL are induced by Zn-ion implantation. The YL intensity for annealed GaN is almost same as the one for un-implanted GaN. The sheet resistance is 1.04 × 102cm-2 Ω/sq. for un-implanted, 3.98 × 109cm-2 Ω/sq. for as-implanted, and 3.77cm-2 Ω/sq. for annealed GaN. The high resistance for as-implanted GaN is attributed to gallium vacancy as a compensation center. The low resistance and the decrease of YL intensity after annealing is attributed to both a shallow nitrogen vacancy and the decrease of gallium vacancy.

Rainbow Scattering of Inert Gas Atoms on Aluminum and Silver Crystal Surfaces

Particle trajectories are calculated to study the rainbow scattering and the focusing of Ar atoms on the Al(111) and Ag(111) crystal surfaces and Ne, Ar, and Kr atoms on the Al(001) crystal surface. The rainbow-scattering-induced features in spectra are used to determine the thermal vibration amplitudes of atoms for the Al(111) and Ag(111) targets. These data agree with the data of independent measurements. The dependence of the position of a rainbow peak on the initial energy of atoms is used to find the atom–surface interaction potentials in the energy range of 0.3–70 eV for the case Ar–Ag and 3–45 eV for other cases. The values and the functional dependences of the potentials on the internuclear distance differ strongly from the well-known pair potential models. This difference is associated with the interaction of a projectile atom with the conduction electrons in a metal.

Negative thermal expansion of ScF3: first principles vs empirical molecular dynamics

The crystal lattice of cubic scandium fluorine (ScF3) exhibits negative thermal expansion (NTE) over a wide range of temperatures from 10 K to 1100 K. Here the NTE effect in ScF3 is studied using atomistic simulations based on empirical and ab initio molecular dynamics (AIMD) in the isobaric-isothermal (NpT) ensemble. The temperature dependence of the average lattice constant, the Sc–F–Sc bond angle distribution and the radial distribution functions were obtained. Crossover from the NTE to positive thermal expansion occurring at about 1100 K is reproduced by AIMD simulations in agreement with the known experiment data. At the same time, empirical MD model fails to reproduce the NTE behaviour and suggests an expansion of the ScF3 lattice with increasing temperature. However, both MD models predict strong anisotropy of fluorine atom thermal vibration amplitude, being larger in the direction orthogonal to the Sc–F–Sc atom chain.

Effect of entanglements on temperature response of gel immobilized microgel photonic crystals

We report here, an evidence of entanglements between polymer chains of thermo-responsive microgels with the immobilizing hydrogel, by studying the temperature dependent dynamics of the microgel-hydrogel composite. The dynamics measurements show a decrease in amplitude of microgel thermal vibrations with an increase in temperature in contrast to the expected amplitude increase, confirming the binding between microgel and hydrogel through the entanglement of their polymer chains. The consequences of these entanglements on the temperature dependence of diffraction of immobilized microgel crystals, across the volume phase transition (VPT) of microgels, have been studied using UV–vis spectroscopy. As an effect of entanglements in immobilized microgel crystals, it is found that the crystalline order (the Bragg diffraction) is retained above VPT with small increase in structural disorder (width of the Bragg diffraction peak). Entanglements restrict thermal motion of microgels leading to retention of crystalline order above the VPT. However, it induces local strain in lattice due to shrinking of microgels upon VPT leading to a small increase in structural disorder.

Energy Spectrum of Relativistic Electrons Channeled Through Single-Wall Carbon Nanotubes

The energy eigenvalues of the channeled electrons through single wall carbon nanotubes (n,m) was calculated. According to the continuum model approximation given by Lindhard for the case of an axial channeling in single crystals, the actual periodic potential of a row of atoms is replaced by a potential averaged over a direction parallel to the row, called continuum potential. The calculations was executed by using the atomic interaction potential as given by Moliere potential. The maximum number of bound states and the energy eigenvalues is calculated for positrons of 100 MeV energy incident in a direction parallel to the nanotube axis, by using WKB method. The calculations showed that the effect of temperature by using Debye approximation of thermal vibration amplitude on the channeling potential is very small and gave the same eigenvalues and the same number of bound states as that for the static nanotubes.

Mode-selective control of thermal Brownian vibration of micro-resonator (Generation of a thermal no-equilibrium state by mechanical feedback control)

Recently, there have been various attempts to dampen the vibration amplitude of the Brownian motion of a microresonator below the thermal vibration amplitude, with the goal of reaching the quantum ground vibration level. To further develop the approach of reaching the quantum ground state, it is essential to clarify whether or not coupling exists between the different vibration modes of the resonator. In this paper, the mode-selective control of thermal Brownian vibration is shown. The first and the second vibration modes of a micro-cantilever moved by a random Brownian motion are cooled selectively and independently below the thermal vibration amplitude, as determined by the statistical thermodynamic theory, using a mechanical feedback control method. This experimental result shows that the thermal no-equilibrium condition was generated by mechanical feedback control.

Quantum effects on thermal vibration of single-walled carbon nanotubes conveying fluid

In this paper, we investigate the microfluid induced vibration of a nanotube in thermal environment. Attention is focused on a special case that the law of energy equipartition is unreliable unless the quantum effect is taken into account. A nonlocal Euler–Bernoulli beam model is used to model the transverse vibration of a single-walled nanotube (SWCNT). Results reveal that the root of mean squared (RMS) amplitude of thermal vibration of the fluid-conveying SWCNT predicted from the quantum theory is lower than that predicted from the law of energy equipartition. The quantum effect on the thermal vibration of the fluid-conveying SWCNT is more significant for the cases of higher-order modes, lower flow velocity, lower temperature, and lower fluid density.

Molecular dynamics simulation of temperature effects on low energy near-surface cascades and surface damage in Cu

The temperature effects on near-surface cascades and surface damage in Cu(001) surface under 500eV argon ion bombardment were studied using molecular dynamics (MD) method. In present MD model, substrate system was fully relaxed for 1ns and a read-restart scheme was introduced to save total computation time. The temperature dependence of damage production was calculated. The evolution of near-surface cascades and spatial distribution of adatoms at varying temperature were analyzed and compared. It was found that near-surface vacancies increased with temperature, which was mainly due to the fact that more atoms initially located in top two layers became adatoms with the decrease of surface binding energy. Moreover, with the increase of temperature, displacement cascades altered from channeling-like structure to branching structure, and the length of collision sequence decreased gradually, because a larger portion of energy of primary knock-on atom (PKA) was scattered out of focused chain. Furthermore, increasing temperature reduced the anisotropy of distribution of adatoms, which can be ascribed to that regular registry of surface lattice atoms was changed with the increase of thermal vibration amplitude of surface atoms.

Study of Silicon Cantilevers by the Photoacoustic Elastic Bending Method

Rectangular silicon cantilevers are studied by the photoacoustic (PA) elastic bending method. Experimental signals versus modulation frequency of the excitation optical beam are measured and analyzed in a frequency range from 20 Hz to 50 000 Hz. The procedure for experimental signal correction to eliminate the frequency characteristics of the measuring system is given. The corrected experimental signal shows a good correlation with theoretically calculated PA signal at frequencies below 32 000 Hz. The corrected experimental PA elastic bending signals for cantilevers with different thicknesses are analyzed. The experimental results allow identifying the resonant frequency (the first resonant mode) of the cantilever vibrations. These values are in good agreement with the theoretically computed values. A theoretical model of the optically excited Si cantilever is derived, taking into account plasmaelastic, thermoelastic, and thermodiffusion mechanisms. Dynamic relations for the amplitude and phase of electronic and thermal elastic vibrations in optically excited cantilevers are derived. The theoretical model is compared to the experimental results.