Anharmonicity Of Atomic Vibrations Research Articles

Study on the conductivity of metal-based epitaxial graphene with vacancy defects and anharmonic effects

Metal-based epitaxial graphene exhibits extremely high conductivity at room temperature, making the study of its conductance crucial for understanding electron transport mechanisms in two-dimensional materials. In this paper, we applied solid-state physics theories and methods to investigate factors influencing the conductivity of metal-based epitaxial graphene. We considered the variation of conductivity and its temperature stability coefficient with temperature, taking into account the anharmonic vibrations of atoms, and explored the impact of anharmonic effects on conductivity. Using copper-based graphene as an example, we established relationships between temperature and several key parameters: electronic conductivity (σe), conductivity contributed by electron–phonon interactions (σp), conductivity contributed by vacancy defects (σn), and total conductivity (σ), along with its temperature stability coefficient (ασ). All research results were obtained within the temperature range of 300 K to 1200 K. The study reveals that σ decreases nonlinearly as temperature increases, with a magnitude on the order of (Ω ∙ m)-1, which is approximately equal to σp. The conductivity of copper-based epitaxial graphene is found to be greater than that of lithium-based epitaxial graphene. The anharmonic effects of atomic vibrations increase σ, and this increase is more pronounced at higher temperatures. The temperature stability coefficient ασ rapidly decreases with increasing temperature before tending to a constant, indicating that conductivity exhibits better temperature stability at higher temperatures. This paper provides theoretical guidance for understanding electron transport characteristics of metal-based epitaxial graphene and contributes to the design and application of high-performance electronic devices.

Thermoelectric transport properties of semiconductor film-based epitaxial monolayer graphene

ABSTRACT Epitaxial graphene on semiconductor films has potential for various applications due to its thermoelectric properties. We investigated factors affecting its thermo power using a solid-state physics approach, considering the interaction between the substrate and graphene, and exploring the effects of chemical potential, temperature, anharmonic vibrations of atoms, phonon-drag, and film thickness. Our results show that anharmonic effects significantly enhance the thermopower caused by electrons, especially at higher temperatures. Additionally, we observed an increase in total thermopower due to phonon-drag, although it has negligible effects at or above room temperature. We found that the thermopower on size-quantized semiconductor films is significantly higher than on metal conductor films and bulk semiconductor substrates. Decreasing the film thickness further increases the thermo power, providing an effective way to enhance the thermo electric properties of epitaxial graphene. Our findings contribute to a better understanding of the thermoelectric properties of epitaxial graphene on semiconductor films and offer valuable insights for future applications.

Carbon monoxide-sensing of SnS nanoflakes induced by the electron-trapped polaron upon the substituted-lithium

Two-dimensional (2D) SnS with wrinkled lattice and strong oxidation resistance exhibits malleable talents and great potential for gas-sensing applications. But it suffers the inherent disadvantage of low sensitivity towards weakly polarized gases like CO. Herein, inspired by the unique atomic real polarization and orbital penetration of lithium, a distinct polarized configuration of 2D Li-substituted SnS is proposed for achieving a moderate CO adsorption-desorption dynamics at room temperature. The 2D nanoflakes of Li-SnS, synthesized via one-step solvothermal method, reveal highly sensitive and selective performances towards trace CO as low as 2 ppm at RT. Conducting with first-principles calculations, the substitutional doping of Li in SnS crystal is unveiled as the knob to modulate the electronic state of SnS. The enhanced electron-deficiency states and the local vibration modes of Li atoms, urge the coupling of electrons and longitudinal-optical phonons to form a polaron on each Li site. These polarons serve as efficient electron traps, and synergize with anharmonic local vibrations of Li atoms to form energy state fluctuation, promoting CO adsorption-desorption dynamics and carrier transport for the SnS system. This work provides novel perspectives for understanding the structure-electrical configurations of 2D materials and the microscopic mechanism of gas adsorption.

Comparative study of high-temperature specific heat for Al–Pd–Mn icosahedral quasicrystals and crystal approximants

Quasicrystals (QCs) have a peculiar structural order characterized by quasiperiodicity and non-crystallographical point group symmetry. To reveal their characteristic physical property reflecting the peculiar structural order, specific heat measurements were performed for Al–Pd–Mn icosahedral QCs (i-QCs) and a series of crystal approximants (CAs) of 2/1- 1/1- and 1/0-cubic types at 400–1200 K. The measured specific heat per atom at constant pressure was converted to that at constant volume by using data of the thermal expansion coefficient and bulk modulus. Below ∼700 K, the values of all the specimens of i-QCs and CAs were close to ( Boltzman’s constant), i.e., they obeyed Dulong–Petit’s law. With further increase in temperature, the i-QCs showed a dramatic increase in with increasing temperature, and reached at 1100 K. In contrast, the 2/1 CAs showed a similar but slightly smaller increase in whereas the 1/1 and 1/0 CAs showed a negligible increase. The systematic behavior of in the order of CAs and QC demonstrates that a large excessive specific heat is a characteristic feature of QCs, reflecting the peculiarity of their structural order. Its possible physical mechanism was discussed in terms of anharmonic atomic vibrations, electronic excitations, and phasonic excitations.

Thermal expansion of solids: review on theories

The coefficient of thermal expansion of a solid can be derived from (1) anharmonicity of atomic vibrations; (2) lattice dynamics; (3) equation of state by G. Mie; (4) equation of state by E. Gruneisen; and (6) potential of interatomic interaction. Only the last theory in this list provides us with the equation describing correctly all features in the thermal expansion: (1) proportionality between thermal expansion and heat capacity; (2) various values of “plateau” for the coefficient of thermal expansion at temperatures close to Debye temperature; and (3) acceleration of the thermal expansion in the vicinity of melting point.

Effects of Doping of Lead Sulfide with Silver on the Lattice and Optical Properties of Pb1 –xAgxS Solid Solutions

Single-phase cubic Pb1 –xAgxS limited solid solutions based on PbS with a metal sublattice doped with Ag are produced. The maximal relative content of Ag in the Pb1 –xAgxS solid solutions reaches up to x = 0.15. The thermal expansion of semiconductor Pb1 –xAgxS solid solutions is first measured by the dilatometry technique in the temperature range from 295 to 580 K. The replacement of Pb atoms by Ag atoms in Pb1 –xAgxS results in a decrease in the coefficient of thermal expansion, which is due to a change in the anharmonicity of atomic vibrations and a slight increase in the elastic properties. For single-crystal PbS particles and Pb1 –xAgxS solid solutions, the spatial distributions of the modulus of elasticity E, the Poisson ratio μ, and the linear compressibility β in relation to the (hkl) direction are determined. The reflectance spectra of synthesized PbS, Ag2S, and Pb1 –xAgxS powders are recorded, and it is shown that the replacement of Pb by Ag in PbS is accompanied by an increase in the band gap.

Эффекты легирования сульфида свинца серебром на решеточных и оптических свойствах твердых растворов Pb-=SUB=-1-x-=/SUB=-Ag-=SUB=-x-=/SUB=-S

Single-phase limited cubic solid solutions Pb1-xAgxS based on PbS with a metal sublattice alloyed with silver are obtained. The maximum relative content of silver in solid solutions Pb1-xAgxS reaches x = 0.15. For the first time the thermal expansion of semiconductor solid solutions Pb1-xAgxS was measured by dilatometry method in the temperature range 295-580 K. Substitution of lead atoms by silver atoms in Pb1-xAgxS leads to a decrease in the coefficient of thermal expansion associated with a change in the anharmonicity of atomic vibrations and a weak increase in the elastic properties. For single-crystal particles PbS and solid solutions Pb1-xAgxS, spatial distributions of the elastic modulus E, Poisson's ratio , and linear compressibility  as a function of the direction (hkl) are found. The reflection spectra of the synthesized powders PbS, Ag2S and Pb1-xAgxS are measured and it is shown that the replacement of lead with silver in PbS is accompanied by an increase in the width of the band gap.

Quantifying Anharmonic Vibrations in Thermoelectric Layered Cobaltites and Their Role in Suppressing Thermal Conductivity

Optimizing multiple materials properties which are simultaneously in competition with each other is one of the chief challenges in thermoelectric materials research. Introducing greater anharmonicity to vibrational modes is one strategy for suppressing phonon thermal transport in crystalline oxides without detrimentally affecting electronic conductivity, so that the overall thermoelectric efficiency can be improved. Based on perturbed molecular dynamics and associated numerical analyses, we show that CoO2 layers in layered cobaltite thermoelectrics NaxCoO2 and Ca3Co4O9 are responsible for most of the in-plane heat transport in these materials, and that the non-conducting intermediate layers in the two materials exhibit different kinds of anharmonicity. More importantly, thermal conduction is shown to be altered by modifying the structure of the intermediate layers. The simulation methods developed to quantify the effect of anharmonic atomic vibrations on thermal conductivity provide a new tool for the rational design of thermoelectric materials, and the insights gained should hasten the attainment of higher conversion efficiencies so that thermoelectrics can be put to widespread practical use.

Second-order structural phase transitions, free energy curvature, and temperature-dependent anharmonic phonons in the self-consistent harmonic approximation: Theory and stochastic implementation

The self-consistent harmonic approximation is an effective harmonic theory to calculate the free energy of systems with strongly anharmonic atomic vibrations, and its stochastic implementation has proved to be an efficient method to study, from first-principles, the anharmonic properties of solids. The free energy as a function of average atomic positions (centroids) can be used to study quantum or thermal lattice instability. In particular the centroids are order parameters in second-order structural phase transitions such as, e.g., charge-density-waves or ferroelectric instabilities. According to Landau's theory, the knowledge of the second derivative of the free energy (i.e. the curvature) with respect to the centroids in a high-symmetry configuration allows the identification of the phase-transition and of the instability modes. In this work we derive the exact analytic formula for the second derivative of the free energy in the self-consistent harmonic approximation for a generic atomic configuration. The analytic derivative is expressed in terms of the atomic displacements and forces in a form that can be evaluated by a stochastic technique using importance sampling. Our approach is particularly suitable for applications based on first-principles density-functional-theory calculations, where the forces on atoms can be obtained with a negligible computational effort compared to total energy determination. Finally we propose a dynamical extension of the theory to calculate spectral properties of strongly anharmonic phonons, as probed by inelastic scattering processes. We illustrate our method with a numerical application on a toy model that mimics the ferroelectric transition in rock-salt crystals such as SnTe or GeTe.

Study of the effect of adhesion and anharmonicity of atomic vibrations on the thermal conductance of “metal–dielectric” interfaces

The method for calculating the thermal conductance of “metal–dielectric” interfaces, which takes into account the adhesive interaction and anharmonicity of atomic vibrations at the interface within the acoustic mismatch model and allows achieving better agreement of calculated and experimental data.

Borates—Crystal Structures of Prospective Nonlinear Optical Materials: High Anisotropy of the Thermal Expansion Caused by Anharmonic Atomic Vibrations

In the present study the thermal structure evolution is reviewed for known nonlinear optical borates such as β-BaB2O4, LiB3O5, CsLiB6O10, Li2B4O7, K2Al2B2O7, and α-BiB3O6, based on single-crystal and powder X-ray diffraction data collected over wide temperature ranges. Temperature-dependent measurements of further borates are presented for the first time: α-BaB2O4 (295–673 K), β-BaB2O4 (98–693 K), LiB3O5 (98–650 K) and K2Al2B2O7 (98–348 K). In addition to the established criteria for nonlinear optical (NLO) properties of crystals, here the role of the anisotropy and anharmonicity of the thermal vibrations of atoms is analysed as well as changes in their coordination spheres and the anisotropy of the thermal expansion of the crystal structure. Non-centrosymmetric borates, especially those that have NLO properties, often show distinct anisotropies for each cation in comparison to centrosymmetric borates. All considered NLO borates contain BO3 triangles, which are the principal cause of the strong anisotropy of the thermal expansion.

Thermal expansion of nanocrystalline and coarse-crystalline silver sulfide Ag2S

In situ studies of the thermal expansion of polymorphic phases of coarse-crystalline and nanocrystalline silver sulfide, namely, monoclinic acanthite α-Ag2S and cubic argentite β-Ag2S, have been performed for the first time by high-temperature X-ray diffraction. The temperature dependences of the unit cell parameters of acanthite and argentite have been measured from temperatures in the range of 300–623 K, and the thermal expansion coefficients of acanthite and argentite have been determined. The observed difference between the thermal expansion coefficients of nano- and coarse-crystalline acanthite is shown to be due to a small size of nanocrystalline silver sulfide particles, which leads to an increase in the anharmonicity of atomic vibrations.

Thermal expansion of nanostructured PbS films and anharmonicity of atomic vibrations

The dependences of the coherent scattering region size and thermal expansion coefficient α of a PbS nanofilm on the annealing temperature in the range of 293–473 K and on the duration of annealing at a constant temperature of 423 K have been measured. It has been found that the thermal expansion coefficient α of the PbS nanofilm is almost twice as much as the coefficient α of coarse-grained lead sulfide. It has been shown that the large difference in the coefficients α is associated with the small size of particles in the film, which leads to an increase in the anharmonicity of atomic vibrations. The contribution from the small size of particles to the thermal expansion coefficient of the PbS nanofilm has been evaluated theoretically.

温度をパラメータとした鉱物結晶学

Application of the Debye model to the temperature dependence of atomic mean square displacements determined by X-ray diffraction provides individual knowledge of dynamic and static natures of atomic displacements, together with characteristic values of crystals such as Debye temperature and one particle potential coefficients. The anharmonic refinement, incorporating the higher-order terms into the Debye-Waller factor, is a useful technique to detect the deformation of the probability density functions from ellipsoidal distribution due to anharmonic thermal vibrations and static disorders of atoms. Here we review our recent research that applied these approaches to Mg3Al2Si3O12 garnet, an important constituent in the Earth's interior. The research has proved the presence of the Mg static disorder, which has long been a controversial issue, and has proposed the possibility of anharmonic thermal vibrations of atoms at high temperature.

Linear Compressibility and Thermal Expansion of KMn[Ag(CN)2]3 Studied by Raman Spectroscopy and First-Principles Calculations

We have investigated the linear compressibility and thermal expansion properties of KMn[Ag(CN)2]3 using Raman spectroscopy and DFT calculations. Phonon frequencies and mode assignments from polarized Raman measurements and DFT calculations agree with each other satisfactorily. Computed linear compressibilities and thermal expansion coefficients corroborate the reported measured values. Pressure variation of mean partial phonon frequencies of KMn[Ag(CN)2]3 shows that large amplitude anharmonic displacements of Ag atoms can occur with minimum enthalpy cost even with increasing pressure. This means that Ag layer can be squeezed relatively easily, which manifests as PLC in the basal plane and coupled NLC along trigonal axis due to the rigid Mn-NC-Ag-CN-Mn chain along ⟨101⟩ crystal direction. Elastic constants of KMn[Ag(CN)2]3 indicate that the crystal is highly anisotropic and becomes unstable with increasing pressure. Directional Gruneisen parameters of KMn[Ag(CN)2]3 are found to be highly anisotropic. These properties show that NLC/NTE and PLC/PTE in KMn[Ag(CN)2]3 are driven by elastic and Gruneisen anisotropies combined with anharmonic lattice vibrations of Ag atoms. Partial phonon frequencies of KMn[Ag(CN)2]3 are found to be higher than those of Ag3[Co(CN)6]. The partial frequency of K atom increases rapidly with pressure and becomes comparable to that of Ag around 2 GPa. This shows that K inclusion stiffens the lattice and changes the dynamics, causing the pressure-induced phase transformation of KMn[Ag(CN)2]3 to occur at a higher pressure rather than at 0.2 GPa as in Ag3[Co(CN)6]. The phase transformation can be attributed to the softening of two low-energy optic modes (A2 and E) and the softening of C44 shear elastic constant and hence the transverse acoustic mode.

Discussion on the structural anisotropy of würtzite-type compounds

The würtzite-type ionic compounds exhibit flattened tetrahedral sites with a decentering of the central atom. The tetrahedral distortion and the relationship between the atom parameter (z) and the c/a ratio were explained on the basis of cell volume optimization respecting the bond valence model, and the role of anharmonic atomic vibrations was emphasized.

Absolute Helmholtz free energy of highly anharmonic crystals: Theory vs Monte Carlo

We discuss the problem of the quantitative theoretical prediction of the absolute free energy for classical highly anharmonic solids. Helmholtz free energy of the Lennard-Jones (LJ) crystal is calculated accurately while accounting for both the anharmonicity of atomic vibrations and the pair and triple correlations in displacements of the atoms from their lattice sites. The comparison with most precise computer simulation data on sublimation and melting lines revealed that theoretical predictions are in excellent agreement with Monte Carlo simulation data in the whole range of temperatures and densities studied.

Fast stochastic librations and slow small-angle rotations of molecules in glasses observed on nitroxide spin probes by stimulated electron spin echo spectroscopy

Abstract Electron spin echo (ESE) spectroscopy as applied to nitroxide spin probes in glasses is sensitive to molecular motions of two types. The first type of motion is fast stochastic librations, with correlation times on the scale of nanoseconds. In this work, these librations were found in glassy glycerol above ∼190 K and in glassy o-terphenyl above ∼250 K (glass transition temperatures for these two solvents are Tg = 185 K and Tg = 243 K, respectively). Most likely, these librations are of the same origin as anharmonic atomic vibrations, as seen in glasses by neutron scattering above a so-called dynamical transition temperature. The second type of motion is slow millisecond inertial rotations, which are observed in the experimentally accessible microsecond time scale as developing within an angular range of ∼0.1–2°. Over the temperature range studied, the square of the characteristic rotation rate was found to be proportional to the dielectric α-relaxation rate that is known for glycerol and o-terphenyl from literature. This empirical fact probably means that small-angle inertial rotations of spin probes and dielectric α-relaxation in the solvent are interrelated phenomena.

Ionoluminescence in the presence of ionizing radiation

An increase in the ionoluminescence intensity from a ZnS-CdS:Ag sample by a factor of more than 20 upon additional electronic excitation by UV light has been found. The effect decreases in magnitude with an increase in the energy of bombarding H2+ ions and peaks at an energy below 175 eV. This effect manifests itself in samples having a system of shallow electron traps and is due to the relaxation of highly excited anharmonic atomic vibrations, caused by the ion impact, through the electronic channel. A mechanism is proposed and computed for the phenomenon revealed.

Charge ordering and elastic anomalies in NaxCoO2

Abstract We report in-plane resistivity and elastic constant C33 measurements on the Na0.8CoO2 and Na0.5CoO2 systems. An ordering transition is found at T0=280 K for Na0.8CoO2. The temperature dependence of the elastic constant C33 propagating perpendicular to the CoO2 layers is interpreted, in a phenomenological approach, as being due to the anharmonicity of atomic vibrations. The effective Gruneisen parameter γeff deduced directly from the temperature dependence of C33 exhibits important changes at the charge ordering, magnetic and metal-insulator phase transitions.