Anharmonicity Of Lattice Vibrations Research Articles

Polytelluride square planar chain-induced anharmonicity results in ultralow thermal conductivity and high thermoelectric efficiency in Al2Te5 monolayers.

Two-dimensional (2D) metal chalcogenides provide rich ground for the development of nanoscale thermoelectrics, although achieving optimal thermoelectric efficiency is still a challenge. Here, we leverage the unique chemistry of tellurium (Te), renowned for its hypervalent bonding and catenation abilities, to tackle this challenge as manifested in Al2Te3 and Al2Te5 monolayers. While the former forms a straightforward covalent Al-Te network, the latter adopts a more intricate bonding mechanism, enabled by eccentric features of Te chemistry, to maintain charge balance. In Al2Te5, a square planar chain (SPC) known as polytelluride [Te3]2- is neutralized by the covalently bonded [Al2Te2]2+ framework. The hypervalent nature of Te results in bizarre Born effective charges of 7 and -4 for adjacent Te atoms within the square planar chain, a feature that induces significant anharmonicity in Al2Te5 monolayers. Enhanced anharmonic lattice vibrations and the accordion pattern bestow glass-like, strongly anisotropic thermal conductivity to the Al2Te5 monolayer. The calculated κL values of 1.8 and 0.5 W m-1 K-1 along the a- and b-axes at 600 K are one order of magnitude lower than those of Al2Te3, and even lower than monolayers that contain heavy cations like Bi2Te3. Moreover, the tellurium chain dominates the valence band maximum and conduction band minimum of Al2Te5, leading to a high valley degeneracy of 10, and thus a high power factor and figure of merit (zT). Using rigorous first-principles calculations of electron relaxation time, the estimated hole-doped and electron-doped zT of, respectively, 1.5 and 0.5 at 600 K is achieved for Al2Te5. The pioneering zT of Al2Te5 compared to that of Al2Te3 is rooted merely in its amorphous-like lattice thermal transport and its polytelluride chain. These findings underscore the importance of aluminum telluride and polymeric-based inorganic compounds as practical and cost-effective thermoelectric materials, pending further experimental validation.

Interface‐Enhanced High‐Temperature Thermoelectricity in Cu1.99Se/B4C Composites with Synergistically Improved Mechanical Strength

AbstractDegenerate semiconductors usually demonstrate a metallic‐like conduction behavior, showing limited carrier mobility at high temperatures. Herein, by incorporating B4C nanoparticles into the Cu1.99Se system, an unusual switch from the “degenerate” to “non‐degenerate” semiconducting behavior is revealed as a result of the engineered interfaces. Heterogeneous interfaces and disordered Cu2Se amorphous phases are introduced in the Cu1.99Se/B4C composites, which generate a trapping effect against the mobile Cu ions, leading to a distinctive “hump” signature for electrical conductivity. Benefiting from this rare high‐temperature thermoelectric response, a high power factor is obtained due to reduced carrier concentration and enhanced mobility, and low lattice thermal conductivity is retained because of relatively stronger anharmonic lattice vibrations. Consequently, the Cu1.99Se + 0.9 vol.% B4C sample at least achieves a maximum thermoelectric figure of merit (ZT) of 2.6 at 1025 K with synergistically enhanced mechanical robustness. The present interface engineering strategy may be applicable to other thermoelectric materials with ionic migration characteristics.

Isotopic effect in thermodynamic properties of solid neon

Isotopic effects in mean-square displacement, specific heat at constant pressure and linear thermal expansion coefficient of solid neon have been considered using the statistical moment method in statistical mechanics. This approach allows us to study these effects including the anharmonicity of lattice vibrations. We implement calculations for 20Ne and 22Ne isotopes in temperature range from 0 K to the melting temperature (24.6 K) using Lennard-Jones potential to describe the interaction between Ne quantum particles. Our numerical results are compared with those of path-integral Monte Carlo simulations and previous experimental data showing the good agreement. This research presents an effective statistical approach to study isotopic effects in thermodynamic quantities of materials.

Investigation on the bond characteristics and microwave dielectric properties of rock salt-structured Li2Mg0.5nTiO3+0.5n (n = 1–8) ceramics based on the complex chemical bond theory

Cubic rock salt structured ceramics are of great interest due to their outstanding microwave dielectric properties. Complex chemical bond theory and polarization theory combined with XRD refinement as well as XPS were employed to reveal the mechanisms of the compositional effect on the microwave dielectric properties of Li2Mg0.5nTiO3+0.5n ceramics with a rock salt structure. It was demonstrated that when n = 1, the microwave dielectric properties exhibit a biphasic structure. However, as n increased to 2 and higher levels, the specimens were consisted of a single cubic rock salt phase. εr of single-phased samples decreased with an increase in the n value, which was due to the decreases in both the bond ionicity and polarizability of unit cell. Meanwhile, as lattice energy increased, the formation of oxygen vacancies was effectively suppressed, and anharmonic lattice vibrations were weakened, leading to an increase in Q×f. Moreover, τf showed a negative shift due to an increase in the aL,ave of the chemical bond and an decrease in the bond energy. The optimal microwave dielectric properties of εr= 17.3, Q×f= 81,000 GHz, and τf = −7.7 ppm/℃ were achieved in the component with n = 1 when sintered at 1350 °C for 4 h.

Temperature effects on thermodynamic properties of rare-earth ytterbium

Thermodynamic quantities (including Debye temperature and frequency, atomic mean-square displacement, specific heats at constant volume and constant pressure, linear thermal expansion coefficient, and total entropy) of face-centered cubic ytterbium metal have been studied by means of the statistical moment method in statistical mechanics. This theoretical approach allows us to calculate these thermodynamic quantities taking into account the anharmonicity of lattice vibrations. Numerical calculations for ytterbium have been conducted in temperature range from 0 K to 1100 K using Lennard-Jones potential to describe the interaction between ytterbium atoms. Our derived results are compared with those of mean-field potential approach as well as previous experimental data showing the good agreement. We have shown that the atomic mean-square displacement contains the zero-point vibration (quantum effect) at low temperature. At high temperature it changes linearly with respect to temperature. Furthermore, our theoretical calculations have also pointed out the anharmonic contribution to specific heat at constant volume of ytterbium metal is negative with temperature. This research presents an effective statistical approach to study temperature effects on thermodynamic quantities of materials.

Magnetic-Field-Induced Sign Changes of Thermal Expansion in DyCrO4

The anharmonicity of lattice vibration is mainly responsible for the coefficient of thermal expansion (CTE) of materials. External stimuli, such as magnetic and electric fields, thus cannot effectively change the CTE, much less the sign variation from positive to negative or vice versa. In this study, we report significant magnetic field effects on the CTE of zircon- and scheelite-type DyCrO4 prepared at ambient and high pressures, respectively. At zero field, the zircon-type DyCrO4 exhibits a negative CTE below the ferromagnetic-order temperature of 23 K. With increasing field up to ≥1.0 T, however, the sign of the CTE changes from negative to positive. In the scheelite phase, magnetic field can change the initially positive CTE to be negative with a field up to 2.0 T, and then a reentrant positive CTE is induced by enhanced fields ≥3.5 T. Both zircon and scheelite phases exhibit considerable magnetostrictive effects with the absolute values as high as ∼ 800 ppm at 2 K and 10 T. The strong spin–lattice coupling is discussed to understand the unprecedented sign changes of the CTE caused by applying magnetic fields. The current DyCrO4 provides the first example of field-induced sign change of thermal expansion, opening up a way to readily control the thermal expansion beyond the conventional chemical substitution.

Significantly reduced lattice thermal conductivity with anharmonic lattice vibrations and band edge effect in electronic thermal conductivity in Ag2S1-xSex (0 ≤ x ≤ 0.6)

The composition dependence of the unusual behaviors in electronic and lattice thermal conductivity, κele and κlat, in Ag2S1-xSex (x = 0–0.6 in steps of 0.1, 300 K) is investigated in detail by means of precise electron and heat transport properties measurement, synchrotron X-ray crystal structure and electron density distribution analyses, and sound velocity measurement. We reveal that the κele of Ag2S1-xSex is strongly affected by the fine electronic structure of the conduction band edge near the chemical potential and the thermoelectric motive force; therefore, these effects make the κele of Ag2S1-xSe far different from that calculated by the Wiedemann–Franz law, κele = L0σT, with the Lorentz number L0 = π2kB2/(3e2). It is also clearly demonstrated that the κlat of Ag2S1-xSex is greatly reduced by anharmonic lattice vibrations and that the magnitude of κlat is quantitatively reproduced by an equation representing the thermal conductivity under the strongest scattering limit. The κlat decreases with increasing x and saturates at 0.4 W m−1 K−1 at x ≥ 0.4. This is caused by the increasing anharmonic lattice vibrations with x, and its saturating behavior is determined by the strongest scattering limit. On the other hand, a negligibly small κele at x = 0 turns out to be non-trivial at x ≥ 0.4 owing to the increasing carrier density with x, most likely contributed by the increasing interstitial Ag defects. Consequently, the total thermal conductivity of Ag2S1−xSex becomes minimum not at x = 0.5 (composition of the maximum structure entropy) but at x = 0.3.

High-Temperature Thermodynamics of Uranium from Ab Initio Modeling

We present high-temperature thermodynamic properties for uranium in its γ phase (γ-U) from first-principles, relativistic, and anharmonic theory. The results are compared to CALPHAD modeling. The ab initio electronic structure is obtained from density-functional theory (DFT) that includes spin–orbit coupling and an added self-consistent orbital-polarization (OP) mechanism for more accurate treatment of magnetism. The first-principles method is coupled to a lattice dynamics scheme that is used to model anharmonic lattice vibrations, namely, Self-Consistent Ab Initio Lattice Dynamics (SCAILD). The methodology can be summarized in the acronym DFT + OP + SCAILD. Upon thermal expansion, γ-U develops non-negligible magnetic moments that are included for the first time in thermodynamic theory. The all-electron DFT approach is shown to model γ-U better than the commonly used pseudopotential method. In addition to CALPHAD, DFT + OP + SCAILD thermodynamic properties are compared with other ab initio and semiempirical modeling and experiments. Our first-principles approach produces Gibbs free energy that is essentially identical to CALPHAD. The DFT + OP + SCAILD heat capacity is close to CALPHAD and most experimental data and is predicted to have a significant thermal dependence due to the electronic contribution.

Broadband emission originating from the stereochemical expression of 6s2 lone pairs in two-dimensional lead bromide perovskites.

The stereochemical expression of the 6s2 lone pair on the lead atom has a significant impact on the crystal structures and physical properties of lead halide perovskites. Two-dimensional (2D) lead bromide perovskites often exhibit a broadband emission, yet the structural origin of the broadband emission has been under debate. Here, we report the synthesis and characterization of a 2D lead bromide hybrid (4-chlorophenylammonium)2PbBr4 that consists of a combination of the octahedral unit PbBr6 and the rarely observed capped octahedral unit PbBr7 through corner-sharing and edge-sharing linkages. The seven-coordination geometry indicates a strong stereo-active lone pair on the Pb2+ cation. By comparing this structure with two representative 2D perovskites, (benzylammonium)2PbBr4 and (4-aminotetrahydropyran)2PbBr4, we establish how the lone pair expression affects the local coordination geometry of the Pb2+ cation and the resulting optical and electronic properties. As the Pb-Br bond length increases, the lone pair expression leads to off-centering displacement of Pb2+ within the octahedra and then the formation of seven-coordination capped octahedra. Density functional theory calculations indicate that the off-centering distorted octahedra and capped octahedra are due to the asymmetric distribution of the Pb electrons that have both s and p orbital characteristics. Spectroscopic studies show the photoluminescence spectra evolving from narrowband emission to broadband emission with increasing LPE, as well as softer and more anharmonic lattice vibrations that facilitate exciton self-trapping. Our results demonstrate that lone pairs could be a powerful design rule for developing light emitting materials.

High-Temperature Thermodynamics Modeling of Graphite

We present high-temperature thermodynamic properties for graphite from first-principles anharmonic theory. The ab initio electronic structure is obtained from density-functional theory coupled to a lattice dynamics method that is used to model anharmonic lattice vibrations. This combined approach produces free energies and specific heats for graphite that compare well with available experiments and results from models that empirically represent experimental data, such as CALPHAD. We show that anharmonic theory for the phonons is essential for accurate thermodynamic quantities above about 1000 K.

Materials informatics for dielectric loss tangent in the millimeter wave region

For the prediction of the dielectric loss tangent in the millimeter wave region, machine-learning approaches based on the first-principles calculations were carried out. The data set was prepared by the first-principles calculations considering the anharmonicity of lattice vibrations. The two-phonon density of states, which is correlated with the dielectric loss tangent, was calculated and confirmed the connection with the difference in crystal structures. Machine-learning models to predict the dielectric loss tangent were created considering both atomic compositions and crystal structures as descriptors. In addition, transfer-learning models, in which a pretrained model for the two-phonon density of states was used as the new descriptor, were compared with models from scratch. The transfer-learning model showed 25% higher prediction accuracy than the scratch model.

Unveiling the effect of vacancy defects on structural, mechanical, electronic and diffusion properties of copper (I) iodide

Effects of vacancy defects on formation energies, mechanical stability, electronic properties and diffusion coefficients in copper (I) iodide (CuI) are investigated by first-principles calculations. A temperature-dependent behavior for vacancy formation energy is observed that is explained by the anharmonicity of lattice vibrations at high temperatures. Both Cu and I vacancy defects enhance the electronic conductivity. Cu diffusion is more predominant, because CuI has a less stable structure in the presence of Cu vacancy and atomic bonds of CuI also possess the least stability with Cu vacancies. This study found that the diffusivity increases with an increase of defect concentration and temperature, and Cu diffusion is dominant in CuI regardless of the type of the defect or temperature.

The Effect of Solution Treatment on the Si Particles’ Morphology Evolution and the Thermal Conductivity and Tensile Properties of Sb-Modified Al-8Si-0.6Mg Alloys

The effects of solution treatment time on the morphology evolution of Si particles and the thermal conductivity and tensile properties of Sb-modified alloys were studied. The results show that the evolution of Si particles follows four mechanisms: spheroidization, necking and splitting of particles with large aspect ratios, fusion of spherical particles, and coarsening controlled by diffusion. The first three mechanisms mainly occur at the early stage of solution treatment. The addition of Sb does not change the evolution law of the Si particles, but it does change the contribution of various evolution mechanisms, including promoting spheroidization, fusion, and coalescence, as well as significantly reducing the coarsening rate, which makes the thermal modification of Sb-modified alloys more effective. The increase in thermal conductivity during solution treatment is related to the decrease of the anharmonicity of lattice vibration, lattice wave scattering, and electron scattering of Si particles. The 0.4 wt. % Sb-modified alloy exhibits excellent tensile strength and elongation under as-cast T4- and T6-heat-treated conditions, because the modification significantly reduces the stress concentration of the Si particles and delays the germination and propagation of microcracks.

Crystal structure, lattice vibration and microwave dielectric properties of 3CaO·2SiO2·xCaF2 (0 ≤ x ≤ 1.5) ceramics

The crystal structure, lattice vibration and microwave dielectric properties of 3CaO·2SiO2·xCaF2 ceramics were investigated in this work. With the increasing of x value, the crystal structure of 3CaO·2SiO2·xCaF2 ceramics transfers from rankinite (Ca3Si2O7) to cuspidine (Ca4Si2O7F2). The increase of the vibration energy and shrinkage of [SiO4] tetrahedral unit hampers the ionic polarization and thus reduces relative permittivity (εr). The enlarged FWHM of the Si–O stretching peak reflects a more drastic anharmonic lattice vibration, resulting in a lower quality factor (Q × f value). The Raman shift of O/F–Ca–O/F bending peak is positively correlated with the temperature coefficient of resonant frequency (τf). The microwave dielectric properties of εr and Q × f value (∼@11 GHz) ranging from 7.89 to 8.42, and 21805–46098 GHz, respectively. The stable complex permittivity (εr∗) in the frequency range of 20–110 GHz indicates that the fluoride cuspidine ceramics could be a promising candidate for microwave device applications.

Anharmonicity of lattice vibrations in thin film α-Ga2O3 investigated by temperature dependent Raman spectroscopy

Gallium oxide is a promising candidate for several future electronic devices to replace common technologies. For this reason, an understanding of fundamental physical processes is needed. In this work, we investigate the Raman excitations of a α-Ga2O3 thin film under temperature variation from 80 K up to 790 K. This yields detailed information about anharmonic processes in the crystal. For the two dominant phonon modes for each of the two Raman-active phonon mode symmetries (A1g and Eg), model calculations are performed in order to quantify the contributions of different decay mechanisms. It is shown that our experimental data can be well described by the applied theoretical models. The determined coefficients of cubic and quartic decay for both, phonon energy and linewidth, are compared with those from hexagonal GaN and AlN as well as with those from α-Al2O3. We observe that for the two selected phonon modes of α-Ga2O3, the shifts of frequency and broadening under temperature variation are significantly smaller than in GaN and AlN, but similar to α-Al2O3.

Phonon anharmonicity: a pertinent review of recent progress and perspective

Anharmonic lattice vibrations govern the thermal dynamics in materials and present how the atoms interact and how they conduct heat. An indepth understanding of the microscopic mechanism of phonon anharmonicity in condensed systems is critical for developing better functional and energy materials. In recent years, a variety of novel behaviors in condense matters are driven by phonon anharmonic effects in some way or another, such as soft mode phase transition, negative thermal expansion, multiferroicity, ultralow thermal conductivity or high thermal resistance, and high-temperature superconductivity, etc. All these properties have endowed anharmonicity with many promising applications and provided remarkable opportunities for developing anharmonicity engineering, regulating heat transport towards excellent performance in materials. In this work, we review the recent development of the study on phonon anharmonic effect and summarize its origination, influence and mechanism, research methods, and applications. Besides, the remaining challenges, future trends, and prospects of phonon anharmonicity are also put forward.

Low-temperature peculiarities of thermal properties of EuF2.16 europium fluoride and (SrF2)0.5(EuF2.16)0.5 solid solution

The heat capacity and lattice parameters of europium fluoride EuF2.16 and (SrF2)0.5(EuF2.16)0.5 solid solution are experimentally investigated at temperatures 2–300 K. The revealed anomalies in the heat capacity are due to magnetic phase transition and disorder in fluorides crystal structures. The dependencies studied were analyzed using the Debye–Einstein approximation, taking into account the influence of the magnetic phase transition, two-level systems, and anharmonicity of lattice vibrations on their thermodynamic properties. We determined the parameters of the Debye and Einstein models – the characteristic temperatures as well as the magnitudes their respective contributions to the overall thermodynamic characteristics, the parameters characterizing crystal structure disorder, and the exchange parameters characterizing interaction in magnetic subsystems of fluorides. Dependences studied for solid solution deviate from the additive values. We further established that the mechanisms causing these are based on the disorder in the crystal structures of europium fluoride and its solid solution.

Temperature-dependent influence of disorder on the thermodynamic properties of Sn20.5□3.5As20I8, a vacancy-driven superstructure of the type-I clathrate

ABSTRACT A polycrystalline sample of the Sn20.5□3.5As22I8 clathrate was synthesised by a standard ampoule method from elements. Temperature dependencies of the heat capacity Cp (T) and unit cell parameter a(T) experimentally studied at the temperatures of 2–300 K revealed abnormal behaviour of CP (T) and a(T) dependencies at the lowest (2–30 K) and elevated (200–300 K) temperatures. This was attributed to disorder in the clathrate crystal structure due to significant number of vacancies in the clathrate host matrix. The dependencies studied were analysed within the Debye–Einstein approach taking into account soft atomic potential theory, vibrations of two-level system (TLS) at the lowest temperatures, and anharmonicity of lattice vibration at elevated temperatures, which allows determining parameters of different contributions to thermodynamic characteristics of the studied clathrate. A comparison of the temperature dependence of Grüneisen parameter, which was determined from experimental data, with the temperature dependence of the calculated Grüneisen mode parameters revealed specific modes that have a decisive influence on the anomalous behaviour of the thermodynamic characteristics of the title clathrate in different parts of the studied temperature range. The dimensionless Grüneisen parameter reaches γ = 4 at moderately high temperatures, which indicates a significant degree of structural disorder and its influence on thermodynamic properties of clathrates and correlates well with low thermal conductivity of the title clathrate.

Structures, and Thermophysical Properties Characterizations of (La1-xHox)3NbO7 Solid Solutions as Thermal Barrier Coatings

A sequence of (La1-xHox)3NbO7 solid solutions were fabricated in this work, which were studied as candidate for thermal insulation materials. The lattices were identified via XRD, when SEM and EDS were used to characterize the microstructures and element distributions. The results showed that the highest modulus, hardness, and toughness of (La1-xHox)3NbO7 were 196 GPa, 9.2 GPa, and 1.6 MPa m1/2, respectively, and they accorded with the mechanical property requirements. Also, a low thermal conductivity (1.06 W m−1 K−1) and high thermal expansion coefficients (TECs: 11.3 × 10−6 K−1) were simultaneously realized in (La3/6Ho3/6)3NbO7, at high temperatures. No phase transition was detected up to 1,200°C, which proved their good high-temperature lattice stability. The intense anharmonic lattice vibrations might contribute to the outstanding thermal properties of (La1-xHox)3NbO7 ceramics. The suitable modulus, high hardness, low thermal conductivity, and high TECs of (La1-xHox)3NbO7 solid solutions proclaimed that they were exceptional thermal insulation ceramics.

Ab initio molecular dynamics investigation of the elastic properties of superionic Li2O under high temperature and pressure

Theoretical prediction on the elastic properties of superionic material is challenging due to the fast diffusion of cation/anion in the lattice. Here, we investigated the elastic properties of ${\mathrm{Li}}_{2}\mathrm{O}$ at elevated temperature and pressure using ab initio molecular dynamics (AIMD). We observed the superionic transition above 1300 K, and the highly diffusive ${\mathrm{Li}}^{+}$ leads to local structure change with significant influence on the elasticity of ${\mathrm{Li}}_{2}\mathrm{O}$. We successfully predicted the significant ${C}_{11}$ softening above 1300 K, and the calculated elastic constants fit the previous experimental results very well. It suggests the anharmonic lattice vibration before superionic transition and the diffusion of ${\mathrm{Li}}^{+}$ after superionic transition are very important for the prediction on the elastic properties, and the AIMD method is able to describe the superionic behavior accurately. In addition, we calculated the bulk and shear moduli, sound velocities, as well as elastic and sound velocity anisotropies. We found that the superionic state transition also leads to the weakening of the elastic and sound velocity anisotropies in ${\mathrm{Li}}_{2}\mathrm{O}$. Pressure has negative effect on the mobility of ${\mathrm{Li}}^{+}$, which strengthens the elastic stiffening effect of superionic ${\mathrm{Li}}_{2}\mathrm{O}$ with increasing pressure.