Quartic Anharmonicity Research Articles

Classical Chaos in a Driven One-Dimensional Quartic Anharmonic Oscillator

In this work, we investigate the transition from regular dynamics to chaotic behavior in a one-dimensional quartic anharmonic classical oscillator driven by a time-dependent external square-wave force. Owing to energy conservation, the motion of an undriven quartic anharmonic oscillator is regular, periodic, and stable. For a driven quartic anharmonic oscillator, the equations of motion cannot be solved analytically due to the presence of an anharmonic term in the potential energy function. Using the fourth-order Runge–Kutta method to numerically solve the equations of motion for the driven quartic anharmonic oscillator, we find that the oscillator motion under the influence of a sufficiently small driving force remains regular, while by gradually increasing the driving force, a series of nonlinear resonances can occur, grow, overlap, and ultimately disappear due to the emergence of chaos.

The influence of lattice anharmonicity on the thermal transport properties of two-dimensional MgF2

Abstract Graphene research has ignited interest in two-dimensional (2D) materials. In addition to their unique electronic, mechanical, and optical properties, 2D materials exhibit distinctive thermal transport characteristics. A profound understanding of the microscopic mechanisms underlying the thermal transport properties of 2D materials is crucial for applications in energy conversion and storage devices. However, current studies lack insights into the influence of higher-order lattice anharmonicity on the transport behavior of 2D materials. Thus, this paper focuses on the 2D 1T phase MgF2, analyzing its microscopic thermal transport properties through an anharmonic lattice dynamics approach. Our methodology comprehensively accounts for the effects of quartic anharmonicity and four-phonon scattering on the thermal transport properties of 2D materials.

Synergistic effect of lone-pair electron and atomic distortion in introducing anomalous phonon transport in layered PbXSeF (X= Cu, Ag) compounds with low lattice thermal conductivity

Using first-principles calculations, self-consistent phonon theory and Boltzmann transport theory, the crystal structure, phonon and electronic transport, and thermoelectric (TE) properties of PbXSeF (X = Cu, Ag) compounds are comprehensive explored in the current work. The heterogeneous bonding characteristics along the in-plane and out-of-plane directions lead to low lattice thermal conductivities in PbXSeF (X = Cu, Ag) compounds. The low lattice thermal conductivity is primarily attributed to strong anharmonicity caused by the lone-pair electrons of Pb. Notably, the PbCuSeF compound, despite the lighter mass in comparison with PbAgSeF, exhibits relatively lower lattice thermal conductivity. Such finding can be attributed to the distortion introduced by Cu atom, which leads to strong quartic anharmonicity, and thereby suppressing the heat-carrying phonons through the rattling-like behavior of Cu atom. The lone-pair electrons of Pb2+ and the heterogeneous bonding characteristics in PbXSeF (X = Cu, Ag) compounds contribute the multi-valley band degeneracy, resulting the decoupling of Seebeck coefficient and electrical conductivity with carrier concentration while generating in a high power factor. Our current work not only illustrates the fundamental insights into the low lattice thermal conductivity and related anomaly of layered PbXSeF (X = Cu, Ag) compounds based on the four-phonon scattering and multiple carrier scattering rates, but also highlights the anisotropic feature of electronic and thermal transport properties.

Comparison of ultra-low lattice thermal conductivity of the full-Heusler compound Li2Rb(Cs)Bi after considering strong quartic anharmonicity

This paper conducts a detailed study on the thermal transport and thermoelectric properties of Li2Rb(Cs)Bi and analyzes the optical phonon frequency shift caused by considering anharmonicity. We mainly focus on studying the microscopic mechanism of the difference in lattice thermal conductivity (κL) of the two materials. By calculating the group velocity, scattering rate, scattering phase space and scattering sub-process, it is concluded that κL is mainly dominated by the acoustic branch. Due to its small group velocity and large scattering rate, Li2CsBi has a low κL, which is 0.60 W m−1K−1 at 300 K. Research results show that n-type Li2CsBi has a higher ZT value of about 2.1 at T = 900 K, while p-type Li2RbBi has a higher ZT value of about 1.5 at the same temperature. These results provide an important theoretical basis for the application of Li2Rb(Cs)Bi in the field of thermoelectric conversion.

Excellent thermoelectric properties and significant anisotropy for filled-tetragonal NaZnAs caused by strong anharmonicity

We have theoretically investigated the transport properties of the filled-tetrahedral NaZnAs using first-principles calculations in combination with self-consistent phonon theory and the Boltzmann transport equation. The results show that the transport behavior of NaZnAs exhibits obvious anisotropy, and the influence of quartic anharmonicity on the lattice thermal conductivity cannot be neglected as shown by the thermal conductivity results obtained from different computational models. Both the increase in scattering rates(SRs) and the decrease in group velocity signify a strong anharmonicity. We further find that the special vibrational modes due to the weak bonding of Zn atoms are the main source of anharmonicity. We find that considering the bubble diagram for the phonon self-energy correction reduces the κL by up to 28.04% at 700 K, which favors the capture of large ZT values. In addition, The ZT value of NaZnAs can reach 3.07 at 700 K, which shows great potential for thermoelectric applications.

Hierarchical characterization of thermoelectric performance in copper-based chalcogenide CsCu3S2: Unveiling the role of anharmonic lattice dynamics

Fundamental understanding of anharmonic lattice dynamics and heat conductance physics in crystalline compounds is critical for the development of thermoelectric energy conversion devices. Herein, we thoroughly investigate the microscopic mechanisms of thermal transport in CsCu3S2 by coupling the self-consistent phonon (SCP) theory with the linearized Wigner transport equation (LWTE). We explicitly consider both phonon energy shifts and broadening arising from both cubic and quartic anharmonicities, as well as diagonal/non-diagonal terms of heat flux operators in thermal conductivity. Our findings show that the strong anharmonicity of CsCu3S2 primarily arises from the presence of p-d anti-bonding hybridization between Cu and S atoms, coupled with the random oscillations of Cs atoms. Notably, the competition between phonon hardening described by the loop diagram and softening induced by the bubble diagram significantly influences particle-like propagation, predominantly reflected in group velocity and energy-conservation rule. Additionally, the electrical transport properties are determined by employing the precise momentum relaxation-time approximation (MRTA). At high temperatures, the thermoelectric performance of p-type CsCu3S2 reaches its optimum theoretical value of 0.94 along the in-plane direction based on advanced phonon renormalization theory. In striking contrast, the harmonic approximation theory significantly overestimates the thermoelectric efficiency at the same temperatures, rendering it an impractical expectation. Conversely, the first-order renormalization approach leads to a serious underestimation of the thermoelectric properties due to the over-correction of phonon energy. Our study not only reveals the pivotal role of anharmonic lattice dynamics in accurately assessing thermoelectric properties but also underscores the potential thermoelectric applications for novel copper-based chalcogenides.

Influence of quartic anharmonicity on lattice dynamics and thermal transport properties of 16 antifluorite structures

Influence of quartic anharmonicity on lattice dynamics and thermal transport properties of 16 antifluorite structures

Effects of Rattling Behavior of K and Cd Atoms along Different Directions in Anisotropic KCdAs on Lattice Thermal Transport and Thermoelectric Properties

We employ advanced first principles methodology, merging self‐consistent phonon theory and the Boltzmann transport equation, to comprehensively explore the thermal transport and thermoelectric properties of KCdAs. Notably, the study accounts for the impact of quartic anharmonicity on phonon group velocities in the pursuit of lattice thermal conductivity and investigates 3ph and 4ph scattering processes on phonon lifetimes. Through various methodologies, including examining atomic vibrational modes and analyzing 3ph and 4ph scattering processes, the article unveils microphysical mechanisms contributing to the low κL within KCdAs. Key features include significant anisotropy in Cd atoms, pronounced anharmonicity in K atoms, and relative vibrations in non‐equivalent As atomic layers. Cd atoms, situated between As layers, exhibit rattling modes and strong lattice anharmonicity, contributing to the observed low κL. Remarkably flat bands near the valence band maximum translate into high PF, aligning with ultralow κL for exceptional thermoelectric performance. Under optimal temperature and carrier concentration doping, outstanding ZT values are achieved: 4.25 (a(b)‐axis, p‐type, 3 × 1019 cm−3, 500 K), 0.90 (c‐axis, p‐type, 5 × 1020 cm−3, 700 K), 1.61 (a(b)‐axis, n‐type, 2 × 1018 cm−3, 700 K), and 3.06 (c‐axis, n‐type, 9 × 1017 cm−3, 700 K).

The relation between the atomic mass ratio and quartic anharmonicity in alkali metal hydrides

Phonons play a crucial role in understanding various aspects of solid-state physics, including thermal expansion, phase transition, interfacial thermal resistance, and lattice thermal conductivity (κL). Usually, the three-phonon (3ph) scattering processes have been considered the dominant mechanism governing thermal transport in solids. However, recent studies have revealed that quartic anharmonicity can fill the gap between theoretical calculations based on 3ph interactions and experimental values in a range of materials, such as BAs, perovskite CsPbBr3, and thermoelectric PbTe. Typically, the vibration frequency of phonons is proportional to the inverse square root of the atomic mass. Some semiconductors with heavy atoms have a big mass ratio which leads to a gap between acoustic and optical phonon modes. This phenomenon concurrently suppresses 3ph scattering. The influence of 4ph scattering on κL becomes more important. We investigate the relation between the atomic mass ratio and quartic anharmonicity using rocksalt alkali metal hydrides XH (X = Li, Na, K, Rb, Cs). Our finding reveals a positive correlation between the atomic mass ratio and quartic anharmonicity.

Exotic Quartic Anharmonicity Induced by Rattling Effect in Layered Isostructural Compounds

Exotic Quartic Anharmonicity Induced by Rattling Effect in Layered Isostructural Compounds

Unravelling ultralow thermal conductivity in perovskite Cs2AgBiBr6: dominant wave-like phonon tunnelling and strong anharmonicity

Understanding the lattice dynamics and heat transport physics in the lead-free halide double perovskites remains an outstanding challenge due to their lattice dynamical instability and strong anharmonicity. In this work, we investigate the microscopic mechanisms of anharmonic lattice dynamics and thermal transport in lead-free halide double perovskite Cs2AgBiBr6 from first principles. We combine self-consistent phonon calculations with bubble diagram correction and a unified theory of lattice thermal transport that considers both the particle-like phonon propagation and wave-like tunnelling of phonons. An ultra-low thermal conductivity at room temperature (~0.21 Wm−1K−1) is predicted with weak temperature dependence( ~ T−0.34), in sharp contrast to the conventional ~T−1 dependence. Particularly, the vibrational properties of Cs2AgBiBr6 are featured by strong anharmonicity and wave-like tunnelling of phonons. Anharmonic phonon renormalization from both the cubic and quartic anharmonicities are found essential in precisely predicting the phase transition temperature in Cs2AgBiBr6 while the negative phonon energy shifts induced by cubic anharmonicity has a significant influence on particle-like phonon propagation. Further, the contribution of the wave-like tunnelling to the total thermal conductivity surpasses that of the particle-like propagation above around 310 K, indicating the breakdown of the phonon gas picture conventionally used in the Peierls-Boltzmann Transport Equation. Importantly, further including four-phonon scatterings is required in achieving the dominance of wave-like tunnelling, as compared to the dominant particle-like propagation channel when considering only three-phonon scatterings. Our work highlights the importance of lattice anharmonicity and wave-like tunnelling of phonons in the thermal transport in lead-free halide double perovskites.

Role of atypical temperature-responsive lattice thermal transport on the thermoelectric properties of antiperovskites Mg3XN (X = P, As, Sb, Bi)

Antiperovskite materials have garnered significant attention due to their rich array of physical properties. In this study, we undertake a theoretical exploration into the phase stabilities, and the thermal and electronic transport properties of magnesium-based antiperovskite Mg3XN (X = P, As, Sb, and Bi) based on density functional theory (DFT) calculations, aiming at designing promising thermoelectric materials. The Mg3PN and Mg3AsN possess potential lattice distortion and strong quartic anharmonicity associated with the tilting displacement of Mg6N octahedra. After phonon renormalization, the thermal conductivity of Mg3PN and Mg3AsN exhibits relatively subdued temperature responsiveness with T−0.47 and T−0.62, respectively. Of note, the thermal conductivity of Mg3BiN drops the lowest at 900 K because of its distinctive rattle-dominated flat vibrational modes and strong temperature responsiveness with T−0.96, despite having a high initial value. Moreover, the combination of multiple degeneracy pockets and lighter dispersion band edges in Mg3XN ensures high Seebeck coefficient and impressive electronic conductivity, respectively. Ultimately, Mg3BiN achieves the optimal power factor, which also guarantees its excellent thermoelectric performance with the ZT values of 1.03 and 1.01 for n-type and p-type at 900 K, respectively. Our findings shed light on the significant impact of unconventional temperature-responsive lattice thermal conductivity on thermoelectric materials for high-temperature applications.

Study on lattice dynamics and thermal conductivity of fluorite AF2 (A = Ca, Sr, Ba) based on first principles calculations.

Fluorite materials have received particular attention in electron optics due to their favorable optical properties. However, further exploration of these materials in the thermoelectric (TE) field is hampered by the lack of studies on their lattice thermal transport properties. In this work, we use first-principles calculations, combined with self-consistent phonon theory, compressive sensing lattice dynamics and the Boltzmann transport equation, to study the microscopic mechanism of lattice thermal transport properties in AF2 (A = Ca, Sr, Ba) with a fluorite structure. We investigate the effects of three-phonon and four-phonon scattering and quartic anharmonic renormalization of phonon frequencies on this system. The results show that the bonding strength of atoms A (Ca, Sr, and Ba) plays an important role in the thermal transport process, and the third-order anharmonicity also plays an important role in this system. Meanwhile, the role of the quartic anharmonicity cannot be ignored. Our findings not only fill in the gaps in the study of lattice thermal transport of fluorite materials, but also deepen the comprehensive understanding of the high κL value of fluorite materials.

Lattice Thermal Conductivity in XMg2Sb2(X = Ca or Mg) Compounds: Temperature and High-Order Anharmonicity Effect

The binary compound Mg3Sb2 (also written as MgMg2Sb2) exhibits a much lower lattice thermal conductivity (κL) than its ternary analog CaMg2Sb2, despite its relatively low mass density and simple crystalline structure. Here, we perform a comparative first-principles study of the lattice dynamics in MgMg2Sb2 and CaMg2Sb2 based on the density functional theory, together with the self-consistent phonon theory and the Boltzmann transport theory. We show that the modest anharmonicity of CaMg2Sb2 renders the three-phonon processes dominant, and the temperature dependence of κL approximately follows the T−1 relationship. In contrast, the strong quartic anharmonicity of MgMg2Sb2 leads to the ultralow κL and weak temperature dependence, in agreement with the experimental observations. A comprehensive analysis reveals that the κLs in the two compounds are mainly carried by the acoustic phonons associated with the Sb atoms, and the different behaviors of κL result from the chemical bond changes around Sb atoms, which bond more covalently with the Mg atoms than the Ca atoms and thus lead to high-order anharmonicity in MgMg2Sb2. These results give us insights into the understanding of the anomalous thermal transport in thermoelectric materials.

Scaling theory of critical strain-stiffening in disordered elastic networks

Disordered elastic networks provide a framework for describing a wide variety of physical systems, ranging from amorphous solids, through polymeric fibrous materials to confluent cell tissues. In many cases, such networks feature two widely separated rigidity scales and are nearly floppy, yet they undergo a dramatic stiffening transition when driven to sufficiently large strains. We present a complete scaling theory of the critical strain-stiffened state in terms of the small ratio between the rigidity scales, which is conceptualized in the framework of a singular perturbation theory. The critical state features quartic anharmonicity, from which a set of nonlinear scaling relations is derived. Scaling predictions for the macroscopic elastic modulus beyond the critical state are derived as well, revealing a previously unidentified characteristic strain scale. The predictions are quantitatively compared to a broad range of available numerical data on biopolymer network models and future research questions are discussed.

The filled tetrahedral compound NaZnP with strong quartic anharmonicity and good thermoelectric properties

Based on first-principles calculations, self-consistent phonon (SCP) theory, and the Boltzmann transport equation, we investigate the thermal transport and thermoelectric properties of the Nowotny-Juza filled tetrahedral compound NaZnP. The effects of anharmonic phonon renormalization and four-phonon scattering on the heat transport of NaZnP are also considered. The weak binding and rattling-like vibrational behavior of Na atoms lead to strong lattice anharmonicity, and the results show that NaZnP has low lattice thermal conductivity. Furthermore, the coexistence of high dispersion and high degeneracy of valence band maxima leads to high power factor under p-type doping. The combination of low lattice thermal conductivity and good electrical transport properties results in high thermoelectric performance. This indicates that NaZnP is a promising p-type high-temperature thermoelectric material.

Effect of four-phonon scattering on the intrinsic thermal conductivity of penta-graphene

Penta-graphene (PG), as a novel and stable pentagonal structure, has attracted considerable attention due to its large band gap, ultrahigh strength, negative Poisson's ratio, which indicates promising potential in nanoelectronics and nanomechanics. Thermal conductivity is a key physical quantity for the potential applications of PG based nano-devices. However, previous studies focused on the thermal conductivity of PG dominated by the well-known cubic anharmonic effect, and the quartic anharmonicity, although probably significant, was still neglected. In this work, we study the effect of four-phonon scattering on the thermal transport in PG through using first-principles calculations and solving the Boltzmann transport equation (BTE). We find that the intrinsic lattice thermal conductivity of PG is 182.1 W/mK at room temperature after including four-phonon scattering, which is reduced by 73.5 % as compared to the obtained results with only three-phonon scattering. Meanwhile, the relative contribution of the flexural acoustic (ZA) branch is reduced from 60.5 % to 32.5 % when four-phonon scattering is included. Thus, the large reduction in thermal conductivity can be ascribed to the large four-phonon scattering rates, which are completely comparable with those of three-phonon processes in the acoustic phonon frequency range even at 300 K. It is well believed that this finding is not a special case but should exist in other 2D materials with similar phonon features. Furthermore, the validity of the sum of three- and four-phonon scattering rates has been verified by the results based on the MD simulations. Our finding provides critical revisit and valuable insight to the exact thermal conductivity value of PG.

The thermal transport and scattering channel of body centered cubic carbon BC14 using self-consistent phonon theory

Using the self-consistent phonon (SCP) theory, lattice thermal expansion, and Boltzmann transport equation (BTE), both thermal conductivity and scattering channel are studied by considering the cubic and quartic anharmonicity. The increase of phonon group velocity is caused by phonon frequency shifts at about 12 THz, but the phonon group velocity decreases slightly above 15 THz, agreeing with the decrease of phonon frequency induced by quartic anharmonic renormalization. The relaxation time of SCP is larger than that of HA, leading to the increase of thermal conductivity under SCP. The glass-like thermal conductivity of HA+ 3 ph, HA+ 3 ph + 4 ph, SCP+ 3 ph and SCP+ 3 ph + 4 ph is 0.12517 W/mK, 0.15713 W/mK, 0.1187 W/mK, 0.28551 W/mK, respectively. The three-phonon weighted phase space of HA is slightly larger than that of SCP, while the four-phonon weighted phase space of HA is nearly the same as the phase space of SCP. The major contributions to the scattering channels are X + ZA/TA/LA→O, X→O+ZA/TA/LA, X + O+ZA/TA→O, X + O-O/TA/LA→O, X + O-O→ZA/TA/LA, and X-O-ZA/TA→O. The weak C-C bonding is responsible for the low thermal conductivity of BC14. Moreover, these findings help us to understand the physical mechanism of thermal transport with the effect of quartic anharmonic renormalization.

Low lattice thermal conductivity with two-channel thermal transport in the superatomic crystal PH4AlBr4

Designing novel crystalline materials composed of light and nontoxic elements, but with ultralow thermal conductivity insensitive to temperature, has been a long-standing challenge. One effective strategy is to utilize superatoms as building blocks to introduce hierarchical bonding and vibration for suppressing phonon velocity and enhancing high-order scattering. However, far fewer theoretical efforts have been made to understand the lattice dynamics and thermal transport in superatom-based materials. Herein, different from most of the existing works reported hitherto on atom-superatom hybrid systems, we carry out a comprehensive study on the phonon interaction and thermal transport in superatomic crystal $\mathrm{P}{\mathrm{H}}_{4}\mathrm{Al}{\mathrm{Br}}_{4}$ solely consisting of superatoms (superalkali and superhalogen), by employing homogeneous nonequilibrium molecular dynamics with active-learning potential, combined with density functional theory and unified theory of phonon thermal transport. We find that the supersalt $\mathrm{P}{\mathrm{H}}_{4}\mathrm{Al}{\mathrm{Br}}_{4}$ crystal exhibits amorphouslike ultralow lattice thermal conductivity of $0.329\ensuremath{-}0.286\phantom{\rule{0.16em}{0ex}}\mathrm{W}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ from 200 to 600 K. In particular, due to the strong quartic anharmonicity, the contribution of four-phonon scattering reaches 38% of total scattering rates at 300 K, while the phonon coherence's contribution is comparable with that of population, resulting from significant phonon localization. These theoretical findings demonstrate that superatom-assembled materials exhibit features distinguished from atom-based crystals and provide a unique platform for exploring ultralow thermal conductivity with enhanced two-channel thermal transport.

The influence of strong anharmonicity on high thermoelectric properties for the ternary compound NaMgX (X = As, Sb)

We theoretically analyzed the thermoelectric characteristics of the tetragonal NaMgX (X = As, Sb) compounds with strongly quartic anharmonicity based on an incorporation of first-principles calculations with self-consistent phonon theory and Boltzmann transport equations. These two materials show the low lattice thermal conductivity due to the low phonon group velocity. Since the flat band and the dispersion band coexist near the Fermi surface, the ZT values of p-type NaMgAs and NaMgSb at 900 K along the a(b) axis are 1.27 and 2.29, respectively. These results show that these two materials have good thermoelectric properties.