Strong anharmonicity-assisted low lattice thermal conductivities and high thermoelectric performance in double-anion Mo_(2)AB_(2)(A=S,Se,Te;B=Cl,Br,I)semiconductors

The thermoelectric properties of layered Mo_(2)AB_(2)(A=S,Se,Te;B=Cl,Br,I)materials are systematically investigated by first-principles approach.Soft transverse acoustic modes and direct Mo d–Mo d couplings give rise to strong anharmonicities and low lattice thermal conductivities.The double anions with distinctly different electronegativities of Mo_(2)AB_(2)monolayers can reduce the correlation between electron transport and phonon scattering,and further benefit much to their good thermoelectric properties.Thermoelectric properties of these Mo_(2)AB_(2)monolayers exhibit obvious anisotropies due to the direction-dependent chemical bondings and transport properties.Furthermore,their thermoelectric properties strongly depend on carrier type(n-type or p-type),carrier concentration and temperature.It is found that n-type Mo_(2)AB_(2)monolayers can be excellent thermoelectric materials with high electric conductivity,σ,and figures of merit,ZT.Choosing the types of A and B anions of Mo_(2)AB_(2)is an effective strategy to optimize their thermoelectric performance.These results provide rigorous understanding on thermoelectric properties of double-anions compounds and important guidance for achieving high thermoelectric performance in multi-anion compounds.

Tunable anharmonicity versus high-performance thermoelectrics and permeation in multilayer(GaN)_(1-x)(ZnO)_(x)

Nonisovalent(GaN)_(1-x)(ZnO)_(x)alloys are more technologically promising than their binary counterparts because of the abruptly reduced band gap.Unfortunately,the lack of two-dimensional(2D)configurations as well as complete stoichiometries hinders to further explore the thermal transport,thermoelectrics,and adsorption/permeation.We identify that multilayer(GaN)_(1-x)(ZnO)_(x)stabilize as wurtzite-like Pm-(GaN)_(3)(ZnO)_(1),Pmc2_(1)-(Ga N)_(1)(ZnO)_(1),P3m1-(GaN)_(1)(ZnO)_(2),and haeckelite C2/m-(GaN)_(1)(ZnO)_(3)via structural searches.P3m1-(GaN)_(1)(ZnO)_(2)shares the excellent thermoelectrics with the figure of merit ZT as high as 3.08 at 900 K for the p-type doping due to the ultralow lattice thermal conductivity,which mainly arises from the strong anharmonicity by the interlayer asymmetrical charge distributions.The p–d coupling is prohibited from the group theory in C2/m-(Ga N)_(1)(ZnO)_(3),which thereby results in the anomalous band structure versus Zn O composition.To unveil the adsorption/permeation of H^(+),Na^(+),and OH^(-)ions in AA-stacking configurations,the potential wells and barriers are explored from the Coulomb interaction and the ionic size.Our work is helpful in experimental fabrication of novel optoelectronic and thermoelectric devices by 2D(GaN)_(1-x)(ZnO)_(x)alloys.

Electronic origin of the unusual thermal properties of copper-based semiconductors:The s-d coupling-induced large phonon anharmonicity

Copper(Cu)-based materials(such as cuprates,Cu chalcogenides,and Cu halides)often exhibit unusual properties such as superconductivity,ultralow thermal conductivity,and superionicity.However,the electronic origin of these unusual behaviors remains elusive.In this study,we demonstrate that the high-lying occupied 3d orbital of Cu causes a strong s-d coupling with its unoccupied 4s state when local symmetry is reduced.This leads to strong phonon anharmonicity and is responsible for these intriguing properties.For example,during thermal transport,symmetry-controlled s-d coupling can substantially lower the lattice potential barrier,thereby enhancing the anharmonicity and scattering between phonons and ultimately significantly reducing lattice thermal conductivity.We confirmed this understanding with Raman spectra measurements,which demonstrated a remarkable red shift in the phonon vibrational frequency with an increase in the temperature of Cu-based semiconductors.Our study shows that the cause of phonon anharmonicity is related to the fundamental electronic structures,which can also explain other unusual physical properties of the Cu compounds.

Band modification towards high thermoelectric performance of SnSb_(2)Te_(4) with strong anharmonicity driven by cation disorder

As a typical (IV–VI)_(x)(V_(2)VI_(3))_(y) compound, the tetradymite-like layered SnSb_(2)Te_(4) -based compounds have attracted increasing attention in the thermoelectric community owing to the intrinsically low lattice thermal conductivity. Nevertheless, the effect of cations disorder on the inherent physical characteristics remains puzzling, and its inferior Seebeck coefficient is the bottleneck to achieving high thermoelectric performance. In this work, the thermoelectric properties of polycrystalline In_(x)Sn_(1−x)Sb_(2)(Te_(1−y)Se_(y))_(4) (0≤x≤0.1,0≤y≤0.15) samples are comprehensively investigated. In conjunction with the calculated band structure and experimental results, the Seebeck coefficient and power factor are markedly improved after the introduction of indium and selenium, which originates from the combined effects of the emergent resonant states and converged valence bands along with optimal carrier concentration. Additionally, compared with the ordered lattice structure, the disordered cations occupancy in SnSb_(2)Te_(4) further strengthens lattice anharmonicity and reduces phonon group velocity verified by first-principles calculations, securing intrinsically low lattice thermal conductivity. Finally, a record zT value of ∼0.6 at 670 K and an average zT of ∼0.4 between 320 and 720 K are obtained in the In0.1 Sn0.9 Sb2 Te3.4 Se0.6 sample, being one of the highest zT values among SnSb2 Te4 -based materials. This work not only demonstrates that SnSb2 Te4 -based compounds are promising thermoelectric candidates, but also provides guidance for the promotion of thermoelectric performance in a broad temperature range.

Phonon transport properties of Janus Pb_(2)XAs(X=P,Sb,and Bi)monolayers:A DFT study

Grasping the underlying mechanisms behind the low lattice thermal conductivity of materials is essential for the efficient design and development of high-performance thermoelectric materials and thermal barrier coating materials.In this paper,we present a first-principles calculations of the phonon transport properties of Janus Pb_(2)PAs and Pb_(2)SbAs monolayers.Both materials possess low lattice thermal conductivity,at least two orders of magnitude lower than graphene and h-BN.The room temperature thermal conductivity of Pb_(2)SbAs(0.91 W/m K)is only a quarter of that of Pb_(2)PAs(3.88 W/m K).We analyze in depth the bonding,lattice dynamics,and phonon mode level information of these materials.Ultimately,it is determined that the synergistic effect of low group velocity due to weak bonding and strong phonon anharmonicity is the fundamental cause of the intrinsic low thermal conductivity in these Janus structures.Relative regular residual analysis further indicates that the four-phonon processes are limited in Pb_(2)PAs and Pb_(2)SbAs,and the three-phonon scattering is sufficient to describe their anharmonicity.In this study,the thermal transport properties of Janus Pb_(2)PAs and Pb_(2)SbAs monolayers are illuminated based on fundamental physical mechanisms,and the low lattice thermal conductivity endows them with the potential applications in the field of thermal barriers and thermoelectrics.

Anharmonicity induced thermal modulation in stressed graphene

Thermal properties are essentially decided by atomic geometry and thus stress is the most direct way for manipulating. In this paper, we investigate stress modulation of thermal conductivity of graphene by molecular dynamics simulations and discuss the underlying microscopic mechanism. It is found that thermal conductivity of flexural-free graphene increases with compression and decreases with strain, while thermal conductivity of flexural-included graphene decreases with both compression and strain. Such difference in thermal behavior originates from the changes in the anharmonicity of the interatomic potential, where the wrinkle scattering is responsible for the thermal conductivity diminishment in flexural-included graphene under strain. By comparing the results obtained from the Tersoff and AIREBO potentials, it is revealed that the degree of the symmetry of interatomic potential determines the thermal conductivity variation of graphene. Our results indicate that the symmetry of interatomic potential should be taken into careful consideration in constructing the lattice model of graphene.

Phonon anharmonicity:a pertinent review of recent progress and perspective

Anharmonic lattice vibrations play pivotal roles in the thermal dynamics in condense matters and affect how the atoms interact and conduct heat.An in-depth understanding of the microscopic mechanism of phonon anharmonicity in condensed systems is critical for developing better functional and energy materials.In recent years,various novel behaviors in condense matters driven by phonon anharmonic effects were discovered,such as soft mode phase transition,negative thermal expansion(NTE),multiferroicity,ultralow thermal conductivity(κ),high thermal resistance,and high-temperature superconductivity.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 studies on phonon anharmonic effect and summarize its origin,mechanism,research methods,and applications.Besides,the remaining challenges,future trends,and prospects of phonon anharmonicity are also discussed.

Phonon anharmonicity and thermal conductivity of two-dimensional van der Waals materials: A review

Two-dimensional(2D) van der Waals(vdW) materials have extraordinary thermal properties due to the effect of quantum confinement, making them promising for thermoelectric energy conversion and thermal management in microelectronic devices.In this review, the mechanism of phonon anharmonicity originating from three-and four-phonon interactions is derived. The phonon anharmonicity of 2D vdW materials, involving the Grüneisen parameter, phonon lifetime, and thermal conductivity, is summarized and derived in detail. The size-dependent thermal conductivity of representative 2D vdW materials is discussed experimentally and theoretically. This review will present fundamental and advanced knowledge on how to evaluate the phonon anharmonicity in 2D vdW materials, which will aid the design of new structures and materials for applications related to energy transfer and conversion.

Hydrogen mean force and anharmonicity in polycrystalline and amorphous ice

The hydrogen mean force from experimental neutron Compton profiles is derived using deep inelastic neutron scattering on amorphous and polycrystalline ice. The formalism of mean force is extended to probe its sensitivity to anharmonicity in the hydrogen-nucleus effective potential. The shape of the mean force for amorphous and polycrystalline ice is primarily determined by the anisotropy of the underlying quasi-harmonic effective potential. The data from amorphous ice show an additional curvature reflecting the more pronounced anharmonicity of the effective potential with respect to that of ice Ih.

Anti-Stokes/Stokes temperature calibration and its application in laser-heating diamond anvil cells

Anti-Stokes/Stokes Raman peak intensity ratio was used to infer sample temperatures,but the influence factors of system correction factors were not clear.Non-contact in-situ anti-Stokes/Stokes temperature calibration was carried out for up to 1500 K based on six different samples under two excitation light sources(±50 K within 1000 K,±100 K above1000 K),and the system correction factorγwas systematically investigated.The results show that the correction factorγof anti-Stokes/Stokes thermometry is affected by the wavelength of the excitation light source,Raman mode peak position,temperature measurement region and other factors.The anti-Stokes/Stokes thermometry was applied to the laser-heating diamond anvil cell(LHDAC)experiment to investigate the anharmonic effect of h BN under high temperature and high pressure.It is concluded that the strong anharmonic effect caused by phonon scattering at low pressure gradually changes into the predominance of localized molecular lattice thermal expansion at high pressure.

Normal thermal conduction in lattice models with asymmetric harmonic interparticle interactions

We study the thermal conduction behaviors of one-dimensional lattice models with asymmetric harmonic interparticle interactions. Normal thermal conductivity that is independent of system size is observed when the lattice chains are long enough. Because only the harmonic interactions are involved, the result confirms, without ambiguity, that asymmetry plays a key role in normal thermal conduction in one-dimensional momentum conserving lattices. Both equilibrium and nonequilibrium simulations are performed to support the conclusion.

A Model Effective Mass Quantum Anharmonic Oscillator and Its Thermodynamic Characterization

Using a model anharmonic oscillator with asymptotically decreasing effective mass to study the effect of compositional grading on the quantum mechanical properties of a semiconductor heterostructure, we determine the exact bound states and spectral values of the system. Furthermore, we show that ordering ambiguity only brings about a spectral shift on the quantum anharmonic oscillator with spatially varying effective mass. A study of thermodynamic properties of the system reveals a resonance condition dependent on the magnitude of the anharmonicity parameter. This resonance condition is seen to set a critical value on the said parameter beyond which a complex valued entropy which is discussed, emerges.

High-temperature thermodynamics of silver:Semi-empirical approach

We report high-temperature thermodynamics for fcc silver by combining ab initio phonon dynamics to empirical quadratic temperature-dependent term for anharmonic part of Helmholtz free energy. The electronic free energy is added through an interpolation scheme, which connects ambient condition free electron gas model to Thomas-Fermi results.The present study shows good agreement with experimental and reported findings for several thermal properties, and the discrepancy observed in some caloric properties is addressed. The decreases in the product of volume thermal expansion coefficient and isothermal bulk modulus and in the constant volume anharmonic lattice specific heat at high temperature are the clear evidences of proper account of anharmonicity. The present study also reveals that T-2-dependent anharmonic free energy is sufficient for correct evaluation of thermal pressure and conventional Grüneisen parameter. We observe that the intrinsic phonon anharmonicity starts dominating above characteristic temperature, which is attributed to higher order anharmonicity and can be related to higher order potential derivatives. We conclude that the uncorrelated and largeamplitude lattice vibrations at high temperature raise dominating intrinsic thermal stress mechanism, which surpasses the phonon-anharmonism and requires future consideration.

Theory of Electron Density of States of High Temperature Impurity Induced Anharmonic Superconductors

The expression for the electron density of states (EDOS) of high temperature superconductors (HTS) has been derived taking the disorder and anharmonicity effects as a central problem. This has been dealt with the help of double time thermodynamic Green’s function theory for electrons via a generalized Hamiltonian which consists of the contribution due to 1) unperturbed electrons;2) unperturbed phonons;3) isotopic impurities;4) anharmonicities (no BCS type Hamiltonian has been taken up in the formulation);and 5) electron-phonon interactions. The renormalization effects and emergence of pairons appears as a unique feature of the theory and dependence of EDOS on impurity concentration and temperature has been discussed in details with special reference to the HTS.

Phase transition and thermodynamic properties of ThO2： Quasi-harmonic approximation calculations and anharmonic effects

The thermodynamic properties and the phase transition of ThO2 from the cubic structure to the orthorhombic structure are investigated using the first-principles projector-augmented wave method. The vibrational contribution to Helmholtz free energy is evaluated from the first-principles phonon calculations. The anharmonic contribution to quasi-harmonic free energy is accounted for by using an effective method （2010 Phys. Rev. B 81 172301）. The results reveal that at ambient temperature, the phase transition from the cubic phase to the orthorhombic phase occurs at 26.45 GPa, which is consistent with the experimental and theoretical data. With increasing temperature, the transition pressure decreases almost linearly. By comparing the experimental results with the calculation results, it is shown that the thermodynamic properties of ThO2 at high temperature improve substantially after including the anharmonic correction to quasi-harmonic free energy.

Study on the relationships between Raman shifts and temperature range for α-plane GaN using temperature-dependent Raman scattering

In this paper,Raman shifts of a-plane GaN layers grown on r-plane sapphire substrates by low-pressure metal-organic chemical vapor deposition（LPMOCVD） are investigated.We compare the crystal qualities and study the relationships between Raman shift and temperature for conventional a-plane GaN epilayer and insertion AlN/AlGaN superlattice layers for a-plane GaN epilayer using temperature-dependent Raman scattering in a temperature range from 83 K to 503 K.The temperature-dependences of GaN phonon modes（A1（TO）,E2（high）,and E1（TO）） and the linewidths of E2（high） phonon peak are studied.The results indicate that there exist two mechanisms between phonon peaks in the whole temperature range,and the relationship can be fitted to the pseudo-Voigt function.From analytic results we find a critical temperature existing in the relationship,which can characterize the anharmonic effects of a-plane GaN in different temperature ranges.In the range of higher temperature,the relationship exhibits an approximately linear behavior,which is consistent with the analyzed results theoretically.

Raman spectroscopic study of ceramic Sr2Bi4Ti5O18

Raman spectra of ceramic Sr2Bi4Ti5O18 （SBTi5） are reported to consist of four different Raman bands. Temperature-dependent spectra reveal the relationship between the lattice vibration and the material＇s structure. There appears a relatively large change in structure of the material at about 273K, The anharmonic potential of the material has a great influence on its phonon mode full width at half maximum （FWHM）, which can be expressed by a function of temperature. Theoretical fittings of the FWHMs for the two modes at around 312 cm^-1 and 464cm^-1 indicate that the latter phonon mode is more anharmonic than the former one.

Effects of anharmonic lattice distortion on orbital and magnetic orderings in KCuF_3

Lattice, magnetic and orbital structures in KCuF3 are self-consistently determined by our cluster self-consistent field approach based on a spin-orbital-lattice Hamiltonian. Two stable structures are obtained and found to be degenerate, which confirms the presence of the coexistent phases observed experimentally. We clearly show that due to the inherent frustration, the ground state of the system only with the superexchange interaction is degenerate; while the Jahn-Teller distortion, especially the anharmonic effect, stabilizes the orbital ordered phase at about 23% in the x2-y2 orbit and at 77% in the 3z2-r2 orbit. Meanwhile the magnetic moment of Cu is considerably reduced to 0.56μB, and magnetic coupling strengths are highly anisotropic, Jx/Jxy ≈ 18. These results are in good agreement with the experiments, implying that the anharmonic Jahn-Teller effect plays an essential role in stabilising the orbital ordered ground state of KCuF3.

Generation-channel interference of high-order harmonics of an anharmonic oscillator driven by bi-chrime laser fields and its mechanism

A method to describe the generation channels of high-order harmonics is proposed. According to this method, the mechanism of generation-channel interference of high-order harmonics is revealed clearly. We take the anharmonic oscillator driven by bi-chrome fields as an example to illustrate that this method can be used to understand the effect of generation-channel interference.

Critical rotation of an anharmonically trapped Bose-Einstein condensate

We consider rotational motion of an interacting atomic Bose-Einstein condensate （BEC） with both two- and three- body interactions in a quadratic-plus-quartic and harmonic-plus-Gaussian trap. By using the variational method, the influence of the three-body interaction and the anharmonicity of the trap on the lowest energy surface mode excitation and the spontaneous shape deformation （responsible for the vortex formation） in a rotating BEC is discussed in detail. It is found that the repulsive three-body interaction helps the formation of the vortex and reduces the lowest energy surface mode frequency and the critical rotational frequency of the system. Moreover, the critical rotational frequency for the vortex formation in the harmonic-plus-Gaussian potential is lower than that in the quadratic-plus-quartic potential.