Self-consistent Phonon Theory Research Articles

Excellent thermoelectric performance in alkali metal phosphides M3P (M = Na and K) with phonon-glass electron-crystal like behaviour.

Identifying ideal thermoelectric materials presents a formidable challenge due to the intricate coupling relationship between thermal conductivity and power factor. Here, based on first-principles calculations, along with self-consistent phonon theory and the Boltzmann transport equation, we theoretically investigate the thermoelectric properties of alkali metal phosphides M3P (M = Na and K). The evident 'avoided crossing' phenomenon indicates the phonon glass behavior of M3P (M = Na and K). Due to the strong lattice anharmonicity induced by alkali metal elements, accounting for quartic anharmonic corrections, the lattice thermal conductivities of Na3P and K3P at room temperature are merely 0.25 and 0.12 W m-1 K-1, respectively. Furthermore, the high degeneracy and 'pudding-mold-type' band structure lead to high p-type PF in M3P (M = Na and K). At 300 K, the p-type power factors (PF) of Na3P and K3P can reach 3.90 and 0.80 mW mK-2, respectively. The combination of ultralow κL and high PF leads to excellent thermoelectric figure of merit (ZT) values of 1.70 (3.38) and 1.18 (2.13) for p-type Na3P and K3P under optimal doping concentration at 300 K (500 K), respectively, surpassing traditional thermoelectric materials. These findings demonstrate that M3P (M = Na and K) exhibits behavior similar to phonon-glass electron crystals, thereby indicating a direction for the search for high-performance thermoelectric materials.

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.

Comparison of the excellent thermoelectric properties of the half-Heusler compounds RbMgSb with a host-guest structure and LiMgSb

In this work, we systematically studied the thermoelectric (TE) transport properties of the half-Heusler compounds AMgSb (A = Li, Rb) based on an incorporation of first-principles calculations with self-consistent phonon theory and Boltzmann transport equations. We noted significant changes in the vibrational behavior of alkali metal atoms with a substantial increase in atomic mass. This alteration led to the formation of a host-guest structure in RbMgSb. In contrast, the stronger harmonic vibrations in LiMgSb results in it maintaining a Half-Heusler structure, without the pronounced anharmonicity found in RbMgSb. The calculation results reveal that RbMgSb has ultra-low lattice thermal conductivity κL, which is ten times lower than LiMgSb. We show that rattlers cause tenfold reductions in the thermal conductivity by increasing the phonon–phonon scattering probability, occurred in a wide frequency range. In addition, after careful consideration of multiple scattering mechanisms, the multiple valleys, high dispersion, flat band edges and band asymmetry near the Fermi level give both materials excellent electron transport properties. At the same time, LiMgSb itself already has a very low electron thermal conductivity κe, but the κe of RbMgSb is ten times smaller than that. As a consequence, remarkable ZT values of 2.51 and 3.45 at 900 K are captured in n-type LiMgSb and p-type RbMgSb, respectively. These findings reveal the promising potential of AMgSb in TE applications.

Ultralow thermal conductivity and high thermoelectric performance induced by dimensionality reduction in chain-like compounds X2PtSe2 (X=K, rb)

Balancing low lattice thermal conductivity (κL) with a high power factor is a major challenge in the research of thermoelectric (TE) materials. In this paper, we report on a class of chain-like compounds, X2PtSe2(X = K, Rb), characterized by strong lattice anharmonicity, weak bonds, and low phonon group velocities. Using first-principles calculations in conjunction with self-consistent phonon theory and the Boltzmann transport equation, we systematically investigate the thermal and electrical transport properties of X2PtSe2(X = K, Rb). At room temperature, the κL of K2PtSe2 and Rb2PtSe2 in the direction perpendicular to the Pt–Se chains is only 0.15 and 0.10 Wm−1K−1, respectively. Additionally, due to the low-dimensional nature of the Pt–Se chains, these compounds exhibit a ‘pudding-mold type’ band structure, contributing to a TE power factor. At 300K, under n-type doping, K2PtSe2 and Rb2PtSe2 achieve TE figures of merit (ZT) values of 1.66 and 1.67, respectively, in the direction perpendicular to the Pt–Se chains. At 500K, the ZT value of Rb2PtSe2 approaches 4, far surpassing traditional TE materials. These results indicate that the chain-like compounds X2PtSe2(X = K, Rb) exhibit excellent TE performance, achieving energy conversion efficiencies comparable to commercial transducer devices.

Terahertz electric-field-driven dynamical multiferroicity in SrTiO3

The emergence of collective order in matter is among the most fundamental and intriguing phenomena in physics. In recent years, the dynamical control and creation of novel ordered states of matter not accessible in thermodynamic equilibrium is receiving much attention1–6. The theoretical concept of dynamical multiferroicity has been introduced to describe the emergence of magnetization due to time-dependent electric polarization in non-ferromagnetic materials7,8. In simple terms, the coherent rotating motion of the ions in a crystal induces a magnetic moment along the axis of rotation. Here we provide experimental evidence of room-temperature magnetization in the archetypal paraelectric perovskite SrTiO3 due to this mechanism. We resonantly drive the infrared-active soft phonon mode with an intense circularly polarized terahertz electric field and detect the time-resolved magneto-optical Kerr effect. A simple model, which includes two coupled nonlinear oscillators whose forces and couplings are derived with ab initio calculations using self-consistent phonon theory at a finite temperature9, reproduces qualitatively our experimental observations. A quantitatively correct magnitude was obtained for the effect by also considering the phonon analogue of the reciprocal of the Einstein–de Haas effect, which is also called the Barnett effect, in which the total angular momentum from the phonon order is transferred to the electronic one. Our findings show a new path for the control of magnetism, for example, for ultrafast magnetic switches, by coherently controlling the lattice vibrations with light.

Anomalous thermal conductivity in 2D silica nanocages of immobilizing noble gas atom

Noble gas atoms such as Kr and Xe are byproducts of nuclear fission in nuclear plants. How to trap and confine these volatile even radioactive gases is particularly challenging. Recent studies have shown that they can be trapped in nanocages of ultrathin silica. Here, we exhibit with self-consistent phonon theory and four-phonon (4ph) scattering where the adsorption of noble gases results in an anomalous increase in lattice thermal conductivity (κL), while the presence of Cu atoms doping leads to a reduction in κL. We trace this behavior in host–guest 2D silica to an interplay of tensile strain, rattling phonon modes, and redistribution of electrons. We also find that 4ph scatterings play indispensable roles in κL of 2D silica. Our work illustrates the microscopic heat transfer mechanism in 2D silica nanocages with the immobilization of noble gas atoms and inspires further exploring materials with the kagome and glasslike κL.

Intrinsic ultralow lattice thermal conductivity in lead-free halide perovskites Cs3Bi2X9 (X = Br, I).

Lead-free halide perovskites have recently garnered significant attention due to their rich structural diversity and exceptionally ultralow lattice thermal conductivity (κL). Here, we employ first-principles calculations in conjunction with self-consistent phonon theory and Boltzmann transport equations to investigate the crystal structure, electronic structure, mechanical properties, and κLs of two typical vacancy-ordered halide perovskites, denoted with the general formula Cs3Bi2X9 (X = Br, I). Ultralow κLs of 0.401 and 0.262 W mK-1 at 300 K are predicted for Cs3Bi2Br9 and Cs3Bi2I9, respectively. Our findings reveal that the ultralow κLs are mainly associated with the Cs rattling-like motion, vibrations of halide polyhedral frameworks, and strong scattering in the acoustic and low-frequency optical phonon branches. The structural analysis indicates that these phonon dynamic properties are closely relevant to the bonding hierarchy. The presence of the extended Bi-X antibonding states at the valence band maximum contributes to the soft elastic lattice and low phonon group velocities. Compared to Cs3Bi2Br9, the face-sharing feature and weaker bond strength in Cs3Bi2I9 lead to a softer elasticity modulus and stronger anharmonicity. Additionally, we demonstrate the presence of wave-like κC in Cs3Bi2X9 by evaluating the coherent contribution. Our work provides the physical microscopic mechanisms of the wave-like κC in two typical lead-free halide perovskites, which are beneficial to designing intrinsic materials with the feature of ultralow κL.

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.

Room temperature high thermoelectric performance of Bi-based full-Heusler compounds CsxRb[formula omitted]Bi with strong anharmonicity

Bismuth-based compounds have been identified as a class of promising candidates for the realization of high-performance thermoelectrics, derived from their exceptional electrical conductivity and intrinsic low lattice thermal conductivity κL. Here, we employed first-principles calculations, self-consistent phonon theory, and compressive sensing technique in conjunction with the Boltzmann transport equation to investigate the anharmonic thermoelectric properties of full-heusler bismuth compounds CsxRb3−xBi. As the Cs content increases, the κL of CsxRb3−xBi decreases due to impurity scattering effects, and then increases. Among them, at 300 K, Rb3Bi has the largest κL of 0.69 Wm−1K−1, while Cs2RbBi has the smallest κL of 0.45 Wm−1K−1, both of which are lower than the κL of traditional bismuth-based thermoelectric materials. The ultralow κL originates from the strong lattice anharmonicity. In addition, the coexistence of high dispersion and flat band edges leads to high thermoelectric power factor at optimal doping concentration. As a result, the largest thermoelectric figure of merit ZT values of 2.59 (4.19) at 300 (500) K were obtained for CsRb2Bi at optimal hole doping level. These findings suggest that CsxRb3−xBi compounds are superior for thermal management and thermoelectric applications.

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.

Extremely Large Response of Phonon Coherence in Twisted Penta-NiN2 Bilayer.

Twisting has recently been demonstrated as an effective strategy for tuning the interactions between particles or quasi-particles in layered materials. Motivated by the recent experimental synthesis of pentagonal NiN2 sheet [ACS Nano 2021, 15, 13539], for the first time, the response of phonon coherence to twisting in bilayer penta-NiN2 , going beyond the particle-like phonon transport is studied. By using the unified theory of phonon transport and high order lattice anharmonicity, together with the self-consistent phonon theory, it is found that the lattice thermal conductivity is reduced by 80.6% from 33.35 to 6.47Wm-1 K-1 at 300K when the layers are twisted. In particular, the contribution of phonon coherence is increased sharply by an order of magnitude, from 0.21 to 2.40Wm-1 K-1 , due to the reduced differences between the phonon frequencies and enhanced anharmonicity after the introduction of twist. The work provides a fundamental understanding of the phonon interaction in twisted pentagonal sheets.

Ab initio investigations on lattice dynamics and thermal transport properties of ThO2

Thorium dioxide (ThO2) is considered as a potential substitute for uranium dioxide due to its higher melting point, higher thermal conductivity and lower thermal expansion coefficient. In this paper, based on first-principles calculations and Boltzmann transport equations (BTE), we calculate the temperature-dependent phonon dispersion and lattice thermal conductivity using self-consistent phonon (SCP) theory and the results are in good agreement with experimental values. It is worth noting that the optical vibration modes in the range of 5.5 THz to 10 THz harden significantly with the increase of temperature, leading to the gradual separation of the overlapping of the longitudinal acoustic branch and the transverse optical branch, and finally generate a band gap of 0.2 THz at 1500K, which was not found in previous studies on ThO2. After verifying the accuracy of SCP + BTE method in calculating the lattice thermal conductivity of ThO2, we predict the lattice thermal conductivity of cubic phase ThO2 in the range of 0 GPa to 30 GPa at 300K. The lattice thermal conductivity of ThO2 is 14.4 W/mK at 0 GPa and will increases to 61.9 W/mK at 30 GPa. Analysis of pressure-related thermal transport parameters reveals that the large increase in lattice thermal conductivity is mainly due to a nearly threefold increase in phonon relaxation time from 0 GPa to 30 GPa. Our analysis is of great significance for understanding the thermodynamic behavior of this new nuclear fuel at high pressure. It makes up for the lack of study on the thermal transport properties of cubic phase ThO2 under high pressure.

Study on the thermoelectric characteristics of the ternary alkali metal compound XMgSb (X = K, Rb, Cs)

We conducted a comprehensive analysis of the mechanical, transport, and thermoelectric (TE) characteristics of XMgSb (X = K, Rb, Cs) alkali metal compounds using first-principles calculations, self-consistent phonon theory, pressive sensing lattice dynamics, and the Boltzmann transport equation. Our results show that the very low lattice thermal conductivity of these materials is mainly attributed to the strong anharmonicity of the alkali metal atoms, and the lattice thermal conductivity is negatively correlated with the mass of X atoms. Furthermore, we consider five scattering mechanisms to accurately calculate transport properties and electron relaxation times. Notably, we observed that the large electronic dispersion band near the valence band maximum leads to the high conductivity of these three compounds, with a flat electronic energy band at the Γ-Z point, which generally implies a larger Seebeck coefficient. The coexistence of good electronic band dispersion and flat electronic bands leads to high conductivity and large Seebeck coefficient, resulting in high TE power. Low lattice thermal conductivity and high TE power factor jointly determine the development potential of alkali metal compound XMgSb (X = K, Rb, Cs) in the field of TE.

Ultralow lattice thermal conductivities and excellent thermoelectric properties of hypervalent triiodides XI3 (X = Rb, Cs) discovered by machine learning method.

Thermal conductivity and power factor are key factors in evaluating heat transfer performance and designing thermoelectric conversion devices. To search for materials with ultralow thermal conductivity and a high power factor, we proposed a set of universal statistical interaction descriptors (SIDs) and developed accurate machine learning models for the prediction of thermoelectric properties. For lattice thermal conductivity prediction, the SID-based model achieved the state-of-the-art results with an average absolute error of 1.76W m-1 K-1. The well-performing models predicted that hypervalent triiodides XI3 (X = Rb, Cs) have ultralow thermal conductivities and high power factors. Combining first-principles calculations, the self-consistent phonon theory, and the Boltzmann transport equation, we obtained the anharmonic lattice thermal conductivities of 0.10 and 0.13W m-1 K-1 for CsI3 and RbI3 in the c-axis direction at 300K, respectively. Further studies show that the ultralow thermal conductivity of XI3 arises from the competition of vibrations between alkali metal atoms and halogen atoms. In addition, at 700K, the thermoelectric figure of merit ZT values of CsI3 and RbI3 are 4.10 and 1.52, respectively, at the optimal hole doping level, which indicates hypervalent triiodides are potential high performance thermoelectric materials.

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.

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.

Investigation on transport properties and anomalously heat-carrying optical phonons in KXY (X = Ca, Mg; Y = Sb, Bi)

In this work, we systematically studied the thermal transport properties of ternary zintl compound KXY using self-consistent phonon theory combined with compressive sensing technology and the Boltzmann transport equation. The effects of quartic anharmonic induced phonon renormalization and 4 - phonon scattering on the results are fully considered. Vibrational mode visualization reveals that the anomalous contribution of optical phonons to lattice thermal conductivity in KCaBi originates from high-speed out-of-phase vibrations of Ca atoms. We analyzed the microscopic mechanism of heat transport from the perspective of atomic bonding combined with the results of group velocity, scattering rate, Gru¨neisen parameter, mean free path, etc. In addition, we verified and predicted the mechanical properties in KXY by calculation.

Impact of quartic anharmonicity on lattice thermal transport in EuTiO3: A comparative theoretical and experimental investigation

We investigate the role of the quartic anharmonicity in the lattice dynamics and thermal transport of the cubic EuTiO3 by combining ab initio self-consistent phonon theory with compressive sensing techniques and experimental thermal conductivity determination measurement. The antiferromagnetic G-type magnetic structure is used to mimic the para-magnetic EuTiO3. We find that the strong quartic anharmonicity of oxygen atoms plays an important role in the phonon quasiparticles free from imaginary frequencies in EuTiO3 and causes the hardening of vibrational frequencies of soft modes. Based on these results, the lattice thermal transport properties are predicted through the Boltzmann transport equation within the relaxation time approximation. The hardened modes thereby affect calculated lattice thermal conductivity significantly, resulting in an improved agreement with experimental results, including the deviation from κL ∝ T−1 at high temperatures. The calculated thermal conductivity of 8.2 W/mK at 300 K matched the experimental value of 6.1 W/mK. When considering the boundary scattering, the calculated thermal conductivity is reduced to 6.9 W/mK at 300 K, which agrees better with the experiment.