Transverse Acoustic Branch Research Articles

Anomalous Thermal Transport across the Superionic Transition in Ice

Superionic ices with highly mobile protons within stable oxygen sub-lattices occupy an important proportion of the phase diagram of ice and widely exist in the interior of icy giants and throughout the Universe. Understanding the thermal transport in superionic ice is vital for the thermal evolution of icy planets. However, it is highly challenging due to the extreme thermodynamic conditions and dynamical nature of protons, beyond the capability of the traditional lattice dynamics and empirical potential molecular dynamics approaches. By utilizing the deep potential molecular dynamics approach, we investigate the thermal conductivity of ice-VII and superionic ice-VII″ along the isobar of P = 30 GPa. A non-monotonic trend of thermal conductivity with elevated temperature is observed. Through heat flux decomposition and trajectory-based spectra analysis, we show that the thermally activated proton diffusion in ice-VII and superionic ice-VII″ contribute significantly to heat convection, while the broadening in vibrational energy peaks and significant softening of transverse acoustic branches lead to a reduction in heat conduction. The competition between proton diffusion and phonon scattering results in anomalous thermal transport across the superionic transition in ice. This work unravels the important role of proton diffusion in the thermal transport of high-pressure ice. Our approach provides new insights into modeling the thermal transport and atomistic dynamics in superionic materials.

Overdamped Phonon Diffusion and Nontrivial Electronic Structure Leading to a High Thermoelectric Figure of Merit in KCu5Se3.

Thermoelectric copper selenides are highly attractive owing to not only their constituent nontoxic, abundant elements but also their ultralow liquid-like lattice thermal conductivity (κlat). For the first time, the promising thermoelectric properties of the new KCu5Se3 are reported herein, showing a high power factor (PF = 9.0 μWcm-1 K-2) and an intrinsically ultralow κlat = 0.48 Wm-1 K-1. The doped K1-xBaxCu5Se3 (x = 0.03) realizes a figure-of-merit ZT = 1.3 at 950 K. The crystallographic structure of KCu5Se3 allows complex lattice dynamics that obey a rare dual-phonon transport model well describing a high scattering rate and an extremely short phonon lifetime that are attributed to interband phonon tunneling, confinement of the transverse acoustic branches, and temperature-dependent anharmonic renormalization, all of which generate an unprecedently high contribution of the diffusive phonons (70% at 300 K). The overall weak chemical bonding feature of KCu5Se3 gives K+ cations a quiescence behavior that further blocks the heat flux transfer. In addition, the valence band edge energy dispersion of KCu5Se3 is quasilinear that allows a large Seebeck coefficient even at high hole concentrations. These in-depth understandings of the ultralow lattice thermal conductivity provide new insights into the property-oriented design and synthesis of advanced complex chalcogenide materials.

Anharmonic lattice dynamics and the origin of intrinsic ultralow thermal conductivity in AgI materials

Ionic conductors such as AgI with ultralow thermal conductivities $({\ensuremath{\kappa}}_{l})$ are of increasing interest because of their excellent thermoelectric properties. However, the origin of their intrinsic low ${\ensuremath{\kappa}}_{l}$ values remain elusive. In this study, comprehensive theoretical calculations of the lattice dynamics and the thermal transport properties of $\ensuremath{\gamma}\text{\ensuremath{-}}\mathrm{AgI}$ (zinc-blende structure) and $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{AgI}$ (wurtzite structure) as functions of temperature were carried out based on many-body perturbation theory and phonon Boltzmann transport theory. First, the mean-squared displacements (MSDs) of ${\mathrm{Ag}}^{+}$ were significantly larger than those of ${\mathrm{I}}^{\ensuremath{-}}$ in both $\ensuremath{\gamma}\text{\ensuremath{-}}$ and \ensuremath{\beta}-phases below the order-disorder phase transition temperature $({T}_{\mathrm{c}})$, which led to a characteristic ``rattling'' feature and low-frequency, nearly flat local phonon vibrations. According to our previous work [Xie et al., Phys. Rev. Lett. 125, 245901 (2020)], such nondispersive flat phonon band structures are expected to give rise to four-phonon resonance and result in a dramatic increase in the four-phonon scattering over the conventional three-phonon scattering. For $\ensuremath{\gamma}\text{\ensuremath{-}}\mathrm{AgI}$, similar four-phonon resonance behavior was also discovered for the low-lying transverse acoustic phonon branches, and it was found that their four-phonon scattering rates were an order of magnitude larger than the corresponding three-phonon scattering rates. Considering the four-phonon scattering, the theoretical ${\ensuremath{\kappa}}_{l}$ of $\ensuremath{\gamma}\text{\ensuremath{-}}\mathrm{AgI}$ was predicted to be $\ensuremath{\sim}0.32$ W/m K at 300 K, which was in good agreement with the value deduced from our experiments ($\ensuremath{\sim}0.36$ W/m K at 300 K). Compared to $\ensuremath{\gamma}\text{\ensuremath{-}}\mathrm{AgI}$, the acoustic phonons in $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{AgI}$ were more dispersive, and they intertwined with low-energy optical phonons at the zone boundaries. It was found that three-phonon resonance became as important as four-phonon resonance for the nearly flat longitudinal phonon band. The theoretical ${\ensuremath{\kappa}}_{l}$ for $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{AgI}$ was determined to be around $\ensuremath{\sim}0.32$ W/m K at room temperature, closely reproducing our measurement value $\ensuremath{\sim}0.29$ W/m K. Our results for AgI demonstrate the strong quartic anharmonicity in materials characterized by the rattling of weak bonding atoms as well as dispersionless phonon band structures. It is believed that this intimate relationship between the low-${\ensuremath{\kappa}}_{l}$ and flat phonon dispersion can be employed as a good indicator when searching for material systems with ultralow ${\ensuremath{\kappa}}_{l}$ values, e.g., cagelike rattling structures, quasi-two-dimensional structures, and chainlike structures.

Ultrafast Suppression of the Ferroelectric Instability in KTaO_{3}.

We use an x-ray free-electron laser to study the lattice dynamics following photoexcitation with ultrafast near-UV light (wavelength 266nm, 50fs pulse duration) of the incipient ferroelectric potassium tantalate, KTaO_{3}. By probing the lattice dynamics corresponding to multiple Brillouin zones through the x-ray diffuse scattering with pulses from the Linac Coherent Light Source (LCLS) (wavelength 1.3Å and <10 fs pulse duration), we observe changes in the diffuse intensity associated with a hardening of the transverse acoustic phonon branches along Γ to X and Γ to M. Using force constants from density functional theory, we fit the quasiequilibrium intensity and obtain the instantaneous lattice temperature and density of photoexcited charge carriers. The density functional theory calculations demonstrate that photoexcitation transfers charge from oxygen 2p derived π-bonding orbitals to Ta 5d derived antibonding orbitals, further suppressing the ferroelectric instability and increasing the stability of the cubic, paraelectric structure.

Thermal conductivity of two stable bilayer phosphorene stackings: A computation study

We report the thermal conductivity of two dynamically stable bilayer phosphorene stackings, i.e., a twisted phase with a twist angle of ∼70.5° (or 2O-tαP phase) and a shifting phase with half of the lattice constants (or AB phase). This was achieved by using the first-principles-driven lattice dynamics calculations and a fully iterative solver of the Boltzmann transport equation, the latter including an anharmonic phonon–phonon scattering effect. At room temperature, the thermal conductivity of the 2O-tαP phase is 146 and 108 W/mK along its two orthogonal lattice basis vectors, respectively, larger than that along the armchair direction (69 W/mK) of the AB phase, while smaller than that along the AB zigzag direction (164 W/mK); with an increasing temperature, the conductivity decreases along the basis vectors of the 2O-tαP and AB stackings, and the anisotropy lessens for both stackings. The thermal transport anisotropies for the two kinds of bilayer stacking can be attributed to the different proportions of their acoustic branches along different directions. In particular, the phonon mean free path showed that the in-plane transverse acoustic branch is the main contribution of the thermal conductivity along the short lattice constant direction of the 2O-tαP phase due to the twist angle extending the propagation path of transverse acoustic waves in the direction. Finally, the thermal conductivity accumulation was revealed to increase in the form of a hyperbolic tangent with mean free path of the phonons, which can be used to evaluate the size effect of the stacking materials in practice.

Boson-peak-like anomaly caused by transverse phonon softening in strain glass

Strain glass is a glassy state with frozen ferroelastic/martensitic nanodomains in shape memory alloys, yet its nature remains unclear. Here, we report a glassy feature in strain glass that was thought to be only present in structural glasses. An abnormal hump is observed in strain glass around 10 K upon normalizing the specific heat by cubed temperature, similar to the boson peak in metallic glass. The simulation studies show that this boson-peak-like anomaly is caused by the phonon softening of the non-transforming matrix surrounding martensitic domains, which occurs in a transverse acoustic branch not associated with the martensitic transformation displacements. Therefore, this anomaly neither is a relic of van Hove singularity nor can be explained by other theories relying on structural disorder, while it verifies a recent theoretical model without any assumptions of disorder. This work might provide fresh insights in understanding the nature of glassy states and associated vibrational properties.

Optical phonon contribution to the thermal conductivity of a quantum paraelectric

Motivated by recent experimental findings, we study the contribution of a quantum critical optical phonon branch to the thermal conductivity of a paraelectric system. We consider the proximity of the optical phonon branch to transverse acoustic phonon branch and calculate its contribution to the thermal conductivity within the Kubo formalism. We find a low temperature power law dependence of the thermal conductivity as T α , with 1 < α < 2, (lower than T 3 behavior) due to optical phonons near the quantum critical point. This result is in accord with the experimental findings and indicates the importance of quantum fluctuations in the thermal conduction in these materials.

Raman scattering from highly-stressed anvil diamond* *Project support by the National Natural Science Foundation of China (Grant No. 11774247).

The high-frequency edge of the first-order Raman mode of diamond reflects the stress state at the culet of anvil, and is often used for the pressure calibration in diamond anvil cell (DAC) experiments. Here we point out that the high-frequency edge of the diamond Raman phonon corresponds to the Brillouin zone (BZ) center Γ point as a function of pressure. The diamond Raman pressure gauge relies on the stability of crystal lattice of diamond under high stress. Upon the diamond anvil occurs failure under the uniaxial stress (197 GPa), the loss of intensity of the first-order Raman phonon and a stress-dependent broad Raman band centered at 600 cm−1 are observed, which is associated with a strain-induced local mode corresponding to the BZ edge phonon of the L 1 transverse acoustic phonon branch.

Uncertainty quantification in first-principles predictions of phonon properties and lattice thermal conductivity

We present a framework for quantifying the uncertainty that results from the choice of exchange-correlation (XC) functional in predictions of phonon properties and thermal conductivity that use density functional theory (DFT) to calculate the atomic force constants. The energy ensemble capabilities of the BEEF-vdW XC functional are first applied to determine an ensemble of interatomic force constants, which are then used as inputs to lattice dynamics calculations and a solution of the Boltzmann transport equation. The framework is applied to isotopically-pure silicon. We find that the uncertainty estimates bound property predictions (e.g., phonon dispersions, specific heat, thermal conductivity) from other XC functionals and experiments. We distinguish between properties that are correlated with the predicted thermal conductivity [e.g., the transverse acoustic branch sound speed ($R^2=0.89$) and average Gr\"uneisen parameter ($R^2=0.85$)] and those that are not [e.g., longitudinal acoustic branch sound speed ($R^2=0.23$) and specific heat ($R^2=0.00$)]. We find that differences in ensemble predictions of thermal conductivity are correlated with the behavior of phonons with mean free paths between $100$ and $300$ nm. The framework systematically accounts for XC uncertainty in phonon calculations and should be used whenever it is suspected that the choice of XC functional is influencing physical interpretations.

Probing the physical and superconducting properties of hexagonal ZrRuAs: A first-principles calculation

In the presented work, ab initio pseudopotential calculations have been realized on structural, electronic, elastic, mechanical, phonon and electron-phonon interaction properties for ZrRuAs with the hexagonal ZrNiAl-type layer crystal structure. In the vicinity of the Fermi level, Ru 4d and Zr 4d states dominate and mainly contribute to the conduction properties of ZrRuAs. A critical assessment of elastic and mechanical properties for ZrRuAs reveals that, this superconductor is soft (ductile) due to remarkable metallic bonding. Phonon anomalies have been observed in the phonon spectrum of ZrRuAs for the lowest transverse acoustic branch and low-frequency transverse optical branches along the Γ-K and Γ-M-K symmetry directions. Our electron-phonon interaction calculations indicated that ZrRuAs is a conventional phonon-mediated superconductor with strong electron-phonon coupling parameter of 1.32. The strong electron-phonon coupling parameter of ZrRuAs produces its superconducting transition temperature to be 11.12 K which accords nicely with its experimental values of 12 K.

Anharmonic decay of high-frequency LA modes in quasi-isotropic III-nitrides

We report for the first time an estimation of the spontaneous decay rates at room temperature in a selection of nitride-based nanostructures that are quasi-isotropic. We numerically calculate the phonon distribution functions and the decay rates and find that the decay channel LA → TA + TA dominates over the decay channel LA → LA + TA, which confirms Klemens’ prediction [] that LA phonon will primarily split into two doubly degenerate TA phonons through a greater variety of decay channels compared to the decay of LA into two modes, one belonging to the longitudinal acoustic and the other to the transverse acoustic branch.

Investigating the normal state and superconducting state properties of orthorhombic and hexagonal ZrRuP: A first-principles study

We have executed ab initio pseudopotential calculations on the structural, electronic, elastic, mechanical, vibrational, and electron-phonon interaction properties of hexagonal ZrRuP (h-ZrRuP) and orthorhombic ZrRuP (o-ZrRuP). The electronic states of both phases near the Fermi energy are found to be dominated by the $d$ electrons of transition metal atoms, suggesting that they play a more active role in the generation of superconducting state for both phases of ZrRuP. A critical assessment of their elastic and mechanical properties reveals that the lattice of h-ZrRuP is softer than that of o-ZrRuP. A comparison of phonon dispersion curves for both phases indicates that the lower transverse acoustic branch of h-ZrRuP is much softer than that of o-ZrRuP. The soft character of this phonon branch gives rise to strong electron-phonon interaction in h-ZrRuP. Therefore the electron-phonon coupling parameter for h-ZrRuP equals to 1.25 which is considerably larger than the corresponding value of 0.57 for o-ZrRuP. As a consequence, phonon and electron-phonon interaction properties are crucial in making superconducting transition temperature much higher for h-ZrRuP than o-ZrRuP. At the end, the value of this temperature is found to be 12.49 K for h-ZrRuP and 3.89 K for o-ZrRuP which coincide with their experimental values of 12.93 and 3.82 K.

Body-centered-cubic structure and weak anharmonic phonon scattering in tungsten

It was recently found that the anharmonic phonon–phonon scattering in tungsten is extremely weak at high frequencies, leading to a predominance of electron–phonon scattering and consequently anomalous phonon transport behaviors. In this work, we calculate the phonon linewidths of W along high-symmetry directions from first principles. We find that the weak phonon–phonon scattering can be traced back to two factors. The first is the triple degeneracy of the phonon branches at the P and H points, a universal property of elemental body-centered-cubic (bcc) structures. The second is a relatively isotropic character of the phonon dispersions. When both are met, phonon–phonon scattering rates must vanish at the P and H points. The weak phonon–phonon scattering feature is also applicable to Mo and Cr. However, in other elemental bcc substances like Na, the isotropy condition is violated due to the unusually soft character of the lower transverse acoustic phonon branch along the Γ-N direction, opening emission channels and leading to much stronger phonon–phonon scattering. We also look into the distributions of electron mean-free paths (MFPs) at room temperature in tungsten, which can help engineer the resistivity of nanostructured W for applications such as interconnects.

Mindlin–Eringen anisotropic micromorphic elasticity and lattice dynamics representation

ABSTRACTTo account for certain essential features of material such as dispersive behaviour and optical branches in dispersion curves, a fundamental departure from classical elasticity to polar theories is required. Among the polar theories, micromorphic elasticity of appropriate grades and anisotropy is capable of capturing these physical phenomena completely. In the mathematical framework of micromorphic elasticity, in addition to the traditional elastic constants, some additional constants are introduced in the pertinent governing equations of motion. A precise evaluation of the numerical values of the aforementioned elastic constants in the realm of the experimentations poses serious difficulties. Thus this paper aims to provide a remedy as how to determine the micromorphic elastic constants theoretically in terms of the atomic force constants and lattice parameters of the crystalline solid with general anisotropy. In this treatment capture of the discrete nature of matter becomes an essential factor. To this end, the discrete lattice dynamics equations of a crystal are related to the pertinent anisotropic micromorphic equations of motion. This approach allows incorporating the symmetry groups of the crystals within lattice dynamics equations conveniently. For the illustration of the current theoretical developments, the micromorphic elastic constants of diamond and silicon crystals are computed in conjunction with ab initio density functional perturbation theory (DFPT). Moreover, the longitudinal and transverse optical and acoustic branches pertinent to [100] and [110] directions are presented. The accuracy of the results is verified by comparing the dispersion curves derived from the micromorphic theory, those of available experiments, and those directly obtained from DFPT calculations.

Anomalous thermal expansion and chiral phonons in BiB3O6

The origins of anomalous thermal expansion in the chiral monoclinic solid $\alpha$-BiB$_{3}$O$_{6}$ have been studied through ab initio calculations. Positive and negative axial thermal expansion are shown to be driven by librations of borate units, elastic anisotropy, and most notably by chiral acoustic phonons involving elliptical revolutions of bismuth atoms. The chirality of the lattice gives rise to these modes by allowing the transverse acoustic branches to have opposite circular polarizations, only one of which couples strongly to the lattice strains. These results further understanding of relationships between crystallographic symmetry and physical properties.

Thermal transport properties in monolayer GeS

Utilizing the first-principle techniques combined with the Boltzmann transport equation, we investigate the thermal transport properties of monolayer GeS. The calculated lattice thermal conductivity κL is fairly low, e.g., 11.76 (12.53) Wm−1K−1 at 300 K, along the x (y) axis, which is much lower than the values for phosphorene, monolayer MoS2, graphene, etc. Our analysis reveals that the low lattice thermal conductivity is resulted from the strong three-phonon scattering process and the low phonon group velocity. Due to the weak anisotropy of GeS, we study the contribution of each phonon branch to the heat transport along x and y axis, and find that the longitudinal acoustic (LA) mode contributes most of the total κL along x axis, while the transverse acoustic (TA) branch has the largest contribution to the total κL along y axis. Additionally, the size dependence of thermal conductivity with respect to the nanoribbon width is also studied for the design of nanometer devices.

Probing the acoustic phonon dispersion and sound velocity of graphene by Raman spectroscopy

The extraordinary thermal and elastic properties of graphene, mainly originating from its unique acoustic phonon branches near Γ point in Brillouin zone, have attracted great attention in its fundamental researches and practical applications. Here, we introduce an optical technique to accurately probe longitudinal acoustic (LA) and transverse acoustic (TA) phonon branches of graphene near Γ point by double resonant Raman scattering of the combination phonon modes in the range of 1650−2150 cm−1 along with the overtone 2D' mode at ∼3200 cm−1. The corresponding sound velocities (νTA=12.9km/s,νLA=19.9km/s) of graphene have been accessed, which are about 10% smaller than those of graphite. Based on νTA and νLA, the two-dimensional (2d) elastic stiffness (tension) coefficients c11 and c66, Young's modulus Y2d and Poisson's ratio σ2d can be estimated. The results demonstrate again that double resonant Raman spectroscopy is a powerful tool to probe the fundamental properties of graphene.

Comment on "Giant electromechanical coupling of relaxor ferroelectrics controlled by polar nanoregion vibrations".

Manley et al. (Science Advances, 16 September 2016, p. e1501814) report the splitting of a transverse acoustic phonon branch below T C in the relaxor ferroelectric Pb[(Mg1/3Nb2/3)1-x Ti x ]O3 with x = 0.30 using neutron scattering methods. Manley et al. argue that this splitting occurs because these phonons hybridize with local, harmonic lattice vibrations associated with polar nanoregions. We show that splitting is absent when the measurement is made using a different neutron wavelength, and we suggest an alternative interpretation.

Remarkable thermoelectric performance in BaPdS2 via pudding-mold band structure, band convergence, and ultralow lattice thermal conductivity

Efficient thermoelectric materials require a rare and contraindicated combination of materials properties: large electrical conductivity, large Seebeck coefficient, and low thermal conductivity. One strategy to achieve the first two properties is via low-energy electronic bands containing both flat and dispersive parts in different regions of crystal momentum space, known as a pudding-mold band structure. Here, we illustrate that ${\mathrm{BaPdS}}_{2}$ successfully achieves the pudding-mold band structure for the valence band, contributing to a large $p$-type thermoelectric power factor, due to its anisotropic crystal structure containing zigzag chains of edge-sharing square planar ${\mathrm{PdS}}_{4}$ units; large power factor is achieved for $n$-type doping as well due to band convergence. In addition, ${\mathrm{BaPdS}}_{2}$ exhibits ultralow lattice thermal conductivity, and thus also achieves the third property, due to extremely soft and anharmonic interactions in its transverse acoustic phonon branch. We predict a remarkably large thermoelectric figure of merit, with peak values between 2 and 3 for two of the three crystallographic directions, suggesting ${\mathrm{BaPdS}}_{2}$ warrants experimental investigation.

Soft-phonon dynamics of the thermoelectric β-SnSe at high temperatures

Results of inelastic neutron scattering experiments on SnSe single crystals at high temperatures along with theoretical studies based on the density functional theory are reported. Our experiments reveal significant softening of the transverse acoustic branch along the [0,ξ,0] direction in the low-temperature α-SnSe of Pbnm symmetry as temperature approaches Tc=807 K from below. This process is followed by a condensation of the zone-boundary Y-phonon of the high-temperature β-SnSe with Cmcm symmetry at the onset of phase transition. The employed theoretical approach supports experimental observations and demonstrates that the phase change in SnSe is mediated by an unstable zone-boundary phonon with the Y2+ irreducible representation within the Cmcm symmetry space group of the high-temperature β-SnSe. The present work provides a detailed understanding of the soft-mode dynamics in SnSe and conclusively shows that the α⇌β structural transformation in this currently topical thermoelectric material is of displacive type.