Anharmonic Interatomic Force Constants Research Articles

Thermal transport properties of two-dimensional boron dichalcogenides from a first-principles and machine learning approach

The investigation of thermal transport is crucial to the thermal management of modern electronic devices. To obtain the thermal conductivity through solution of the Boltzmann transport equation, calculation of the anharmonic interatomic force constants has a high computational cost based on the current method of single-point density functional theory force calculation. The recent suggested machine learning interatomic potentials (MLIPs) method can avoid these huge computational demands. In this work, we study the thermal conductivity of two-dimensional MoS2-like hexagonal boron dichalcogenides (H-B2 VI 2; VI = S, Se, Te) with a combination of MLIPs and the phonon Boltzmann transport equation. The room-temperature thermal conductivity of H-B2S2 can reach up to 336 W⋅m−1⋅K−1, obviously larger than that of H-B2Se2 and H-B2Te2. This is mainly due to the difference in phonon group velocity. By substituting the different chalcogen elements in the second sublayer, H-B2 VIVI′ have lower thermal conductivity than H-B2 VI 2. The room-temperature thermal conductivity of B2STe is only 11% of that of H-B2S2. This can be explained by comparing phonon group velocity and phonon relaxation time. The MLIP method is proved to be an efficient method for studying the thermal conductivity of materials, and H-B2S2-based nanodevices have excellent thermal conduction.

Anomalous thermal response of bulk diamond to uniaxial (100) strain: A first-principles prediction

Diamond, a material that exhibits ultrahigh thermal conductivity with a sensitive thermal response to stress, is an ideal heat-sink material in the embedded cooling paradigm. This study uses first-principles calculations with the phonon Boltzmann transport equation to predict the variation rules of the thermal conductivity of diamond along the $\ensuremath{\langle}100\ensuremath{\rangle}$ crystal direction under strains at three orders of magnitude: 0.1%, 1%, and 10.5%. Density functional theory is used to predict the stress--strain dependence of diamond and the temperature-dependent thermal conductivity of unstrained diamond. The predictions are in good agreement with the experimental results. The calculated uniaxial strain--thermal conductivity dependence results reveal that the thermal conductivity of diamond abnormally increases by approximately 15% under small-scale uniaxial strain because of the weakened anharmonic interatomic force constants. Under large-scale strain, the thermal conductivity considerably decreases because of reduced phonon group velocities and increased numbers of phonon scattering channels. The findings in this study will guide analyses of the dependence of thermal conductivity on strain in other diamondlike structures, such as Group IV element-based materials. The abnormal thermal response at small strain is expected to lead to the realization of an artificial thermal conduction channel.

Conformational Gap Control in CsTaS3.

Simple arguments based on orbital energies and crystal symmetry suggest the band gap of CsTaS3 to be suitable for solar cell photovoltaics. Here, we combine chemical theory with sophisticated calculations to describe an intricate relationship between the structure and optical properties of this material. Orbital interactions govern both the presence and nature of CsTaS3's gap. In the first place, through a second-order Jahn-Teller (JT) distortion, which slides the Ta ion along the axial direction of TaS3 chains. This displacement creates a gap that remains direct in the face of minor distortions. Using an advanced methodology, compressive sensing lattice dynamics, we compute the anharmonic interatomic force constants up to the fourth order and use them to renormalize the phonons at finite temperatures. This analysis predicts CsTaS3 to undergo the JT metal-to-semiconductor transition at temperatures below 1000 K. At around room temperature, we find a second distortion that moves the Ta ion along the equatorial direction of the TaS3 chains, giving rise to many possible supercell conformations. By relaxing all symmetry-inequivalent structures with Ta ion displacements, in supercells with up to 12 formula units, we obtain 204 symmetrically distinct conformations and sort them by energy and (direct) band gap magnitude. Since all structures with a gap lie within an energy range of 30 meV/Ta above the ground state, we expect CsTaS3's optical properties to be controlled by the full polymorphic ensemble of gapped conformations. Using the GW-Bethe-Salpeter approach, we predict a band gap of 1.3-1.4 eV as well as potent absorption in the visible range.

Thermoelectric transport properties of two-dimensional materials <i>X</i>Te<sub>2</sub> (<i>X</i> = Pd, Pt) via first-principles calculations

<sec>Developing efficient thermoelectric materials has never lost the attraction due to their promising performances in the energy conversion. The different mechanisms of phonon scattering lead to the various outstanding performances of layered materials in thermoelectric properties. So we investigate the structure, electronic and thermoelectric transport properties of Penta-<i>X</i>Te<sub>2</sub> (<i>X</i> = Pd, Pt) layers based on the density functional theory and Boltzmann transport theory. Those monolayers have a beautiful penta-graphene-like buckled structure with a space group of <i>P</i>2_1/<i>c</i> (No.14). The values of optimized lattice constant <i>a</i> (<i>b</i>) are 6.437 Å (6.145 Å) and 6.423 Å (6.12 Å) for PdTe<sub>2</sub> and PtTe<sub>2</sub> monolayers, respectively. In order to assess the stability, we calculate the phonon dispersion along the high symmetry lines in the Brillouin zone. The second-order harmonic and third-order anharmonic interatomic force constants (IFCs) are calculated by using 5 × 5 × 1 supercell and 4 × 4 × 1 supercell based on the relaxed unit cell. All these results indicate that those monolayers are thermodynamically stable. Energy band structure is essential in obtaining reliable transport properties. So we calculate the band structures of penta-<i>X</i>Te<sub>2</sub>. Both PdTe<sub>2</sub> and PtTe<sub>2</sub> are semiconductors with indirect band gaps of 1.24 eV and 1.38 eV, respectively, which are in good agreement with previous experimental and theoretical results.</sec><sec>The lattice thermal conductivity of <i>X</i>Te<sub>2</sub> decreases with temperature increasing, but the electronic thermal conductivity varies with temperature in the opposite way exactly. It is found that the thermal conductivity comes from the contribution of the lattice thermal conductivity at low temperature. The room-temperature total thermal conductivities in the <i>x</i> (<i>y</i>) direction of the PdTe<sub>2</sub> and PtTe<sub>2</sub> monolayers are 3.95 W/(m·K) (2.7 W/(m·K)) and 3.27 W/(m·K)(1.04 W/(m·K)), respectively. The contribution of low thermal conductivity indicates that the thermoelectric properties of PtTe<sub>2</sub> monolayer may be better than those of PdTe<sub>2</sub> monolayer.</sec><sec>The relaxation time (<i>τ</i>) and carrier mobility (<i>μ</i>) are obtained based on the Bardeen-Shockley deformation potential (DP) theory in two-dimensional materials. Remarkably, they have the higher hole mobility than the electron mobility. The anisotropic electronic transport properties of <i>X</i>Te<sub>2</sub> are obtained by solving Boltzmann transport equation. The electrical conductivity over relaxation time (<i>σ</i>/<i>τ</i>) and Seebeck coefficient (<i>S</i>) contribute to the figure of merit <i>ZT</i>. High Seebeck coefficient (<i>S</i>) with the value larger than 400 μV/K can be found in both p-type and n-type cases, suggesting that the TE performance of <i>X</i>Te<sub>2</sub> may be considerable. The room-temperature largest <i>ZT</i> values of penta-<i>X</i>Te<sub>2</sub> (<i>X</i> = Pd, Pt) at p-type are 0.83 and 2.75 respectively. The monolayer PtTe<sub>2</sub> is a potential thermoelectric material.</sec>

Accelerating first-principles estimation of thermal conductivity by machine-learning interatomic potentials: A MTP/ShengBTE solution

Accurate evaluation of the thermal conductivity of a material can be a challenging task from both experimental and theoretical points of view. In particular for the nanostructured materials, the experimental measurement of thermal conductivity is associated with diverse sources of uncertainty. As a viable alternative to experiment, the combination of density functional theory (DFT) simulations and the solution of Boltzmann transport equation is currently considered as the most trusted approach to examine thermal conductivity. The main bottleneck of the aforementioned method is to acquire the anharmonic interatomic force constants using the computationally demanding DFT calculations. In this work we propose a substantially accelerated approach for the evaluation of anharmonic interatomic force constants via employing machine-learning interatomic potentials (MLIPs) trained over short ab initio molecular dynamics trajectories. The remarkable accuracy of the proposed accelerated method is confirmed by comparing the estimated thermal conductivities of several bulk and two-dimensional materials with those computed by the full-DFT approach. The MLIP-based method proposed in this study can be employed as a standard tool, which would substantially accelerate and facilitate the estimation of lattice thermal conductivity in comparison with the commonly used full-DFT solution.

Density functional theory study of the structural, mechanical and thermal conductivity of uranium dialuminide (UAl2)

In this work, we present a systematic study on the structural, mechanical, and thermal conductivity of uranium dialuminide (UAl2) using the ab initio calculation, based on the density functional theory (DFT). The structural and mechanical properties such as the volume expansion, thermal expansion coefficient, density variation and the bulk modulus of UAl2 as a function of temperature (between 300 K and 1500 K) are evaluated within quasiharmonic approximation (QHA). The total thermal conductivity (κTot) of UAl2 as a function of temperature were predicted considering both the lattice thermal conductivity (κph) and the electronic contribution (κe). The κph was estimated by solving the Boltzmann Transport Equation (BTE) using the harmonic and anharmonic interatomic force constants. Whereas, the κe was evaluated using the Wiedemann-Franz law. The absolute value of electrical conductivity (σ) required for the Wiedemann-Franz law was evaluated employing the BoltzTraP code and the Electron-Phonon Wannier (EPW) code. In addition to the total thermal conductivity κTot=κe+κph, the mode-dependent phonon scattering rates and the group velocities, as well as their impacts on the lattice thermal conductivity, are discussed in detail. The results obtained demonstrated that κTot of UAl2 decreased with increasing temperature up to 600 K and then remained nearly invariant at ∼5.9 Wm−1K−1 up to 1500 K. Moreover, a large optical mode contribution (31% at 300 K) to the κph was predicted for UAl2.

Revisiting PbTe to identify how thermal conductivity is really limited

Due to the long range interaction in lead telluride (PbTe), the transverse optical (TO) phonon becomes soft around the Brillouin zone center. Previous studies have postulated that this zone-center softening causes the low thermal conductivity of PbTe through either enlarged phonon scattering phase space and/or strengthened lattice anharmonicity. In this work, we reported an extensive sensitivity analysis of the PbTe thermal conductivity to various factors: range and magnitude of harmonic and anharmonic interatomic force constants, and phonon wavevectors in the three-phonon scattering processes. The analysis reveals that the softening by long range harmonic interaction itself does not reduce thermal conductivity and it is the large magnitude of the anharmonic (cubic) force constants that realizes low thermal conductivity, however, not through the TO phonons around the zone center but dominantly through the ones with larger wavevectors in the middle of Brillion zone. The work clarifies that local band softening cannot be a direct finger print for low thermal conductivity and the entire Brillion zone needs to be characterized on exploring low thermal conductivity materials.

Temperature-dependent infrared optical properties of 3C-, 4H- and 6H-SiC

The temperature-dependent optical properties of cubic (3C) and hexagonal (4H and 6H) silicon carbide are investigated in the infrared range of 2–16 μm both by experimental measurements and numerical simulations. The temperature in experimental measurement is up to 593 K, while the numerical method can predict the optical properties at elevated temperatures. To investigate the temperature effect, the temperature-dependent damping parameter in the Lorentz model is calculated based on anharmonic lattice dynamics method, in which the harmonic and anharmonic interatomic force constants are determined from first-principles calculations. The infrared phonon modes of silicon carbide are determined from first-principles calculations. Based on first-principles calculations, the Lorentz model is parameterized without any experimental fitting data and the temperature effect is considered. In our investigations, we find that the increasing temperature induces a small reduction of the reflectivity in the range of 10–13 μm. More importantly, it also shows that our first-principles calculations can predict the infrared optical properties at high-temperature effectively which is not easy to be obtained through experimental measurements.

Thermal transport and microscopic dynamics in filled skutterudite YbFe4Sb12 studied by ab initio molecular dynamics simulation

Filled skutterudite is a typical thermoelectric material with high thermoelectric figure of merit at intermediate temperatures. One of the important features is the low lattice thermal conductivity (L) caused by the low frequency vibrations of filler atoms in the oversized void cages. In the past decades, it has been still under debate whether the underlying phonon scattering mechanism should be considered to be resonant scattering or enhanced three-phonon process. To clarify the role played by the filler atoms in reducing the lattice thermal conductivity, we study the microscopic dynamical process of filler and related interactions by means of ab initio molecular dynamics (AIMD) and temperature dependent effective potential (TDEP) technique. Firstly, we simulate the dynamical trajectories of fully filled skutterudite YbFe4Sb12 at different temperatures through AIMD. In this approach, the nonlinear guest-host interactions at finite temperatures are taken into consideration naturally from dynamical trajectories. Then, we extract the effective temperature-dependent harmonic and anharmonic interatomic force constants (IFCs) by TDEP method through the statistical analyses of both trajectories and forces. The atomic participation ratios and lifetimes of phonon modes are calculated based on the effective IFCs. The results demonstrate that the local vibration modes of Yb couple with acoustic branches and reduce the lifetimes of the lattice phonons significantly. However, the calculated L, which is on the assumption that the filler interacts with lattice phonons through three-phonon collision, still deviates from the experimental result. In order to rationalize the discrepancy, we analyze the correlation properties between different Yb atoms by velocity coherence in atomic dynamical motions. The localized and independent vibration characteristic of Yb is found in this analysis. This implies that the motions of Yb atoms deviate from the periodic and collective vibration excitation paradigm of phonon. Therefore, the mechanism for how filler atoms scatter lattice phonon and enhance thermal resistance is beyond three-phonon scattering process. We thus introduce resonant scattering into the lifetimes of Yb-dominant localized vibration modes, and so-calculated L is in a good agreement with the experimental data. Overall, we come to a conclusion that both the phonon-phonon interaction and the resonant scattering due to the localized oscillators cause the low lattice thermal conductivity of YbFe4Sb12.

Anharmonic interatomic force constants and thermal conductivity from Grüneisen parameters: An application to graphene

Phonon-mediated thermal conductivity, which is of great technological relevance, fundamentally arises due to anharmonic scattering from interatomic potentials. Despite its prevalence, accurate first-principles calculations of thermal conductivity remain challenging, primarily due to the high computational cost of anharmonic interatomic force constant (IFCs) calculations. Meanwhile, the related anharmonic phenomenon of thermal expansion is much more tractable, being computable from the Gr\"uneisen parameters associated with phonon frequency shifts due to crystal deformations. In this work, we propose a novel approach for computing the largest cubic IFCs from the Gr\"uneisen parameter data. This allows an approximate determination of the thermal conductivity via a much less expensive route. The key insight is that although the Gr\"uneisen parameters cannot possibly contain all the information on the cubic IFCs, being derivable from spatially uniform deformations, they can still unambiguously and accurately determine the largest and most physically relevant ones. By fitting the anisotropic Gr\"uneisen parameter data along judiciously designed deformations, we can deduce (i.e., reverse engineer) the dominant cubic IFCs and estimate three-phonon scattering amplitudes. We illustrate our approach by explicitly computing the largest cubic IFCs and thermal conductivity of graphene, especially for its out-of-plane (flexural) modes that exhibit anomalously large anharmonic shifts and thermal conductivity contributions. Our calculations on graphene not only exhibits reasonable agreement with established DFT results, but also presents a pedagogical opportunity for introducing an elegant analytic treatment of the Gr\"uneisen parameters of generic two-band models. Our approach can be readily extended to more complicated crystalline materials with nontrivial anharmonic lattice effects.

A first principles study of the electronic structure, elastic and thermal properties of UB2

Uranium diboride (UB2) has been widely deployed for refractory use and is a proposed material for Accident Tolerant Fuel (ATF) due to its high thermal conductivity. However, the applicability of UB2 towards high temperature usage in a nuclear reactor requires the need to investigate the thermomechanical properties, and recent studies have failed in highlighting applicable properties. In this work, we present an in-depth theoretical outlook of the structural and thermophysical properties of UB2, including but not limited to elastic, electronic and thermal transport properties. These calculations were performed within the framework of Density Functional Theory (DFT) + U approach, using Quantum ESPRESSO (QE) code considering the addition of Coulomb correlations on the uranium atom. The phonon spectra and elastic constant analysis show the dynamic and mechanical stability of UB2 structure respectively. The electronic structure of UB2 was investigated using full potential linear augmented plane waves plus local orbitals method (FP-LAPW+lo) as implemented in WIEN2k code. The absence of a band gap in the total and partial density of states confirms the metallic nature while the valence electron density plot reveals the presence of covalent bond between adjacent B-B atoms. We predicted the lattice thermal conductivity (kL) by solving Boltzmann Transport Equation (BTE) using ShengBTE. The second order harmonic and third-order anharmonic interatomic force constants required as input to ShengBTE was calculated using the Density-functional perturbation theory (DFPT). However, we predicted the electronic thermal conductivity (kel) using Wiedemann-Franz law as implemented in Boltztrap code. We also show that the sound velocity along ‘a’ and ‘c’ axes exhibit high anisotropy, which accounts for the anisotropic thermal conductivity of UB2.

Lattice dynamics and thermal conductivity of cesium chloride via first-principles investigation

The lattice thermal conductivity of CsCl crystal is theoretically investigated from a first-principles theoretical approach based on an iterative solution of the Boltzmann transport equation. Real-space finite-difference supercell approach is employed to generate the harmonic and anharmonic interatomic force constants. Phonon frequencies, velocities, and specific heat capacity as well as anharmonic properties are then obtained and applied to calculate the bulk thermal conductivity of CsCl crystal at the temperatures ranging from 20K to 700K. The calculated lattice thermal conductivity 1.14W/mK of CsCl at room temperature agrees well with the experimental value, demonstrating that this parameter-free approach can provide a good description for the thermal transport of this material. The RTA and iterative solution of BTE are both presented. Our results show that both methods can obtain the thermal conductivity successfully.

Anisotropic lattice thermal conductivity in chiral tellurium from first principles

Using ab initio based calculations, we have calculated the intrinsic lattice thermal conductivity of chiral tellurium. We show that the interplay between the strong covalent intrachain and weak van der Waals interchain interactions gives rise to the phonon band gap between the lower and higher optical phonon branches. The underlying mechanism of the large anisotropy of the thermal conductivity is the anisotropy of the phonon group velocities and of the anharmonic interatomic force constants (IFCs), where large interchain anharmonic IFCs are associated with the lone electron pairs. We predict that tellurium has a large three-phonon scattering phase space that results in low thermal conductivity. The thermal conductivity anisotropy decreases under applied hydrostatic pressure.

Ab initio phonon properties of half-Heusler NiTiSn, NiZrSn and NiHfSn

A theoretical investigation of phonon properties from first-principles calculations is carried out for the half-Heusler compounds NiXSn, , Zr and Hf. The crystal structures are optimised via ab initio calculations within the framework of density functional theory. The phonon properties are retrieved from harmonic and anharmonic interatomic force constants calculations using the finite size displacements method and many-body perturbation theory. A solution to the linearized phonon Boltzmann transport equation is then used to compute the ab initio thermal conductivities. For X = Ti, Zr and Hf, we found 15.4, 13.3 and 15.8 W m−1 K−1 at 300 K, respectively. Thanks to a spectral analysis of the velocities and lifetimes we were able appreciate the differences in the thermal conductivities between the three compounds under study. Our results provide insights to understand the behaviour of the thermal conductivity and therefore to improve the thermoelectric figure of merit for such materials.

Importance of local force fields on lattice thermal conductivity reduction in PbTe1−xSex alloys

Lattice thermal conductivity of PbTe1−xSex alloyed crystals has been calculated by molecular-dynamics simulations with anharmonic interatomic force constants (a-IFCs) obtained from first principles. The a-IFCs of pure PbTe and PbSe were calculated by the real-space displacement method with care of the stability for molecular-dynamics simulations. An empirical mixing rule of a-IFCs has been developed to account for both mass and local force-field differences in alloys. The obtained alloy-fraction dependence of lattice thermal conductivity reduction agrees well with the experiments. The comparative study shows that the local force-field difference significantly impacts the lattice thermal conductivity.

Ab initiothermal transport in compound semiconductors

We use a recently developed ab initio approach to calculate the lattice thermal conductivities of compound semiconductors. An exact numerical solution of the phonon Boltzmann transport equation is implemented, which uses harmonic and anharmonic interatomic force constants determined from density functional theory as inputs. We discuss the method for calculating the anharmonic interatomic force constants in some detail, and we describe their role in providing accurate thermal conductivities in a range of systems. This first-principles approach obtains good agreement with experimental results for well-characterized systems (Si, Ge, and GaAs). We determine the intrinsic upper bound to the thermal conductivities of cubic aluminum-V, gallium-V, and indium-V compounds as limited by anharmonic phonon scattering. The effects of phonon-isotope scattering on the thermal conductivities are examined in these materials and compared to available experimental data. We also obtain the lattice thermal conductivities of other technologically important materials, AlN and SiC. For most materials, good agreement with the experimental lattice thermal conductivities for naturally occurring isotopic compositions is found. We show that the overall frequency scale of the acoustic phonons and the size of the gap between acoustic and optic phonons play important roles in determining the lattice thermal conductivity of each system. The first-principles approach used here can provide quantitative predictions of thermal transport in a wide range of systems.

Spectral phonon conduction and dominant scattering pathways in graphene

In this paper, we examine the lattice thermal conductivity and dominant phonon scattering mechanisms of graphene. The interatomic interactions are modeled using the Tersoff interatomic potential and perturbation theory is applied to calculate the transition probabilities for three-phonon scattering. The matrix elements of the perturbing Hamiltonian are calculated using the anharmonic interatomic force constants obtained from the interatomic potential as well. The linearized Boltzmann transport equation is applied to compute the thermal conductivity of graphene for a wide range of parameters giving spectral and polarization-resolved information. The complete spectral detail of selection rules, important phonon scattering pathways, and phonon relaxation times in graphene are provided. We also highlight the specific scattering processes that are important in Raman spectroscopy-based measurements of graphene thermal conductivity, and provide a plausible explanation for the observed dependence on laser spot size.

Thermal conductivity of half-Heusler compounds from first-principles calculations

We demonstrate successful application of first-principles-based thermal conductivity calculation on half-Heusler compounds that are promising, environmentally friendly thermoelectric materials. Taking the case of a $p$-type half-Heusler structure, the harmonic and anharmonic interatomic force constants were obtained from a set of force-displacement data calculated by the density functional theory. Thermal conductivity was obtained by two different methods: (1) Boltzmann-Peierls formula with phonon relaxation times calculated by either Fermi's golden rule of three-phonon scattering processes or spectral analysis of molecular dynamics phase space trajectories and (2) Green-Kubo formula for heat current obtained by equilibrium molecular dynamics simulations. The calculated temperature dependence of thermal conductivity is in reasonable agreement with experiments. The method was extended to alloy crystals assuming the transferability of interatomic force constants. By having access to accurate phonon-dependent transport properties, the contribution from an arbitral subset of phonon modes can be quantified. This helps understanding the influence of nanostructures on thermal conductivity.

Ab initiotheory of the lattice thermal conductivity in diamond

We present a first-principles theoretical approach to calculate the lattice thermal conductivity of diamond based on an exact solution of the Boltzmann transport equation. Density-functional perturbation theory is employed to generate the harmonic and third-order anharmonic interatomic force constants that are required as input. A central feature of this approach is that it provides accurate representations of the interatomic forces and at the same time introduced no adjustable parameters. The calculated lattice thermal conductivities for isotopically enriched and naturally occurring diamond are both in very good agreement with experimental data. The role of the scattering of heat-carrying acoustic phonons by optic branch phonons is also investigated. We show that inclusion of this scattering channel is indispensable in properly describing the thermal conductivity of semiconductors and insulators. The accurate adjustable-parameter-free results obtained herein highlight the promise of this approach in providing predictive descriptions of the lattice thermal conductivity of materials.

Intrinsic lattice thermal conductivity of semiconductors from first principles

We present an ab initio theoretical approach to accurately describe phonon thermal transport in semiconductors and insulators free of adjustable parameters. This technique combines a Boltzmann formalism with density functional calculations of harmonic and anharmonic interatomic force constants. Without any fitting parameters, we obtain excellent agreement (<5% difference at room temperature) between the calculated and measured intrinsic lattice thermal conductivities of silicon and germanium. As such, this method may provide predictive theoretical guidance to experimental thermal transport studies of bulk and nanomaterials as well as facilitating the design of new materials.