Anharmonic Lattice Dynamics Calculations Research Articles

Computational Study of the Thermal Rectification Properties of a Graphene-Based Nanostructure.

Thermally rectifying materials would have important implications for thermal management, thermal circuits, and the field of phononics in general. Graphene-based nanostructures have very high intrinsic thermal conductance, but they normally display no thermal rectification effects. The present study relates to a thermally rectifying material and, more particularly, to a graphene-based nanomaterial for controlling heat flux and the associated method determining the rectification coefficient. Thermal rectifiers using a graphene-based nanostructure as thermal conductors were designed. Vacancy defects were introduced into one end of the nanostructure to produce an axially non-uniform mass distribution. Modified Monte Carlo methods were used to investigate the effects of defect size and shape, vacancy concentration, and ribbon length on the thermal rectification properties. Anharmonic lattice dynamics calculations were carried out to obtain the frequency-dependent phonon properties. The results indicated that the nanoscale system conducts heat asymmetrically, with a maximum available rectification coefficient of about 70%. Thermal rectification has been achieved, and the difference in temperature dependence of thermal conductivity is responsible for the phenomenon. Defects can be tailored to modulate the temperature dependence of thermal conductivity. The power-law exponent can be negative or positive, depending upon the ribbon length and vacancy concentration. A computational method has been developed, whereby the numerous variables used to determine the rectification coefficient can be summarized by two parameters: the power-law exponent and the thermal resistance ratio. Accordingly, the rectification coefficient can be obtained by solving a simple algebraic expression. There are several structure factors that cause noticeable effects on the thermal rectification properties. Defect size, vacancy concentration, and ribbon length can affect the thermal conductance of the nanostructure symmetrically and significantly. Graphene-based nanostructure thermal rectifiers can be arranged in an array so as to provide thermal rectification on a macroscopic scale.

Density functional study of thermodynamic properties, thermal expansion and lattice thermal conductivity of Fe2VAl in the high-temperature region

Here, we present the phonon calculations for thermodynamic properties, thermal expansion and lattice thermal conductivity of Fe2VAl in the temperature range of and compare them with existing experiment. Phonon dispersion is computed using the finite displacement method and supercell approach. The positive frequencies of all the phonon modes indicate the mechanical stability of the compound. The specific heat at constant volume and Helmholtz free energy are calculated under harmonic approximation, while calculation of thermal expansion is done under quasi-harmonic approximation. Lattice thermal conductivity is calculated using first-principle anharmonic lattice dynamics calculations. The zero-point energy and Debye temperature are computed as and 638 K, respectively. The calculated thermal expansions are found to be and at 300 and 800 K, respectively. A significant deviation between calculated () and experimental () values of are observed at 300 K. But, as the temperature increases, the calculated and experimental come closer with the corresponding values of and at 800 K. The possible reasons for the deviation of are addressed. The temperature dependence of phonon lifetime is computed in order to understand the feature of . The present study suggests that DFT-based phononic calculations provide reasonably good explanations of available experimental phonon-related properties of Fe2VAl in the high-temperature range of .

First principle design of new thermoelectrics from TiNiSn based pentanary alloys based on 18 valence electron rule

In this study we have reported electronic structure, lattice dynamics, and thermoelectric (TE) transport properties of a new family of pentanary substituted TiNiSn systems using the 18 valence electron count (VEC) rule. We have modeled the pentanary substituted TiNiSn by supercell approach with the aliovalent substitution, inspite of the traditional isoelectronic substitution. We have performed the detailed analysis of electronic structure, lattice dynamics, and TE transport properties of selected systems from this family. From our calculated band structures and density of states we show that by preserving the 18 VEC through aliovalent substitutions at Ti site of TiNiSn semiconducting behavior can be achieved and hence one can tune the band structure and band gap to maximize the thermoelectric figure of merit (ZT) value. Two approaches have been used for calculating the lattice thermal conductivity (κL), one by fully solving the linearized phonon Boltzmann transport (LBTE) equation from first-principles anharmonic lattice dynamics calculations implemented in Phono3py code and other using Slack’s equation with calculated Debye temperature and Grüneisen parameter using the calculated elastic constant values. At high temperatures the calculated κL and ZT values from both these methods show very good agreement. The calculated κL values decreases from parent TiNiSn to pentanary substituted TiNiSn systems as expected due to fluctuation in atomic mass. The substitution of atoms with different mass creates more phonon scattering centers and hence lower the κL value. The calculated κL for Hf containing systems La0.25Hf0.5V0.25NiSn and non Hf containing system La0.25Zr0.5V0.25NiSn calculated from Phono3py (Slack’s equation) are found to be 0.37 (1.04) and 0.16 (0.95) W/mK, at 550K, respectively and the corresponding ZT value are found to be 0.54 (0.4) and 0.77 (0.53). Among the considered systems, the calculated phonon spectra and heat capacity show that La0.25Hf0.5V0.25NiSn has more optical-acoustic band mixing which creates more phonon–phonon scattering and hence lower the κL value and maximizing the ZT. Based on the calculated results we conclude that one can design high efficiency thermoelectric materials by considering 18 VEC rule with aliovalent substitution.

P-TRANS: A Monte Carlo ray-tracing software to simulate phonon transport in arbitrary nanostructures

P-TRANS is a software to simulate phonon transport in arbitrary nanostructures based on the Boltzmann transport theory. The core part of the software is a Monte Carlo ray-tracing solver that uses the stochastic method to sample phonon transport in various nanostructures. The solver is written in FORTRAN with well-organized modules and utilizing the OpenMP and MPI parallelization to achieve high performance. The software can handle a typical calculation of nanostructures with a feature size of ∼1000 nm on a normal PC within seconds, which is useful when exploring the wide variety of structures, for instance for structural optimization or high-throughput screening in material informatics. The software takes the bulk phonon properties obtained from the first-principles anharmonic lattice dynamics calculations as inputs. The database of bulk phonon properties is available on the software webpage, which currently contains more than 60 materials and will increase in the future. We also provide a graphical user interface to design the nanostructures and to run the simulation for non-expert users. In this paper, we introduce the theoretical background, the technical details and implementation, and the applications of the software. Program summaryProgram title:P-TRANSCPC Library link to program files:https://doi.org/10.17632/n76jpj3fnz.1Developer's repository link:https://github.com/TEEL-UTokyo/P-TRANSCode Ocean capsule:https://codeocean.com/capsule/9387119Licensing provisions: GPLv3Programming language: FortranSupplementary material:http://www.phonon.t.u-tokyo.ac.jp/p-trans/Nature of problem: Knowing the effective thermal conductivity of nanostructures is important for numerous applications. Phonons are the dominate heat carriers in dielectrics and their transport is influenced by the voids, grain boundaries, and free surfaces in the nanostructure. Here we are focusing on the effective thermal conductivities of nanostructures with complex geometries and boundaries.Solution method: Monte Carlo ray tracing simulations.

First-principles phonon calculations for lattice dynamics, thermal expansion and lattice thermal conductivity of CoSi in the high temperature region

This study presents the first-principles phonon calculations to understand the experimental thermal expansion () and lattice thermal conductivity of CoSi in the high temperature region. Phonon dispersion is computed using the finite displacement method and supercell approach by taking the equilibrium crystal structures obtained from DFT. The calculation of is done under quasi-harmonic approximation. The is calculated using first-principle anharmonic lattice dynamics calculations under single-mode relaxation time approximation. The calculated in the temperature range 0–1300 K gives a good match with existing experimental data. The calculated value of (∼8.0 W/mK) at 300 K is found to be in good agreement with the experimental value of ∼8.3 W/mK. The temperature dependence of phonon lifetime due to phonon-phonon interaction is calculated to understand the behaviour of . The present study suggests that ground state phonon dispersion obtained from DFT-based methods gives reasonably good explanation of experimental and .

Surface phonons limit heat conduction in thin films

Understanding microscopic heat conduction in thin films is important for nano/micro heat transfer and thermal management for advanced electronics. As the thickness of thin films is comparable to or shorter than a phonon wavelength, phonon dispersion relations and transport properties are significantly modulated, which should be taken into account for heat conduction in thin films. Although phonon confinement and depletion effects have been considered, it should be emphasized that surface-localized phonons (surface phonons) arise whose influence on heat conduction may not be negligible due to the high surface-to-volume ratio. However, the role of surface phonons in heat conduction has received little attention thus far. In the present work, we performed anharmonic lattice dynamics calculations to investigate the thickness and temperature dependence of in-plane thermal conductivity of silicon thin films with sub-10-nm thickness in terms of surface phonons. Through systematic analysis of the influences of surface phonons, we found that anharmonic coupling between surface and internal phonons localized in thin films significantly suppresses overall in-plane heat conduction in thin films. We also discovered that specific low-frequency surface phonons significantly contribute to surface--internal phonon scattering and heat conduction suppression. Our findings are beneficial for the thermal management of electronics and phononic devices and may lead to surface phonon engineering for thermal conductivity control.

Efficient anharmonic lattice dynamics calculations of thermal transport in crystalline and disordered solids

Understanding heat transport in semiconductors and insulators is of fundamental importance because of its technological impact in electronics and renewable energy harvesting and conversion. Anharmonic lattice dynamics provides a powerful framework for the description of heat transport at the nanoscale. One of the advantages of this method is that it naturally includes quantum effects due to atoms vibrations, which are needed to compute the thermal properties of semiconductors widely used in nanotechnology, like silicon and carbon, even at room temperature. While the heat transport picture substantially differs between amorphous and crystalline semiconductors from a microscopic standpoint, a unified approach to simulate both crystals and glasses has been devised. Here, we introduce a unified workflow, which implements both the Boltzmann Transport equation and the quasi-harmonic Green-Kubo methods. We discuss how the theory can be optimized to exploit modern parallel architectures, and how it is implemented in κALDo: a versatile and scalable open-source software to compute phonon transport in solids. This approach is applied to crystalline and partially disordered silicon-based systems, including bulk silicon and clathrates, and on silicon–germanium alloy clathrates with largely reduced thermal conductivity.

Structural, stability and thermoelectric properties for the monoclinic phase of NaSbS2 and NaSbSe2: A theoretical investigation

This study is the first attempt towards establishing computational insight into the structural, electronic, mechanical, dynamical and thermoelectric properties of the monoclinic phases of NaSbS2 and NaSbSe2. The mechanical properties are predicted using the Hill approximation. Dynamical stability was investigated by computing the phonon frequency to check for the absence of imaginary modes. Lattice thermal conductivity was calculated by using a single-mode relaxation-time approximation in the linearized phonon Boltzmann equation from first-principles an-harmonic lattice dynamics calculations. We found that the lattice thermal conductivity of NaSbS2 and NaSbSe2 are anisotropic, with values ranging between 0.753 and 1.173 Wm−1 K−1 at room temperature (300 K). The calculated values of the lattice thermal conductivity are small, especially along the x-axis. The charge transport properties are predicted using Boltzmann transport equations. The highest values attained for the figure of merit are high as 4.22 and 2.88 when the electron concentration is 1018 cm−3 at 600 K for NaSbS2 and NaSbSe2, respectively. This highlights the potential of using NaSbS2 and NaSbSe2 in designing thermoelectric materials since low lattice thermal conductivity and high figure of merit are a requisite for maximizing the efficiency of thermoelectric materials.

A scattering rate model for accelerated evaluation of lattice thermal conductivity bypassing anharmonic force constants

Predicting the lattice thermal conductivity from the atomic structure is important to many scientific and engineering applications. However, the state-of-the-art method based on first-principles calculations of the three-phonon scattering process is bound with high computational cost, while semiempirical models such as the Slack equation are less accurate. In this work, we examined the theoretical background of the commonly used computational models for thermal conductivity evaluation and proposed an improved quasiharmonic model based on an early approximation for three-phonon scattering strength. This model has significantly reduced computational cost as compared to the full anharmonic lattice dynamics calculations but retains a fairly good quantitative accuracy comparing to many semiempirical models. It also allows one to include normal processes in phonon-phonon scattering and obtain the phonon relaxation times.

Anharmonic stabilization and lattice heat transport in rocksalt β-GeTe

Peierls-Boltzmann transport equation, coupled with third-order anharmonic lattice dynamics calculations, has been widely used to model lattice thermal conductivity (κl) in bulk crystals. However, its application to materials with structural phase transition at relatively high temperature is fundamentally challenged by the presence of lattice instabilities (imaginary phonon modes). Additionally, its accuracy suffers from the absence of higher-than-third-order phonon scattering processes, which are important near/above the Debye temperature. In this letter, we present an effective scheme that combines temperature-induced anharmonic phonon renormalization and four-phonon scattering to resolve these two theoretical challenges. We apply this scheme to investigate the lattice dynamics and thermal transport properties of GeTe, which undergoes a second-order ferroelectric phase transition from rhombohedral α-GeTe to rocksalt β-GeTe at about 700 K. Our results on the high-temperature phase β-GeTe at 800 K confirm the stabilization of β-GeTe by temperature effects. We find that considering only three-phonon scattering leads to significantly overestimated κl of 3.8 W/mK at 800 K, whereas including four-phonon scattering reduces κl to 1.7 W/mK, a value comparable with experiments. To explore the possibility to further suppress κl, we show that alloying β-GeTe with heavy cations such as Pb and Bi can effectively reduce κl to about 1.0 W/mK, whereas particle size needs to be around 10 nm through nanostructuring to achieve a comparable reduction in κl.

A theoretical investigation of structural, mechanical, electronic and thermoelectric properties of orthorhombic CH3NH3PbI3

The structural, mechanical, electronic and thermoelectric properties of the low temperature orthorhombic perovskite phase of CH3NH3PbI3 have been investigated using density functional theory (DFT). Elastic parameters bulk modulus B, Young’s modulus E, shear modulus G, Poisson’s ratio ν and anisotropy value A have been calculated by the Voigt–Reuss–Hill averaging scheme. Phonon dispersions of the structure were investigated using a finite displacement method. The relaxed system is dynamically stable, and the equilibrium elastic constants satisfy all the mechanical stability criteria for orthorhombic crystals, showing stability against the influence of external forces. The lattice thermal conductivity was calculated within the single-mode relaxation-time approximation of the Boltzmann equation from first-principles anharmonic lattice dynamics calculations. Our results show that lattice thermal conductivity is anisotropic, and the corresponding lattice thermal conductivity at 150 K was found to be 0.189, 0.138, and 0.530 Wm−1K−1 in the a, b, and c directions. Electronic structure calculations demonstrate that this compound has a DFT direct band gap at the gamma point of about 1.57 eV. The electronic transport properties have been calculated by solving the semiclassical Boltzmann transport equation on top of DFT calculations, within the constant relaxation time approximation. The Seebeck coefficient S is almost constant from 50 to 150 K. At temperatures 100 and 150 K, the maximal figure of merit is found to be 0.06 and 0.122 in the direction of the c-axis, respectively.

Lattice thermal conductivity and bandgap engineering of a three-dimensional [formula omitted]-hybridized Dirac carbon material: HS-C48

A sp2 hybridized three-dimensional Dirac carbon material, HS-C48, is predicted by means of first principles calculations. The evaluation of mechanical, thermodynamic and kinetic stabilities shows HS-C48 is a potential carbon allotrope to be prepared. By solving linearized phonon Boltzmann equation from first-principles anharmonic lattice dynamics calculations, we find that the lattice thermal conductivity of HS-C48 is anisotropic and quite low relative to sp2 hybridized graphene or nanotubes. Electronic structure calculation shows it is a metallic carbon with Dirac linear dispersion near Fermi level. By means of triaxial strain engineering, the bandgap of HS-C48 could be opened, especially when the positive strains εz is applied.

First principles study of the structural, stability properties and lattice thermal conductivity of bulk ReSe2

Thermoelectric devices can convert heat into an electric current and have immense potential for efficient use of the available energy. This includes converting heat energy from internal combustion engines, conventional power plants and solar cells into usable energy. Research into finding efficient thermoelectric materials has intensified over the past decade. One of the desired features of efficient thermoelectric materials is a low lattice thermal conductivity. In other words, the thermal energy transported by the motion of the atoms in thermoelectric materials should be small. Recent research suggests that some layered materials may possess this property. In this study we used first-principles calculations to investigate the structural, mechanical, and vibrational properties of bulk ReSe2, a layered material. The lattice thermal conductivity was calculated by using a single-mode relaxation-time approximation in the linearized phonon Boltzmann equation from first-principles an-harmonic lattice dynamics calculations. We find that the lattice thermal conductivity of ReSe2 is non-isotropic, with the highest value of 18.58W(mK)-1 along the a-axis and lowest one of 0.69W(mK)-1 along the c-axis at room temperature. These values make this an interesting material as a potential active component in a thermoelectric device.

Abnormal negative thermal expansion of sodium: A first-principles discovery at high pressures

Negative thermal expansion coefficients ($\ensuremath{\alpha}$) are found in the fcc and cI16 (a distorted bcc structure) phases of sodium at pressures above 90 GPa from first principles. At room temperature, the most significant negative $\ensuremath{\alpha}$ of about $\ensuremath{-}4.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\phantom{\rule{4pt}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ is predicted in fcc sodium at 120 GPa, which represents the first prediction of a robust negative $\ensuremath{\alpha}$ in a simple metal. Anharmonic lattice dynamics calculations were carried out to rationalize this intriguing behavior. We find that the negative thermal expansion of fcc sodium originates from the transverse acoustic modes with large negative Gr\uneisen parameters. Furthermore, full phonon spectra of fcc sodium at elevated temperatures are calculated from perturbation theory. The phonon-phonon couplings in fcc sodium are found to increase abnormally under high pressures.

Harmonic phonon theory for calculating thermal conductivity spectrum from first-principles dispersion relations

In recent years, nanostructuring of dielectric and semiconducting crystals has enhanced controllability of their thermal conductivity. To carry out computational materials search for nanostructured materials with desirable thermal conductivity, a key property is the thermal conductivity spectrum of the original single crystal, which determines the appropriate length scale of nanostructures and mutual adaptability of different kinds of nanostructures. Although the first-principles phonon transport calculations have become accessible, the anharmonic lattice dynamics calculations are still expensive to scan many materials. To this end, we have developed an empirical model that describes the thermal conductivity spectrum in terms only of harmonic phonon properties and bulk thermal conductivity. The model was tested for several crystals with different structures and thermal conductivities, and was confirmed to reproduce the overall profiles of thermal conductivity spectra and their accumulation functions obtained by the first-principles anharmonic calculations.

Prediction of Low-Thermal-Conductivity Compounds with First-Principles Anharmonic Lattice-Dynamics Calculations and Bayesian Optimization.

Compounds of low lattice thermal conductivity (LTC) are essential for seeking thermoelectric materials with high conversion efficiency. Some strategies have been used to decrease LTC. However, such trials have yielded successes only within a limited exploration space. Here, we report the virtual screening of a library containing 54,779 compounds. Our strategy is to search the library through Bayesian optimization using for the initial data the LTC obtained from first-principles anharmonic lattice-dynamics calculations for a set of 101 compounds. We discovered 221 materials with very low LTC. Two of them even have an electronic band gap <1 eV, which makes them exceptional candidates for thermoelectric applications. In addition to those newly discovered thermoelectric materials, the present strategy is believed to be powerful for many other applications in which the chemistry of materials is required to be optimized.

Distributions of phonon lifetimes in Brillouin zones

Lattice thermal conductivities of zincblende- and wurtzite-type compounds with 33 combinations of elements are calculated with the single-mode relaxation-time approximation and linearized phonon Boltzmann equation from first-principles anharmonic lattice dynamics calculations. In 9 zincblende-type compounds, distributions of phonon linewidths (inverse phonon lifetimes) are discussed in detail. The phonon linewidths vary non-smoothly with respect to wave vector, which is explained from the imaginary parts of the self energies. It is presented that detailed combination of phonon-phonon interaction strength and three phonon selection rule is critically important to determine phonon lifetime for these compounds. This indicates difficulty to predict phonon lifetime quantitatively without anharmonic force constants. However it is shown that joint density of states weighted by phonon numbers, which is calculated only from harmonic force constants, can be potentially used for a screening of the lattice thermal conductivity of materials.

Thermal conductivity of silicene calculated using an optimized Stillinger-Weber potential

Silicene, the silicon-based counterpart of graphene with a two-dimensional honeycomb lattice, has attracted tremendous interest both theoretically and experimentally due to its significant potential industrial applications. From the aspect of theoretical study, the widely used classical molecular dynamics simulation is an appropriate way to investigate the transport phenomena and mechanisms in nanostructures such as silicene. Unfortunately, no available interatomic potential can precisely characterize the unique features of silicene. Here, we optimized the Stillinger-Weber potential parameters specifically for a single-layer Si sheet, which can accurately reproduce the low buckling structure of silicene and the full phonon dispersion curves obtained from ab initio calculations. By performing equilibrium and nonequilibrium molecular dynamics simulations and anharmonic lattice dynamics calculations with the new potential, we reveal that the three methods consistently yield an extremely low thermal conductivity of silicene and a short phonon mean-free path, suggesting silicene as a potential candidate for high-efficiency thermoelectric materials. Moreover, by qualifying the relative contributions of lattice vibrations in different directions, we found that the longitudinal phonon modes dominate the thermal transport in silicene, which is fundamentally different from graphene, despite the similarity of their two-dimensional honeycomb lattices.

Thermal conductivity of one-, two- and three-dimensional sp2 carbon

Carbon atoms can form structures in one, two and three dimensions due to their unique chemical versatility. In terms of thermal conductivity, carbon polymorphs cover a wide range from very low values with amorphous carbon to very high values with diamond, carbon nanotubes and graphene. Schwarzites are a class of three-dimensional fully covalent sp2-bonded carbon polymorphs, with the same local chemical environment as graphene and carbon nanotubes, but negative Gaussian curvature. We calculate the thermal conductivity of a (10,0) carbon nanotube, graphene and two schwarzites with different curvature, by molecular dynamics simulations based on the Tersoff empirical potential. We find that schwarzites present a thermal conductivity two orders of magnitude smaller than nanotubes and graphene. The reason for such large difference is explained by anharmonic lattice dynamics calculations, which show that phonon group velocities and mean free paths are much smaller in schwarzites than in nanotubes and graphene. Their reduced thermal conductivity, in addition to tunable electronic properties, indicate that schwarzites could pave the way towards all-carbon thermoelectric technology with high conversion efficiency.

Phonon transport in periodic silicon nanoporous films with feature sizes greater than 100 nm

The thermal conductivities of solid silicon thin films and silicon thin films with periodic pore arrays are predicted using a Monte Carlo technique to include phonon-boundary scattering and the Boltzmann transport equation. The bulk phonon properties required as input are obtained from harmonic and anharmonic lattice dynamics calculations. The force constants required for the lattice dynamics calculations are obtained from forces calculated using density functional theory. For both solid and porous films, the in-plane thermal conductivity predictions capture the magnitudes and trends of previous experimental measurements. Because the prediction methodology treats the phonons as particles with bulk properties, the results indicate that coherent phonon modes associated with the secondary periodicity of the pores do not contribute to thermal transport in porous films with feature sizes greater than 100 nm.