Anharmonic Force Constants Research Articles

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.

Self-consistent phonon calculations of lattice dynamical properties in cubicSrTiO3with first-principles anharmonic force constants

We present an \textit{ab initio} framework to calculate anharmonic phonon frequency and phonon lifetime that is applicable to severely anharmonic systems. We employ self-consistent phonon (SCPH) theory with microscopic anharmonic force constants, which are extracted from density-functional calculations using the least absolute shrinkage and selection operator technique. We apply the method to the high-temperature phase of SrTiO$_{3}$ and obtain well-defined phonon quasiparticles that are free from imaginary frequencies. Here we show that the anharmonic phonon frequency of the antiferrodistortive mode depends significantly on the system size near the critical temperature of the cubic-to-tetragonal phase transition. By applying perturbation theory to the SCPH result, phonon lifetimes are calculated for cubic SrTiO$_{3}$, which are then employed to predict lattice thermal conductivity using the Boltzmann transport equation within the relaxation-time approximation. The presented methodology is efficient and accurate, paving the way toward a reliable description of thermodynamic, dynamic, and transport properties of systems with severe anharmonicity, including thermoelectric, ferroelectric, and superconducting materials.

Linear transformation of anharmonic molecular force constants between normal and Cartesian coordinates.

A full derivation of the analytic transformation of the quadratic, cubic, and quartic force constants from normal coordinates to Cartesian coordinates is given. Previous attempts at this transformation have resulted in non-linear transformations; however, for the first time, a simple linear transformation is presented here. Two different approaches have been formulated and implemented, one of which does not require prior knowledge of the translation-rotation eigenvectors from diagonalization of the Hessian matrix. The validity of this method is tested using two molecules H2O and c-C3H2D(+).

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.

Stochastic algorithm for size-extensive vibrational self-consistent field methods on fully anharmonic potential energy surfaces.

A stochastic algorithm based on Metropolis Monte Carlo (MC) is presented for the size-extensive vibrational self-consistent field methods (XVSCF(n) and XVSCF[n]) for anharmonic molecular vibrations. The new MC-XVSCF methods substitute stochastic evaluations of a small number of high-dimensional integrals of functions of the potential energy surface (PES), which is sampled on demand, for diagrammatic equations involving high-order anharmonic force constants. This algorithm obviates the need to evaluate and store any high-dimensional partial derivatives of the potential and can be applied to the fully anharmonic PES without any Taylor-series approximation in an intrinsically parallelizable algorithm. The MC-XVSCF methods reproduce deterministic XVSCF calculations on the same Taylor-series PES in all energies, frequencies, and geometries. Calculations using the fully anharmonic PES evaluated on the fly with electronic structure methods report anharmonic effects on frequencies and geometries of much greater magnitude than deterministic XVSCF calculations, reflecting an underestimation of anharmonic effects in a Taylor-series approximation to the PES.

Lattice-dynamical model for the filled skutteruditeLaFe4Sb12: Harmonic and anharmonic couplings

The filled skutterudite ${\mathrm{LaFe}}_{4}{\mathrm{Sb}}_{12}$ shows greatly reduced thermal conductivity compared to that of the related unfilled compound ${\mathrm{CoSb}}_{3}$, although the microscopic reasons for this are unclear. We calculate harmonic and anharmonic force constants for the interaction of the La filler atom with the framework atoms. We find that force constants show a general trend of decaying rapidly with distance and are very small for the interaction of the La with its next-nearest-neighbor Sb and nearest-neighbor La. However, a few rather long-range interactions, such as with the next-nearest-neighbor La and with the third neighbor Sb, are surprisingly strong, although still small. We test the central-force approximation and find significant deviations from it. Using our force constants we calculate a bare La mode Gruneisen parameter and find a value of 3--4, substantially higher than values associated with cage atom anharmonicity, i.e., a value of about 1 for ${\mathrm{CoSb}}_{3}$ but much smaller than a previous estimate [Bernstein et al., Phys. Rev. B 81, 134301 (2010)]. This latter difference is primarily due to the previously used overestimate of the La-Fe cubic force constants. We also find a substantial negative contribution to this bare La Gruneisen parameter from the aforementioned third-neighbor La-Sb interaction. Our results underscore the need for rather long-range interactions in describing the role of anharmonicity on the dynamics in this material.

Anharmonic force constants extracted from first-principles molecular dynamics: applications to heat transfer simulations

A systematic method to calculate anharmonic force constants of crystals is presented. The method employs the direct-method approach, where anharmonic force constants are extracted from the trajectory of first-principles molecular dynamics simulations at high temperature. The method is applied to Si where accurate cubic and quartic force constants are obtained. We observe that higher-order correction is crucial to obtain accurate force constants from the trajectory with large atomic displacements. The calculated harmonic and anharmonic force constants are, then, combined with the Boltzmann transport equation (BTE) and non-equilibrium molecular dynamics (NEMD) methods in calculating the thermal conductivity. The BTE approach successfully predicts the lattice thermal conductivity of bulk Si, whereas NEMD shows considerable underestimates. To evaluate the linear extrapolation method employed in NEMD to estimate bulk values, we analyze the size dependence in NEMD based on BTE calculations. We observe strong nonlinearity in the size dependence of NEMD in Si, which can be ascribed to acoustic phonons having long mean-free-paths and carrying considerable heat. Subsequently, we also apply the whole method to a thermoelectric material Mg2Si and demonstrate the reliability of the NEMD method for systems with low thermal conductivities.

Lattice thermal conductivity of Bi, Sb, and Bi-Sb alloy from first principles

Using first principles, we calculate the lattice thermal conductivity of Bi, Sb, and Bi-Sb alloys, which are of great importance for thermoelectric and thermomagnetic cooling applications. Our calculation reveals that the ninth-neighbor harmonic and anharmonic force constants are significant; accordingly, they largely affect the lattice thermal conductivity. Several features of the thermal transport in these materials are studied: (1) the relative contributions from phonons and electrons to the total thermal conductivity as a function of temperature are estimated by comparing the calculated lattice thermal conductivity to the measured total thermal conductivity, (2) the anisotropy of the lattice thermal conductivity is calculated and compared to that of the electronic contribution in Bi, and (3) the phonon mean free path distributions, which are useful for developing nanostructures to reduce the lattice thermal conductivity, are calculated. The phonon mean free paths are found to range from 10 to 100 nm for Bi at 100 K.

Prediction of Spectral Phonon Mean Free Path and Thermal Conductivity with Applications to Thermoelectrics and Thermal Management: A Review

We give a review of the theoretical approaches for predicting spectral phonon mean free path and thermal conductivity of solids. The methods can be summarized into two categories: anharmonic lattice dynamics calculation and molecular dynamics simulation. In the anharmonic lattice dynamics calculation, the anharmonic force constants are used first to calculate the phonon scattering rates, and then the Boltzmann transport equations are solved using either standard single mode relaxation time approximation or the Iterative Scheme method for the thermal conductivity. The MD method involves the time domain or frequency domain normal mode analysis. We present the theoretical frameworks of the methods for the prediction of phonon dispersion, spectral phonon relaxation time, and thermal conductivity of pure bulk materials, layer and tube structures, nanowires, defective materials, and superlattices. Several examples of their applications in thermal management and thermoelectric materials are given. The strength and limitations of these methods are compared in several different aspects. For more efficient and accurate predictions, the improvements of those methods are still needed.

Ab initiostudy of the unusual thermal transport properties of boron arsenide and related materials

Recently, using a first principles approach, we predicted that zinc blende boron arsenide (BAs) will have an ultrahigh lattice thermal conductivity, \ensuremath{\kappa}, of over 2000 Wm${}^{\ensuremath{-}1}$K${}^{\ensuremath{-}1}$ at room temperature (RT), comparable to that of diamond. Here, we provide a detailed ab initio examination of phonon thermal transport in boron arsenide, contrasting its unconventional behavior with that of other related materials, including the zinc blende crystals boron nitride (BN), boron phosphide, boron antimonide, and gallium nitride (GaN). The unusual vibrational properties of BAs contribute to its weak phonon-phonon scattering and phonon-isotope scattering, which are responsible for its exceptionally high \ensuremath{\kappa}. The thermal conductivity of BAs has contributions from phonons with anomalously large mean free paths (\ensuremath{\sim}2 \ensuremath{\mu}m), two to three times those of diamond and BN. This makes \ensuremath{\kappa} in BAs sensitive to phonon scattering from crystal boundaries. An order of magnitude smaller RT thermal conductivity in a similar material, zinc blende GaN, is connected to more separated acoustic phonon branches, larger anharmonic force constants, and a large isotope mixture on the heavy rather than the light constituent atom. The striking difference in \ensuremath{\kappa} for BAs and GaN demonstrates the importance of using a microscopic first principles thermal transport approach for calculating \ensuremath{\kappa}. BAs also has an advantageous RT coefficient of thermal expansion, which, combined with the high \ensuremath{\kappa} value, suggests that it is a promising material for use in thermal management applications.

Vibrational Spectroscopy of Picolinamide and Water: From Dimers to Condensed Phase

Because of the presence of polar groups in picolinamide, its aqueous solvation is characterized by formation of multiple hydrogen bonds, which are responsible for differences in vibrational spectra of picolinamide in the gas phase and its aqueous solution. In this contribution, we try to identify dominant interactions between the solute and the solvent molecules that are the origin of the observed spectral changes. For this purpose, we analyzed the vibrational properties of picolinamide (a single molecule and also embedded in the environment described with an implicit solvent model) and picolinamide-water dimers: by comparing their vibrational frequencies with experimentally observed values of picolinamides' aqueous solution and by analyzing the computed anharmonic force constants, it is possible to recognize whether and in which way the solvent causes changes in the vibrational properties of the title compound. Calculations performed on the picolinamide three-hydrate confirm conclusions obtained by analyzing monohydrates.

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.

The discovery of the Stark effect and its early theoretical explanations

After Pieter Zeeman had discovered in the fall of 1896 that an external magnetic field causes spectral lines to split in several components,1 the logical next step was to investigate whether an electric field would also have an influence on the shape or frequency of spectral lines. The first to publish the results of a systematic theoretical investigation of the possible effect of electric fields was the Gottingen physicist Woldemar Voigt [2]. Voigt used a modified version of the purely classical model for the explanation of spectral lines that was used for the description of magnetooptic effects. In this model, devised by Hendrik Lorentz, atoms contain electrons that are bound to a center with a harmonic force. In Voigt’s version these forces are no longer purely harmonic, but contain an anharmonic part as well. This anharmonic component was needed because an electric field has no influence on the frequency of a harmonically vibrating charged particle, as can be easily seen from its equation of motion. On the basis of his model and estimates (based on experimental results for electric double refraction) for the value of the anharmonic force constant for various substances, Voigt came to the

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.

Erratum: Method to extract anharmonic force constants from first principles calculations [Phys. Rev. B77, 144112 (2008)

Erratum: Method to extract anharmonic force constants from first principles calculations [Phys. Rev. B<b>77</b>, 144112 (2008)

Spectroscopic properties, potential energy surfaces and interaction energies of RgClF (Rg = Kr and Xe) van der Waals complexes

Spectroscopic properties, dissociation energies, potential energy surfaces (PES) and interaction energies of linear, anti-linear and T-shaped isomers of KrClF and XeClF van der Waals complexes have been studied in detail using MP2 and CCSD(T) methods in conjunction with correlation consistent triple-ζ and quadruple-ζ basis sets. A method has been developed to calculate the depth of the potential well and cubic anharmonic force constant of the complexes. In this method, the Lennard-Jones potential is used to describe the van der Waals complexes. Both potential method and supermolecular approach are applied to accurately calculate the depth of the potential well and dissociation energy and also to check the consistency of the calculated values. Well depths obtained from potential energy curves are in harmony with that calculated by potential method. Most of the spectroscopic properties and depth of the potential well for these complexes are reported for the first time. Three potential minima corresponding to linear, anti-linear and nearly asymmetric T-shaped isomers are found for RgClF complexes. Linear isomers are more stable than the T-shaped and anti-linear isomers.

O–H Stretch in Phenol and Its Hydrogen-Bonded Complexes: Band Position and Relaxation Pathways

Anharmonic force fields are a suitable means for identification of vibrational degrees of freedom responsible for the peculiar shape of molecular spectra and the existence of diverse relaxation pathways. In this contribution, we investigated interactions that govern the position of the O-H stretching band in phenol and its dimers with water and ammonia. Dominant couplings are identified, and the nature of relaxation channels is analyzed. The effect of hydrogen bonding on O-H stretching motion and vibrational energy redistribution time through intra- and intermolecular interactions is studied, and possible vibrational predissociation upon O-H stretch excitation is addressed. The results based on computed anharmonic force constants are in accord with the available experimental findings.

High Thermal Conductivity in Short-Period Superlattices

The thermal conductivity of ideal short-period superlattices is computed using harmonic and anharmonic force constants derived from density-functional perturbation theory and by solving the Boltzmann transport equation in the single-mode relaxation time approximation, using silicon-germanium as a paradigmatic case. We show that in the limit of small superlattice period the computed thermal conductivity of the superlattice can exceed that of both the constituent materials. This is found to be due to a dramatic reduction in the scattering of acoustic phonons by optical phonons, leading to very long phonon lifetimes. By variation of the mass mismatch between the constituent materials in the superlattice, it is found that this enhancement in thermal conductivity can be engineered, providing avenues to achieve high thermal conductivities in nanostructured materials.

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.