Atomic Force Constants Research Articles

Phononic heat conductance of gold atomic contacts: Coherent versus incoherent transport

We present here a theoretical method to determine the phononic contribution to the thermal conductance of nanoscale systems in the phase-coherent regime. Our approach makes use of classical molecular dynamics (MD) simulations to calculate the temperature-dependent dynamical matrix, and the phononic heat conductance is subsequently computed within the Landauer-B\"uttiker formalism with the help of nonequilibrium Green's function techniques. Tailored to nanostructures, crucial steps of force constant and heat transport calculations are performed directly in real space. As compared to conventional density functional theory (DFT) approaches, the advantage of our method is two-fold. First, interatomic interactions can be described with the method of choice. Semiempirical potentials may lead to large computational speedups, enabling the study of much larger systems. Second, the method naturally takes into account the temperature dependence of atomic force constants, an aspect that is ignored in typical static DFT-based calculations. We illustrate our method by analyzing the temperature dependence of the phononic thermal conductance of gold (Au) chains with lengths ranging from 1 to 12 atoms. Moreover, in order to evaluate the importance of anharmonic effects in these atomic-scale wires, we compare the phase-coherent approach with nonequilibrium MD (NEMD) simulations. We find that the predictions of the phase-coherent method and the classical NEMD approach largely agree above the Debye temperature for all studied chain lengths, which shows that heat transport is coherent and that our phase-coherent approach is well suited for such nanostructures.

Atomistic simulation of phonon heat transport across metallic vacuum nanogaps

The understanding and modeling of the heat transport across nanometer and sub-nanometer gaps where the distinction between thermal radiation and conduction become blurred remains an open question. In this work, we present a three-dimensional atomistic simulation framework by combining the molecular dynamics (MD) and phonon non-equilibrium Green's function (NEGF) methods. The relaxed atomic configuration and interaction force constants of metallic nanogaps are generated from MD as inputs into harmonic phonon NEGF. Phonon tunneling across gold-gold and copper-copper nanogaps is quantified, and is shown to be a significant heat transport channel below gap size of 1nm. We demonstrate that lattice anharmonicity contributes to within 20-30% of phonon tunneling depending on gap size, whereas electrostatic interactions turn out to have negligible effect for the small bias voltage typically used in experimental measurements. This work provides detailed information of the heat current spectrum and interprets the recent experimental determination of thermal conductance across gold-gold nanogaps. Our study contributes to deeper insight into heat transport in the extremely near-field regime, as well as hints for the future experimental investigation.

Effect of carbon vacancies and oxygen impurities on the dynamical and thermal properties of uranium monocarbide

An influence of carbon vacancies and substitutional oxygen impurities on the phonon dynamics and thermal properties of uranium monocarbide is investigated within the density functional theory incorporating strong local Coulomb and spin-orbit interactions. Anharmonicity of lattice vibrations is taken into account via the quasi-harmonic theory. Results obtained for the modeled UC1−x and UC1−xOx compositions with x=3% show that the changes in atomic displacements and force constants induced by mono-vacancies and substitutional oxygen impurities in the carbon sublattice of UC remain restricted to the immediate neighborhood of the incorporated defects. The most sensitive to point defects in the carbon sublattice of UC are the optical phonon branches, while the phonon densities of states and the phonon-dependent thermodynamical properties remain affected to a lesser extent. The X-ray powder diffraction experiments have been performed to examine the temperature evolution of the lattice parameter of highly stoichiometric UC between 20 and 310 K. The present experimental studies supplement existing literature data by extending description of the uranium monocarbide structure below room temperature. They also support and validate our theoretical predictions about behavior of the investigated system at low temperatures.

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.

Weakly nonlocal micromorphic elasticity for diamond structures vis-à-vis lattice dynamics

In this work, after formulating the weakly nonlocal micromorphic equations of motion for non-Bravais crystals with general anisotropy, specialization to diamond structures is made. A critical dilemma is the determination of the elastic moduli tensor appearing in the equations of motion. From the equivalency of these equations with the pertinent equations obtained in the context of lattice dynamics, the expressions of the components of the elastic moduli tensors in terms of the atomic force constants are derived analytically. Subsequently, the atomic force constants are calculated via ab initio density functional perturbation theory (DFPT) with high precision. As a benchmark for the accuracy and potency of the proposed theory, it is shown that the theory can capture not only all the acoustic branches but also all the optical branches of the dispersion curves for non-Bravais crystals like diamond and silicon over the entire first Brillouin zone. The accuracy of the results depends on the implemented order of the approximation of weakly nonlocal micromorphic theory. For illustration, the zeroth, tenth, and twentieth order approximations are employed to probe the dispersion curves pertinent to the crystallographic directions [100], [110], and [111] for diamond and silicon. For verification, the results are compared to those obtained independently from ab initio DFPT calculations.

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.

Phonon Spectrum and Resonance with Acoustic Wave of Lithium by Lattice Dynamics and the Modified Analytic Embedded-Atom Method

The phonon spectrum and resonance are studied by lattice dynamics and using the second nearest-neighbor (2NN) modified analytic embedded-atom method (MAEAM). Through deriving the expressions for atomic force constants, the phonon spectrum of lithium metal is calculated along three principal directions ([100], [110], [111]). The calculated and experimental values are in good agreement. On this basis, the phonon dispersion of acoustic wave is added to the phonon spectrum of lithium metal and the transverse wave and longitudinal wave of resonance frequencies are calculated. It is proposed that terahertz acoustic wave can be used to produce resonance with metal lithium electrodes, which would break the detrimental lithium dendrites during the charge process of Li batteries. The method can also be used to calculate the phonon spectrum and the resonance frequencies of other metal electrodes.

Lattice dynamics of epitaxial strain-free interfaces

We report a systematic lattice dynamics study of the technologically important ${\mathrm{Fe}}_{3}\mathrm{Si}$/GaAs heterostructure for ${\mathrm{Fe}}_{3}\mathrm{Si}$ layer thicknesses of 3, 6, 8, and 36 monolayers. The Fe-partial phonon density of states obtained by nuclear inelastic scattering exhibits up to a twofold enhancement of the low-energy phonon states compared to the bulk material for layer thicknesses of 8 monolayers and below. First-principles calculations explain the observed effect by interface-specific phonon states originating from the significantly reduced atomic force constants and allow for achieving a comprehensive understanding of the lattice dynamics of epitaxial strain-free interfaces.

Evaluation of Tension, Bending and Twisting Rigidities of Single-Layer Graphene Sheets by an Analytical Asymptotic Homogenization Model

In the present study, the method of asymptotic homogenization is used to estimate elastic properties as well as tension, bending and twisting rigidities of single-layer graphene sheets (SLGSs). To this end, asymptotic homogenization of a reinforced composite is developed for modeling of SLGS by assuming that the covalent bond between carbon atoms can be represented by reinforcements. Applicable formulas are obtained for the elastic properties and rigidities of SLGS directly from the interatomic interactions through three types of potentials. It is proved that force field constants significantly affect the elastic properties of SLGS. Herein, the elastic moduli are obtained based on different types of atomic force constants. The results of the present analytical model are in close agreements with the similar theoretical results and experimental measurements. This approach can be developed to represent mechanical properties of nanotubes, nanocomposites and other nanostructures. DOI: http://dx.doi.org/10.5755/j01.mech.24.2.17822

Toupin–Mindlin first strain gradient theory revisited for cubic crystals of hexoctahedral class: Analytical expression of the material parameters in terms of the atomic force constants and evaluation via ab initio DFT

Capture of the discrete nature of crystalline solids for the purpose of the determination of their mechanical behavior with high precision is of interest. To achieve this objective, two fundamental contributing factors are on top of the list: (1) formulation in the mathematical framework of an appropriate higher order continuum theory rather than using classical treatment, and (2) incorporation of the true anisotropy of the media. The present work revisits Toupin–Mindlin first strain gradient theory for media with general anisotropy, and then specialize it to cubic crystals of hexoctahedral class. This formulation in addition to 3 classical material constants encountered in classical theory of elasticity, gives rise to 11 additional material parameters peculiar to first strain gradient theory. To date, there is no experimental method in the literature for the measurement of these parameters. A methodology incorporating lattice dynamics is proposed, by which all the material parameters including the classic ones are analytically expressed in terms of the atomic force constants. Subsequently, the analytical expressions for the nonzero components of the 4th and 6th order elastic moduli tensors as well as 6 characteristic lengths are derived. Finally, with the aid of ab initio calculations all the material properties in Toupin–Mindlin first strain gradient theory are numerically obtained with high precision. In this work the transformation matrices of cubic crystals of diploidal class which also falls under centrosymmetric point groups are discussed as well.

Anharmonic phonon properties in Eu0.5Ba0.5TiO3

Abstract Phonon properties have been studied using reduced sound velocity of Eu0.5Ba0.5TiO3 (EBTO). To achieve this aim, the anharmonic phonon-phonon interaction and the spin-phonon interaction were used. It was shown that the reduced sound velocity of multiferroic EBTO exhibits a kink at TN = 1.9 K. This anomalously reduced sound velocity can be interpreted as an effect of vanishing magnetic ordering above TN. What’s more, the ferroelectric subsystem cannot be influenced by the magnetic subsystem above TN for TN ≪TC in the EBTO. It was found that the reduced sound velocity decreases as T increases near ferroelectric transition TC. That is to say, the sound velocity softens near ferroelectric transition TC. It is also noteworthy that the reduced sound velocity softens when the RE (the coupling between the ferroelectric pseudo-spins and phonons), V(3) and |V(4)| (the third- and fourth-order atomic force constants of the anharmonic phonons, respectively) increase. These conclusions are all in good accordance with the experimental data and theoretical results.

Anomalous reduced sound velocity of multiferroic TbMn2O5

The anomalous reduced sound velocity of multiferroic TbMn2O5 (TMO) has been studied using Green's function technique. To achieve this aim, the anharmonic phonon-phonon interaction and the spin-phonon interaction were used. It was shown that the reduced velocity of sound of TMO exhibits a kink at the ferroelectric phase transition temperature TC. This can be explained as an effect of vanishing ferroelectric ordering above TC. It was found that the reduced sound velocity increases with increasing V(3) (the third-order atomic force constants of the anharmonic phonons) in the interval T < TC, whereas the reduced sound velocity remains unchanged in the interval TC < T < TN. It was also found that the reduced sound velocity increases with the increase of V(4) (the fourth-order atomic force constants of the anharmonic phonons) in the interval T < TN. In addition, the ferroelectric phase transition temperature TC decreases when V(4) increases in the interval T < TN. Those theoretical results are in agreement with the experimental data.

Thermal transport in monolayer InSe

Two-dimensional InSe, a recently synthesized semiconductor having a moderate band gap, has gained attention due to its ultra high mobility and high photo-responsivity. In this work, we calculate the lattice thermal conductivity (κ) of monolayer InSe by solving the phonon Boltzmann transport equation (BTE) with first-principles calculated inter atomic force constants. κ of monolayer InSe is isotropic and found to be around 27.6 W m at room temperature along the in-plane direction. The size dependence of κ shows the size effect can persist up to 20 μm. Further, κ can be reduced to half by tuning the sample size to 300 nm. This low value suggests that κ might be a limiting factor for emerging nanoelectronic applications of monolayer InSe.

Mode decomposition based on crystallographic symmetry in the band-unfolding method

The band-unfolding method is widely used to calculate the effective band structures of a disordered system from its supercell model. The unfolded band structures show the crystallographic symmetry of the underlying structure, where the difference of chemical components and the local atomic relaxation are ignored. It has been, however, still difficult to decompose the unfolded band structures into the modes based on the crystallographic symmetry of the underlying structure, and therefore detailed analyses of the unfolded band structures have been restricted. In this study, we develop a procedure to decompose the unfolded band structures according to the small representations (SRs) of the little groups. For this purpose, we derive the projection operators for SRs based on the group representation theory. We also introduce another type of projection operators for chemical elements, which enables us to decompose the unfolded band structures into the contributions of different combinations of chemical elements. Using the current method, we investigate the phonon band structure of disordered face-centered cubic Cu0.75Au0.25, which has large variations of atomic masses and force constants among the atomic sites due to the chemical disorder. We find several peculiar behaviors such as discontinuous and split branches in the unfolded phonon band structure. They are found to occur because different combinations of the chemical elements contribute to different regions of frequency.

Inter atomic force constants of binary and ternary tetrahedral semiconductors

In this paper, we present the expressions relating the inter atomic force constants like as bond-stretching force constant (α in N/m) and bond-bending force constant (β in N/m) for the binary (zinc blende structure) and ternary (chalcopyrite structure) semiconductors with the product of ionic charges (PIC) and crystal ionicity (fi). Interatomic force constants of these compounds exhibit a linear relationship; when plot a graph between Interatomic force constants and the nearest neighbor distance d (A) with crystal ionicity (fi), but fall on different straight lines according to the product of ionic charges of these compounds. A fairly good agreement has been found between the observed and calculated values of the α and β for binary and ternary tetrahedral semiconductors.

A density-functional study on the electronic and vibrational properties of layered antimony telluride

We present a comprehensive survey of electronic and lattice-dynamical properties of crystalline antimony telluride (Sb2Te3). In a first step, the electronic structure and chemical bonding have been investigated, followed by calculations of the atomic force constants, phonon dispersion relationships and densities of states. Then, (macroscopic) physical properties of Sb2Te3 have been computed, namely, the atomic thermal displacement parameters, the Grüneisen parameter γ, the volume expansion of the lattice, and finally the bulk modulus B. We compare theoretical results from three popular and economic density-functional theory (DFT) approaches: the local density approximation (LDA), the generalized gradient approximation (GGA), and a posteriori dispersion corrections to the latter. Despite its simplicity, the LDA shows excellent performance for all properties investigated—including the Grüneisen parameter, which only the LDA is able to recover with confidence. In the absence of computationally more demanding hybrid DFT methods, the LDA seems to be a good choice for further lattice dynamical studies of Sb2Te3 and related layered telluride materials.

A combined first principles and analytical determination of the modulus of cohesion, surface energy, and the additional constants in the second strain gradient elasticity

Mindlin’s (1965) second strain gradient theory due to its competency in capturing the effects of edges, corners, and surfaces is of particular interest. Formulation in this framework, in addition to the usual Lamé constants, requires the knowledge of sixteen additional materials constants. To date, there are no successful experimental techniques for measuring these material parameters which reflect the discrete nature of matter. The present work gives an accurate remedy for the atomistic calculations of these parameters by utilizing the first principles density functional theory (DFT) for the calculations of the atomic force constants combined with an analytical formulation. It will be shown that writing the consistency conditions obtained from the equivalency between the atomistic crystal lattice dynamics of the bulk material and its counterpart in the second strain gradient elasticity is insufficient for the calculations of all the additional constants. As it will be discussed, there are two missing conditions which are then provided by consideration of the free standing film problem that bring the surface effect into account. As a consequence of surface effect consideration, the modulus of cohesion which is one of the important additional constants is calculated. Moreover, an analytical expression for the surface energy in terms of the modulus of cohesion, Lamé constants, materials characteristic lengths, and the film thickness is presented. If the film thickness is much bigger than the magnitude of the characteristic lengths of the material, then the surface energy would no longer depend on the film thickness.

Phonon Dispersion in the Fcc Metals Ca, Sr and Yb

Within the harmonic approximation and adiabatic approximation, the expressions of atomic force constants have been derived. Phonon dispersion curves along four major symmetry directions and four off-symmetry directions have been simulated for alkaline-earth metals Ca, Sr and the rare-earth metal Yb by combining the modified analytic embedded atom method with the theory of lattice dynamics. The simulated phonon dispersion curves for the fcc metals Ca, Sr and Yb along four major symmetry directions have been compared to the corresponding experimental data. The results show that the simulated results are general consistent with available experimental results, with a maximum deviation of approximately 14 %. The simulated phonon frequencies of the fcc metals Ca, Sr and Yb lay a significant foundation for guiding and judging relative experiment results, especially for the phonon dispersion relation along off-symmetry directions.

Solvent effect on the vibrational spectra of Carvedilol

Carvedilol (CRV) is an important medicament for heart arrhythmia. The aim of this work was the interpretation of its vibrational spectra with consideration on the solvent effect. Infrared and Raman spectra were recorded in solid state as well in solution. The experimental spectra were evaluated using DFT quantum chemical calculations computing the optimized structure, atomic net charges, vibrational frequencies and force constants. The same calculations were done for the molecule in DMSO and aqueous solutions applying the PCM method. The calculated force constants were scaled to the experimentally observed solid state frequencies. The characters of the vibrational modes were determined by their potential energy distributions. Solvent effects on the molecular properties were interpreted. Based on these results vibrational spectra were simulated.

Gas phase infrared spectra of small polyatomic ions as a benchmark for theory

Infrared multiple photon dissociation (IRMPD) provides a method for examining vibrational spectroscopy of ions in the gas phase. Comparison of such experiments with the IR spectra of neutral molecules shows that the strength of a bond between a trigonal center and an attached methyl group tends to diminish after fluoride attacks to make the central atom tetrahedral. For selected main group species, the change becomes more pronounced as the central atom becomes more electropositive. Trimethylboron displays a more dramatic alteration than do silicon analogs, which indicates an effect beyond that of electronegativity by itself. In comparing gaseous trimethylboron with the negative ions derived from it, CH hyperconjugation ought to operate to a much greater extent in the neutral than in the anions. Anharmonic vibrational calculations using Density Functional Theory (DFT) match the experimental vibrational spectra and confirm that interpretation, providing evidence in favor of substantial hyperconjugative stabilization. However, further simplification of vibrational spectroscopy in terms of “atomic force constants” does not show much promise. Atoms in molecules (AIM) comparison of C–C bond orders in cations with B–C bond orders in neutral boranes is consistent with hyperconjugation.