Effect of the accuracy of interatomic force constants on the prediction of lattice thermal conductivity
University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University（密歇根大学-上海交通大学联合学院，上海交通大学）；Institute of Engineering Thermophysics, School of Mechanical Engineering, Shanghai Jiao Tong University（上海交通大学机械工程学院工程热物理研究所）
Solving Peierls-Boltzmann transport equation with interatomic force constants (IFCs) from first-principles calculations has been a widely used method for predicting lattice thermal conductivity of three-dimensional materials. With the increasing research interests in two-dimensional materials, this method is directly applied to them but different works show quite different results. In this work, classical potential was used to investigate the effect of the accuracy of IFCs on the predicted thermal conductivity. Inaccuracies were introduced to the third-order IFCs by generating errors in the input forces. When the force error lies in the typical value of first-principles calculations, the calculated thermal conductivity would be quite different from the benchmark result. It is found that imposing translational invariance conditions cannot always guarantee a better thermal conductivity result. It is also shown that Grüneisen parameters cannot be used as a necessary and sufficient criterion for the accuracy of third-order IFCs in the aspect of predicting thermal conductivity.
Thermal management materials are of critical importance for engineering miniaturized electronic devices, where theoretical design of such materials demands the evaluation of thermal conductivities which are numerically expensive. In this work, we applied the recently developed machine learning interatomic potential (MLIP) to evaluate the thermal conductivity of hexagonal boron nitride monolayers. The MLIP is obtained using the Gaussian approximation potential (GAP) method, and the resulting lattice dynamical properties and thermal conductivity are compared with those obtained from explicit fro…
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 a…
Thermal and mechanical properties of two-dimensional nanomaterials are commonly studied by calculating force constants using the density functional theory (DFT) and classical molecular dynamics (MD) simulations. Although DFT simulations offer accurate estimations, the computational cost is high. On the other hand, MD simulations strongly depend on the accuracy of interatomic potentials. Here, we investigate thermal conductivity and elastic modulus of nitrogenated holey graphene (C2N) using passively fitted machine-learning interatomic potentials (MLIPs), which depend on computationally inexpen…
Phonons are essential for understanding the thermal properties in monolayer transition metal dichalcogenides, which limit their thermal performance for potential applications. We investigate the lattice dynamics and thermodynamic properties of MoS2, MoSe2, and WS2 by first principles calculations. The obtained phonon frequencies and thermal conductivities agree well with the measurements. Our results show that the thermal conductivity of MoS2 is highest among the three materials due to its much lower average atomic mass. We also discuss the competition between mass effect, interatomic bonding …
The system of particles interacting via multibody interatomic potential of general form is considered. Possible variants of partition of the total force acting on a single particle into pair contributions are discussed. Two definitions for the force acting between a pair of particles are compared. The forces coincide only if the particles interact via pair or embedded-atom potentials. However in literature both definitions are used in order to determine Cauchy stress tensor. A simplest example of the linear pure shear of perfect square lattice is analyzed. It is shown that, Hardy's definition …
Crystalline materials with ultralow thermal conductivity are highly desirable for thermoelectric applications. Many known crystalline materials with low thermal conductivity, including PbTe and Bi2Te3, possess a special kind of chemical bond called "resonant bond". Resonant bonds consist of superposition of degenerate bonding configurations that leads to structural instability, anomalous long-range interatomic interaction and soft optical phonons. These factors contribute to large lattice anharmonicity and strong phonon-phonon scattering, which result in low thermal conductivity. In this work,…
We apply standard, first-principles calculations to a complete treatment of lattice dynamics in the harmonic approximation. The algorithm makes use of the straightforward ``frozen-phonon'' approach to the calculation of vibrational spectra and addresses some limitations of the method. Our prescription's validity is independent of crystal structure. It treats polar crystals in a general way, and it incorporates interatomic-force constants reaching beyond the supercell that is considered. For a range of materials, phonon dispersion exhibits the close agreement with experiment that is now charact…
We determine experimentally the excited-state interatomic forces in photoexcited bismuth. The forces are obtained by a constrained least-squares fit of the excited-state dispersion obtained by femtosecond time-resolved x-ray diffuse scattering to a fifteen-nearest neighbor Born-von Karman model. We find that the observed softening of the zone-center $A_{1g}$ optical mode and transverse acoustic modes with photoexcitation are primarily due to a weakening of three nearest neighbor forces along the bonding direction. This provides a more complete picture of what drives the partial reversal of the…
We report a classical interatomic force field for TiO$_2$, which has been parameterized using density functional theory forces, energies, and stresses in the rutile crystal structure. The reliability of this new classical potential is tested by evaluating the structural properties, equation of state, phonon properties, thermal expansion, and some thermodynamic quantities such as entropy, free energy, and specific heat under constant volume. The good agreement of our results with {\em ab initio} calculations and with experimental data, indicates that our force-field describes the atomic interac…
The phonon dispersion curves of cubic BaTiO_3 have been computed within a first-principles approach and the results compared to the experimental data. The curves obtained are very similar to those reported for KNbO_3 by Yu and Krakauer [Phys. Rev. Lett. 74, 4067 (1995)]. They reveal that correlated atomic displacements along <100> chains are at the origin of the ferroelectric instability. A simplified model illustrates that spontaneous collective displacements will occur when a dozen of aligned atoms are coupled. The longitudinal interatomic force constant between nearest neighbour Ti and O at…
The redshifts and asymmetric broadening observed in nanocrystal Raman Spectra are attributed to the quantum confinement effects by some authors. But others show that they may come from the local heating caused by the incident laser as well. In this study we demonstrate that in the Si nanocrystal case the latter at most has obvious effects on the broadening but has negligible effects on the 1LO peak shift, while the former contributes most of the 1LO peak shift. We also demonstrate that after assigning appropriate interatomic force constants in the calculation of Raman Spectrum by bond polariza…
We explore the possibility for the reconstruction of the generative physical models describing interactions between atomic units in solids from observational electron microscopy data. Here, scanning transmission electron microscopy (STEM) is used to observe the dynamic motion of Si atoms at the edge of monolayer graphene under continuous electron beam illumination. The resulting time-lapsed STEM images represent the snapshots of observed chemical states of the system. We use two approaches: potential of mean force (PMF) calculation using a radial distribution function (RDF) and a direct fittin…
We present a methodology for fitting interatomic potentials to ab initio data, using the particle swarm optimization (PSO) algorithm, needing only a set of positions and energies as input. The prediction error of energies associated with the fitted parameters can be close to 1 meV/atom or lower, for reference energies having a standard deviation of about 0.5 eV/atom. We tested our method by fitting a Sutton-Chen potential for copper from \emph{ab initio} data, which is able to recover structural and dynamical properties, and obtain a better agreement of the predicted melting point versus the e…
}We present a formalism for extending the second moment tight-binding model, incorporating ferro- and anti-ferromagn etic interaction terms which are needed for the FeCr system. For antiferromagnetic and paramagnetic materials, an explicit additional variable representing the spin is required. In a mean-field approximation this spin can be eliminated, and the potential becomes explicitly temperature dependent. For ferromagnetic interactions, this degree of freedom can be eliminated, and the formalism reduces to the embedded atom method (EAM) and we show the equivale nce of existing EAM potenti…
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 Grüneisen parameters associated with phonon frequency shifts due to crystal deformations. In this work, we pro…
Grimme's DFT-D dispersion contribution to interatomic forces constants, required for the computation of the phonon band structures in density-functional perturbation theory, has been derived analytically. The implementation has then been validated with respect to frozen phonons, and applied on materials where weak cohesive forces play a major role i.e. argon, graphite, benzene. We show that these dispersive contributions have to be considered to properly reproduce the experimental vibrational properties of these materials, although the lattice parameter change, coming from the ground-state rel…
One of the ultimate goals of computational modeling in condensed matter is to be able to accurately compute materials properties with minimal empirical information. First-principles approaches such as the density functional theory (DFT) provide the best possible accuracy on electronic properties but they are limited to systems up to a few hundreds, or at most thousands of atoms. On the other hand, classical molecular dynamics (CMD) simulations and finite element method (FEM) are extensively employed to study larger and more realistic systems, but conversely depend on empirical information. Her…
In recent years, many types of machine learning potentials (MLPs) have been introduced, which are able to represent high-dimensional potential-energy surfaces (PES) with close to first-principles accuracy. Most current MLPs rely on atomic energy contributions given as a function of the local chemical environments. Frequently, in addition to total energies also atomic forces are used to construct the potentials, as they provide detailed local information about the PES. Since many systems are too large for electronic structure calculations, obtaining reliable reference forces from smaller subsys…
Benchmarking machine-learning interatomic potentials using classical force fields
Université de Lille（里尔大学）；CNRS, Unité Matériaux et Transformations（法国国家科学研究中心，材料转化单元）；Université Marie et Louis Pasteur（玛丽·路易·巴斯德大学）；CNRS, LmB (UMR 6623)（法国国家科学研究中心，LmB（联合研究单位6623））
First-principles phonon calculations have been widely performed for studying vibrational properties of condensed matter, where the dynamical matrix is commonly constructed via supercell force-constant calculations or the linear response approach. With different manners, a supercell can be introduced in both methods. Unless the supercell is large enough, the interpolated phonon property highly depends on the shape and size of the supercell and the imposed periodicity could give unphysical results that can be easily overlooked. Along this line, the concept of partition of force constants is disc…
In this work, we investigated tensile and compression forces effect on the thermal conductivity of silicon. We used equilibrium molecular dynamics approach for the evaluation of thermal conductivity considering different interatomic potentials. More specifically, we tested Stillinger-Weber, Tersoff, Environment-Dependent Interatomic Potential and Modified Embedded Atom Method potentials for the description of silicon atom motion under different strain and temperature conditions. Additionally, we extracted phonon density of states and dispersion curves from molecular dynamics simulations. These…
In this contribution we assess the performance of two different exchange-correlation functionals in the first-principle prediction of the lattice thermal conductivity of bulk semiconductors, namely the local density approximation (LDA) and the Perdew-Burke-Ernzerhof implementation of the generalized gradient approximation (GGA). Both functionals are shown to give results in good agreement with experimental measurements. Such a consistency between the two functionals may seem a bit surprising, as the LDA is known to overbind and the GGA to soften the interatomic bonds. Such features ought to gr…
The temperature dependent effective potential (TDEP) method is generalized beyond pair interactions. The second and third order force constants are determined consistently from ab initio molecular dynamics simulations at finite temperature. The reliability of the approach is demonstrated by calculations of the Mode Grüneisen parameters for Si. We show that the extension of TDEP to higher order allows for an efficient calculation of the phonon life time, in Si as well as in $ε$-FeSi, a system that exhibits anomalous softening with temperature.
The highly anisotropic thermal conductivity in layered materials is crucial for a broad range of applications such as thermal management of electronic devices, thermal insulation, and thermoelectrics. Understanding of anisotropic thermal transport in layered materials largely depends on atomistic simulations based on density functional theory (DFT) or empirical potentials, which however suffer either low computational efficiency or accuracy. Recently, machine learning interatomic potentials (MLIPs) are emerging as a powerful tool to bridge the gap. Despite the recent progress in developing MLI…
Molecular dynamics simulations provide a versatile framework to study interfacial heat transport, but their accuracy remains limited by the accuracy of available interatomic potentials. In the past, researchers have adopted the use of analytic potentials and simple mixing rules to model interfacial systems, with minimal justification for their use. On the other hand, contemporary machine learned interatomic potentials have greater complexity, but have not seen rigorous validation of interfacial heat transport properties. Moreover, when fitting to ab initio data, it is not known whether interfa…
The lattice thermal conductivity of thermoelectric material CuInTe2 is predicted using classical molecular dynamics simulations, where a simple but effective Morse-type interatomic potential is constructed by fitting first-principles total energy calculations. In a broad temperature range from 300 to 900 K, our simulated results agree well with those measured experimentally, as well as those obtained from phonon Boltzmann transport equation. By introducing the Cd impurity and Cu vacancy, the thermal conductivity of CuInTe2 can be effectively reduced to further enhance the thermoelectric perfor…
The process of deriving an interatomic potentials represents an attempt to integrate out the electronic degrees of freedom from the full quantum description of a condensed matter system. In practice it is the derivatives of the interatomic potentials which are used in molecular dynamics, as a model for the forces on a system. These forces should be the derivative of the free energy of the electronic system, which includes contributions from the entropy of the electronic states. This free energy is weakly temperature dependent, and although this can be safely neglected in many cases there are s…
Machine-learned interatomic potentials enable realistic finite temperature calculations of complex materials properties with first-principles accuracy. It is not yet clear, however, how accurately they describe anharmonic properties, which are crucial for predicting the lattice thermal conductivity and phase transitions in solids and, thus, shape their technological applications. Here we employ a recently developed on-the-fly learning technique based on molecular dynamics and Bayesian inference in order to generate an interatomic potential capable to describe the thermodynamic properties of zi…
Driving force of atomic ordering in Fe$_{1-x}$Pt$_{x}$, investigated by density functional theory and machine-learning interatomic potentials Monte Carlo simulations
The length dependence of the thermal conductivity over more than two decades is systematically studied for a range of materials, interatomic potentials and temperatures, by the atomistic approach-to-equilibrium molecular dynamics method (AEMD). By comparing the values of conductivity obtained for a given supercell length and maximum phonon mean-free-path (MFP), we find that such values are strongly correlated, demonstrating that the AEMD calculation with a supercell of finite length, actually probes the thermal conductivity corresponding to a maximum phonon MFP. As a consequence, the less pron…
We develop a fundamental theory of the long-range electrostatic interactions in two-dimensional crystals by performing a rigorous study of the nonanalyticities of the Coulomb kernel. We find that the dielectric functions are best represented by $2\times 2$ matrices, with nonuniform macroscopic potentials that are two-component hyperbolic functions of the out-of-plane coordinate, $z$. We demonstrate our arguments by deriving the long-range interatomic forces in the adiabatic regime, where we identify a formerly overlooked dipolar coupling involving the out-of-plane components of the dynamical c…
Large-scale atomistic simulations of materials heavily rely on interatomic potentials, which predict the system energy and atomic forces. One of the recent developments in the field is constructing interatomic potentials by machine-learning (ML) methods. ML potentials predict the energy and forces by numerical interpolation using a large reference database generated by quantum-mechanical calculations. While high accuracy of interpolation can be achieved, extrapolation to unknown atomic environments is unpredictable. The recently proposed physically-informed neural network (PINN) model signific…
Interatomic potentials have been widely used in atomistic simulations such as molecular dynamics. Recently, frameworks to construct accurate interatomic potentials that combine a systematic set of density functional theory (DFT) calculations with machine learning techniques have been proposed. One of these methods is to use compressed sensing to derive a sparse representation for the interatomic potential. This facilitates the control of the accuracy of interatomic potentials. In this study, we demonstrate the applicability of compressed sensing to deriving the interatomic potential of ten ele…
We use recent theoretical advances to develop a new functional form for interatomic forces in bulk silicon. The theoretical results underlying the model include a novel analysis of elastic properties for the diamond and graphitic structures and inversions of ab initio cohesive energy curves. The interaction model includes two-body and three-body terms which depend on the local atomic environment through an effective coordination number. This formulation is able to capture successfully: (i) the energetics and elastic properties of the ground state diamond lattice; (ii) the covalent re-hybridiza…
Upscaling DFT-trained machine-learning interatomic potential toward Quantum Monte Carlo accuracy: Sulfur-vacancy migration in monolayer MoS$_2$ as a testbed
Institute of Informatics, Slovak Academy of Sciences（斯洛伐克科学院信息学研究所）；Faculty of Informatics and Information Technologies, Slovak University of Technology（斯洛伐克技术大学信息技术学院）；Computational Science Division, Argonne National Laboratory（阿贡国家实验室计算科学部）；Institute of Physics, Slovak Academy of Sciences（斯洛伐克科学院物理研究所）
Defect-limited thermal transport in AlN using pretrained machine-learning interatomic potentials
Seoul National University（首尔大学）；Research Institute of Advanced Materials, Seoul National University（首尔大学先进材料研究所）；Center for AI and Natural Sciences, Korea Institute for Advanced Study（韩国高等研究院人工智能与自然科学中心）；Incheon National University（仁川国立大学）
FourPhonon is a computational package that can calculate four-phonon scattering rates in crystals. It is built within ShengBTE framework, which is a well-recognized lattice thermal conductivity solver based on Boltzmann transport equation. An adaptive energy broadening scheme is implemented for the calculation of four-phonon scattering rates. In analogy with $thirdorder.py$ in ShengBTE, we also provide a separate python script, $Fourthorder.py$, to calculate fourth-order interatomic force-constants. The extension module preserves all the nice features of the well-recognized lattice thermal con…
The method and the advantages of an evolutionary computing based approach using a steady state genetic algorithm (GA) for the parameterization of interatomic potentials for metal oxides within the shell model framework are developed and described. We show that the GA based methodology for the parameterization of interatomic force field functions is capable of (a) simultaneous optimization of the multiple phases or properties of a material in a single run, (b) facilitates the incremental re-optimization of the whole system as more data is available for either additional phases or material prope…
We present a novel scheme to accurately predict atomic forces as vector quantities, rather than sets of scalar components, by Gaussian Process (GP) Regression. This is based on matrix-valued kernel functions, on which we impose the requirements that the predicted force rotates with the target configuration and is independent of any rotations applied to the configuration database entries. We show that such covariant GP kernels can be obtained by integration over the elements of the rotation group SO(d) for the relevant dimensionality d. Remarkably, in specific cases the integration can be carri…
Artifacts in the collective desorption map of the detector hits impede a truthful reconstruction, including enhanced "zone lines" with high atomic impact intensity. Since APT is destructive, simulation is the only approach to explain the origin of these zone lines, but previous work couldn't reproduce them. Here, we use a new simulation technique that adds the full electrostatic forces to the interatomic forces in a molecular-dynamics simulation and eliminates the previous ad-hoc assumptions. We find for the canonical example of tungsten that evaporation happens when the electrostatic force ov…
Towards Accurate and Scalable High-throughput MOF Adsorption Screening: Merging Classical Force Fields and Universal Machine Learned Interatomic Potentials
By means of first-principles calculations, we investigate the thermal properties of silica as it evolves, under hydrostatic compression, from a stishovite phase into a CaCl$_2$-type structure. We compute the thermal conductivity tensor by solving the linearized Boltzmann transport equation iteratively in a wide temperature range, using for this the pressure-dependent harmonic and anharmonic interatomic couplings obtained from first principles. Most remarkably, we find that, at low temperatures, SiO$_2$ displays a large peak in the in-plane thermal conductivity and a highly anisotropic behavior…
A new simulation approach of field evaporation is presented. The model combines classical electrostatics with molecular dynamics (MD) simulations. Unlike previous atomic-level simulation approaches, our method does not rely on an evaporation criterion based on thermal activation theory, instead, electric-field-induced forces on atoms are explicitly calculated and added to the interatomic forces. Atoms then simply move according to the laws of classical molecular dynamics and are "evaporated" when the external force overcomes interatomic bonding. This approach thus makes no ad-hoc assumptions c…
We carry out a systematic study of the thermal conductivity of four single-layer transition metal dichalcogenides, MX$_2$ (M = Mo, W; X = S, Se) from first-principles by solving the Boltzmann Transport Equation (BTE). We compare three different theoretical frameworks to solve the BTE beyond the Relaxation Time Approximation (RTA), using the same set of interatomic force constants computed within density functional theory (DFT), finding that the RTA severely underpredicts the thermal conductivity of MS$_2$ materials. Calculations of the different phonon scattering relaxation times of the main c…
Parameterizing empirical interatomic potentials for predicting thermophysical properties via an irreducible derivative approach: the case of ThO$_2$ and UO$_2$
Idaho National Laboratory（爱达荷国家实验室）；Columbia University（哥伦比亚大学）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；The Pennsylvania State University（宾夕法尼亚州立大学）；The Ohio State University（俄亥俄州立大学）
Ferroelectric perovskites have been ubiquitously applied in piezoelectric devices for decades, among which, eco-friendly lead-free (K,Na)NbO3-based materials have been recently demonstrated to be an excellent candidate for sustainable development. Molecular dynamics is a versatile theoretical calculation approach for the investigation of the dynamical properties of ferroelectric perovskites. However, molecular dynamics simulation of ferroelectric perovskites has been limited to simple systems, since the conventional construction of interatomic potential is rather difficult and inefficient. In …
High performance thermoelectric devices requires materials with low lattice thermal conductivities. Many strategies, such as phonon engineering, have been made to reduce lattice thermal conductivity without simultaneously decrease of the charge transport performance. It is a simple and effective approach to use materials with heavy element to reduce the lattice thermal conductivity. Here, based on the first-principles calculations and phonon Boltzmann transport equations, we find the replacement of Zr with heavy element Hf in ZrNCl doesn't reduce the lattice thermal conductivity, instead, it s…
While machine learning approaches have been successfully used to represent interatomic potentials, their speed has typically lagged behind conventional formalisms. This is often due to the complexity of the structural fingerprints used to describe the local atomic environment and the large cutoff radii and neighbor lists used in the calculation of these fingerprints. Even recent machine learned methods are at least 10 times slower than traditional formalisms. An implementation of a rapid artificial neural network (RANN) style potential in the LAMMPS molecular dynamics package is presented here…
