Pushing thermal conductivity to its lower limit in crystals with simple structures.

Materials with low thermal conductivity usually have complex crystal structures. Herein we experimentally find that a simple crystal structure material AgTlI2 (I4/mcm) owns an extremely low thermal conductivity of 0.25 W/mK at room temperature. To understand this anomaly, we perform in-depth theoretical studies based on ab initio molecular dynamics simulations and anharmonic lattice dynamics. We find that the unique atomic arrangement and weak chemical bonding provide a permissive environment for strong oscillations of Ag atoms, leading to a considerable rattling behaviour and giant lattice anharmonicity. This feature is also verified by the experimental probability density function refinement of single-crystal diffraction. The particularly strong anharmonicity breaks down the conventional phonon gas model, giving rise to non-negligible wavelike phonon behaviours in AgTlI2 at 300 K. Intriguingly, unlike many strongly anharmonic materials where a small propagative thermal conductivity is often accompanied by a large diffusive thermal conductivity, we find an unusual coexistence of ultralow propagative and diffusive thermal conductivities in AgTlI2 based on the thermal transport unified theory. This study underscores the potential of simple crystal structures in achieving low thermal conductivity and encourages further experimental research to enrich the family of materials with ultralow thermal conductivity.

Tensorial Properties via the Neuroevolution Potential Framework: Fast Simulation of Infrared and Raman Spectra.

Infrared and Raman spectroscopy are widely used for the characterization of gases, liquids, and solids, as the spectra contain a wealth of information concerning, in particular, the dynamics of these systems. Atomic scale simulations can be used to predict such spectra but are often severely limited due to high computational cost or the need for strong approximations that limit the application range and reliability. Here, we introduce a machine learning (ML) accelerated approach that addresses these shortcomings and provides a significant performance boost in terms of data and computational efficiency compared with earlier ML schemes. To this end, we generalize the neuroevolution potential approach to enable the prediction of rank one and two tensors to obtain the tensorial neuroevolution potential (TNEP) scheme. We apply the resulting framework to construct models for the dipole moment, polarizability, and susceptibility of molecules, liquids, and solids and show that our approach compares favorably with several ML models from the literature with respect to accuracy and computational efficiency. Finally, we demonstrate the application of the TNEP approach to the prediction of infrared and Raman spectra of liquid water, a molecule (PTAF-), and a prototypical perovskite with strong anharmonicity (BaZrO3). The TNEP approach is implemented in the free and open source software package gpumd, which makes this methodology readily available to the scientific community.

Combining linear-scaling quantum transport and machine-learning molecular dynamics to study thermal and electronic transports in complex materials.

We propose an efficient approach for simultaneous prediction of thermal and electronic transport properties in complex materials. Firstly, a highly efficient machine-learned neuroevolution potential (NEP) is trained using reference data from quantum-mechanical density-functional theory calculations. This trained potential is then applied in large-scale molecular dynamics simulations, enabling the generation of realistic structures and accurate characterization of thermal transport properties. In addition, molecular dynamics simulations of atoms and linear-scaling quantum transport calculations of electrons are coupled to account for the electron-phonon scattering and other disorders that affect the charge carriers governing the electronic transport properties. We demonstrate the usefulness of this unified approach by studying electronic transport in pristine graphene and thermoelectric transport properties of a graphene antidot lattice, with a general-purpose NEP developed for carbon systems based on an extensive dataset.

Transferability of Machine Learning Models for Predicting Raman Spectra.

Theoretical prediction of vibrational Raman spectra enables a detailed interpretation of experimental spectra, and the advent of machine learning techniques makes it possible to predict Raman spectra while achieving a good balance between efficiency and accuracy. However, the transferability of machine learning models across different molecules remains poorly understood. This work proposed a new strategy whereby machine learning-based polarizability models were trained on similar but smaller alkane molecules to predict spectra of larger alkanes, avoiding extensive first-principles calculations on certain systems. Results showed that the developed polarizability model for alkanes with a maximum of nine carbon atoms can exhibit high accuracy in the predictions of polarizabilities and Raman spectra for the n-undecane molecule (11 carbon atoms), validating its reasonable extrapolation capability. Additionally, a descriptor space analysis method was further introduced to evaluate the transferability, demonstrating potentials for accurate and efficient Raman predictions of large molecules using limited training data labeled for smaller molecules.

Combining the D3 dispersion correction with the neuroevolution machine-learned potential.

Machine-learned potentials (MLPs) have become a popular approach of modeling interatomic interactions in atomistic simulations, but to keep the computational cost under control, a relatively short cutoff must be imposed, which put serious restrictions on the capability of the MLPs for modeling relatively long-ranged dispersion interactions. In this paper, we propose to combine the neuroevolution potential (NEP) with the popular D3 correction to achieve a unified NEP-D3 model that can simultaneously model relatively short-ranged bonded interactions and relatively long-ranged dispersion interactions. We show that improved descriptions of the binding and sliding energies in bilayer graphene can be obtained by the NEP-D3 approach compared to the pure NEP approach. We implement the D3 part into thegpumdpackage such that it can be used out of the box for many exchange-correlation functionals. As a realistic application, we show that dispersion interactions result in approximately a 10% reduction in thermal conductivity for three typical metal-organic frameworks.

Tuning the Through-Plane Lattice Thermal Conductivity in van der Waals Structures through Rotational (Dis)ordering.

It has recently been demonstrated that MoS2 with irregular interlayer rotations can achieve an extreme anisotropy in the lattice thermal conductivity (LTC), which is, for example, of interest for applications in waste heat management in integrated circuits. Here, we show by atomic-scale simulations based on machine-learned potentials that this principle extends to other two-dimensional materials, including C and BN. In all three materials, introducing rotational disorder drives the through-plane LTC to the glass limit, while the in-plane LTC remains almost unchanged compared to those of the ideal bulk materials. We demonstrate that the ultralow through-plane LTC is connected to the collapse of their transverse acoustic modes in the through-plane direction. Furthermore, we find that the twist angle in periodic moiré structures representing rotational order provides an efficient means for tuning the through-plane LTC that operates for all chemistries considered here. The minimal through-plane LTC is obtained for angles between 1 and 4° depending on the material, with the biggest effect in MoS2. The angular dependence is correlated with the degree of stacking disorder in the materials, which in turn is connected to the slip surface. This provides a simple descriptor for predicting the optimal conditions at which the LTC is expected to become minimal.

Sub-Micrometer Phonon Mean Free Paths in Metal-Organic Frameworks Revealed by Machine Learning Molecular Dynamics Simulations.

Metal-organic frameworks (MOFs) are a family of materials that have high porosity and structural tunability and hold great potential in various applications, many of which require a proper understanding of the thermal transport properties. Molecular dynamics (MD) simulations play an important role in characterizing the thermal transport properties of various materials. However, due to the complexity of the structures, it is difficult to construct accurate empirical interatomic potentials for reliable MD simulations of MOFs. To this end, we develop a set of accurate yet highly efficient machine-learned potentials for three typical MOFs, including MOF-5, HKUST-1, and ZIF-8, using the neuroevolution potential approach as implemented in the GPUMD package, and perform extensive MD simulations to study thermal transport in the three MOFs. Although the lattice thermal conductivity values of the three MOFs are all predicted to be smaller than 1 W/(m K) at room temperature, the phonon mean free paths (MFPs) are found to reach the sub-micrometer scale in the low-frequency region. As a consequence, the apparent thermal conductivity only converges to the diffusive limit for micrometer single crystals, which means that the thermal conductivity is heavily reduced in nanocrystalline MOFs. The sub-micrometer phonon MFPs are also found to be correlated with a moderate temperature dependence of thermal conductivity between those in typical crystalline and amorphous materials. Both the large phonon MFPs and the moderate temperature dependence of thermal conductivity fundamentally change our understanding of thermal transport in MOFs.

Accurate prediction of heat conductivity of water by a neuroevolution potential.

We propose an approach that can accurately predict the heat conductivity of liquid water. On the one hand, we develop an accurate machine-learned potential based on the neuroevolution-potential approach that can achieve quantum-mechanical accuracy at the cost of empirical force fields. On the other hand, we combine the Green-Kubo method and the spectral decomposition method within the homogeneous nonequilibrium molecular dynamics framework to account for the quantum-statistical effects of high-frequency vibrations. Excellent agreement with experiments under both isobaric and isochoric conditions within a wide range of temperatures is achieved using our approach.

Technical note: TERMA scaling as an effective heterogeneity correction model for convolution-based external-beam photon dose calculations.

BACKGROUND: In highly heterogeneous medium, such as one with lung tissue or air cavities, the dose in the low-density region or after it, as calculated by the conventional methods based on convolution with an energy-spreading kernel, is usually overestimated in comparison with measurements or more accurate predictions. PURPOSE: To correct the overestimation, we propose a method of scaling the total energy released per mass (TERMA). METHODS: The scaling depends on both the density distribution and the effective beam size in the lateral direction. RESULTS: The corrected convolution method achieved a significantly improved accuracy in both the lung-like tissue and the water-like region after air, compared to the uncorrected method. The TERMA correction only adds about 10% to the overall computational cost. CONCLUSIONS: Due to the improvement in accuracy and the preservation of computational efficiency, the proposed dose calculation method will be valuable for inverse treatment planning.

Correction to "Structure and Pore Size Distribution in Nanoporous Carbon".

[This corrects the article DOI: 10.1021/acs.chemmater.1c03279.].

GPUMD: A package for constructing accurate machine-learned potentials and performing highly efficient atomistic simulations.

We present our latest advancements of machine-learned potentials (MLPs) based on the neuroevolution potential (NEP) framework introduced in Fan et al. [Phys. Rev. B 104, 104309 (2021)] and their implementation in the open-source package gpumd. We increase the accuracy of NEP models both by improving the radial functions in the atomic-environment descriptor using a linear combination of Chebyshev basis functions and by extending the angular descriptor with some four-body and five-body contributions as in the atomic cluster expansion approach. We also detail our efficient implementation of the NEP approach in graphics processing units as well as our workflow for the construction of NEP models and demonstrate their application in large-scale atomistic simulations. By comparing to state-of-the-art MLPs, we show that the NEP approach not only achieves above-average accuracy but also is far more computationally efficient. These results demonstrate that the gpumd package is a promising tool for solving challenging problems requiring highly accurate, large-scale atomistic simulations. To enable the construction of MLPs using a minimal training set, we propose an active-learning scheme based on the latent space of a pre-trained NEP model. Finally, we introduce three separate Python packages, viz., gpyumd, calorine, and pynep, that enable the integration of gpumd into Python workflows.

Improving the accuracy of the neuroevolution machine learning potential for multi-component systems.

In a previous paper Fanet al(2021Phys. Rev.B104, 104309), we developed the neuroevolution potential (NEP), a framework of training neural network based machine-learning potentials using a natural evolution strategy and performing molecular dynamics (MD) simulations using the trained potentials. The atom-environment descriptor in NEP was constructed based on a set of radial and angular functions. For multi-component systems, all the radial functions between two atoms are multiplied by some fixed factors that depend on the types of the two atoms only. In this paper, we introduce an improved descriptor for multi-component systems, in which different radial functions are multiplied by different factors that are also optimized during the training process, and show that it can significantly improve the regression accuracy without increasing the computational cost in MD simulations.

GPU_PBTE: an efficient solver for three and four phonon scattering rates on graphics processing units.

Lattice thermal conductivity (LTC) is a key parameter for many technological applications. Based on the Peierls-Boltzmann transport equation (PBTE), many unique phonon transport properties of various materials were revealed. Accurate calculation of LTC with PBTE, however, is a time-consuming task, especially for compounds with a complex crystal structure or taking high-order phonon scattering into consideration. Graphical processing units (GPUs) have been extensively used to accelerate scientific simulations, making it possible to use a single desktop workstation for calculations that used to require supercomputers. Due to its fundamental differences from traditional processors, GPUs are especially suited for executing a large group of similar tasks with minimal communication, but require completely different algorithm design. In this paper, we provide a new algorithm optimized for GPUs, where a two-kernel method is used to avoid divergent branching. A new open-source code, GPU_PBTE, is developed based on the proposed algorithm. As demonstrations, we investigate the thermal transport properties of silicon and silicon carbide, and find that accurate and reliable LTC can be obtained by our software. GPU_PBTE performed on NVIDIA Tesla V100 can extensively improve double precision performance, making it two to three orders of magnitude faster than our CPU version performed on Intel Xeon CPU Gold 6248 @2.5 GHz. Our work also provides an idea of accelerating calculations with other novel hardware that may come out in the future.

Ultrahigh Convergent Thermal Conductivity of Carbon Nanotubes from Comprehensive Atomistic Modeling.

Anomalous heat transport in one-dimensional nanostructures, such as nanotubes and nanowires, is a widely debated problem in condensed matter and statistical physics, with contradicting pieces of evidence from experiments and simulations. Using a comprehensive modeling approach, comprised of lattice dynamics and molecular dynamics simulations, we proved that the infinite length limit of the thermal conductivity of a (10,0) single-wall carbon nanotube is finite but this limit is reached only for macroscopic lengths due to a thermal phonon mean free path of several millimeters. Our calculations showed that the extremely high thermal conductivity of this system at room temperature is dictated by quantum effects. Modal analysis showed that the divergent nature of thermal conductivity, observed in one-dimensional model systems, is suppressed in carbon nanotubes by anharmonic scattering channels provided by the flexural and optical modes with polarization in the plane orthogonal to the transport direction.

Anomalous thermal conductivity enhancement in low dimensional resonant nanostructures due to imperfections.

Nanophononic metamaterials have broad applications in fields such as heat management, thermoelectric energy conversion, and nanoelectronics. Phonon resonance in pillared low-dimensional structures has been suggested to be a feasible approach to reduce thermal conductivity (TC). In this work, we study the effects of imperfections in pillared nanostructures based on graphene nanoribbons (GNR), using classical molecular dynamics simulations and harmonic lattice dynamics. The TC of perfect pillared GNR is only about 13% of that of pristine GNR due to the strong phonon resonant hybridization in pillared GNR. However, introducing imperfections such as vacancy defects and mass mismatch between the pillars and the base material, and alloy disorder in the pillars, can weaken the resonant hybridization and abnormally increase the TC. We show that both vacancy defects and mass mismatch can reduce the penetration of the resonant modes from the pillars into the base material, while the alloy disorder in the pillars can scatter the phonons inside them, which turns regular resonance into a random one with weaker hybridization. Our work provides useful insight into the phonon resonance mechanisms in experimentally relevant low dimensional nanostructures containing various imperfections.

A minimal Tersoff potential for diamond silicon with improved descriptions of elastic and phonon transport properties.

Silicon is an important material and many empirical interatomic potentials have been developed for atomistic simulations of it. Among them, the Tersoff potential and its variants are the most popular ones. However, all the existing Tersoff-like potentials fail to reproduce the experimentally measured thermal conductivity of diamond silicon. Here we propose a modified Tersoff potential and develop an efficient open source code called GPUGA (graphics processing units genetic algorithm) based on the genetic algorithm and use it to fit the potential parameters against energy, virial and force data from quantum density functional theory calculations. This potential, which is implemented in the efficient open source GPUMD (graphics processing units molecular dynamics) code, gives significantly improved descriptions of the thermal conductivity and phonon dispersion of diamond silicon as compared to previous Tersoff potentials and at the same time well reproduces the elastic constants. Furthermore, we find that quantum effects on the thermal conductivity of diamond silicon at room temperature are non-negligible but small: using classical statistics underestimates the thermal conductivity by about 10% as compared to using quantum statistics.

Influence of thermostatting on nonequilibrium molecular dynamics simulations of heat conduction in solids.

Nonequilibrium molecular dynamics (NEMD) has been extensively used to study thermal transport at various length scales in many materials. In this method, two local thermostats at different temperatures are used to generate a nonequilibrium steady state with a constant heat flux. Conventionally, the thermal conductivity of a finite system is calculated as the ratio between the heat flux and the temperature gradient extracted from the linear part of the temperature profile away from the local thermostats. Here, we show that, with a proper choice of the thermostat, the nonlinear part of the temperature profile should actually not be excluded in thermal transport calculations. We compare NEMD results against those from the atomistic Green's function method in the ballistic regime and those from the homogeneous nonequilibrium molecular dynamics method in the ballistic-to-diffusive regime. These comparisons suggest that in all the transport regimes, one should directly calculate the thermal conductance from the temperature difference between the heat source and sink and, if needed, convert it into the thermal conductivity by multiplying it with the system length. Furthermore, we find that the Langevin thermostat outperforms the Nosé-Hoover (chain) thermostat in NEMD simulations because of its stochastic and local nature. We show that this is particularly important for studying asymmetric carbon-based nanostructures, for which the Nosé-Hoover thermostat can produce artifacts leading to unphysical thermal rectification.

Heat transport in pristine and polycrystalline single-layer hexagonal boron nitride.

We use a phase field crystal model to generate large-scale bicrystalline and polycrystalline single-layer hexagonal boron nitride (h-BN) samples and employ molecular dynamics (MD) simulations with the Tersoff many-body potential to study their heat transport properties. The Kapitza thermal resistance across individual h-BN grain boundaries is calculated using the inhomogeneous nonequilibrium MD method. The resistance displays strong dependence on the tilt angle, the line tension and the defect density of the grain boundaries. We also calculate the thermal conductivity of pristine h-BN and polycrystalline h-BN with different grain sizes using an efficient homogeneous nonequilibrium MD method. The in-plane and the out-of-plane (flexural) phonons exhibit different grain size scalings of the thermal conductivity in polycrystalline h-BN and the extracted Kapitza conductance is close to that of large-tilt-angle grain boundaries in bicrystals.