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Phonon coherence and minimum thermal conductivity in disordered superlattices
Molecular dynamics (MD) simulations play an important role in understanding and engineering heat transport properties of complex materials. An essential requirement for reliably predicting heat transport properties is the use of accurate and efficient interatomic potentials. Recently, machine-learned potentials (MLPs) have shown great promise in providing the required accuracy for a broad range of materials. In this mini-review and tutorial, we delve into the fundamentals of heat transport, explore pertinent MD simulation methods, and survey the applications of MLPs in MD simulations of heat transport. Furthermore, we provide a step-by-step tutorial on developing MLPs for highly efficient and predictive heat transport simulations, utilizing the neuroevolution potentials as implemented in the GPUMD package. Our aim with this mini-review and tutorial is to empower researchers with valuable insights into cutting-edge methodologies that can significantly enhance the accuracy and efficiency of MD simulations for heat transport studies.
Transition metal dichalcogenides (TMDs) are a class of layered materials that hold great promise for a wide range of applications. Their practical use can be limited by their thermal transport properties, which have proven challenging to determine accurately, both from a theoretical and experimental perspective. We have conducted a thorough theoretical investigation of the thermal conductivity of four common TMDs, MoSe 2 , WSe 2 , MoS 2 , and WS 2 , at room temperature, to determine the key factors that influence their thermal behavior. We analyze these materials using calculations performed with the program, anharmonic lattice dynamics and the Boltzmann transport equation formalism, as implemented in the temperature-dependent effective potentials method. Within this framework, we analyze the microscopic parameters influencing the thermal conductivity, such as the phonon dispersion and the phonon lifetimes. The aim is to precisely identify the origin of differences in thermal conductivity among these canonical TMD materials. We compare their in-plane thermal properties in monolayer and bulk form, and we analyze how the thickness and the chemical composition affect the thermal transport behavior. We showcase how bonding and the crystal structure influence the thermal properties by comparing the TMDs with silicon, reporting the cases of bulk silicon and monolayer silicene. We find that the interlayer bond type (covalent vs. van der Waals) involved in the structure is crucial in the heat transport. In two-dimensional silicene, we observe a reduction by a factor ∼ 15 compared to the Si bulk thermal conductivity due to the smaller group velocities and shorter phonon lifetimes. In the TMDs, where the group velocities and the phonon bands do not vary significantly passing from the bulk to the monolayer limit, we do not see as strong a decrease in the thermal conductivity: only a factor 2–3. Moreover, our analysis reveals that differences in the thermal conductivity arise from variations in atomic species, bond strengths, and phonon lifetimes. These factors are closely interconnected and collectively impact the overall thermal conductivity. We inspect each of them separately and explain how they influence the heat transport. We also study artificial TMDs with modified masses, in order to assess how the chemistry of the compounds modifies the microscopic quantities and thus the thermal conductivity.
Published by the American Physical Society 2024
Heterostructures find wide-ranging applications in fields such as thermal management, thermoelectric energy conversion, and nanoelectronics. This study provides new insights into the thermal conductivity of parallel heterointerfaces by investigating a longitudinal heterostructure composed of graphene and hexagonal boron nitride (h-BN) using molecular dynamics simulations. Interestingly, it is observed that this unique heterostructure possesses a lower thermal conductivity compared to pure h-BN. The analysis reveals that phonon scattering is enhanced by stress at the interface of the heterostructure and the mass distribution through it. The heterostructure model introduced in this study presents new insights for controlling phonon transportation in nanoscale structures.
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.
Efficient waste heat dissipation has become increasingly challenging as transistor size has decreased to nanometers. As governed by universal Umklapp phonon scattering, the thermal conductivity of semiconductors decreases at higher temperatures and causes heat transfer deterioration under high-power conditions. In this study, we realized simultaneous electrical and thermal rectification (TR) in a monolayer MoSe2-WSe2 lateral heterostructure. The atomically thin MoSe2-WSe2 heterojunction forms an electrical diode with a high ON/OFF ratio up to 104. Meanwhile, a preferred heat dissipation channel was formed from MoSe2 to WSe2 in the ON state of the heterojunction diode at high bias voltage with a TR factor as high as 96%. Higher thermal conductivity was achieved at higher temperatures owing to the TR effect caused by the local temperature gradient. Furthermore, the TR factor could be regulated from maximum to zero by rotating the angle of the monolayer heterojunction interface. This result opens a path for designing novel nanoelectronic devices with enhanced thermal dissipation.
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 we 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, GPYUMD, CALORINE, and PYNEP, which enable the integration of GPUMD into Python workflows.
Thermal transport in amorphous materials has remained one of the fundamental questions in solid state physics while involving a very large field of applications. Using a heat conduction theory incorporating coherence, we demonstrate that the strong phase correlation between local and non-propagating modes, commonly named diffusons in the terminology of amorphous systems, triggers the conduction of heat. By treating the thermal vibrations as collective excitations, the significant contribution of diffusons, predominantly relying on coherence, further reveals interesting temperature and length dependences of thermal conductivity. The propagation length of diffuson clusters is found to reach the micron, overpassing the one of propagons. The explored wavelike behavior of diffusons uncovers the unsolved physical picture of mode correlation in prevailing models and further provides an interpretation of their ability to transport heat. This work introduces a framework for understanding thermal vibrations and transport in amorphous materials, as well as an unexpected insight into the wave nature of thermal vibrations.
Thermal transport at the nanoscale level is attracting attention not only because of its physically interesting features such as the peculiar behavior of phonons due to their pronounced ballistic and wave-like properties but also because of its potential applications in alleviating heat dissipation problems in electronic and optical devices and thermoelectric energy harvesting. In the last quarter-century, researchers have elucidated the thermal transport properties of various nanostructured materials, including phononic crystals (PnCs): artificial periodic structures for phonons. PnCs are excellent platforms for investigating thermal transport owing to their well-defined structural parameters. In addition, it is interesting to control thermal transport by interference, as demonstrated in the low-frequency regime with elastic waves and sounds. In this article, we focus on high-frequency phonons and review the thermal transport in semiconductor PnCs. This comprehensive review provides an understanding of recent studies and trends, organized as theoretical and experimental, in terms of the quasiparticle and wave aspects.
In a previous paper [Fan Z et al. 2021 Phys. Rev. B, 104, 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.
We develop a neuroevolution-potential (NEP) framework for generating neural network-based machine-learning potentials. They are trained using an evolutionary strategy for performing large-scale molecular dynamics (MD) simulations. A descriptor of the atomic environment is constructed based on Chebyshev and Legendre polynomials. The method is implemented in graphic processing units within the open-source gpumd package, which can attain a computational speed over 107 atom-step per second using one Nvidia Tesla V100. Furthermore, per-atom heat current is available in NEP, which paves the way for efficient and accurate MD simulations of heat transport in materials with strong phonon anharmonicity or spatial disorder, which usually cannot be accurately treated either with traditional empirical potentials or with perturbative methods.
Anderson localization of thermal phonons has been shown only in few nanostructures with strong random disorder by the exponential decay
of transmission to zero and a thermal conductivity maximum when increasing the system length. In this work, we present a path to demonstrate
the phonon localization with distinctive features in graded superlattices with short-range order and long-range disorder. A thermal
conductivity minimum with system length appears due to the exponential decay of transmission to a non-zero constant, which is a feature
of partial phonon localization caused by the moderate disorder. We provide clear evidence of localization through the combined analysis of
the participation ratio, transmission, and real-space phonon number density distribution based on our quantum transport simulation. The
present work would promote heat conduction engineering by localization via the wave nature of phonons.
Our direct atomic simulations reveal that a thermally activated phonon mode involves a large population of elastic wave packets. These excitations are characterized by a wide distribution of lifetimes and coherence times expressing particlelike and wavelike natures. In agreement with direct simulations, our theoretical derivation yields a generalized law for the decay of the phonon number taking into account coherent effects. Before the conventional exponential decay due to phonon-phonon scattering, this law introduces a delay proportional to the square of the coherence time. This additional regime leads to a moderate increase of the relaxation times and to a different dependence of phonon relaxation to those. This work opens new horizons in the understanding of the origin and the treatment of thermal phonons.
Lattice heat conduction can be modulated via nanostructure interfaces. Although advances have been made by viewing phonons as particles, the controllability should be enhanced by fully utilizing their wave nature. By considering phonons as coherent waves, herein we design an optimized aperiodic superlattice that minimizes the coherent phonon heat conduction by alternatingly coupling coherent phonon transport calculations and machine learning. The thermal conductivity of the fabricated aperiodic superlattice agrees well with the calculations over a temperature range of 77–300 K, indicating that complex aperiodic wave interference of coherent phonons can be controlled. The thermal conductivity of the aperiodic superlattice is significantly smaller than the conventional periodic superlattice due to enhanced phonon localization. The optimized aperiodic structure is formed by connecting weakly correlated local structures that introduce interference over broad phonon frequencies. Controlling coherent phonons by aperiodic interferences opens a new route for phonon engineering.
We show that aperiodic superlattices exhibit intriguing interplay between phononic coherent wave interference effects and incoherent transport. In particular, broadband Anderson localization results in a drastic thermal conductivity reduction of 98% at room temperature, providing an ultralow value of 1.3 W m−1 K−1, and further yields an anomalously large thermal anisotropy ratio of ∼102 in aperiodic Si/Ge superlattices. A maximum in the thermal conductivity emerges as an unambiguous consequence of phonon Anderson localization at a system length scale bridging the extended and localized transport regimes. The frequency-resolved picture, combined with our lattice dynamical description of Anderson localization, elucidates the rich transport characteristics in these systems and the potential of correlated disorder for sub- to few-THz phononic engineering of heat transport in thermoelectric applications.
The standard equilibrium Green–Kubo and nonequilibrium molecular dynamics (MD) methods for computing thermal transport coefficients in solids typically require relatively long simulation times and large system sizes. To this end, we revisit here the homogeneous nonequilibrium MD method by Evans [Phys. Lett. A 91, 457 (1982)] and generalize it to many-body potentials that are required for more realistic materials modeling. We also propose a method for obtaining spectral conductivity and phonon mean-free path from the simulation data. This spectral decomposition method does not require lattice dynamics calculations and can find important applications in spatially complex structures. We benchmark the method by calculating thermal conductivities of three-dimensional silicon, two-dimensional graphene, and a quasi-one-dimensional carbon nanotube and show that the method is about one to two orders of magnitude more efficient than the Green–Kubo method. We apply the spectral decomposition method to examine the long-standing dispute over thermal conductivity convergence vs divergence in carbon nanotubes.
Superlattices are ideal model systems for the realization and understanding of coherent (wave-like) and incoherent (particle-like) phonon thermal transport. Single layer heterostructures of graphene and hexagonal boron nitride have been produced recently with sharp edges and controlled domain sizes. In this study we employ nonequilibrium molecular dynamics simulations to investigate the thermal conductivity of superlattice nanoribbons with equal-sized domains of graphene and hexagonal boron nitride. We analyze the dependence of the conductivity with the domain sizes, and with the total length of the ribbons. We determine that the thermal conductivity reaches a minimum value of 89 W m−1K−1 for ribbons with a superlattice period of 3.43 nm. The effective phonon mean free path is also determined and shows a minimum value of 32 nm for the same superlattice period. Our results also reveal that a crossover from coherent to incoherent phonon transport is present at room temperature for BNC nanoribbons, as
In this article, we first summarize and compare the phonon properties, such as phonon dispersion and relaxation time, of emerging pristine two-dimensional (2-D) materials with the single layer graphene to understand the role of crystal structure on their thermal conductivity. We then compare the phonon properties, between an idealized 2-D crystal, realistic 2-D crystals, and 3-D crystals, and present the physical picture on how the thermal conductivity of 2-D materials changes with sample sizes. The geometric effects, such as layer numbers and width, and other physical effects like defects, mechanical strains, and substrates, on the thermal properties of 2-D materials are discussed. We also briefly discuss the challenges in theoretical and experimental studies of phonon and thermal transport in 2-D materials. The rich and special phonon physics in 2-D materials make them promising candidates for exploring novel phenomena like topological phonon effect and applications like phononic quantum devices, as discussed in the outlook.
Two-dimensional materials have unusual phonon spectra due to the presence of flexural (out-of-plane) modes. Although molecular dynamics simulations have been extensively used to study heat transport in such materials, conventional formalisms treat the phonon dynamics isotropically. Here, we decompose the microscopic heat current in atomistic simulations into in-plane and out-of-plane components, corresponding to in-plane and out-of-plane phonon dynamics, respectively. This decomposition allows for direct computation of the corresponding thermal conductivity components in two-dimensional materials. We apply this decomposition to study heat transport in suspended graphene, using both equilibrium and nonequilibrium molecular dynamics simulations. We show that the flexural component is responsible for about two-thirds of the total thermal conductivity in unstrained graphene, and the acoustic flexural component is responsible for the logarithmic divergence of the conductivity when a sufficiently large tensile strain is applied.
The isolation of single- to few-layer transition metal dichalcogenides opens new directions in the application of two-dimensional materials to nanoelectronics. The characterization of thermal transport in these new low-dimensional materials is needed for their efficient implementation, either for general overheating issues or specific applications in thermoelectric devices. In this study, the lattice thermal conductivities of single-layer MoS2 and MoSe2 are evaluated using classical molecular dynamics methods. The interactions between atoms are defined by Stillinger-Weber-type empirical potentials that are developed to represent the structural, mechanical, and vibrational properties of the given materials. In the parameterization of the potentials, a stochastic optimization algorithm, namely particle swarm optimization, is utilized. The final parameter sets produce quite consistent results with density functional theory in terms of lattice parameters, bond distances, elastic constants, and vibrational properties of both single-layer MoS2 and MoSe2. The predicted thermal properties of both materials are in very good agreement with earlier first-principles calculations. The discrepancies between the calculations and experimental measurements are most probably caused by the pristine nature of the structures in our simulations.
Nonequilibrium molecular dynamics (NEMD) simulations on conceptual binary Lennard-Jones systems show that the thermal conductivity (\kappa) of a superlattice (SL) can be significantly reduced by randomizing the thicknesses of its layers, by which a SL becomes a random multilayer (RML). Such reduction in \kappa is a clear signature of coherent phonon that can be localized in RMLs. We build a two-phonon model that divides the overall heat conduction into coherent and incoherent phonon contributions. In SL both coherent and incoherent phonons contribute to heat conduction, while in RML coherent phonons are localized so only incoherent phonons contribute. This model can fit the length dependence of the thermal conductances predicted in our NEMD simulations very well. The ballistic-limit thermal conductance and the intrinsic mean free path (MFP) of both coherent and incoherent phonons, and the localization length of coherent phonons, are obtained by fitting our model to the NEMD simulation results. The significant increase in \kappa of SL with total length is due to the long MFP of coherent phonons, and the lower \kappa of RML than SL is caused by the localization of coherent phonons.
We demonstrate the existence of a coherent transport of thermal energy in superlattices by introducing a microscopic definition of the phonon coherence length. A criterion is provided to distinguish the coherent transport regime from diffuse interface scattering and discuss how these can be specifically controlled by several physical parameters. Our approach provides a convenient framework for the interpretation of previous thermal conductivity measurements and calculations; it also paves the way for the design of a new class of thermal interface materials.
Two-dimensional transition metal dichalcogenides (TMDCs) are finding
promising electronic and optical applications due to their unique properties.
In this letter, we systematically study the phonon transport and thermal
conductivity of eight semiconducting single-layer TMDCs, MX2 (M=Mo, W, Zr and
Hf, X=S and Se), by using the first-principles-driven phonon Boltzmann
transport equation approach. The validity of the single-mode relaxation time
approximation to predict the thermal conductivity of TMDCs is assessed by
comparing the results with the iterative solution of the phonon Boltzmann
transport equation. We find that the phononic thermal conductivities of 2H-type
TMDCs are above 50 W/mK at room temperature while the thermal conductivity
values of the 1T-type TMDCs are much lower, when the size of the sample is 1
{\mu}m. A very high thermal conductivity value of 142 W/mK was found in
single-layer WS2. The large atomic weight difference between W and S leads to a
very large phonon bandgap which in turn forbids the scattering between acoustic
and optical phonon modes and thus resulting in very long phonon relaxation
time.
Amorphous silica (a-SiO2) is a foundational disordered material for which the thermal transport properties are important for various applications. To accurately model the interatomic interactions in classical molecular dynamics (MD) simulations of thermal transport in a-SiO2, we herein develop an accurate yet highly efficient machine-learned potential model that allows us to generate a-SiO2 samples closely resembling experimentally produced ones. Using the homogeneous nonequilibrium MD method and a proper quantum-statistical correction to the classical MD results, quantitative agreement with experiments is achieved for the thermal conductivities of bulk and 190-nm-thick a-SiO2 films over a wide range of temperatures. To interrogate the thermal vibrations at different temperatures, we calculated the current correlation functions corresponding to the transverse acoustic and longitudinal acoustic collective vibrations. The results reveal that, below the Ioffe-Regel crossover frequency, phonons as well-defined excitations remain applicable in a-SiO2 and play a predominant role at low temperatures, resulting in a temperature-dependent increase in thermal conductivity. In the high-temperature region, more phonons are excited, accompanied by a more intense liquidlike diffusion event. We attribute the temperature-independent thermal conductivity in the high-temperature range of a-SiO2 to the collaborative involvement of excited phonon scattering and liquidlike diffusion in heat conduction. These findings provide physical insights into the thermal transport of a-SiO2 and are expected to be applied to a vast range of amorphous materials.
This is a graduate level textbook in nanoscale heat transfer and energy conversion that can also be used as a reference for researchers in the developing field of nanoengineering. It provides a comprehensive overview of microscale heat transfer, focusing on thermal energy storage and transport. Chen broadens the readership by incorporating results from related disciplines, from the point of view of thermal energy storage and transport, and presents related topics on the transport of electrons, phonons, photons, and molecules. This book is part of the MIT-Pappalardo Series in Mechanical Engineering.
Complex problems that cross traditional disciplinary lines between physics, chemistry, biology, and materials science can be studied at an unprecedented level of detail using increasingly sophisticated theoretical methodology and high-speed computing platforms. The tools of statistical mechanics provide the bridge between the atomistic descriptions of these complex systems and the macroscopic observables accessible to experimental investigations and predictable in computer simulations. The aim of this book is to prepare burgeoning users and developers to become active researchers in the theoretical and computational molecular sciences by uniting, in one monograph, the theoretical underpinnings of equilibrium and time-dependent classical and quantum statistical mechanics with modern computational techniques used to put these concepts into practice to address real-world applications. The book contains detailed reviews of classical and quantum mechanics and in-depth discussions of the most commonly used statistical ensembles side by side with modern computational methods such as molecular dynamics, Monte Carlo, advanced configurational and trajectory sampling approaches, free-energy based rare-event sampling approaches, Feynman path integral techniques, linear response theory and time correlation functions, stochastic methods, critical phenomena, and an introduction to machine learning and its uses in statistical mechanics. Readers of this book will be provided, in a pedagogical manner, with a firm foundation in both the theory and practical implementation of statistical mechanical concepts, thus allowing them to approach application technology with an understanding of the underlying algorithms and to become, themselves, creators of new and powerful approaches for solving challenging research problems.
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.
Amorphous silicon (a-Si) is an important thermal-management material and also serves as an ideal playground for studying heat transport in strongly disordered materials. Theoretical prediction of the thermal conductivity of a-Si in a wide range of temperatures and sample sizes is still a challenge. Herein we present a systematic investigation of the thermal transport properties of a-Si by employing large-scale molecular dynamics (MD) simulations with an accurate and efficient machine learned neuroevolution potential (NEP) trained against abundant reference data calculated at the quantum-mechanical density-functional-theory level. The high efficiency of NEP allows us to study the effects of finite size and quenching rate in the formation of a-Si in great detail. We find that a simulation cell up to 64000 atoms (a cubic cell with a linear size of 11 nm) and a quenching rate down to 1011 K s−1 are required for almost convergent thermal conductivity. Structural properties, including short- and medium-range order as characterized by the pair-correlation function, angular-distribution function, coordination number, ring statistics, and structure factor are studied to demonstrate the accuracy of NEP and to further evaluate the role of quenching rate. Using both the heterogeneous and homogeneous nonequilibrium MD methods and the related spectral decomposition techniques, we calculate the temperature- and thickness-dependent thermal conductivity values of a-Si and show that they agree well with available experimental results from 10 K to room temperature. Our results also highlight the importance of quantum effects in the calculated thermal conductivity and support the quantum-correction method based on the spectral thermal conductivity.
Two-dimensional (2D) lateral superlattices, a typical artificial nano-phononic crystal, have stimulated widespread interests and potential application prospects in terms of their physically interesting features. Herein, we have found wave-particle crossover of phonon transport in the graphene (Gr)/2D polyani-line (C 3 N) lateral superlattices, which is an indication of a transition in the phonon transport mechanism from the incoherent to coherent regime. Due to the high structural similarity of C 3 N to Gr, the thermal conductivity of the Gr/C 3 N lateral superlattice can achieve an ultra-wide modulation range of about 500 ∼ 1100 W m −1 K −1 , which is far beyond that of other superlattices. The analysis shows that an increase of the interface density will on the one hand weaken the thermal conductivity by increasing phonon-interface scattering, and on the other hand increase it by lowering the phonon transport barriers and allowing more long-wavelength phonons to participate in the transport. This determines the parabolic trend of thermal conductivity containing the minimum, and also reflects the dual effects of hetero-interfaces on phonon thermal transport. In addition, phonon calculations show that the above variation in thermal conductivity is entirely attributable to differences in the phonon mean free path for different interface densities and is not related to their group velocity.
Controlling thermal transport in nanoporous graphene through wave-like characteristics of phonons beyond the conventional particle regime has attracted widespread interest. Although the existence of wave-like coherent transport in nanoporous graphene has been proposed, the comprehensive impact on phonon transport remains unclear. In this work, we use a rigorous comparison between non-equilibrium molecular dynamics (NEMD) simulation which captures wave effects and mode-resolved phonon Boltzmann transport equation (BTE) which is a particle approach, to quantify the wave effect contribution in the periodic and aperiodic nanoporous graphene. We find that in periodic nanoporous graphene, the wave effect enhances the thermal conductivity compared to solely particle transport. While in aperiodic nanoporous graphene, we observe the coexistence of diverse wave effects that enhance or reduce thermal transport. The competition of these diverse wave effects can lead to an overall enhancement, decrease, or no impact on the thermal conductivity as compared to the particle transport. Our work reveals insights into wave transport in periodic and aperiodic nanoporous structures and provides important guidance for further tuning the thermal conductivity of nanostructures.
The van der Waals (vdW) superlattice, obtained by applying the concept of the periodic superlattice to two-dimensional materials using low-energy vdW physical assembly, is undoubtedly an instrumental avenue for the modulation of material properties. In the field of nanoscale thermal transport, the influence of the periodic structure of superlattice on the wave-particle phonon transport regime arouses substantial interests from the standpoint of basic physics and applied science. In the Graphene/h-BN vdW superlat-tice, we have found the wave-particle crossover of phonon transport, which is reflected in the transition from incoherent to coherent regime as the interface density increases. The analysis reveals that the increased thermal conductivity owing to coherent transport effects will amply compensate for the progressively increasing interface phonon scattering throughout this process. In addition, due to the stronger effects of the above two aspects, the superlattices with higher interface density are more sensitive to changes in temperature and interface coupling strength, which are manifested in the rate of change in thermal conductivity caused by their alteration, respectively. These results establish an in-depth understanding of coherent phonon transport while exploring the possibility of phonon wave-particle crossover in vdW superlattices, providing guidance for related thermal management based on phonon engineering.
Atomistic simulation methods, including anharmonic lattice dynamics combined with the Boltzmann transport equation, equilibrium and non-equilibrium molecular dynamics simulations, and Landauer formalism, are vital for the prediction of thermal conductivity and the understanding of nanoscale thermal transport mechanisms. However, for years, the simulation results using different methods, or even the same method with different simulation setups, lack consistency, leading to many arguments about the underlying physics and proper numerical treatments on these atomistic simulation methods. In this perspective, we review and discuss the recent advances in atomistic simulation methods to predict the thermal conductivity of solid materials. The underlying assumptions of these methods and their consequences on phonon transport properties are comprehensively examined. Using silicon and graphene as examples, we analyze the influence of higher-order phonon scatterings, finite-size effects, quantum effects, and numerical details on the thermal conductivity prediction and clarify how to fairly compare the results from different methods. This perspective concludes with suggestions on obtaining consistent thermal conductivity prediction of different material systems and also provides perspective on efficient and accurate simulations of thermal transport in more complex and realistic conditions.
As the energy problem becomes more prominent, research on thermoelectric (TE) materials has deepened over the past few decades. Low thermal conductivity enables thermoelectric materials better thermal conversion performance. In this study, based on the first principles and phonon Boltzmann transport equation, we studied the thermal conductivities of single-layer WSe2 under several defect conditions using density functional theory (DFT) as implemented in the Vienna Ab-initio Simulation Package (VASP). The lattice thermal conductivities of WSe2 under six kinds of defect states, i.e., PS, SS-c, DS-s, SW-c, SS-e, and DS-d, are 66.1, 41.2, 39.4, 8.8, 42.1, and 38.4 W/(m·K), respectively at 300 K. Defect structures can reduce thermal conductivity up to 86.7% (SW-c) compared with perfect structure. The influences of defect content, type, location factors on thermal properties have been discussed in this research. By introducing atom defects, we can reduce and regulate the thermal property of WSe2, which should provide an interesting idea for other thermoelectric materials to gain a lower thermal conductivity.
Since the classical molecular dynamics simulator LAMMPS was released as an open source code in 2004, it has become a widely-used tool for particle-based modeling of materials at length scales ranging from atomic to mesoscale to continuum. Reasons for its popularity are that it provides a wide variety of particle interaction models for different materials, that it runs on any platform from a single CPU core to the largest supercomputers with accelerators, and that it gives users control over simulation details, either via the input script or by adding code for new interatomic potentials, constraints, diagnostics, or other features needed for their models. As a result, hundreds of people have contributed new capabilities to LAMMPS and it has grown from fifty thousand lines of code in 2004 to a million lines today. In this paper several of the fundamental algorithms used in LAMMPS are described along with the design strategies which have made it flexible for both users and developers. We also highlight some capabilities recently added to the code which were enabled by this flexibility, including dynamic load balancing, on-the-fly visualization, magnetic spin dynamics models, and quantum-accuracy machine learning interatomic potentials.
Program Summary
Program Title: Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS)
CPC Library link to program files: https://doi.org/10.17632/cxbxs9btsv.1
Developer's repository link: https://github.com/lammps/lammps
Licensing provisions: GPLv2
Programming language: C++, Python, C, Fortran
Supplementary material: https://www.lammps.org
Nature of problem: Many science applications in physics, chemistry, materials science, and related fields require parallel, scalable, and efficient generation of long, stable classical particle dynamics trajectories. Within this common problem definition, there lies a great diversity of use cases, distinguished by different particle interaction models, external constraints, as well as timescales and lengthscales ranging from atomic to mesoscale to macroscopic.
Solution method: The LAMMPS code uses neighbor lists, parallel spatial decomposition, and parallel FFTs for long-range Coulombic interactions [1]. The time integration algorithm is based on the Størmer-Verlet symplectic integrator [2], which provides better stability than higher-order non-symplectic methods. In addition, LAMMPS supports a wide range of interatomic potentials, constraints, diagnostics, software interfaces, and pre- and post-processing features.
Additional comments including restrictions and unusual features: This paper serves as the definitive reference for the LAMMPS code.
References
[1]S. Plimpton. Fast parallel algorithms for short-range molecular dynamics. J. Comp. Phys., 117:1–19, 1995.
[2]L. Verlet. Computer experiments on classical fluids: I. Thermodynamical properties of Lennard–Jones molecules. Phys. Rev., 159:98–103, 1967.
The design of applications, especially those based on heterogeneous integration, must rely on detailed knowledge of material properties, such as thermal conductivity (TC). To this end, multiple methods have been developed to study TC as a function of vibrational frequency. Here, we compare three spectral TC methods based on velocity decomposition in homogenous molecular dynamics simulations: Green-Kubo modal analysis (GKMA), the spectral heat current (SHC) method, and a method we propose called homogeneous nonequilibrium modal analysis (HNEMA). First, we derive a convenient per-atom virial expression for systems described by general many-body potentials, enabling compact representations of the heat current, each velocity decomposition method, and other related quantities. Next, we evaluate each method by calculating the spectral TC for carbon nanotubes, graphene, and silicon. We show that each method qualitatively agrees except at optical phonon frequencies, where a combination of mismatched eigenvectors and a large density of states produces artificial TC peaks for modal analysis (MA) methods. Our calculations also show that the HNEMA and SHC methods converge much faster than the GKMA method, with the SHC method being the most computationally efficient. Finally, we demonstrate that our MA implementation in the Graphics Processing Units Molecular Dynamics code on a single graphics processing unit is over 1000 times faster than the existing implementation in the Large-scale Atomic/Molecular Massively Parallel Simulator code on one central processing unit.
Two-dimensional polyaniline (2D-PANI) with semiconductor properties, a single crystalline carbon nitride with a stoichiometry of C3N, has attracted a lot of interest after its successful synthesis. In this study, the thermal transport properties in pristine and defective 2D-PANI were explored by extensive molecular dynamics (MD) simulations. Results based on three different versions of the MD method consistently showed that the lattice thermal conductivity of the pristine 2D-PANI is up to around 2000Wm−1K−1. It decreases significantly after the introduction of structural defects and is essentially in a low-power law with the defects concentration. In addition, the difference in the weakening of thermal conductivity between vacancy and topological defects stems mainly from their respective differential effects on the low-frequency out-of-plane phonons. Remarkably, it also reveals the potential mutual constraints between anharmonic phonon-phonon scattering and phonon-defect scattering. These findings provide guidance for the thermal management of 2D-PANI-based electronic devices and are also expected to advance their application in the field of thermal design of nanomaterials.
Two-dimensional materials such as graphene and transition metal dichalcogenides (TMDCs) have received extensive research interest and investigations in the past decade. In this research, we used a refined opto-thermal Raman technique to explore the thermal transport properties of one popular TMDC material WSe2, in the single-layer (1L), bilayer (2L), and trilayer (3L) forms. This measurement technique is direct without additional processing to the material, and the absorption coefficient of WSe2 is discovered during the measurement process to further increase this technique's precision. By comparing the sample's Raman spectroscopy spectra through two different laser spot sizes, we are able to obtain two parameters-lateral thermal conductivities of 1L-3L WSe2 and the interfacial thermal conductance between 1L-3L WSe2 and the substrate. We also implemented full-atom nonequilibrium molecular dynamics simulations (NEMD) to computationally investigate the thermal conductivities of 1L-3L WSe2 to provide comprehensive evidence and confirm the experimental results. The trend of the layer-dependent lateral thermal conductivities and interfacial thermal conductance of 1L-3L WSe2 is discovered. The room-temperature thermal conductivities for 1L-3L WSe2 are 37 ± 12, 24 ± 12, and 20 ± 6 W/(m·K), respectively. The suspended 1L WSe2 possesses a thermal conductivity of 49 ± 14 W/(m·K). Crucially, the interfacial thermal conductance values between 1L-3L WSe2 and the substrate are found to be 2.95 ± 0.46, 3.45 ± 0.50, and 3.46 ± 0.45 MW/(m2·K), respectively, with a flattened trend starting the 2L, a finding that provides the key information for thermal management and thermoelectric designs.
We elucidate the dependence of the in-plane and interfacial thermal conduction of two-dimensional (2D) transition-metal dichalcogenide (TMDC) materials (including MoS2, WS2, and WSe2) on the materials’ physical features, such as size, layer number, composition, and substrates. The in-plane thermal conductivity k is measured at suspended 2D TMDC materials and the interfacial thermal conductance g is measured at materials supported on substrates, both through Raman thermometry techniques. The thermal conductivity k increases with the radius R of the suspended area following a logarithmic scaling as k∼log(R). k also shows a substantial decrease from monolayer to bilayer, but only changes slightly with a further increase in the layer number. In contrast, the interfacial thermal conductance g has a negligible dependence on the layer number, but g increases with the strength of the interaction between 2D TMDC materials and the substrate, substantially varying among different substrates. The result is consistent with theoretical predictions and clarifies much inconsistence in the literature. This work provides useful guidance for thermal management in 2D TMDC materials and devices.
Predicting the mechanical and thermal properties of quasi-two-dimensional (2D) transition metal dichalcogenides (TMDs) is an essential task necessary for their implementation in device applications. Although rigorous density-functional-theory–based calculations are able to predict mechanical and electronic properties, mostly they are limited to zero temperature. Classical molecular dynamics facilitates the investigation of temperature-dependent properties, but its performance highly depends on the potential used for defining interactions between the atoms. In this study, we calculated temperature-dependent phonon properties of single-layer TMDs, namely, MoS2, MoSe2, WS2, and WSe2, by utilizing Stillinger-Weber–type potentials with optimized sets of parameters with respect to the first-principles results. The phonon lifetimes and contribution of each phonon mode in thermal conductivities in these monolayer crystals are systematically investigated by means of the spectral-energy-density method based on molecular dynamics simulations. The obtained results from this approach are in good agreement with previously available results from the Green-Kubo method. Moreover, detailed analysis of lattice thermal conductivity, including temperature-dependent mode decomposition through the entire Brillouin zone, shed more light on the thermal properties of these 2D crystals. The LA and TA acoustic branches contribute most to the lattice thermal conductivity, while ZA mode contribution is less because of the quadratic dispersion around the Brillouin zone center, particularly in MoSe2 due to the phonon anharmonicity, evident from the redshift, especially in optical modes, by increasing temperature. For all the considered 2D crystals, the phonon lifetime values are compelled by transition metal atoms, whereas the group velocity spectrum is dictated by chalcogen atoms. Overall, the lattice thermal conductivity is linearly proportional with inverse temperature.
The atomic cluster expansion is developed as a complete descriptor of the local atomic environment, including multicomponent materials, and its relation to a number of other descriptors and potentials is discussed. The effort for evaluating the atomic cluster expansion is shown to scale linearly with the number of neighbors, irrespective of the order of the expansion. Application to small Cu clusters demonstrates smooth convergence of the atomic cluster expansion to meV accuracy. By introducing nonlinear functions of the atomic cluster expansion an interatomic potential is obtained that is comparable in accuracy to state-of-the-art machine learning potentials. Because of the efficient convergence of the atomic cluster expansion relevant subspaces can be sampled uniformly and exhaustively. This is demonstrated by testing against a large database of density functional theory calculations for copper.
In this paper, first-principles calculations along with the phonon Boltzmann transport equation are used to study the strain- and size-dependent thermal conductivity of monolayer WSe2. The thermal conductivity of monolayer WSe2 is primarily contributed by the acoustic phonons and decreases with tensile strain due to the reduction in both the group velocity and phonon lifetime. Shrinking the system size also restricts the thermal conductivity significantly by ruling out the contributions of long mean free path phonons. The rate of decrease in thermal conductivity with tensile strain is found to be size dependent, which is attributed to the competition between the phonon-phonon scattering and the phonon-boundary scattering. The decreasing trend of the thermal conductivity of monolayer WSe2 through tensile strain paves the way for high-efficiency thermoelectric materials combining the strain-tuned electronic structure.
Through non-equilibrium molecular dynamics simulations, we report the direct numerical evidence for the coherent phonons participating in thermal transport at room temperature in graphene phononic crystal (GPnC) structure, and evaluate their contribution to thermal conductivity based on the two-phonon model. With decreasing period length in GPnC, the transition from the incoherent to coherent phonon transport is clearly observed. When a random perturbation to the positions of holes is introduced in a graphene sheet, the phonon wave packet simulation reveals the presence of notable localization of coherent phonons, leading to the significant reduction of thermal conductivity and suppressed length dependence. Finally, the effects of period length and temperature on the coherent phonon contribution to thermal conductivity are also discussed. Our work establishes a deep understanding of the coherent phonons transport behavior in periodic phononic structures, which provides effective guidance for engineering thermal transport based on a new path via phonon localization.
Molecular dynamics simulations are performed to investigate the misfit strain induced buckling of the transition-metal dichalcogenide (TMD) lateral heterostructures, which are seamless epitaxial growth of different TMDs along the in-plane direction. The Stillinger-Weber potential is utilized to describe both the interaction for individual TMD and the coupling between different TMDs, i.e., MX2 (with M=Mo, W and X=S, Se, Te). It is found that the misfit strain can induce strong buckling of the free-standing TMD lateral heterostructures of large area, resulting from the TMDs' atomic-thick nature. The buckling phenomenon occurs in a variety of TMD lateral heterostructures of different compositions and in various patterns. Our findings raise a fundamental mechanical challenge for the structural stability of the free-standing TMD lateral heterostructures.
Two prototype transition-metal dichalcogenide (TMDC) materials, MoS2 and MoSe2, have attracted growing attention as promising 2D semiconductors. The heterostructure created by stacking the 2D monolayers in the out-of-plane direction exhibits peculiar properties that can be utilized in electronic applications. The lateral and flexural phonon transport behaviors in MoS2/MoSe2 heterobilayer are comprehensively investigated using classical molecular dynamics simulations. In-plane thermal conductivity (κ) and out-of-plane interfacial thermal resistance (R) are calculated by nonequilibrium molecular dynamics (NEMD) and transient pump–probe methods, respectively. Thermal conductivity of MoS2/MoSe2 bilayer 2D sheet is characterized as 28.8 W/m·K, which preserves the high thermal conductivity of most TMDC materials. The maximum κ reductions of MoS2, MoSe2, and heterobilayer amount to 83.0, 68.9, and 77.1%, respectively, with increasing temperatures from 100 to 500 K. It is also found that the basal-plane thermal performance of MoS2/MoSe2 bilayer will not be affected by interfacial interactions, which is important in industrial applications. The predicted out-of-plane flexural phonon conductance results reveal that heat flux runs preferably from MoS2 to MoSe2 than in the reverse direction.
Nowadays, computer simulations have become a standard tool in essentially all fields of chemistry, condensed matter physics, and materials science. In order to keep up with state-of-the-art experiments and the ever growing complexity of the investigated problems, there is a constantly increasing need for simulations of more realistic, i.e., larger, model systems with improved accuracy. In many cases, the availability of sufficiently efficient interatomic potentials providing reliable energies and forces has become a serious bottleneck for performing these simulations. To address this problem, currently a paradigm change is taking place in the development of interatomic potentials. Since the early days of computer simulations simplified potentials have been derived using physical approximations whenever the direct application of electronic structure methods has been too demanding. Recent advances in machine learning (ML) now offer an alternative approach for the representation of potential-energy surfaces by fitting large data sets from electronic structure calculations. In this perspective, the central ideas underlying these ML potentials, solved problems and remaining challenges are reviewed along with a discussion of their current applicability and limitations.
Two dimensional (2D) MoSe2 and MoS2 monolayers, two prototype transition metal dichalcogenides (TMDCs) materials, have attracted growing interests as promising 2D semiconductors. In this work, thermal conductivity (κ) of the monolayer MoSe2 is computed using large-scale classical non-equilibrium molecular dynamics (NEMD) simulations for the first time. The predicted κ of monolayer MoSe2 with infinite length (or MoSe2 2D sheets) are 43.88 ± 1.33 and 41.63 ± 0.66 W/mK in armchair and zigzag direction, respectively. These simulation results are further confirmed by independent simulations using the Green-Kubo method (GKM) which yields computed κ of 44.38 ± 2.08 and 44.63 ± 2.50 W/mK, respectively. For 2D MoS2 sheet, the computed κ based on the NEMD method are 101.43 ± 1.13 and 110.30 ± 2.07 W/mK, respectively, in armchair and zigzag direction, whereas those based on the GKM are 102.32 ± 6.05 and 108.74 ± 6.68 W/mK, respectively. The predicted κ values of MoS2 monolayer are twice larger than those of MoSe2 monolayer. Both types of 2D monolayers exhibit isotropic properties in thermal conduction. Effects of system dimensions, heat flux, and temperature on κ are investigated comprehensively. The predicted κ value increases monotonically with the system length but decreases with temperature.
Phonons are essential for understanding the thermal properties in monolayer transition metal dichalcogenides. 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 low average atomic mass. We also discuss the competition between mass effect, interatomic bonding and anharmonic vibrations in determining the thermal conductivity of WS2. Strong covalent W–S bonding and low anharmonicity in WS2 are found to be crucial in understanding its much higher thermal conductivity compared to MoSe2.
Atomically thin materials such as graphene and semiconducting transition
metal dichalcogenides (TMDCs) have attracted extensive interest in recent
years, motivating investigation into multiple properties. In this work, we
demonstrate a refined version of the optothermal Raman technique to measure the
thermal transport properties of two TMDC materials, MoS2 and MoSe2, in
single-layer (1L) and bi-layer (2L) forms. This new version incorporates two
crucial improvements over previous implementations. First, we utilize more
direct measurements of the optical absorption of the suspended samples under
study and find values ~40% lower than previously assumed. Second, by comparing
the response of fully supported and suspended samples using different laser
spot sizes, we are able to independently measure the interfacial thermal
conductance to the substrate and the lateral thermal conductivity of the
supported and suspended materials. The approach is validated by examining the
response of a suspended film illuminated in different radial positions. For 1L
MoS2 and MoSe2, the room-temperature thermal conductivities are (84+/-17) W/mK
and (59+/-18) W/mK, respectively. For 2L MoS2 and MoSe2, we obtain values of
(77+/-25) W/mK and (42+/-13) W/mK. Crucially, the interfacial thermal
conductance is found to be of order 0.1-1 MW/m2K, substantially smaller than
previously assumed, a finding that has important implications for design and
modeling of electronic devices.