Symposium DS03—Phonon Properties of Complex Materials—Challenges in Data Generation, Data Availability and Machine Learning Approaches

Thermal transport phenomena are ubiquitous and play a critical role in the performance of various microelectronic and energy-conversion devices. A comprehensive understanding of the underlying heat transfer mechanism through the development of microscopic theories is therefore of fundamental importance, yet it remains elusive because of the challenges arising from explicitly treating higher-order anharmonicity. Recent theoretical and experimental advances have revealed the essential role of quartic anharmonicity in suppressing heat transfer in zinc blende boron arsenide (BAs) with ultrahigh κL. However, critical questions concerning the general effects of higher-order anharmonicity in the broad classes and chemistries of many solids are still unanswered. Using our recently developed high-throughput phonon framework based on first-principles density functional theory calculations, we systematically investigate the lattice dynamics and thermal transport properties of a large number of compounds, with a particular focus on unraveling the impacts of quartic anharmonicity on κL. Our advanced theoretical model for computing κL embraces current state-of-the-art methods, featuring a complete treatment of quartic anharmonicity for both phonon frequencies and lifetimes at finite temperatures, as well as contributions from off-diagonal terms in the heat-flux operator. We illustrate the physical insights gained from studies of a large number of binary rocksalt and zincblende compounds, Tl3VSe4, and Cu12Sb4S13.

Metastable nitrides are an emerging class of materials with potential applications in solar energy conversion, thermoelectrics, power electronics, coatings, and superconductivity. Their unique electronic and bonding characteristics, as well as their general tolerance to structural defects, allow for a wide range of novel, tuneable functionalities. Despite their desirable characteristics, they are relatively unexplored due to their metastability and the comparative difficulty of their synthesis, so that roughly ten times more oxides are reported in the Inorganic Crystal Structure Database (ICSD). Recent synthetic and computational advances, however, make them more accessible and an exciting type of compounds to investigate from both a materials design and a fundamental point of view.
Copper tantalum nitride, CuTaN₂, is a particularly promising candidate system for photovoltaic as well as thermoelectric applications because it exhibits favorable optical properties, is non-toxic, and presumably defect-tolerant. At the same time, it is known to exhibit interesting lattice dynamics, likely related to its thermodynamic metastability, and vibrational anharmonicity that drives a finite-temperature stabilization of the crystal. To investigate the lattice-dynamical properties of CuTaN₂ as a representative of the wider class of metastable ternary nitrides, we combine first-principles molecular dynamics and THz Raman spectroscopy, both performed at various temperatures. This allows for probing the effects of anharmonic phonon-phonon interactions and static as well as dynamic disorder in the material, which provides insights into the extent to which these phenomena impact the mechanism of dynamic stabilization.

Complex argyrodite compounds are attracting intense interest for both solid-state electrolytes owing to their superionic behavior, and for thermoelectric applications owing to their ultralow thermal conducitivities. We present a combined experimental and theoretical investigation of atomic dynamics in the complex superionic argyrodite compound Cu₇PSe₆, rationalizing the atomistic diffusion mechanism and the influence of its soft, anharmonic lattice dynamics. Inelastic neutron scattering (INS) and quasi-elastic neutron scattering (QENS) were performed as a function of temperature, and were complemented with ab-initio molecular dynamics extended to long time scales with the use of machine-learned potentials (MLMD). INS data reveal characteristic changes at the onset of superionic behavior, providing insights into the role of the host lattice dynamics, while QENS probes the superionic Cu diffusion. The MLMD simulations reveal that the long-range Cu diffusion is limited by an inter-cluster hopping step, which is strongly coupled to the host phonon dynamics, and directly match the experimental QENS results. Further, MLMD simulations enable us to capture the ultralow lattice thermal conductivity and its various contributions beyond conventional propagative phonons. These results provide detailed insights into the hybrid atomic dynamics in superionic argyrodites, and supersede the traditional quasiharmonic phonon picture to capture the strong anharmonicity in this complex superionic system.

Computing phonons from first-principles is typically considered a solved problem, yet inadequacies in existing techniques continue to yield deficient results in systems with sensitive phonons, like those with soft modes. Here we circumvent this issue using the lone irreducible derivative (LID) and bundled irreducible derivative (BID) approaches to computing phonons via finite displacements, where the former optimizes precision and the latter, efficiency. The strategy behind the irreducible approaches is to convert gains in efficiency into enhanced accuracy. We illustrate our approach on two prominent charge density wave systems, the shape memory alloy AuZn and the vanadium based kagome metal KV₃Sb₅; in addition to metallic lithium. LID is executed using energy and force derivatives, and practical guidelines are developed. For BID, a bundled basis is derived guaranteeing minimal propagation of error and maximal efficiency, and demonstrating that BID faithfully reproduces the LID results. Comparing our resulting phonons in the aforementioned crystals to the literature reveals nontrivial inaccuracies in all cases. Our approaches' unbiased execution can be fully automated, making it well suited for both niche systems of interest and big data approaches.

The high degree of scattering of phonons from compositional disorder in high entropy thermoelectric alloys is predicted to dramatically reduce thermal conductivity and thereby improve thermoelectric performance. Here, we apply a reformulated Klemens model to compute the thermal conductivity of multicomponent alloys. We show that for a given scattering mechanism, such as phonon scattering from mass contrast, scattering is maximized along the binary with the highest mass contrast. The addition of an intermediate size atom reduces the phonon scattering, instead of increasing it. Therefore, the larger atomic disorder does not necessarily lead to the lowest thermal conductivity. Our results suggest that to further increase phonon scattering a second independent scattering mechanism must be targeted. For example, alloy substitution that adds strain fluctuation to an existing mass fluctuation will tend to increase phonon scattering and further lower thermal conductivity.

The attenuation rate of vibrational excitations in various metallic liquids and glasses has been reported to change from the quadratic dependence on wavevector at low wavevectors to the linear dependence at high wavevectors. However, the origin of this behavior is not clear. Here, the analysis of this phenomenon through molecular dynamics is presented for prototypical metallic liquids, Cu₅₆Zr₄₄ and Fe. It is shown that the crossover wavevector is strongly correlated with structural coherence lengths characterizing coarse-grained density correlations. We suggest that the linear dependence is caused by scattering of vibrational excitations by structural activation processes with low activation energies which are distinctively observed in metallic systems.
*This work was supported by the U.S. Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences, Materials and Science and Engineering Division.

Nanostructured porosity has been shown to substantially impede phonon transport in semiconducting materials with comparably less detriment to electrical transport, thereby improving their thermoelectric efficiency. Current strategies focus on increasing phonon scattering and reducing the mean-free-path of phonons across the spectrum. In previous work, we identified an unusual anticorrelated specular phonon scattering effect that resulted in a decrease of up to 80% in the thermal conductivity of close-packed ordered pores compared to non-close-packed ordered pores, at equivalent porosities. In this work, we have determined that this reduction in thermal conductivity stems from the heat trapping of phonons between the pores, resulting in anticorrelated heat flux fluctuations and consequently the super-suppression of mean-free-paths below the characteristic length of the nanostructuring. This realization offers a route for minimizing thermal conductivity by affecting large mean-free-paths (and thus long wavelengths) preferentially, as well as the possibility for the design of ‘band-pass’ phonon filtering. These results stem from large-scale equilibrium molecular dynamics (MD) simulations of nanoporous silicon which have been corroborated through the development of a ray-tracing model that allowed us to identify a unique signature in the heat current autocorrelation function of different forms of correlated scattering. We further present a map, based on the ray tracing analysis, of experimentally accessible geometries where mean-free-path super suppression is expected to occur.

In heat conduction through a homogenous nanomaterial, various phonons may exhibit diverse temperatures even at the same location at a steady state, known as the local phonon nonequilibrium phenomenon. Different phonons are often considered to behave independently, and the phonons with longer mean free paths (MFPs) have smaller temperature gradients. That is, the temperature gradient exhibits the following order: ballistic phonons < semiballistic phonons ≈ lattice (average) temperature gradient < diffusive phonons, where ballistic phonons have MFPs much larger than the characteristic length, semiballistic phonons have MFPs like the characteristic length, and diffusive phonons have MFPs much smaller than the characteristic length. However, in this paper, we reveal that the effect of phonon-phonon coupling leads nonequilibrium phonon temperature gradients to the following trend: diffusive phonon temperature gradients will decrease to the lattice temperature, and temperature gradients of some semiballistic phonons even surpass that of diffusive phonons. The diffusive phonon temperature is merged onto the lattice temperature since they have large scattering rates and can be equilibrated quickly to the lattice temperature after traveling for a short distance away from the boundaries into the nanomaterial. The semiballistic phonons have large scattering rates but not large enough to bring them down to the lattice temperature. To obtain a further understanding of the nonequilibrium phonon temperatures, we have also derived a simple analytical model which can accurately predict the temperature profiles of all individual phonons given their MFPs. Using this model, we find that, near the boundary, phonon temperatures decay with position exponentially (instead of linearly), with a rate inversely proportional to their MFPs. Our findings offer insight for the understanding and prediction of phonon nonequilibrium temperatures within nanodevices.

Molecular dynamics (MD) simulations are important tools to study atomic and molecular systems in material science. Integrating the MD equations of motion with the Green's function formalism has allowed to probe vibration processes in larger time scales than the ones achieved by the conventional MD velocity-Verlet algorithm [1,2]. In the Green's function MD (GFMD), the total interaction potential is expanded up to the quadratic terms enabling an exact solution of the equations of motion for problems within the harmonic approximation, reasonable energy conservation, and fast temporal convergence. However, due to the high computational cost, mainly caused by the diagonalization of the dynamical matrix within its main loop, the use of GFMD has been limited. In this work, we were able to accelerate GFMD simulations by treating the full system (N atoms) as a collection of smaller systems. Diagonalization is then performed for smaller dynamical matrices rather than the one for the full system. The eigenvalues and eigenvectors are then used in the GFMD equations to update the atomic positions and velocities. We have applied the method for one-dimensional lattices of oscillators and found a fast convergence to the exact solution as the size of the smaller systems increases. The computational time of the proposed method scales linearly with N, providing a considerable gain with respect to the N³ cost of the diagonalization of the full dynamical matrix. Results from a parallel version using OpenMP show a speed up of 14x for N = 50000 in affordable computers. The method also exhibits better accuracy and energy conservation than the conventional velocity-Verlet algorithm.These findings indicate that GFMD can be an alternative integration technique for molecular dynamics simulations.
[1] V.K. Tewary, Extending the time scale in molecular dynamics simulations: Propagation of ripples in graphene, Phys. Rev. B 80 (2009) 161409.
[2] V.R. Coluci, S.O. Dantas, V.K. Tewary, Generalized green's function molecular dynamics for canonical ensemble simulations, Phys. Rev. E 97 (2018) 053310.

In heat conduction through a homogenous nanomaterial, various phonons may exhibit diverse temperatures even at the same location at a steady state, known as the local phonon nonequilibrium phenomenon. Different phonons are often considered to behave independently, and the phonons with longer mean free paths (MFPs) have smaller temperature gradients. That is, the temperature gradient exhibits the following order: ballistic phonons < semiballistic phonons ≈ lattice (average) temperature gradient < diffusive phonons, where ballistic phonons have MFPs much larger than the characteristic length, semiballistic phonons have MFPs like the characteristic length, and diffusive phonons have MFPs much smaller than the characteristic length. However, in this paper, we reveal that the effect of phonon-phonon coupling leads nonequilibrium phonon temperature gradients to the following trend: diffusive phonon temperature gradients will decrease to the lattice temperature, and temperature gradients of some semiballistic phonons even surpass that of diffusive phonons. The diffusive phonon temperature is merged onto the lattice temperature since they have large scattering rates and can be equilibrated quickly to the lattice temperature after traveling for a short distance away from the boundaries into the nanomaterial. The semiballistic phonons have large scattering rates but not large enough to bring them down to the lattice temperature. To obtain a further understanding of the nonequilibrium phonon temperatures, we have also derived a simple analytical model which can accurately predict the temperature profiles of all individual phonons given their MFPs. Using this model, we find that, near the boundary, phonon temperatures decay with position exponentially (instead of linearly), with a rate inversely proportional to their MFPs. Our findings offer insight for the understanding and prediction of phonon nonequilibrium temperatures within nanodevices.

Thermal conductivity is an important property for developing applications in energy harvesting, thermal dissipation, and quantum computing. One of the most used approach to predict the thermal conductivity is by integrating the heat flux auto-correlation function determined by equilibrium molecular dynamics simulations. To achieve accurate predictions for the thermal conductivity, long simulations (~ 100 ns) are usually required. Carrying out such simulations using conventional molecular dynamics is a formidable task even for modern computers. Alternatively, Green's function molecular dynamics (GFMD) simulations have been proven to extend the simulation time scale by 6-8 orders of magnitude (pico to microseconds) and to provide accurate trajectories in the phase space in certain idealized non-linear elastic problems [1,2]. These aspects suggest that GFMD can be a promise technique to calculate the thermal conductivity. Thus, in this work, we applied GFMD simulations, coupled with the Green-Kubo technique, to study the effect of simulation parameters (e.g. time-step size and correlation time) on the convergence of the auto-correlation function in idealized 1D and 2D systems. We have found GFMD is able to correctly describe the velocity autocorrelation function - a commonly used function in molecular dynamics simulations to probe phonon density of states – especially for time ranges related to low-frequency phonons, which contribute significantly to the thermal conductivity. Results also indicated that GFMD can reduce the averaging and time integration errors in estimations of the thermal conductivity.

[1] V.K. Tewary, Extending the time scale in molecular dynamics simulations: Propagation of ripples in graphene, Phys. Rev. B 80 (2009) 161409.
[2] V.R. Coluci, S.O. Dantas, V.K. Tewary, Generalized green's function molecular dynamics for canonical ensemble simulations, Phys. Rev. E 97 (2018) 053310.

Molecular dynamics (MD) simulations are important tools to study atomic and molecular systems in material science. Integrating the MD equations of motion with the Green's function formalism has allowed to probe vibration processes in larger time scales than the ones achieved by the conventional MD velocity-Verlet algorithm [1,2]. In the Green's function MD (GFMD), the total interaction potential is expanded up to the quadratic terms enabling an exact solution of the equations of motion for problems within the harmonic approximation, reasonable energy conservation, and fast temporal convergence. However, due to the high computational cost, mainly caused by the diagonalization of the dynamical matrix within its main loop, the use of GFMD has been limited. In this work, we were able to accelerate GFMD simulations by treating the full system (N atoms) as a collection of smaller systems. Diagonalization is then performed for smaller dynamical matrices rather than the one for the full system. The eigenvalues and eigenvectors are then used in the GFMD equations to update the atomic positions and velocities. We have applied the method for one-dimensional lattices of oscillators and found a fast convergence to the exact solution as the size of the smaller systems increases. The computational time of the proposed method scales linearly with N, providing a considerable gain with respect to the N³ cost of the diagonalization of the full dynamical matrix. Results from a parallel version using OpenMP show a speed up of 14x for N = 50000 in affordable computers. The method also exhibits better accuracy and energy conservation than the conventional velocity-Verlet algorithm.These findings indicate that GFMD can be an alternative integration technique for molecular dynamics simulations.
[1] V.K. Tewary, Extending the time scale in molecular dynamics simulations: Propagation of ripples in graphene, Phys. Rev. B 80 (2009) 161409.
[2] V.R. Coluci, S.O. Dantas, V.K. Tewary, Generalized green's function molecular dynamics for canonical ensemble simulations, Phys. Rev. E 97 (2018) 053310.

The axial thermal conductivity of polymer chain lattices usually exhibits an interesting one-dimensional (1D) to three-dimensional (3D) transition in the phonon heat conduction where polymer chains in a lower dimension have a higher axial thermal conductivity. For example, a single polyethylene or polydimethylsiloxane chain has a higher axial thermal conductivity than the double-chain or crystal counterparts due to the chain-chain anharmonic scatterings. We show that this trend can be the opposite in poly(para-phenylene) (PPP). Molecular dynamics simulations were performed to study the thermal transport in PPP chains from 1D to 3D. The axial thermal conductivity of PPP chains shows an anomalous dimensionality dependence where the thermal conductivity increases from 1D to 3D crystalline structure. The confinement of the rotation of benzene rings and the formation of long-range order is observed by analyzing the dihedral angle probability distribution, which is further confirmed by the temperature-dependent thermal conductivity results. Our simulation results provide a new perspective to search for thermally conductive polymers.

The metal-organic–framework (MOF) MIL-53 has a framework geometry with a wine-rack motif that enables it to transition between open and closed structures either under pressure or due to gas sorption. Here we show that in these breathing MOFs the thermal conductivity, an important property for gas sorption performance, also changes between the open and closed-pore conformations. We present a very simple geometric network model of conductivity in these materials that underpins the base trend of the thermal conductivity and test it against equilibrium molecular dynamics thermal conductivity calculations. In addition, a self-consistent-charge density functional tight binding (SCC-DFTB) approach using the DFTB+ software package has been used to compute phonon properties for both the open- and closed-pore MIL-53(Al). While we observe only small changes in the density of states between both configurations, the dispersion relations suggest the emergence of rattling behavior due to the geometric changes in the framework. A phenomenon of considerable technological interest in the phonon transport community is Phonon focusing, which has been proposed to enable materials with ultra-low thermal conductivity. Our work indicates that the anisotropy in the thermal conductivity stems from a phonon focusing effect tempered by scattering from the non-propagating rattler modes.

Nanostructured porosity has been shown to substantially impede phonon transport in semiconducting materials with comparably less detriment to electrical transport, thereby improving their thermoelectric efficiency. Current strategies focus on increasing phonon scattering and reducing the mean-free-path of phonons across the spectrum. In previous work, we identified an unusual anticorrelated specular phonon scattering effect that resulted in a decrease of up to 80% in the thermal conductivity of close-packed ordered pores compared to non-close-packed ordered pores, at equivalent porosities. In this work, we have determined that this reduction in thermal conductivity stems from the heat trapping of phonons between the pores, resulting in anticorrelated heat flux fluctuations and consequently the super-suppression of mean-free-paths below the characteristic length of the nanostructuring. This realization offers a route for minimizing thermal conductivity by affecting large mean-free-paths (and thus long wavelengths) preferentially, as well as the possibility for the design of ‘band-pass’ phonon filtering. These results stem from large-scale equilibrium molecular dynamics (MD) simulations of nanoporous silicon which have been corroborated through the development of a ray-tracing model that allowed us to identify a unique signature in the heat current autocorrelation function of different forms of correlated scattering. We further present a map, based on the ray tracing analysis, of experimentally accessible geometries where mean-free-path super suppression is expected to occur.

Modeling and simulation are critical for predicting the performance and safety of high explosives (HE), in particular their response to moderate insults in accident scenarios. Thermal conductivity, notably, is a key component of HE modeling: heat localization leads to the creation of “hot spots” where chemical reactions occur, ultimately causing events such as deflagration of detonation; heat conduction limits the temperatures accessible in hot spots and thus has a major impact on these phenomena. However, experimental information on thermal conductivity is usually scarce, and rarely accounts for temperature, pressure, and orientation dependence, which are critical input to higher-scale simulations. In this work, we use reverse non-equilibrium molecular dynamics (RNEMD) to determine the thermal conductivity of three important HEs: orthorhombic α-1,3,5-trinitro-1,3,5-triazinane (α-RDX), monoclinic β-1,3,5,7-tetranitro-1,3,5,7-tetrazoctane (β-HMX), and tetragonal pentaerythritol tetranitrate (PETN). Importantly, we compute the full thermal conductivity tensor for these compounds, as a function of temperature and pressure, allowing for the determination of heat transport in any direction, and for thermodynamic conditions that span the stability range of the material.

Thermal barrier coating (TBC) is a system to protect hot components of gas turbine or aviation engine operating at harsh environment. Ceramic materials with low thermal conductivity and excellent thermal durability have been employed as TBC material. Yttria-stabilized zirconia (YSZ) is conventionally used as a TBC material. However, there is increasing demand for further thermal insulating material which is applicable in a higher operating temperature above 1200 degrees for higher thermal conversion efficiency. In this study, a high-entropy approach was employed to design a new single-phase A₂B₂O₇ oxide for thermal insulation applications. Multicomponent high-entropy oxides, containing up to seven different cations, were successfully synthesized in a single defective fluorite structure. We observed that the integration of the functional cation Zn²⁺ effectively blocks thermal radiation by reducing the phonon mean free path and further reduces high-temperature thermal conductivity due to the larger free carrier concentration resulting from a large number of oxygen vacancies. Although a large amount of Zn²⁺ slightly reduced thermal expansion, this study suggests that functional cations can be easily integrated above the general doping level.

In the last two decades, solutions of the Boltzmann transport equation for phonons based on first principles have become a mainstream tool to obtain parameter-free estimates of the thermal conductivity of crystalline solids. More recently, such approaches have been successfully extended to systems with a lower degree of translation symmetry, including crystals with defects, interfaces between bulk crystals, and heterogeneous nanostructures. The key ingredients in the basic formulation of those methods are second- and third-order interatomic force constants (IFCs), i.e., second- and third-order derivatives of the potential energy with respect to atomic displacements around the equilibrium position. Even for a single crystal and taking full advantage of symmetry, a direct calculation of all the required IFCs typically requires three orders of magnitude more computational effort than the local minimization used to find that equilibrium. IFC calculations are therefore a major limiting factor to even more widespread use of these methods. Problems can quickly become intractable when large localized defects, complex unit cells, multiple phases, collections of several materials, explicit temperature dependences or higher-order IFCs come into play, all of which are common requirements in realistic materials for technological applications.

In this talk, I will discuss several possible strategies to accelerate IFC calculations in realistic situations, with an analysis of their advantages and drawbacks based on experience with practical applications. Machine-learning models constitute the foundation of all of these approaches, but several clearly distinct families can be identified. A first possibility is to use first-principles data for the material under study only, trying to make more efficient use of the information than in a direct IFC calculation. Techniques in this category include high-dimensional neural-network interatomic potentials, high-order Taylor expansions, differentiable code, and regression models for the IFCs themselves. The critical issue of local vs. global approximations of the potential energy surface will be addressed in detail in connection with this family. An alternative is to exploit regularities in the IFC tensors of a family of compounds in the context of a high-throughput calculation. To conclude, I will discuss the possibility of avoiding IFC calculations altogether by switching to other families of methods, and how machine learning models shift the traditional value propositions of those.

The anharmonic phonon properties of type-I filled inorganic clathrates Ba8 Ga16 Ge30 and Sr8 Ga16 Ge30 are obtained from the first-principles calculations by considering the temperature-dependent sampling of the potential energy surface and quartic phonon renormalization. Owing to the weak binding of guest atoms with the host lattice, the obtained guest modes undergo strong renormalization with temperature and become stiffer by up to 50% at room temperature in Sr8Ga16Ge30. The calculated phonon frequencies and associated thermal mean squared displacements are comparable with experiments despite the on-centering of guest atoms at cage centers in both clathrates. Lattice thermal conductivities are obtained in the temperature range of 50- 300 K accounting for three-phonon scattering processes and multi-channel thermal transport. The contribution of coherent transport channel is significant at room temperature (13% and 22% in Ba8Ga16Ge30 and Sr8Ga16Ge30) but is insufficient to explain the experimentally observed glass-like thermal transport in Sr8Ga16Ge30.

Fueled by our abilities to compute materials properties and characteristics orders of magnitude faster than they can be measured and recent advancements in harnessing literature data, we are entering the era of the fourth paradigm of science: data-driven materials design. The Materials Project (www.materialsproject.org) uses supercomputing together with state-of-the-art quantum mechanical theory to compute the properties of all known inorganic materials and beyond, design novel materials and offer the data for free to the community together with online analysis and design algorithms. The current release contains data derived from quantum mechanical calculations for over 150,000 materials and millions of properties. The resource supports a growing community of data-rich materials research, currently supporting over 200,000 registered users and tens of millions of data records are served each day through the API. In this talk we will focus on our efforts relevant to vibrational properties and their connection to phase transformations. The Materials Project currently disseminates phonon dispersion curves for over 2,000 materials, including their corresponding entropy and heat capacity. The data has provided rich information on phase stability and even allowed for design of novel multiferroic materials. Formulating an automatic algorithm for identifying shortest path transformation between polymorphs, we are exploring the vast landscape of phonon-enabled, diffusion-less phase transformations; which is anticipated to aid the design of novel materials with emergent properties.

The microscopic manifestation of temperature in lattice dynamics is generally understood through the harmonic approximation, where atomic motion is mapped onto a set of vibrational normal modes (i.e., phonons). Modern studies into lattice dynamics of solids significantly expand on this view to account for anharmonic phenomena such as thermal expansion and phase transitions. In contrast, studies into the electronic properties of solids rarely go beyond a quasi-harmonic treatment.
We combine ab-initio simulations and Raman scattering measurements to demonstrate explicit anharmonic effects in the temperature dependent dielectric response of a NaCl single crystal. Measuring the temperature evolution of its Raman spectrum demonstrates the necessity of including anharmonic lattice dynamics to explain the dielectric response of NaCl, as it is manifested in Raman scattering.
We discuss how considering an experimentally accessible tensor structure for inelastic light scattering can account for anharmonic spectra, while also directly incorporating all relevant symmetry constraints.

First principles and atomistic simulations play a significant role in the study of phonon properties of materials. There are several important questions regarding these simulations, such as how equilibrium and non-equilibrium molecular dynamics (MD) approaches compare with density functional theory (DFT)-based anharmonic phonon interaction approaches, what are the phonon transport properties in mixed-dimensional systems, and how machine learning can be used to determine phonon properties such as vibrational spectra. In this talk, we will discuss comparisons of MD and DFT-based approaches for thermal conductivity simulations, different MD approaches for thermal conductivity prediction of mixed-dimensional and complex nanostructured systems, and discuss machine learning prediction of vibrational spectra.

TBD

Coherence of thermal excitations is a long-standing and general problem in physics. The conventional theory of the phonon gas model indeed does not include coherence and its impact on thermal transport.
We propose a general heat conduction formalism based on theoretical arguments and direct atomic simulations, which bridges conventional phonon gas model and the wave picture of thermal phonons.

By naturally introducing wavepackets in the fundamental heat flux expression [1], we derive an original thermal conductivity formula where coherence times and life-times appear [2]. We apply the theory to a complex crystal where interatomic potentials are optimized by a Machine Learning procedure. The simulation reveals an intrinsic and a -previously investigated- mutual coherence appearing in two different temperature ranges.

[1] Zhongwei Zhang, Yangyu Guo, Marc Bescond, Jie Chen, Masahiro Nomura, and Sebastian Volz, Generalized decay law for particlelike and wavelike thermal phonons, Physical Review B 103(18):184307.
[2] Z. Zhang, Y. Guo, M. Bescond, J. Chen, M. Nomura and S. Volz, Heat conduction theory including phonon coherence. Physical Review Letters, accepted.

In this talk we will discuss our efforts for predicting the transport properties of materials from first principles simulations, which span over both the development of novel methods for studying materials transport properties and the development of software for increasing the speed and accuracy of transport simulations.
First, we will discuss the thermoelectric transport properties of Bi₂Se₃. The transport properties of this narrow gap semiconductor are not precisely captured by semiclassical transport models. Not only is Bi₂Se₃ characterized by bipolar transport, given that the carrier’s gap is comparable to thermal energy, transport is also dominated at low doping concentrations by Zener tunneling. This mechanism allows carriers to tunnel between valence and conduction band and thus carrying charge by hopping between states, rather than charge diffusion under the action of an electric field. Here we show how to describe this phenomenon using a novel first-principles model based on the Wigner distribution. Surprisingly, we find that Zener tunneling doesn’t just involve low-energy carriers, but occurs also between band subvalleys of energy larger than the band gap, thanks to a combination of strong dipole interactions and large density of states.
Next, we will discuss the latest developments of Phoebe, an open-source software for computing thermoelectric properties, capable of solving both phonon and electron Boltzmann equations. Phoebe can compute electron-phonon and phonon-phonon scattering properties from first-principles simulations. In a single package, it is now possible to fully characterize the thermoelectric transport properties of a material from ab-initio simulations. The software has been designed to take advantage of the latest high-performance computing architectures, and implemented an efficient mix of MPI, OpenMP and GPU acceleration strategies, allowing us to simulate more complex materials.

Control of heat conduction through the manipulation of phonons as coherent waves have been attracted great interest for the advanced thermal management [1]. Although smooth interfaces were reported to be obtained in artificial superlattices, preparation of coherent interfaces for terahertz phonons having nanoscale periodicity with atomic-scale perfection are still challenging since MOCVD and MBE were nonequilibrium growth process. Therefore, we focus on natural superlattice titanium oxides, in which periodic structures are obtained as thermodynamically stable phases. A homologous series of the titanium oxides is so-called crystallographic shear (CS) structure, in which planar faults are periodically introduced in the mother rutile structure with their spacing depending on the oxygen. Recently we have revealed that the titanium oxide with CS structure possesses the pristine interface, which is expected to behave as coherent interface for almost all phonons [2]. Furthermore, we have successfully demonstrated the tuning of the interspacing in the CS planes in titanium oxides by the addition of chromium oxides to form oxygen deficiency [3]. In the present study, we have investigated thermal conduction in bulk titanium oxide natural superlattices with CS structures prepared by reductive annealing of rutile TiO₂ and crystal growth by the floating zone method. High-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) revealed that (132)_rutile and (121)_rutile CS planes with interspacings of 2.7 and 1.0 nm were introduced in the mother rutile structure. Time-domain thermoreflectance (TDTR) revealed that the thermal conductivity decreased by the introduction of CS planes, but that the decrease is not monotonic with increasing density of CS planes. Calculation of the thermal conductivity and the mean free path for phonons revealed that a crossover from incoherent to coherent thermal conduction took place, and coherent interfaces with nanoscale periodicity were formed as thermodynamically stable phases in bulk titanium oxide natural superlattices.
[1] M. Maldovan, Nature 503 (2013) 209–217.
[2] S. Harada et al., J. Phys. Chem. C 125 (2021) 11175–11181.
[3] S. Harada, S. Sugimoto et al., J. Phys. Chem. C 125 (2021) 15730–15736.

Material systems with nanometer feature sizes exhibit exotic properties and behaviors beyond those observed for bulk materials. Moreover, at nanometer length scales, conventional macroscopic models of materials often fail to accurately describe their physical behavior while traditional measurement techniques struggle to precisely access their functional properties. In particular, thermal transport in nanoscale geometries can differ significantly from bulk models. As the length scales approach the dominant mean free paths of the heat carriers, the phenomenological model of heat diffusion no longer accurately captures the observed behavior, even for nanoscale heat sources on a bulk substrate [1,2]. In such situations, thermal transport cannot be accurately predicted for nanodevices: fundamental models are often too computationally intensive for multi-scale complex geometries while phenomenological models require too many fitting parameters or calibrations to be predictive. Observing and modeling nanoscale heat flow in complex systems is critical to not only improve existing technologies—such as thermal management in nanoelectronics and improved thermoelectrics—but also for new thermal diodes and communication devices.
In this work, we advance both experimental characterization and theoretical predictions for heat flow away from nanoscale heat sources. By utilizing tabletop sources of ultrafast, coherent extreme ultraviolet (EUV) pulses produced via high harmonic generation [3], we uncover non-diffusive thermal transport behavior away from nanostructured heat sources of varying geometries on a variety of materials. In previous work, we revealed a novel and counter-intuitive thermal transport behavior—that closely-packed nanoscale hot spots cool faster than when widely spaced [2,4]. Here, we map the transient, non-diffusive heat flow away from both 1D- and 2D-confined nanoscale heat sources on bulk silicon experimentally demonstrating, for the first time, that closely-spaced 2D-confined heat sources cool faster than widely spaced ones, and that this effect is larger in the 2D- than the 1D-confined geometry [5]. Additionally, we measure the heat dissipation efficiency from similar heat source geometries on a diamond substrate, where longer mean free paths and higher amounts of normal scattering are present.
To understand and predict these novel behaviors, we apply advanced mesoscopic and microscopic theoretical models to capture the interplay between heat source geometry and heat dissipation efficiency. From a mesoscopic viewpoint, we demonstrate that the kinetic-collective model, based on a hydrodynamic-like transport equation with ab initio calculated parameters, predicts the full thermomechanical response of both 1D- and 2D-confined nanostructured transducers on silicon without the need for geometrical fitting parameters [5]. This hydrodynamic identifies two relaxation time-scales and their associated fundamental mechanisms: specifically, a fast time-scale due to the thermal boundary resistance and a longer time scale arising from hydrodynamic-like effects. From a microscopic viewpoint, we utilize advanced atomic-level simulations to capture the fundamental mechanism responsible for the counter-intuitive behavior of enhanced cooling efficiency in closely-spaced heat sources observed by previous experiments [3-5]. Specifically, we show that for heat source periodicities below the phonon mean free path of the substrate, an enhancement of in-plane phonon-phonon scattering leads to increased cross-plane conduction, or directional channeling of thermal transport, a novel phenomenon.
[1] Nat. Mater. 9, 26 (2010). [2] Proc. Natl. Acad. Sci. 112, 4846 (2015). [3] Science 280, 1412 (1998). [4] Phys. Rev. Appl. 11, 024042 (2019). [5] ACS Nano 15, 13019 (2021). [6] Proc. Natl. Acad. Sci. 118, e2109056118 (2021).

Raman spectroscopy captures materials’ vibrational properties in the form of highly resolved fingerprints with characteristic peaks. However, connecting Raman spectra to underlying structural and chemical attributes can be nontrivial, and first principles calculations typically incur a high computational cost. In this work, we apply machine learning methods to address the challenges associated with obtaining Raman spectra from comparatively low-dimensional inputs, which consist only of accessible structural information and single-atom properties. Using an objective function inspired by optimal transport, we first train an autoencoder to obtain learned, low-dimensional representations of Raman spectra. These representations serve as effective prediction targets for more economical machine learning models that then recover Raman spectra from materials’ structural and chemical attributes. To address the limited data available for training these models, we employ the symmetry-constrained Euclidean neural networks¹, which have been used to successfully predict phonon densities of states from limited training samples owing to their restricted functional space². We apply our proposed framework to ab initio Raman spectra of 2D materials and further investigate its application to experimental Raman spectra from spectral databases of mineral compounds with varying complexity. Our approach enables rapid prediction of Raman spectra from structures which accelerates the interpretation of Raman spectroscopy data.

Boltzmann transport equation (BTE) is an ideal tool to describe the multiscale phonon transport phenomena, which are critical to applications like microelectronics cooling. Numerically solving phonon BTE is extremely computationally challenging due to the high dimensionality of such problems, especially when mode-resolved properties are considered. In this work, we demonstrate a data-free deep learning scheme, physics-informed neural network (PINN), to efficiently solve phonon BTE for multiscale thermal transport problems with the consideration of phonon dispersion and polarization. In particular, a PINN framework is devised to predict the phonon energy distribution by minimizing the residuals of governing equations and boundary conditions, without the need for any labeled training data. Moreover, geometric parameters, such as the characteristic length scale, are included as a part of the input to PINN, which enables learning BTE solutions in a parametric setting. In addition, this deep learning scheme can effectively eliminate the need of the usually implemented small temperature assumption to linearize the BTE. The effectiveness of the present scheme is demonstrated by solving a number of phonon transport problems in different spatial dimensions (from 1D to 3D). Compared to existing numerical BTE solvers, the proposed method exhibits superiority in efficiency and accuracy, showing great promises for practical applications, such as the thermal design of electronic devices.

Aperiodic superlattices can localize coherent phonons, leading to low thermal conductivities that can potentially beat the amorphous material limit. The rational design of disorders in the layer thickness of aperiodic superlattice is essential for minimizing its thermal conductivity. In this work, we combine atomistic simulations with machine learning to investigate several critical aspects of phonon properties of aperiodic superlattices.
First, we have identified several structural parameters that can effectively describe the level of disorder in the layer thickness of aperiodic superlattices. Those disorder parameters were found to improve the efficiency of machine-learning prediction and optimization of thermal conductivity of aperiodic superlattices.
Second, we have analyzed the contribution of coherent phonons and incoherent phonons to the overall thermal conductivity of aperiodic and periodic superlattices. Currently, it is still unclear how and to what extent a change in temperature impacts the relative contributions of coherent and incoherent phonons to thermal transport in superlattices. Some seemingly conflicting computational and experimental observations of the temperature dependence of lattice thermal conductivity make the thermal transport behaviors in superlattices even more elusive. Herein we demonstrate that incoherent phonon contribution to thermal transport in superlattices increases as the temperature increases due to elevated inelastic interfacial transmission. On the other hand, the coherent phonon contribution decreases at higher temperatures due to elevated anharmonic scattering. The competition between these two conflicting mechanisms can lead to different trends of lattice thermal conductivity as temperature increases, i.e. increasing, decreasing, or non-monotonic. Finally, we demonstrate that the neural network-based machine learning model can well capture the coherent–incoherent transition of lattice thermal transport in the superlattice, which can greatly aid the understanding and optimization of thermal transport properties of superlattices.

Machine learning has emerged as a promising tool for science and engineering, and in this talk we show our recent work in developing machine learning approaches to optimize or even disrupt thermal transport science.

In the optimization case study, we demonstrate that an intuition-based manual search for aperiodic superlattice structures (random multilayers or RMLs) with the lowest thermal conductivity yields only a local minimum, while a genetic algorithm (GA) based approach can efficiently identify the globally minimum thermal conductivity by only exploring a small fraction of the design space. Our results show that this minimum value occurs at an average RML period that is, surprisingly, smaller than the period corresponding to the minimum SL thermal conductivity. Moreover, the lower limit of the thermal conductivity occurs at a moderate rather than maximum randomness of the layer thickness.

In the disruption case study, we recognize that discovering exceptions has been a major route for advancing sciences but a challenging and risky process. Machine learning has shown effectiveness in high throughput search of materials and nanostructures, but using it to discover exceptions has been out of the norm. In this example we demonstrate the use of genetic algorithm to discover unexpected thermal conductivity enhancement in disordered 2D nanoporous graphene and 1D aperiodic superlattices, as compared to their periodic counterparts. Through structural analysis, we proposed that such unusual enhancement in 2D is due to the effect of shape factor and channel factor dominating over that of the phonon localization. In 1D, it is due to the coherent interfaces that suppress thermal resistance. Such findings not only provide insights in thermal transport in disordered materials but also demonstrate the effectiveness of machine learning to discover small probability events and the intriguing physics behind.

Anomalously high inelastic scattering intensity of cubic, Raman inactive perovskites (e.g. BaTiO₃ and SrTiO₃) has been a long-standing problem in material science. Such high intensity of the Raman inactive phases cannot be rationalized by existing models. This problem became more prominently urgent after the emergence of halide perovskites (e.g. CsPbBr₃) as excellent photovoltaic materials. The broad features in the Raman spectra of both halide and oxide perovskites has been attributed to light scattering by anharmonic fluctuations which are responsible for their unique and efficient optoelectronic performance.
We hypothesize that the enhanced Raman scattering of oxide perovskites also originates from their anharmonic nature, i.e. their disordered structure. However, anharmonic fluctuations cannot be modeled with classical perturbation theory and require molecular dynamics simulations.
In this work, we present an analytical model to explain the enhanced Raman scattering in both oxide and halide perovskites as well as their unique temperature dependence. We use perturbation theory to the cubic structure, while modeling the effect of anharmonicity as a disordered mode. We show that the disorder enhances high order scattering in the otherwise, Raman inactive perovskites. Moreover, we show that the disorder induced enhancement correlates well with the dielectric function at low frequencies, and that in ferroelectric phase transition this disordered mode is responsible for first order Raman scattering that appears as a ‘central peak’.
This model in not exclusive to cubic perovskites and can be employed to explain light scattering in other cubic materials as well as lower symmetry disordered phases which exhibit very broad Raman features.

Databases of computed materials properties are revolutionizing the way materials science is done. A large body of materials properties such as formation energies, band gap, or elastic constants are nowadays available in major computational databases such as the Materials Project, AFLOW or OQMD.
Here, we report on a large database of highly converged phonons obtained using density functional perturbation theory (DFPT). DFPT offers the advantage of not requiring supercells and providing direct access to derived quantities such as electron-phonon coupling matrices. We first discuss how the parameters (k-point, q-point densities, …) have been selected and the high-throughput infrastructure developed to automatically run these computations. We then present the data of more than 2,000 phonons and how it is available on the Materials Project (http://www.materialproject.org). A use case will be presented as well where new ferroelectric materials are detected using this phonon database. This approach identifies A4X2O anti-Ruddlesen-Popper materials as new ferroelectric and even magnetoelectric multiferroic materials. We will also report on our current work in automation of electron-phonon computations and the development of a database of transport properties including full electron-phonon interactions.
The cost of high-quality phonons computations makes challenging to cover all the structures present in the Materials Project database. Machine learning is an obvious path to bypass full phonon computations and we will also highlight our recent work on predicting vibrational entropy using neural networks.

Controlling thermal conductivities of materials is important for a wide range of applications, from thermoelectrics for clean energy generation to electronic devices and thermal barrier coatings. The thermal conductivity is commonly estimated using molecular dynamics simulations within the Green-Kubo formulation. This requires a force field that is both 1) an accurate estimate of the interatomic interactions and 2) fast enough to allow simulations with sufficiently large length and time scales. Traditionally, only empirical force fields have fulfilled both of these requirements, which severely limits the applicability of the method.

In this work, we employ the Gaussian Process-based FLARE force field, which automatically learns the interactions of more complex materials than empirical force fields. The resulting model can then be mapped to a low-dimensional, computationally efficient model. Through GPU-acceleration with LAMMPS and the Kokkos library, we achieve excellent performance and obtain well-converged estimates for the thermal conductivity. Furthermore, we investigate state-of-the-art sampling and spectral denoising methods for further acceleration of the simulations.

The Seebeck coefficient and electrical conductivity are two central quantities to be optimized simultaneously in designing thermoelectric materials, and they are determined by the dynamics of carrier scattering. We uncover a new regime where the presence of multiple electron bands with different effective masses, crossing near the Fermi level, leads to strongly energy-dependent carrier lifetimes due to intrinsic electron-phonon scattering. In this anomalous regime, electrical conductivity decreases with carrier concentration, Seebeck coefficient reverses sign even at high doping, and power factor exhibits an unusual second peak. We explain the origin and magnitude of this effect using a general simplified model as well as first-principles Boltzmann transport calculations in recently discovered half-Heusler alloys. We identify general design rules for using this paradigm to engineer enhanced performance in thermoelectric materials.

Understanding thermal phonon transport processes is essential to designing nano-materials and devices with desired thermal transport properties for thermal energy conversion and management. Despite the significant progress in thermal transport of simple inorganic crystals, phonon transport in complex structures and across interfaces remains largely unexplored. In this talk, I will present my research group’s efforts to understand thermal transport in complex structures and across interfaces, using atomic modeling and experimental characterization. I will start with phonon dynamics in 3D and 2D hybrid organic-inorganic perovskites using inelastic x-ray scattering, where we gained useful insights into their ultralow thermal conductivity and remarkably weak anisotropy in 2D hybrid. Then, I will share our very recent finding on ultrahigh thermal conductivity in 3D covalent organic frameworks using molecular dynamics simulations. Last but not least, our development of rigorous formalism for anharmonic atomistic Green’s function to capture the contribution of inelastic phonon scattering at the interfaces, direct observation of phonon Anderson localization in aperiodic superlattices, and machine-learning-assisted interface design.

Materials with large optomechanical coupling coefficients display nonlinear response properties of possible interest for quantum transduction and quantum machine learning applications. In this talk, I will show using first-principles methods based on time-dependent density functional theory how materials of broken symmetry can display large optomechanical coupling along their amplitude (Higgs) modes.
Using the charge density wave (CDW) state of the layered transition-metal dichalcogenide, Tantalum Disulfide (1T−TaS2) as a case study, I will show how light can couple with structural order parameter in CDW materials, leading to optomechanical coupling coefficients two orders of magnitude larger than the ones of diamond and ErFeO3.
In addition, I will show this physics can be quantitatively captured by a classical model of the light-induced dynamics and that this dynamics can be deterministically controlled to engineer large third-order non-linear optical susceptibilities. These findings suggest nonlinear phononics processes in CDW materials are promising for non-linear optics applications.

We present two novel thienoacene molecular compounds that comprise four central tetrathienyl cores fused with two naphtyl rings, DN4T and isoDN4T. The straight ‘acene like’ structure of DN4T results in high electron densities on the sulfur atoms while these are absent in isoDN4T that adopts a ‘phene like’ structure. Using Density Functional Theory (DFT), we show that this translates into a reduced molecular reorganization energy, enlarged transfer integrals in the herringbone planes, and as a result larger hole mobility values in DN4T vs isoDN4T molecular crystals.
The carrier mobility in these crystals is known to be limited by low frequency phonons collapsing the wavefunction at room temperature. Remarkably, we find that the transfer integrals in DN4T are rather insensitive to the sliding motion of the aromatic cores, reported to be the ‘killer’ mode in related molecules [1]. The full spectral density, as obtained by combining classical Molecular Dynamic simulations to DFT calculations, reveals a rich structure that points to the phonon modes affecting the most charge transport.
[1] Schweicher, Guillaume, et al. "Chasing the “killer” phonon mode for the rational design of low disorder, high mobility molecular semiconductors." Advanced Materials 31.43 (2019): 1902407

While several works in the literature have experimentally examined the reduction in thermal conductivity (k) when two materials are alloyed together, there are comparatively fewer measurements related to the impact on the volumetric heat capacity (C_v) of such alloys systems. In most measurement scenarios utilizing periodic heating, C_v is an important input parameter and often estimated to be a compositional-average of the alloyed materials; sometimes referred to as a virtual-crystal approximation (VCA). New computational methods such as Green-Kubo modal analysis (GKMA) have been used to highlight the inability of the VCA to describe the temperature-dependent k of thin film InGaAs on the basis of the latter being unable to capture the true vibrational mode-character of the alloy. Given that the temperature-dependence of C_v is directly representative of the vibrational mode-character in a material without requiring knowledge and/or assumptions of phonon scattering rates, it is apparent that an ability to measure C_v(T) directly in thin film alloys would likely aid in answering several fundamental questions related to the mode-character in structurally-ordered, chemically-disordered alloy systems.
This presentation chronicles our work measuring k(T) and C_v(T) of InGaAs and InAlAs thin films from 80 – 450 K. The sample set examined consists of alloy films deposited on InP substrates via metal-organic chemical vapor deposition (MOCVD) at In contents suitable for use as well and barrier layers in quantum cascade lasers (QCLs) and thicknesses ranging from ~100 – 500 nm. Several opto-thermal pump-probe measurement techniques including time-domain and steady-state thermoreflectance (TDTR and SSTR, respectively) were utilized to minimize the number and impact of various thermophysical parameters that could otherwise impact our ability to accurately determine k(T) and C_v(T). The resulting measurements of C_v(T) are compared to predictions from several flavors of the VCA employing both Debye-like and full phonon dispersions, highlighting the importance of these measurements for avoiding erroneous assumptions for C_v(T). This work provides important insight to aid in both the development and validation of future computational models focused on thermal transport processes in alloy material systems.

Phonons, quantized lattice vibrations, determine the majority of thermophysical properties and thermal transport of most materials. Phonon centroid energies are often assessed through inelastic or diffuse neutron or x-ray scattering techniques but require large samples and lack spatial resolution. Recent advances in electron energy-loss spectroscopy (EELS) allow for spatially resolved phonon modes but require state-of-the-art monochromated scanning transmission electron microscopes (STEM) and are more sensitive to higher energy phonon modes.
Here, we present electron thermal diffuse scattering patterns using an Electron microscope pixel array detector (EMPAD) as a feasible method to determine spatially resolved phonon dispersion relations throughout the Brillouin zone made possible by high-reciprocal space sampling and the EMPAD’s high-dynamic-range. We measured thermal diffuse scattering in electron diffraction patterns of gold films and performed least-squares fit of thermal diffuse intensities based on a second-order force constant model Hamiltonian. We also compared the diffuse intensities from atomic configurations from state-of-the-art ab initio calculations and classical molecular dynamics using machine-learned and empirical interatomic potentials at finite temperatures. The patterns using the Gaussian approximation potential (GAP) with the smooth overlap of atomic positions (SOAP) kernel based machine-learned interatomic potentials show good agreement with experiments. In contrast, simulated patterns using empirical potentials show large discrepancies due to the errors in phonon energies. The experimentally determined phonon energies agree with neutron scattering data and calculated dispersions from temperature-dependent effective potential method (TDEP) ab initio and machine-learned calculations. These fitted machine-learned interatomic potentials are transferable, accurately depict the lattice dynamics, and allow for quantitative comparisons between experiments and simulations of systems with reasonable experimental thicknesses.

Predicting the effect of nanostructuring on non-diffusive phonon transport requires models, such as the Boltzmann transport equation (BTE), that capture the phonon’s size effects. Although the BTE has been well validated against several key experiments, notably those on nanoporous materials and thin films, its applicability is computationally expensive. Several analytical models have been put forward to estimate the effective lattice thermal conductivity; however, most of them are either based on simple geometries or simplified material descriptions such as the gray-model approximation. Thus cannot accurately capture ballistic effects. To fill the gap, we propose a model that takes into account the whole mean-free-path (MFP) distribution and the complexity of the material's boundaries through using uni-parameter logistic regressions. The model, called “Ballistic Correction Model” (BCM), has been validated against full BTE simulations of a selection of (i) base materials (GaAs, InAs, and Si) with nanoscale porosity, (ii) binary and ternary alloys (GeSn, AlGaAs, InGaP, andAlInAs), and (iii) in-plane and out-plane thermal transports in thin film membranes, obtaining excellent agreement in both diffusive and ballistic regimes. Providing a simple yet accurate estimation of thermal transport in nanostructures, our work sets out to accelerate the discovery of materials for thermal-related applications.

Modeling the scattering of fast electrons by a crystal populated by phonons is an essential aspect of quantitative scanning transmission electron microscopy (STEM) analyses. Specifically, direct quantitative comparisons between experiments and simulations require that the redistribution of electron scattering due to the atomic thermal motion be taken into account. [1] This thermal vibration is typically incorporated in high-angle annular dark-field STEM using the Einstein approximation (uncorrelated thermal motion) via multi-slice methods. [2] Measurable error, however, has been found for scattering at low angles using these uncorrelated simulations, including diffraction patterns and images. [3, 4] Accurately modeling the correlated thermal displacements of the atoms that accounts for this error requires knowledge of the atomic potentials/force constants, and hence the phonon band structure.
In this presentation, we use simulations of electron scattering in Si as a test to demonstrate the sensitivity of the electron scattering to the phonon band structure by comparing thermal displacements incorporated using DFT-based methods with molecular dynamics using empirical and machine-learned (ML) interatomic potentials. With the correlated thermal motion included, we will show how the different models influence the electron scattering as a function of angle, thickness, and projection direction, even though the mean square displacements are nearly the same. Further we will provide insights into sensitivity to this correlated thermal motion using angle-resolved STEM images, pointing to the possibility of robust quantification of correlated thermal displacements at the atomic scale. We emphasize that the influence of correlated thermal vibrations also depends on orientation of the crystal. For example, the [111] orientation shows enhanced sensitivity to the different interatomic potentials, and hence phonon band structure. Overall, we find that the ML potentials more accurately reproduce the electron scattering than the empirical potentials when compared to using the phonon band structures determined with inelastic neutron diffraction.
References:
[1] Wang, Zhong Lin. Micron 34.3–5 (2003): 141–155.
[2] Kirkland, Earl J. Advanced computing in electron microscopy. Vol. 12. New York: Plenum Press, 1998.
[3] Muller, David A., et al. Ultramicroscopy 86.3–4 (2001): 371-380.
[4] Grieb, Tim, et al. Ultramicroscopy 221 (2021): 113175.
[5] We acknowledge support for this work from the Air Force Office of Scientific Research (FA9550–20–0066).

In electrical insulators, heat is carried by the quantized collective lattice vibrations called phonons. Resistance to heat flow in these materials is caused by phonon scattering processes. Thermal phonon transport in these materials is governed by the semi-classical Boltzmann Transport Equation (BTE). Solutions of the BTE are commonly derived assuming the validity of relaxation time approximation (RTA), where all phonon scattering events are assumed to be momentum-dissipative in nature. While the RTA-based BTE solution describes the heat flow in several materials reasonably well, it fails to capture the ultrahigh thermal conductivity and the exceptional phonon transport properties of materials like diamond and boron nitride. Here we present the solutions of the BTE without the RTA for phonon transport through these ultrahigh thermal conductivity materials, and demonstrate that accurately distinguishing momentum-conserving (Normal) and momentum-dissipative (Umklapp) scattering events in our formulation is crucial to correctly predict their thermal transport properties.
This work is supported by the DST-SERB Core Research Grant (CRG/2020/006166).

The combined progress in first-principles simulation codes and supercomputing capabilities has given birth to the so-called high-throughput ab initio approach. This has generated large amounts of materials data (mainly ground-state properties) which has been stored in various open databases. However, for more complex properties (e.g., linear or higher-order responses), this approach is still out of reach because of the required CPU time. To overcome this limitation, artificial intelligence has recently attracted much attention. However, in order to make accurate predictions, current machine-learning approaches generally require large amounts of data, which are precisely not available for complex properties. In this talk, I will introduce the MODNet framework which relies on a feedforward neural network and the selection of physically meaningful features. Next to being faster in terms of training time, this approach is shown to outperform current machine-learning models on small datasets. In particular, the vibrational entropy at 305 K for crystals is predicted with a mean absolute test error of 0.009 meV/K/atom (four times lower than previous studies). Furthermore, joint learning reduces the test error compared to single-target learning and enables the prediction of multiple properties at once, such as temperature functions. Finally, the selection algorithm highlights the most important features and thus helps to understand the underlying physics.

Kohn-Sham density functional theory based calculations have become a cornerstone for material research and discovery. Despite the great advancements in numerical approaches and computational power, performing large scale first-principles DFT calculations is a daunting task. This issue becomes even more prominent while calculating the higher derivatives of energy using linear response theory. In this work, we develop a real-space density functional perturbation theory formulation for phonon calculation for systems with arbitrary boundary conditions and implement it in large-scale massively parallel state-of-the-art real-space DFT code SPARC. The highly efficient parallel architecture of the ground state calculation of the code is leveraged upon and extended to perform large-scale DFPT calculation. Furthermore, we symmetry-adapt the above formulation to non-affine coordinate system to study systems with cyclic and/or helical symmetry. This opens avenues for studying the low-dimensional systems which have been predicted as future thermoelectric and photovoltaic materials. Finally, we study the effect of different functionals (local as well as nonlocal) on phononic properties for a wide variety of systems. Overall, this work opens avenues for first-principles based large scale data generation related to phononic properties of materials as well as understanding the physics of complex materials.

While semi-analytical solutions of the frequency-dependent phonon Boltzmann equation exist in literature to describe thermal transport in simple semiconductor geometries, such solutions are challenging to obtain for complex nanostructures with multiple interfaces and boundaries. Here, we present transient and steady-state numerical solutions of the linearized phonon Boltzmann equation in complex nanoscale semiconductor devices using a Monte-Carlo technique. In our calculations, we treat various scattering processes that the phonons undergo in the nanosctructure - such as the intrinsic phonon-phonon scattering and the geometric specular and diffuse boundary scattering. In these calculations, we relax the commonly used approximation - the relaxation time approximation (RTA) to differentiate Normal (non-dissipative) and Umklapp (dissipative) phonon-scattering processes more accurately. We demonstrate that our computational scheme reproduces the experimental results on the thermal transport in nanoscale devices accurately, while retaining the low computational cost of the semi-analytical solutions reported in the literature for simple geometries.
This work is supported by the Institute of Eminence Post-doctoral fellowship for VR. The authors acknowledge support from a start-up grant offered by the Indian Institute of Science, Bangalore and the DST SERB Core Research Grant (CRG/2020/006166)

Unlike pure liquids, liquid mixtures have highly tuneable thermophysical properties. Thanks to this characteristic, liquid mixtures have been widely adopted in a range of applications such as pharmaceuticals, polymers, and machinery. However, enhancement in one property may come at the expense of another. There is hence a need to finetune the composition of the mixture to achieve the desired outcome. Moreover, the vast parameter space and complex optimization response surfaces make it difficult to determine the optimum ratios manually due to the cost, time, and number of trials required. Automated experimentation systems coupled with machine learning models can expedite the optimization process. Continuous flow systems can provide experimental data to train the machine learning models to predict the optimal composition.
Nanofluids are suspension of nanoparticles (1–100 nm) such as CuO, Al₂O₃, Ag, graphene, and carbon nanotubes (CNTs) in a base fluid. The addition of these nanoparticles has shown to enhance the thermal conductivity of the base fluid, e.g. water and ethylene glycol. Increasing the concentration of nanoparticles often comes at the cost of increased viscosity, which is an issue in practical systems as higher viscosity means more energy expenditure when driving fluid flow. Experimental investigations into nanofluids have generally been performed manually. The ethylene glycol-water ratio is usually fixed while only a few, select concentrations of nanoparticles are investigated. This research aims to build an automated continuous flow system to optimize the thermal conductivity and viscosity of ethylene glycol, water, and nanoparticle mixtures, a mixture often used in anti-freeze applications and automobile coolants.
In this work, we integrate online optimization techniques into an automated continuous flow system to tune the thermophysical properties of ethylene glycol-water-silver nanowire (EG-W-AgW) nanofluids. The system finds the optimal solid-volume ratio that minimizes the viscosity and maximizes the thermal conductivity of the nanofluid. Different mixture ratios were continuously sampled while the viscosity and thermal conductivity were measured inline using modified capillary rheometer and transient hot-wire techniques, minimizing the time and liquid consumption required for each optimization trial. The viscosity of the fluid mixture was calculated by measuring the fluid pressure at two points on the tube. The thermal conductivity was estimated by inducing Joule heating in a platinum wire and observing the temperature rise of the wire.
Several optimization algorithms such as Stable Noisy Optimization by Branch and Fit (SNOBFIT), Thompson Sampling Efficient Multi-objective Optimization (TSEMO), and Multi-Objective Particle Swarm Optimization (MOPSO) are applied to optimize the weighted objective function involving viscosity and thermal conductivity. The optimal ratio of EG-W-AgW predicted by each algorithm is compared. The proposed system enables the optimization algorithm to recommend parameters and the automated measurement system tests the predicted parameters immediately.

The compromise between density functional theory (DFT) accuracy and molecular dynamics (MD) speed from machine learned potentials (MLPs) permits the simulation of larger and longer scales that were previously difficult to realize. A recently developed potential, namely the Deep Potential (DeepPot), is a novel neural network-based atomic potential with excellent DFT-level energy accuracy. However, the scalability of DeepPot with number of elements (M) is non-linear, where N element-specific networks require the allocation of N x M inputs during training. By construction, using a dataset containing many elements slows down training and reduces the quality of the prediction. Here, we present a modified deep neural network potential, named Elemental DeepPot, which introduces species-specific descriptors. For demonstration, we apply our modified deep neural network to a large dataset containing a mixture of ~12,000 metallic and semiconducting materials, totaling >50 unique elements for training. The results show Elemental DeepPot can capture both atomic structure and species with significant improvement to training speed and accuracy. We finally obtained a few thousand phonon dispersions and lattice thermal conductivities with accuracy comparable to full DFT calculations.

The purpose of data-driven materials research is to improve material property and performance of by designing and optimizing material chemical composition, structure and process conditions. For this purpose, interlinked data of material composition, structure and property for comprehensive material systems from element, compound to substance and material, are needed. In fact, these data are obtained with different methods by researchers in different fields, and usually stored in different databases. Therefore, data integration is a key issue of materials big data construction.
In this talk, examples of data-driven studies on interfacial transport properties with integrated materials and substances data will be introduced. Material identification is considered the key issue of data integration. To solve this problem, standardization of material descriptors at different levels are required. Our current work on materials database construction, in which we try to link experimental data of complex material systems such as process condition and property to substance data such as crystal structure and electronic structure by a substance dictionary, will be introduced.

Recently, it has been shown computationally and experimentally that the inclusion of higher-order scattering among four phonons is crucial to accurately represent the phonon thermal conductivities of several strongly-bonded materials like boron arsenide, boron phosphide, silicon carbide and indium phosphide [1-4], as well as weakly-bonded solids like sodium chloride (NaCl) [5]. Here we show, from rigorous first-principles calculations, that four phonon scattering also critically affects the phonon lineshapes of NaCl and other weakly-bonded solids typically observed in inelastic neutron/x-ray scattering and Raman scattering experiments. These calculations are performed by building on the unified first-principles framework [5], which already includes the effects of the lowest-order three-phonon and higher-order four-phonon scattering processes on the thermal conductivity of materials, a many-body self-consistent anharmonic phonon renormalization step to address the possible ill-defined nature of certain phonon quasiparticles in weakly-bonded solids, and the determination of the stable lattice constants at finite temperatures, by explicitly evaluating and minimizing the fourth-order accurate free energy of the crystal. By performing these calculations over a broad range of temperatures, we show that the four-phonon scattering processes significantly broaden the phonon lineshapes compared to their three-phononcounterparts - particularly at high temperatures, and their inclusion into the calculations are pivotal to explain the experimental data.
This work has been supported by a start-up fund from the Indian Institute of Science, Bangalore, India and the Department of Science and Technology (DST-India) - Science and Engineering Research Board (SERB) Core Research Grant (CRG/2020/006166).
[1] Navaneetha K. Ravichandran and D. A. Broido, Nature Comm. 12, 3473 (2021).
[2] Navaneetha K. Ravichandran and D. A. Broido, Phys. Rev. X 10, 021063 (2020).
[3] Navaneetha K. Ravichandran and D. A. Broido, Nature Comm. 10, 827 (2019).
[4] Fei Tian, Bai Song, Xi Chen, Navaneetha K. Ravichandran et al., Science 361, 6402 (2018).
[5] Navaneetha K. Ravichandran and D. A. Broido, Phys. Rev. B 98 (8), 085205 (2018).

Designing interfacial materials with extremely high/low interfacial thermal conductance has great importance and potential applications in heat dissipation for electronic devices, thermal insulation, and thermoelectrics. Due to the limitation of designing parameter selections and coupling effects, the optimal interfacial thermal transport design is often inefficient and with high cost. In this work, we developed a high throughput screening method to design interfacial materials with high/low interfacial thermal conductance. The prediction model was established based on the collection of data via the atomistic green's functions. Descriptors that dominate the interfacial thermal conductance were discussed. Rules for obtaining high/low interfacial thermal conductance were also summarized. The result shows that our developed high throughput screening method can significantly improve the efficiency for interfacial thermal transport design.

Discovering exceptions has been a major route for advancing sciences but a challenging and risky process. Machine learning has shown effectiveness in high throughput search of materials and nanostructures, but using it to discover exceptions has been out of the norm. In this work, we demonstrate the use of genetic algorithm to discover unexpected thermal conductivity enhancement in disordered nanoporous graphene as compared to periodic counterpart. Recent studies have concluded that random pores in nanoporous graphene lead to reduced thermal conductivity than periodic pores, due to phonon Anderson localization. This work, however, aims to challenge this accepted knowledge by searching for exceptions. First, we attempt a manual search for random structures with molecular dynamics simulations and find that thermal conductivities of 21 random porous graphene structures are all lower than the periodically arranged one. Then, a genetic algorithm enabled “two-step” search process is designed, in which BTE simulation is carried out for pre-screening and NEMD simulation is performed to validate the optimal configuration found by genetic algorithm. Unexpected thermal conductivity enhancement is successfully discovered in certain structures with random pores, at a fraction of the computational cost of the manual search. Through an in-depth analysis of the characteristics of the porous structure, we propose that such unusual enhancement is due to the effect of shape factor and channel factor dominating over that of the phonon localization.
Besides nanoporous materials, the microscopic morphology of the pores will also significantly affect the thermal transport of the porous media at the macro scale. However, existing effective medium approaches usually miss the morphology effects, and numerical simulations are expensive and not physically intuitive. Machine learning methods have recently been successful in predicting effective thermal conductivity, but the lack of descriptors limits physical insights. Here we investigate structural features that have significant effects on thermal transport in porous media. Besides shape factor and channel factor, we propose other three physics-based descriptors to characterize the structural characteristics of porous media: bottleneck, perpendicular non-uniformity, and dominant paths. These descriptors can effectively quantify the anisotropy of pore morphology and strongly correlate with effective thermal conductivities. The proposed descriptors are incorporated into machine learning models to predict the effective thermal conductivity of porous media, and the results are shown to be fairly accurate. They provide new insights into the thermal transport mechanisms in complex heterogeneous media.

Van der Waals (vdW) heterostructures vertically stacked from isolated two-dimensional atomic layers like graphene and WS₂ have triggered tremendous attention due to their promising applications in electronic devices including tunneling transistors, barristors and flexible electronics, as well as optoelectronic devices.¹ Thermal transport at the interface of these heterostructures plays a pivotal role in determining their thermal properties and performance. Here, we perform materials informatics to explore the controllability of thermal transport in vdW graphene-WS₂ heterostructures and identify the ultimate heterostructure that gives minimum thermal conductivity. The thermal conductivities of heterostructures are calculated from the non-equilibrium molecular dynamics simulation, and the black-box optimization is conducted by coupling it with machine learning. Prior to the optimization, we investigated the system size effect on the thermal conductivities of graphene, WS₂ and superlattices. Then, heterostructures with different stacking order of graphene and WS₂ are fed into the optimization algorithm to obtain the heterostructure with the lowest thermal conductivity. First choice of the machine learning method is Bayesian optimization, which can realize highly efficient optimization. ^2-3 On the other hand, since Bayesian optimization pursues biased sampling, it may suffer from possibility of being trapped in the local optimum. Therefore, we also implement replica-exchange method, which searches a broader parameter space by fair sampling and is more likely to find the global minimum at the expense of efficiency. This comparative study helps us identify not only the truly global structure but also the underlying physical mechanism by having two datasets biased differently. For that, microscopic properties such as spectral phonon transmissions are also evaluated. The phonon transmissions and their distributions of the heterostructures suggest that the localization of coherent phonons is the main factor for the reduction in thermal conductivity. This research deepens our understanding of the interfacial thermal transport behaviors of van der Waals heterostructures and provides guidance for the design and control of their thermal properties.
(1) Liu, Y.; Weiss, N. O.; Duan, X.; Cheng, H.-C.; Huang, Y.; Duan, X., Van der Waals heterostructures and devices. Nature Reviews Materials 2016, 1 (9), 16042.
(2) Ju, S.; Shiga, T.; Feng, L.; Hou, Z.; Tsuda, K.; Shiomi, J., Designing nanostructures for phonon transport via Bayesian optimization. Physical Review X 2017, 7 (2), 021024.
(3) Hu, S.; Ju, S.; Shao, C.; Guo, J.; Xu, B.; Ohnishi, M.; Shiomi, J., Ultimate impedance of coherent heat conduction in van der Waals graphene-MoS₂ heterostructures. Materials Today Physics 2021, 16, 100324.