Thermal Transport Mechanisms Research Articles

Ultra-High Interfacial Thermal Conductance via Double hBN Encapsulation for Efficient Thermal Management of 2D Electronics.

Heat dissipation is a major limitation of high-performance electronics. This is especially important in emerging nanoelectronic devices consisting of ultra-thin layers, heterostructures, and interfaces, where enhancement in thermal transport is highly desired. Here, ultra-high interfacial thermal conductance in encapsulated van der Waals (vdW) heterostructures with single-layer transition metal dichalcogenides MX2 (MoS2 , WSe2 , WS2 ) sandwiched between two hexagonal boron nitride (hBN) layers is reported. Through Raman spectroscopic measurements of suspended and substrate-supported hBN/MX2 /hBN heterostructures with varying laser power and temperature, the out-of-plane interfacial thermal conductance in the vertical stack is calibrated. The measured interfacial thermal conductance between MX2 and hBN reaches 74 ± 25 MW m-2 K-1 , which is at least ten times higher than the interfacial thermal conductance of MX2 in non-encapsulation structures. Molecular dynamics (MD) calculations verify and explain the experimental results, suggesting a full encapsulation by hBN layers is accounting for the high interfacial conductance. This ultra-high interfacial thermal conductance is attributed to the double heat transfer pathways and the clean and tight vdW interface between two crystalline 2D materials. The findings in this study reveal new thermal transport mechanisms in hBN/MX2 /hBN structures and shed light on building novel hBN-encapsulated nanoelectronic devices with enhanced thermal management.

Size- and temperature-dependent thermal transport across a Cu−diamond interface: Non-equilibrium molecular dynamics simulations

Cu−diamond composites (CDCs) have greatly promising applications in thermal management for high-power electronics because of their outstanding thermophysical properties. Nonetheless, many fundamental mechanisms of interfacial thermal transport for CDCs remain poorly understood at present. Here we focus on investigating the size- and temperature-dependent thermal transport across a Cu−diamond interface using non-equilibrium molecular dynamics simulations. Results show that interfacial thermal conductance (ITC) is proportional to both the system size and ambient temperature. Especially, our predicted room-temperature ITC of 41.12 MW⋅m−2⋅K−1 at an infinitely long system is close to that of the experiments after an interface optimization. Additionally, the ITC at the system with a length of 323.2 Å is increased by over 2.5 times in the temperature range of 100−500 K, up to 36.39 MW⋅ m−2⋅ K−1. Detailed analyses of interfacial disorder and its concomitant effects, related to system size and temperature, are implemented for helping understand the significant improvement of ITC. The underlying mechanism is further uncovered by the phonon density of states as well as the spectral overlap factor at interfacial Cu and diamond. This study provides an important insight into the understanding of interfacial thermal transport in CDCs and a guideline for optimizing the design of CDCs in experiments.

One-dimensional harmonic chain model of vibration-mode matching in solid-liquid interfacial thermal transport.

Understanding the atomistic mechanism of interfacial thermal transport at solid-liquid interfaces is a key challenge in thermal management at the nanoscale. A recent molecular-dynamics study demonstrated that interfacial thermal resistance (ITR) at the interface between a solid and a surfactant solution can be minimized by adjusting the molecular mass of the surfactant. In the present study, we explain the mechanism of this ITR minimization in view of vibration-mode matching using a one-dimensional (1D) harmonic chain model of a solid-liquid interface having an interfacial adsorption layer of surfactant molecules. The equation of motion for the 1D chain is described by a classical Langevin equation and is analytically solved by the nonequilibrium Green's function (NEGF) method. The resultant ITR is expressed in a form of vibrational matching, and its relationship to the overlap of the vibrational density of states is also discussed. The analysis leads to a conclusion that the damping coefficient η in the Langevin equation should be a finite and sufficiently large value to represent the rapid damping of vibration modes at solid-liquid interfaces. This conclusion provides a clue to seamlessly extend the conventional NEGF-phonon transmission picture of solid-solid interfacial thermal transport, which assumes η to be infinitesimal, to solid-liquid interfaces.

Solid and gas thermal conductivity models improvement and validation in various porous insulation materials

In the past few decades, significant efforts have been made to improve the theoretical understanding of thermal transport mechanisms in thermal insulation materials and push the thermal conductivity's lower limits. However, most works focused singularly on specific types of materials, and the models used for thermal conductivity predictions are diverse - a model that fits one material might not fit others. Here, we improve and unify the gas and solid thermal conductivity models for porous materials. Through experimental characterization of several different materials as well as literature data for other materials, these models are validated. We have also found that the pressure-dependent gas thermal conductivity of most materials can be well fitted by using one or two pore sizes without using a complex pore size distribution. With the refined models, we decompose the effective thermal conductivity of several thermal insulation materials into gas, solid, and radiation contributions. For cellular (polystyrene and polyurethane) foams, the relative contributions from air, solid, and radiation are 58–75%, 3–11%, 16–38%, respectively. For granular porous materials (polyurethane and silica in this work), the contributions from air, solid, and radiation are 45–66%, 34–46%, and 0–8%, respectively. This work is expected to provide guidance on the design and optimization of the next generation of thermal insulation materials, for example, through the effort of reducing gas conduction and radiation in foams and suppressing gas and solid conduction in aerogels.

Thermal transport manipulated by vortex domain walls in bulk h-ErMnO3

Topological defects such as structural vortex domain walls (DWs), which induce many intriguing properties and associated physical phenomena in multiferroics, also provide a platform for manipulating thermal transport. Here, we employ time-domain thermoreflectance (TDTR) to study the thermal conductivity of bulk h-ErMnO3 single crystals with different vortex DWs over a wide temperature range. We find that the vortex DWs can effectively and synergistically suppress the thermal conductivity along (κc) and perpendicular (κab) to the c-axis of h-ErMnO3 single crystals. A phonon scattering model is utilized to explain the mechanism of thermal transport manipulated by vortex DWs. This model yields the intrinsic thermal conductivity and the effective phonon mean free path (MFP) of h-ErMnO3. The model also manifests that vortex DWs achieve a maximum reduction of ∼28% for the room-temperature thermal conductivity against the single-domain case. The reduction becomes more significant with decreasing temperature due to the longer effective MFP at lower temperatures, both proved experimentally by the cryogenic experiment and theoretically based on the proposed phonon scattering model. These findings not only provide an essential understanding of heat transport in multiferroics with vortex DWs but also pave the way for their application in next-generation ferroelectric devices.

Microscopic mechanism of low lattice thermal conductivity in natural superlattice materials BaXYF ( X = Cu, Ag; Y = Se, Te) including fully quartic anharmonicity

Layered quaternary fluorochalcogenides with natural superlattice structures have received particular attention in the thermoelectric (TE) field due to their favorable electronic properties. However, further exploration of these materials in the TE field is hindered by the lack of studies on the lattice thermal transport properties. Here, we investigate the microscopic mechanism of lattice thermal transport in natural superlattice materials $\mathrm{Ba}\mathit{XY}\mathrm{F}$ ($\mathit{X}$ = Cu, Ag; $\mathit{Y}$ = Se, Te) using first-principles calculations combined with self-consistent phonon theory, compressive sensing techniques, and Boltzmann transport equations. We consider three- and four-phonon scattering as well as temperature-driven phonon energy shifts due to quartic anharmonicity. We find that the strong quartic anharmonicity plays a crucial role in the lattice stability of BaCuSeF and BaCuTeF. Furthermore, the ${\ensuremath{\kappa}}_{\mathrm{L}}$ of the four materials exhibits significant anisotropy due to different bonding types along the $a$($b$) and $c$ axes. The calculations indicate that the four materials have low lattice thermal conductivities ${\ensuremath{\kappa}}_{\mathrm{L}}$, e.g., 0.85--$1.61\phantom{\rule{4pt}{0ex}}{\mathrm{Wm}}^{\ensuremath{-}1}{\mathrm{K}}^{\ensuremath{-}1}$ at 300 K. Additionally, the results exhibit that a reasonable ${\ensuremath{\kappa}}_{\mathrm{L}}$ and corresponding temperature dependence can be obtained by considering the fully quartic anharmonicity. Our findings not only fill the gap in the lattice thermal transport research of natural superlattice materials, but also deepen a comprehensive understanding of the low ${\ensuremath{\kappa}}_{\mathrm{L}}$ of natural superlattice materials.

Effect of Sn oxides on the thermal conductivity of polycrystalline SnSe

SnSe is a promising thermoelectric material, with intrinsically low lattice thermal conductivity, κL. Surprisingly, in several reports, polycrystalline samples are found to have a higher thermal conductivity than single crystals. This disparity has been attributed to trace amounts of thermally conductive Sn oxides at the grain boundaries of polycrystalline samples. The same culprit was recently proposed to explain the reduction of κL in purified, oxide-free, SnSe polycrystals. Here, we test this hypothesis by: (i) tuning the type of oxide in SnSe by exploiting thermodynamic stability regions, since Sn-rich or Sn-poor compositions favour the formation of SnO or SnO2, respectively; and (ii) varying the quantity of SnO2 by intentionally oxidizing SnSe powder before consolidation, to obtain samples with quantifiable amounts - up to 15% - of SnO2. We find that the κL of SnSe is impervious to changes in the type or the amount of Sn oxide present in the samples. Our results show that a simple “rule of mixtures” cannot be used to estimate the effect of grain boundary oxides on the thermal conductivity of SnSe. These results call for an improved understanding of the intriguing thermal transport mechanisms in SnSe and numerous other systems where a two-phase transport is presumed.

Phonon interference effects in graphene nanomesh

Graphene nanomesh (GNM) is a single-layer graphene material that has a periodic distribution of nanoscale pores. GNM shows great potential applications in various fields such as thermoelectric energy conversion, energy storage, and field-effect transistors. In this study we utilize non-equilibrium molecular dynamics and lattice dynamics method to investigate the thermal transport mechanism of GNM. The thermal conductivity of GNM is mainly affected by the number of nanoscale pores and their horizontal and vertical spacing. Our study finds that as the number of nanoscale pores increases, the thermal conductivity of GNM decreases significantly. Additionally, the increase of the number of nanoscale pores causes phonon branch to be folded and confined, which results in a flatter dispersion curve, wider bandgap, and slower phonon group velocity. Moreover, the horizontal and vertical spacing of the nanoscale pores jointly affect the thermal transport process of GNM. When the horizontal spacing is small, the thermal conductivity of GNM decreases monotonically with the increase of vertical spacing, and increases monotonically with an increase of horizontal spacing. However, as the horizontal spacing increases, the interference effect caused jointly by phonon reflection and superposition leads to significant fluctuations in thermal conductivity. The analysis of the spectral heat flow, density of states, participation rate, and group velocity of GNM indicate that the variation in vertical spacing leads to different phonon contributions to heat flow, resulting in fluctuations in the thermal conductivity of GNM. These findings could serve as a reference for controlling the thermal transport of graphene nanomesh, and are of great significance in regulating the thermal conductivity and designing nanoscale pores in GNM.

Thermal management and waste heat recovery of electronics enabled by highly thermoconductive aramid composites with bridge-type 1D/2D liquid-crystalline thermal conduction networks

As a vital part of electronics, polymer-based thermal management materials effectively accelerate heat dissipation and improve the reliability, stability, and service life of electronics. Herein, a novel strategy of bridge-type 1D SiC nanowires/2D graphite flakes thermal conduction networks with liquid-crystalline orientation is developed to exploit highly thermoconductive aramid/graphite/SiC films (AGSs). The bridge-type 1D/2D liquid-crystalline thermal conduction networks can significantly promote efficient heat transport. The ultrahigh in-plane thermal conductivity of 19.69 ± 0.16 W m−1 K−1 can be achieved in AGSs, about 714 % higher than that of neat aramid. The thermal transport mechanism of composites at the atomic scale was explored based on phonon spectral analysis by molecular dynamics simulation. The developed AGSs can reduce the temperature of the operating phone CPU by about 3.4 °C when used as the heat dissipation material, and the AGSs also can conduct waste heat effectively to generate electric power in a thermoelectric power generation system. This work provides an effective strategy for thermal management and waste heat recovery of electronics by highly thermoconductive nanocomposites with bridge-type 1D/2D liquid-crystalline thermal conduction networks.

Nonlinear thermal transport in graphene nanoribbon: A molecular dynamics study

Effects of different factors on the thermal conductivity of graphene nanoribbons (GNRs) is investigated using nonequilibrium molecular dynamics (NEMD) simulations with LAMMPS code, taking advantage of the optimized Tersoff interatomic potential. The influences of temperature, size, and layer number on thermal transport are considered for both zigzag and armchair GNRs. It is found that increasing the size (length⩽40 nm and width⩽10 nm) enhances the thermal conductivity of both GNR types by a power-law relationship at room temperature. In contrast, the thermal conductivity of GNRs drastically drops as the temperature rises in the range of 50–500 K. The power-law reduction of conductivity, owing to the temperature increase, is faster in zigzag GNR than in armchair one. In addition, in the range of 1–10 layers, the thermal conductivity experiences a power-law decrease with increasing number of GNRs layers because of the out-of-plane scattering of phonons. Our results reveal how boundary scattering, growing phonon number and Umklapp scattering govern nonlinear thermal transport mechanism. This study also demonstrates a dramatic influence of the edge structure of GNR on thermal conduction.

Enhanced heat transmission in methanol-based AA7072/AA7075 tangent hyperbolic hybrid nanofluid flow along a nonlinear expandable surface

The present article emphasizes the bearing of radiative heat flux, Joule heating on the 3D magneto-flow of tangent hyperbolic mixed nanoliquid above a linear/nonlinear expandable surface. The aluminum alloy nanoparticles AA7072 and AA7075 are suspended in methanol liquid to obtain a hybrid nanofluid. The nonlinear partial differential equations are renovated to ordinary differential equations by utilizing appropriate similarity conversions, and further, the solutions are attained via the bvp5c MATLAB package. The novelty of this research is to supply simultaneous outcomes of the radiative hydrodynamic flow along linear and nonlinear extending surface situations. Further, the stimulus of sundry factors on the flow features is reflected with the aid of plots. The thermal transport rate in the nonlinear extending case is twice greater than the linear stretching case under the action of nanoparticles. Also, the existence of unique nanoparticles performs a substantial response in boosting the thermal transport mechanism of the non-Newtonian liquid.

Thermal transport mechanism of AlN/SiG/3C–SiC typical heterostructures

Understanding the heat transfer mechanism of typical structures in high-power chips is essential for chip design with better engineered heat transfer performance. Here, the interfacial thermal resistance (ITR) and in-plane thermal conductivity (TC) of AlN/Si-doped graphene/3C–SiC (AlN/SiG/3C–SiC) heterostructures are systematically studied by molecular dynamics simulation. Silicon doping can reduce the ITR by as much as 31.72% with a concentration of 8%, which is verified furthermore by energy transport and thermal relaxation time. Multiple analyses indicate that Si doping results in the enhancement of strong interaction between 3C–SiC and SiG, the decline of weak interaction between AlN and other two materials due to the accumulation of wrinkles in SiG, and finally promotes the phonon transmission of 0–18 THz at interfaces owing to the dominance of strong interaction. In addition, the in-plane TC is reduced by 11.24% when the Si-doped concentration is 8%. By analyzing the stress field, SiG and two-layer atoms on the interface side of 3C–SiC are mainly responsible for thermal resistance, and SiG leads to the exponential dependence between TC and doping concentration. The results also show that the ITR is sensitive to the random doping positions, while the TC is not. We believe the results in this work will have important guiding significance for enhancing the thermal transport performance of high-power chips.

Bonding Heterogeneity Leads to Hierarchical and Ultralow Lattice Thermal Conductivity in Sodium Metavanadate.

Sodium metavanadate (NaVO3) is a promising low-cost candidate as a cathode material for sodium-ion batteries (SIBs) owing to its high cycle performance. Its thermal transport, although being a central factor limiting its practical applications, remains scarce. Herein, we comprehensively investigate the intrinsic thermal transport properties of the two phases of NaVO3 using the unified theory. Importantly, we identify a hierarchical thermal transport mechanism in NaVO3 and the significant contribution of diffusive thermal transport. With the combined two channels, we reveal that NaVO3 has the anisotropic and ultralow thermal conductivity κ, which is derived from the bonding heterogeneity with the coexistence of strong V-O bonds and weak Na-O bonds, implying the possibility of engineering the κ of SIBs by spatially tuning the sodium concentration distribution. Our work establishes a fundamental understanding of the intrinsic thermal transport of NaVO3 and provides guidance toward designing tunable thermal conductivity cathode materials for SIBs.

Numerical investigation of thermal failure of a fuel subassembly foot wall during molten material relocation under various flow blockage scenarios in sodium-cooled fast reactor

The innovative Fuel Assembly Inner DUct Structure (FAIDUS) design inherently offers a quick relocation path for the molten core material to descend downwards via the inner duct and arrive at the foot of the Subassembly (SA) following the local core meltdown during Total coolant Flow Blockage (TFB) accident. With its high thermal energy and continual heat generation, the amassed molten mass targets the surrounding foot structure, causing the foot wall to fail. The thermal damage progression and discrete failure of the foot wall govern the later phase of the melt relocation that signals the accident state. To understand the thermal damage progression of SA foot, transient numerical simulations are performed using a commercial computational fluid dynamics solver, ANSYS Fluent. An enthalpy-porosity approach based solidification/melting model is employed to predict the wall failure mechanism and associated event sequences. The computational model is validated against the wall failure test results available in the literature. Subsequently, the foot wall failure analysis is undertaken using a 2-D axisymmetric physical model for various plausible blockage occasions that initiate the TFB accident near the SA foot. The numerical solution endeavors to explicate the transient behavior of molten pool, convection-diffusion controlled phase interface development, thermal transport mechanism, liquid front propagation across the foot cross-section, and associated thermal hydraulics. The present findings indicate that the standard SA foot design perpetuates the accident scenario by releasing the molten mass through the ruptured wall segment after failure. To address this, an improved slotted discriminator-based foot design is proposed in the present study, and the effectiveness of the modified foot design in realizing a positive melt relocation to the core catcher is examined. The simulation results suggest that the modified foot design permits the intended melt release to the core catcher, confirming the Controlled Material Relocation (CMR) strategy and restraining the accident propagation to neighboring SA.

Wigner Formulation of Thermal Transport in Solids

A formulation for heat conduction discusses how particle- and wavelike thermal transport mechanisms can emerge and coexist and provides a criterion to assess their relative strength and the crossover where one or the other dominates.

Thermal transport across graphene/GaN and MoS2/GaN interfaces

Graphene/GaN and MoS2/GaN have important applications in optoelectronic devices. The two-dimensional (2D) materials greatly improves the device performance due to its overwhelming advantages. 2D materials introduce multiple interfaces while improving device performance. With the miniaturization of devices, the interfacial thermal transport has crucial effect on the performance and lifetime of optoelectronic devices. The interfacial thermal conductance of Al/graphene/GaN and Al/MoS2/GaN are measured by the time-domain thermoreflectance (TDTR) technique from 100 K to 400 K. The density of states and spectral thermal conductance are calculated based on nonequilibrium molecular dynamics (NEMD) simulations to understand the underlying thermal transport mechanism. The overlap energy is used to understand the thermal transport efficiency. Most interesting, the results are opposite to that measured by TDTR. Moreover, the spectral thermal conductance and phonon dispersion are used to understand the thermal transport mechanism in frequency domain. The results provide experimental and theoretical guidance for thermal management of optoelectronic devices.

An analytical model for sensing microvascular blood flow in flaps and organ grafts

Thrombosis after free flap transfer or solid organ allotransplantation surgeries can lead to flap or organ failure requiring re-transplantation and sometimes leading to death. Current technologies can provide early warnings of thrombosis, but the resulting measurements can be influenced by motions associated with route operations in patient care and by subtle aspects associated with the use of the devices. These systems also require wired interfaces to external data acquisition hardware, which limits patient mobility and subject the sensor to artefact from interface disruption attributable to external tension. Furthermore, many existing systems require that the probe be mounted directly on the anastomosed artery or vein which puts these delicate structures at risk for kinking, avulsion, or other disruption. Recent reports describe a wireless, implantable flow sensing probe technology that exploits thermal transport mechanisms to enable continuous monitoring of microvascular flow velocity within peripheral tissue that is remote from the critical blood supply. The capability is useful for the reliable detection of thrombosis in auto- or allotransplanted flaps or organs. Because the probe directly measures temperature rather than flow velocity, analytical models must be used to interpret the results. Here, such a model, accounting for both heat conduction and heat convection (due to blood flow), is developed to determine the blood flow velocity in flaps and organ grafts for this flow sensing probe. The model is validated by in vitro experiments without and with blood flow and further applied to in vivo experiments to predict the flow velocity. The model serves as an important support for this type of flow sensing probe and ensures reliable and accurate flow monitoring after the transplantation operations.

Thermal Transport through Polymer-Linked Gold Nanoparticles.

Polymer-nanoparticle networks have potential applications in molecular electronics and nanophononics. In this work, we use all-atom molecular dynamics to reveal the fundamental mechanisms of thermal transport in polymer-linked gold nanoparticle (AuNP) dimers at the molecular level. Attachment of the polymers to AuNPs of varying sizes allows the determination of effects from the flexibility of the chains when their ends are not held fixed. We report heat conductance (G) values for six polymers-viz. polyethylene, poly(p-phenylene), polyacene, polyacetylene, polythiophene, and poly(3,4-ethylenedioxythiophene)-that represent a broad range of stiffness. We address the multimode effects of polymer type, AuNP size, polymer chain length, polymer conformation, system temperature, and number of linking polymers on G. The combination of the mechanisms for phonon boundary scattering and intrinsic phonon scattering has a strong effect on G. We find that the values of G are larger for conjugated polymers because of the stiffness in their backbones. They are also larger in the low-temperature region for all polymers owing to the quenching of segmental rotations at low temperature. Our simulations also suggest that the total G is additive as the number of linking polymers in the AuNP dimer increases from 1 to 2 to 3.

Inter-channel conversion between population-/coherence-channel dictates thermal transport in MAPbI3 crystals

Hybrid halide perovskites, with their favorable carrier recombination time and ultrashort phonon mean-free paths, are leading candidates for various energy conversion applications like photovoltaics and thermoelectrics. The origin of the ultralow thermal conductivity of the prototypical methylammonium lead triiodide (MAPbI3) is of intense research interest as it is critical for improving its energy conversion performance. So far, such an understanding remains elusive in the MAPbI3 above room temperatures (c-MAPbI3) despite numerous efforts due to its unstable phonon modes. Here, we report the discovery of several c-MAPbI3 local minimum energy structures that produce stable phonon dispersions to reveal an amorphous-like coherence-channel thermal transport mechanism in these crystals. Interestingly, an inter-channel conversion between the population- and coherence-channel of the phonons occurs when the c-MAPbI3 changes across these different structures at the same temperature. Such an effect is not yet observed in simple atomic crystals. Our work also shows that existing thermal transport intuitions based on the phonon gas model can be misleading in such hybrid crystals. Further, the dominance of the non-traditional coherence-channel of phonons will affect the interpretation of other phonon-mediated processes in MAPbI3 and other hybrid perovskites.

Effects of high-order anharmonicity on anomalous lattice dynamics and thermal transport in fully filled skutterudite YbFe4Sb12

Accurately describing the lattice dynamics and microscopic mechanism of thermal transport in materials with low-lying flat phonon modes remains an outstanding challenge due to the intrinsic strong anharmonicity. In this paper, we investigate the lattice dynamics and thermal transport in skutterudite ${\mathrm{YbFe}}_{4}{\mathrm{Sb}}_{12}$ using a state-of-the-art first-principles-based anharmonic phonon renormalization technique and a unified theory of lattice thermal transport. In contrast to the previous phenomenological models that introduce additional resonant scattering terms or hopping channels, we show that the unusual total lattice thermal conductivity in ${\mathrm{YbFe}}_{4}{\mathrm{Sb}}_{12}$ can be accurately predicted by considering anharmonic phonon renormalization and coherence contributions from the off-diagonal terms of heat flux operators. Both the cubic and quartic anharmonicities are essential for precisely predicting the significant shift in phonon energies. Specifically, the anharmonicity-induced phonon stiffening of the low-lying flat modes significantly enhances the thermal conductivity of particlelike phonons, e.g., by up to a factor of 1.6 at 300 K, by suppressing the cubic coupling strength and altering the scattering phase space, resulting in much-improved agreement with experiments. By further including the coherence contributions, the predicted total thermal conductivity increases by \ensuremath{\sim}22% throughout the entire temperature range, reproducing well the experimental values in both magnitude and temperature dependence. In this paper, we highlight the strong impact of higher-order anharmonicity on lattice dynamics and thermal transport in the filled skutterudite ${\mathrm{YbFe}}_{4}{\mathrm{Sb}}_{12}$. The insights gained in this paper will be helpful for manipulating the thermal properties of skutterudites and potentially other complex materials with strong anharmonicity, which can improve their performance in applications such as thermoelectrics, ferroelectrics, and photovoltaics.