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$\beta-Ga_2O_3$ is a promising material candidate for next-generation high power devices even as its low thermal conductivity ($\kappa$) limits utilization due to an inability to sufficiently dissipate heat. Despite its importance, a significant discrepancy persists between experimental results and computational models regarding $\beta-Ga_2O_3$'s anisotropic thermal conductivity. Specifically, computational results are within experimental error bounds for $\kappa_{100}$ and $\kappa_{001}$ while underpredicting $\kappa_{010}$, suggesting that the bare phonon models used in literature are missing essential physics related to the anisotropic thermal transport. In response, we compute the anisotropic $\kappa$ using first-principles and the Pierels-Boltzmann transport equation (PBTE) under different approximations. For the simplest model, we consider the heat carriers to be harmonic phonons with scattering rates obtained perturbatively. These results are then compared to those obtained by including phonon renormalization and four-phonon scattering. Our results show that accounting for phonon renormalization resolves the discrepancy between experiment and theory. This is because phonon renormalization leads to an anisotropic $\kappa$ enhancement caused by directionally-dependent changes in the phonon group velocities accompanied by a general increase in phonon lifetime. Owing to the crucial role of these anharmonic interactions in accurately describing anisotropic thermal transport, we also explore the anharmonicity of individual atoms and show that the octahedrally-coordinated gallium atom is the most anharmonic and thus most likely responsible for the failure of the harmonic phonon model to describe thermal transport in this material. Finally, we demonstrate that atomic anharmonicities could be used as a useful metric to guide the tailoring of vibrational properties.

FOS, which means light in Greek, is an open-source program for Fast Optical Spectrum calculations of nanoparticle media. This program takes the material properties and a description of the system as input, and outputs the spectral response including the reflectance, absorptance, and transmittance. Previous open-source codes often include only one portion of what is needed to calculate the spectral response of a nanoparticulate medium, such as Mie theory or a Monte Carlo method. FOS is designed to provide a convenient fully integrated format to remove the barrier as well as providing a significantly accelerated implementation with compiled Python code, parallel processing, and pre-trained machine learning predictions. This program can accelerate optimization and high throughput design of optical properties of nanoparticle or nanocomposite media, such as radiative cooling paint and solar heating liquids, allowing for the discovery of new materials and designs. FOS also enables convenient modeling of lunar dust coatings, combustion particulates, and many other particulate systems. In this paper we discuss the methodology used in FOS, features of the program, and provide four case studies., Comment: 38 pages, 6 figures

First-principles prediction of thermal conductivity and radiative properties is crucial. However, computing phonon scattering, especially for four-phonon scattering, could be prohibitively expensive, and the thermal conductivity even for silicon was still under-predicted and not converged in the literature. Here we propose a method to estimate scattering rates from a small sample of scattering processes using maximum likelihood estimation. The computational cost of estimating scattering rates and associated thermal conductivity and radiative properties is dramatically reduced by over 99%. This allows us to use an unprecedented q-mesh of 32*32*32 for silicon and achieve a converged thermal conductivity value that agrees much better with experiments. The accuracy and efficiency of our approach make it ideal for the high-throughput screening of materials for thermal and optical applications.

Inelastic scattering processes typically introduce friction among carriers and reduce the transport properties of photons, phonons, and electrons. However, we predict that in contrast to the role in reducing thermal conductivity, four-phonon scattering dominates near-field radiative heat transfer (NFRHT) in both boron arsenide~(BAs) and boron antimonide. Including four-phonon scattering results in a nearly 400-fold increase in the total heat flux between two BAs thin-films compared to three-phonon scattering alone. This non-intuitive enhancement arises from the large number of NFRHT channels activated by four-phonon scattering outcompete the effect of decreased coupling strength of surface phonon polaritons at the resonance frequency. Additionally, we point out that four-phonon scattering to decrease NFRHT in certain other systems.

The lattice thermal conductivity ($\kappa$) of two ceramic materials, cerium dioxide (CeO$_2$) and magnesium oxide (MgO), is computed up to 1500 K using first principles and the phonon Boltzmann Transport Equation (PBTE) and compared to time-domain thermoreflectance (TDTR) measurements up to 800 K. Phonon renormalization and the four-phonon effect, along with high temperature thermal expansion, are integrated in our \textit{ab initio} molecular dynamics (AIMD) calculations. This is done by first relaxing structures and then fitting to a set of effective force constants employed in a temperature-dependent effective potential (TDEP) method. Both three-phonon and four-phonon scattering rates are computed based on these effective force constants. Our calculated thermal conductivities from the PBTE solver agree well with literature and our TDTR measurements. Other predicted thermal properties including thermal expansion, frequency shift, and phonon linewidth also compare well with available experimental data. Our results show that high temperature softens phonon frequency and reduces four-phonon scattering strength in both ceramics. Compared to MgO, we find that CeO$_2$ has weaker four-phonon effect and renormalization greatly reduces its four-phonon scattering rates.

The thermal conductivity of monolayer graphene is an outstanding challenge with no consensus reached on its exact value and length convergence so far. We consider four-phonon scattering, phonon renormalization, and an exact solution to phonon Boltzmann transport equation (BTE) from first principles. Using this computational formalism with unprecedented sampling grid, we show that when four-phonon scattering is included the thermal conductivity is convergent with system size at a room temperature value of 1300 W/(m$\cdot$K), which is lower than that of diamond. On the contrary, considering three-phonon scattering only yields divergence with size due to the momentum-conserving normal processes of flexural phonons.

From ultraviolet to mid-infrared region, light-matter interaction mechanisms in semiconductors progressively shift from electronic transitions to phononic resonances and are affected by temperature. Here, we present a parallel temperature-dependent treatment of both electrons and phonons entirely from first principles, enabling the prediction of full-spectrum optical responses. At elevated temperatures, $\textit{ab initio}$ molecular dynamics is employed to find thermal perturbations to electronic structures and construct effective force constants describing potential landscape. Four-phonon scattering and phonon renormalization are included in an integrated manner in this approach. As a prototype ceramic material, cerium dioxide (CeO$_2$) is considered in this work. Our first-principles calculated refractive index of CeO$_2$ agrees well with measured data from literature and our own temperature-dependent ellipsometer experiment.

Micro-Raman spectroscopy has become an important tool in probing thermophysical behavior in emerging functional materials such as two-dimensional (2D) layered structures. Localized heating by the focused Raman excitation laser beam is expected to produce both stress and nonequilibrium temperature distributions in the material. Here we investigate the effects of hot optical phonons in the Raman spectra of molybdenum disulphide (MoS2) and distinguish them from those caused by thermally-induced compressive stress, which causes a Raman frequency blue shift in the focused Raman laser spot. With the stress effect accounted for in micro-Raman measurements, the degree of nonequilibrium between the hot optical phonons and the acoustic phonon bath is found to be much smaller than those observed in prior micro-Raman measurements of suspended graphene. The observation agrees with a first-principles based theoretical prediction of overpopulated zone-center optical phonons compared to other optical phonons in the Brillouin zone and acoustic phonons. The findings provide detailed insight into the energy relaxation processes in this emerging 2D transition metal dichalcogenide (TMD) electronic and optoelectronic material and clarify an important question in micro-Raman measurements of thermal transport in this and other 2D materials., Comment: 19 pages. 4 figures

Previous multitemperature model (MTM) resolving phonon temperatures at the polarization level and measurements have uncovered remarkable nonequilibrium among different phonon polarizations in laser irradiated graphene and metals. Here, we develop a semiconductor-specific MTM (SC-MTM) by including electron-hole pair generation, diffusion, and recombination, and show that a phonon polarization-level model does not yield observable polarization-based nonequilibrium in laser-irradiated molybdenum disulfide (MoS$_2$). In contrast, appreciable nonequilibrium is predicted between zone-center optical phonons and the other modes. The momentum-based nonequilibrium ratio is found to increase with decreasing laser spot size and interaction with a substrate. This finding is relevant to the understanding of the energy relaxation process in two-dimensional optoelectronic devices and Raman measurements of thermal transport.

The Raman peak position and linewidth provide insight into phonon anharmonicity and electron-phonon interactions (EPI) in materials. For monolayer graphene, prior first-principles calculations have yielded decreasing linewidth with increasing temperature, which is opposite to measurement results. Here, we explicitly consider four-phonon anharmonicity, phonon renormalization, and electron-phonon coupling, and find all to be important to successfully explain both the $G$ peak frequency shift and linewidths in our suspended graphene sample at a wide temperature range. Four-phonon scattering contributes a prominent linewidth that increases with temperature, while temperature dependence from EPI is found to be reversed above a doping threshold ($\hbar\omega_G/2$, with $\omega_G$ being the frequency of the $G$ phonon).

FourPhonon is a computational package that can calculate four-phonon scattering rates in crystals. It is built within ShengBTE framework, which is a well-recognized lattice thermal conductivity solver based on Boltzmann transport equation. An adaptive energy broadening scheme is implemented for the calculation of four-phonon scattering rates. In analogy with $thirdorder.py$ in ShengBTE, we also provide a separate python script, $Fourthorder.py$, to calculate fourth-order interatomic force-constants. The extension module preserves all the nice features of the well-recognized lattice thermal conductivity solver ShengBTE, including good parallelism and straightforward workflow. In this paper, we discuss the general theory, program design, and example calculations on Si, BAs and $\mathrm{LiCoO_2}$.

Radiative cooling has recently revived due to its significant potential as an environmentally friendly cooling technology. However, the design of particle-matrix cooling nanocomposites was generally carried out via tedious trial-and-error approaches, and the atomistic physics for efficient radiative cooling was not well understood. In this work, we identify the atomistic metrics of Barium Sulfate (BaSO$_4$) nanocomposite, which is an ultra-efficient radiative cooling material, using a predictive first-principles approach coupled with Monte Carlo simulations. Our results show that BaSO$_4$-acrylic nanocomposites not only attain high total solar reflectance of 92.5% (0.28 - 4.0 um), but also simultaneously demonstrate high normal emittance of 96.0% in the sky window region (8 - 13 um), outperforming the commonly used $\alpha$-quartz ($\alpha$-SiO$_2$). We identify two pertinent characters of ultra-efficient radiative cooling paints: i) a balanced band gap and refractive index, which enables strong scattering while negating absorption in the solar spectrum, and ii) a sufficient number of infrared-active optical resonance phonon modes resulting in abundant Reststrahlen bands and high emissivity in the sky window. The first principles approach and the resulted physical insights in this work pave the way for further search of ultra-efficient radiative cooling materials., Comment: 5 pages, 4 figures

While machine learning (ML) has shown increasing effectiveness in optimizing materials properties under known physics, its application in challenging conventional wisdom and discovering new physics still remains challenging due to its interpolative nature. In this work, we demonstrate the potential of using ML for such applications by implementing an adaptive ML-accelerated search process that can discover unexpected lattice thermal conductivity ($\kappa_l$) enhancement instead of reduction in aperiodic superlattices (SLs) as compared to periodic superlattices. We use non-equilibrium molecular dynamics (NEMD) simulations for high-fidelity calculations of $\kappa_l$ for a small fraction of SLs in the search space, along with a convolutional neural network (CNN) which can rapidly predict $\kappa_l$ for a large number of structures. To ensure accurate prediction by the CNN for the target unknown structures, we iteratively identify aperiodic SLs containing structural features which lead to locally enhanced thermal transport, and include them as additional training data for the CNN in each iteration. As a result, our CNN can accurately predict the high $\kappa_l$ of aperiodic SLs that are absent from the initial training dataset, which allows us to identify the previously unseen exceptional structures. The identified RML structures exhibit increased coherent phonon contribution to thermal conductivity owing to the presence of closely spaced interfaces. Our work describes a general purpose machine learning approach for identifying low-probability-of-occurrence exceptional solutions within an extremely large subspace and discovering the underlying physics.

Radiative cooling is a passive cooling technology that offers great promises to reduce space cooling cost, combat the urban island effect and alleviate the global warming. To achieve passive daytime radiative cooling, current state-of-the-art solutions often utilize complicated multilayer structures or a reflective metal layer, limiting their applications in many fields. Attempts have been made to achieve passive daytime radiative cooling with single-layer paints, but they often require a thick coating or show partial daytime cooling. In this work, we experimentally demonstrate remarkable full daytime sub-ambient cooling performance with both BaSO4 nanoparticle films and BaSO4 nanocomposite paints. BaSO4 has a high electron bandgap for low solar absorptance and phonon resonance at 9 um for high sky window emissivity. With an appropriate particle size and a broad particle size distribution, BaSO4 nanoparticle film reaches an ultra-high solar reflectance of 97.6% and high sky window emissivity of 0.96. During field tests, BaSO4 film stays more than 4.5C below ambient temperature or achieves average cooling power of 117 W/m2. BaSO4-acrylic paint is developed with 60% volume concentration to enhance the reliability in outdoor applications, achieving solar reflectance of 98.1% and sky window emissivity of 0.95. Field tests indicate similar cooling performance to the BaSO4 films. Overall, our BaSO4-acrylic paint shows standard figure of merit of 0.77 which is among the highest of radiative cooling solutions, while providing great reliability, the convenient paint form, ease of use and the compatibility with commercial paint fabrication process., Comment: 23 pages, 7 figures, 1 video. For associate video file (Video S1.mp4), see https://www.dropbox.com/s/9cwcdeoyqhv959y/Video%20S1.mp4

A fundamental limit of current radiative cooling systems is that only the top surface facing deep-space can provide the radiative cooling effect, while the bottom surface cannot. Here, we propose and experimentally demonstrate a concept of "concentrated radiative cooling" by nesting a radiative cooling system in a mid-infrared reflective trough, so that the lower surface, which does not contribute to radiative cooling in previous systems, can radiate heat to deep-space via the reflective trough. Field experiments show that the temperature drop of a radiative cooling pipe with the trough is more than double that of the standalone radiative cooling pipe. Furthermore, by integrating the concentrated radiative cooling system as a preconditioner in an air conditioning system, we predict electricity savings of $>75\%$ in Phoenix, AZ, and $>80\%$ in Reno, NV, for a single-story commercial building.

Radiative cooling is a passive cooling technology by reflecting sunlight and emitting radiation in the atmospheric sky window. Although highly desired, full daytime sub-ambient radiative cooling in commercial-like single-layer particle-matrix paints is yet to be achieved. In this work, we have demonstrated full daytime sub-ambient radiative cooling in CaCO3-acrylic paint by adopting large bandgap fillers, a high particle concentration and a broad size distribution. Our paint shows the highest solar reflectance of 95.5% among paints and a high sky-window emissivity of 0.94. Field tests show cooling power exceeding 37 W/m2 and lower surface temperature more than 1.7C below ambient at noon. A figure of merit RC is proposed to compare the cooling performance under different weather conditions. The RC of our cooling paint is 0.62, among the best radiative cooling performance while offering unprecedented benefits of the convenient paint form, low cost, and the compatibility with commercial paint fabrication process., Comment: 14 pages, 8 figures, 1 video. For associate video file (Movie S1.mp4), see https://www.dropbox.com/s/wow1vr523km7rwc/MovieS1.mp4

Transparent oxide materials, such as $CuAlO_{2}$, a p-type transparent conducting oxide (TCO), have recently been studied for high temperature thermoelectric power generators and coolers for waste heat. TCO materials are generally low cost and non-toxic. The potential to engineer them through strain and nano-structuring are two promising avenues toward continuously tuning the electronic and thermal properties to achieve high zT values and low cost/kW-hr devices. In this work, the strain-dependent lattice thermal conductivity of 2H $CuAlO_{2}$ is computed by solving the phonon Boltzmann transport equation with interatomic force constants extracted from first-principles calculations. While the average bulk thermal conductivity is around 32 W/(K-m) at room temperature, it drops to between 5-15 W/(K-m) for typical experimental grain sizes from 3nm to 30nm at room temperature. We find that strain can offer both an increase as well as a decrease in the thermal conductivity as expected, however the overall inclusion of small grain sizes dictates the potential for low thermal conductivity in this material.

The non-equilibrium Green's function (NEGF) method with B\"uttiker probe scattering self-energies is assessed by comparing its predictions for the thermal boundary resistance with molecular dynamics (MD) simulations. For simplicity, the interface of Si/heavy-Si is considered, where heavy-Si differs from Si only in the mass value. With B\"uttiker probe scattering parameters tuned against MD in homogeneous Si, the NEGF-predicted thermal boundary resistance quantitatively agrees with MD for wide mass ratios. Artificial resistances that the unaltered Landauer approach yield at virtual interfaces in homogeneous systems are absent in the present NEGF approach. Spectral information result from NEGF in its natural representation without further transformations. The spectral results show that the scattering between different phonon modes plays a crucial role in thermal transport across interfaces. B\"uttiker probes provide an efficient and reliable way to include anharmonicity in phonon related NEGF. NEGF including the B\"uttiker probes can reliably predict phonon transport across interfaces and at finite temperatures., Comment: 4 pages, 5 figures

Recent studies reveal that four-phonon scattering is generally important in determining thermal conductivities of solids. However, these studies have been focused on materials where thermal conductivity $\kappa$ is dominated by acoustic phonons, and the impact of four phonon scattering, although significant, is still generally smaller than three-phonon scattering. In this work, taking AlSb as example, we demonstrated that four-phonon scattering is even more critical to three-phonon scattering as it diminishes optical phonon thermal transport, and therefore significantly reduces the thermal conductivities of materials in which optical branches have long three-phonon lifetimes. Also, our calculations show that four-phonon scattering can play an extremely important role in weakening the isotope effect on $\kappa$. Specifically, four-phonon scattering reduces the room-temperature $\kappa$ of the isotopically pure and natural-occurring AlSb by 70$\%$ and 50$\%$, respectively. The reduction for isotopically pure and natural-occurring c-GaN is about 34$\%$ and 27$\%$, respectively. For isotopically-pure w-GaN, the reduction is about 13$\%$ at room temperature and 25$\%$ at 400 K. These results provided important guidance for experimentalists for achieving high thermal conductivities in III-V compounds for applications in semiconductor industry.

Zone-center optical phonon linewidth is a key parameter for infrared and Raman spectra as well as the Lorenz oscillator model. While three-phonon scattering was often assumed to be the leading contribution, in this work we find, surprisingly, that higher-order phonon scattering universally plays a significant or even dominant role over three-phonon scattering at room temperature, and more so at elevated temperatures, for a wide range of materials including diamond, Si, Ge, boron arsenide (BAs), cubic silicon carbide (3C-SiC), and $\alpha$-quartz. This is enabled by the large fourphonon scattering phase space of zone-center optical phonons, and distinct from heat conduction where at room temperature four-phonon scattering is still secondary to three-phonon scattering. Moreover, our results imply that five-phonon and even higher-order scattering may be significant for some large band-gap materials, e.g., BAs. Our predicted infrared optical properties through the Lorenz oscillator model, after including four-phonon scattering, show much better agreement with experimental measurements than those three-phonon based predictions. This work will raise broad interest of studying high-order scattering in various areas beyond heat conduction.

Separating electron and phonon thermal conductivity components is imperative for understanding the principle thermal transport mechanisms in metals and highly desirable in many applications. In this work, we predict the mode-dependent electron and phonon thermal conductivities of 18 different metals at room-temperature from first-principles. Our first-principles predictions, in general, agree well with experimental data. We find that the phonon thermal conductivity is in the range of 2 - 18 $W/mK$, which accounts for 1% - 40% of the total thermal conductivity. It is also found that the phonon thermal conductivities in transition metals and transition-intermetallic-compounds (TICs) are non-negligible compared to noble metals due to their high phonon group velocities. Besides, the electron-phonon coupling effect on phonon thermal conductivity in transition metals and intermetallic compounds is stronger than that of nobles, which is attributed to the larger electron-phonon coupling constant with a high electron density of state within Fermi window and high phonon frequency. The noble metals have higher electron thermal conductivities compared to transition metals and TICs, which is mainly due to the weak electron-phonon coupling in noble metals. It is also shown that the Lorenz ratios of transition metals and transition-intermetallic-compounds hold larger deviations from the Sommerfeld value $L_0=2.44 \times 10^{-8} W \Omega K^{-2}$. We also find the mean free paths (MFPs) for phonon (within 10 nm) are smaller than those of electron (5 - 25 nm). The electrical conductivity and electron thermal conductivity are strongly related to the MFPs of the electron., Comment: 23pages,10 figures, 2 tables

Thermal boundary conductance (TBC) is critical in many thermal and energy applications. A decades-old puzzle has been that many of the measured TBCs, such as those well characterized across Al/Si and ZnO/GaN interfaces, significantly exceed theoretical results or even the absolute upper limit called the ``radiation limit", suggesting the failure of the theory. Here, we identify that for high-transmission interfaces, the commonly assumed phonon local thermal equilibrium adjacent to the interface fails, and the measurable phonon temperatures are not their emission temperature. We hence develop a ``nonequilibrium Landauer approach" and define the unique ``dressed" and ``intrinsic" TBCs. Combining our approach even with a simple diffuse mismatch model (DMM) nearly doubles the theoretical TBCs across the Al/Si and ZnO/GaN interfaces, and the theoretical results agree with experiments for the first time. The radiation limit is also redefined and found to increase over 100\% over the original radiation limit, and it can now well bound all the experimental data.

Phonon energies at finite temperatures shift away from their harmonic values due to anharmonicity. In this paper, we have realized the rigorous calculation of phonon energy shifts of silicon by three and four-phonon scattering from first principles. The anharmonic fourth-order force constants are calculated by considering up to the fifth nearest neighbors. The results agree reasonably well with available data from inelastic neutron scattering throughout the Brillouin zone. Surprisingly, the frequency shifts of optical phonon modes near the $\Gamma$ point are sensitive to the cutoff radius of the fourth-order force constants, in contrast to the four-phonon scattering rates, which nearly saturate when considering the second nearest neighbors. We have also compared the results with ab initio molecular dynamics simulations and found that the higher order of anharmonicity is important for optical phonons. Our work provides critical insight into the anharmonic phonon frequency shift and will have significant impact on the thermal and optical applications.

Although extensive experimental and theoretical works have been conducted to understand the ballistic and diffusive phonon transport in nanomaterials recently, direct observation of temperature and thermal nonequilibrium of different phonon modes has not been realized. Herein, we have developed a method within the framework of molecular dynamics to calculate the temperatures of phonon in both real and phase spaces. Taking silicon thin film and graphene as examples, we directly obtained the spectral phonon temperature (SPT) and observed the local thermal nonequilibrium between the ballistic and diffusive phonons. Such nonequilibrium also generally exists across interfaces and is surprisingly large, and it provides an additional thermal interfacial resistance mechanism. Our SPT results directly show that the vertical thermal transport across the dimensionally mismatched graphene/substrate interface is through the coupling between flexural acoustic phonons of graphene and the longitudinal phonons in the substrate with mode conversion. In the dimensionally matched interfaces, e.g. graphene/graphene junction and graphene/boron nitride planar interfaces, strong coupling occurs between the acoustic phonon modes on both sides, and the coupling decreases with interfacial mixing. The SPT method together with the spectral heat flux can eliminate the size effect of the thermal conductivity prediction induced from ballistic transport. Our work shows that in thin films and across interfaces, phonons are in local thermal nonequilibrium., Comment: 14 pages, 10 figures

We report compressive mechanical response of graphene foams (GFs) and the thermal resistance ($R_{TIM}$) between copper (Cu) and GFs, where GFs were prepared by the chemical vapor deposition (CVD) method. We observe that Young's modulus ($E_{GF}$) and compressive strength ($\sigma_{GF}$) of GFs have a power law dependence on increasing density ($\rho_{GF}$) of GFs. The maximum efficiency of absorbed energy ($\eta_{max}$) for all GFs during the compression is larger than ~0.39. We also find that a GF with a higher $\rho_{GF}$ shows a larger $\eta_{max}$. In addition, we observe that the measured $R_{TIM}$ of Cu/GFs at room temperature with a contact pressure of 0.25 MP applied increases from ~50 to ~90 $mm^2K/W$ when $\rho_{GF}$ increases from 4.7 to 31.9 $mg/cm^3$.

The measured frequencies and intensities of different first- and second- order Raman peaks of suspended graphene are used to show that optical phonons and different acoustic phonon polarizations are driven out of local equilibrium inside a sub-micron laser spot. The experimental results are correlated with a first principles-based multiple temperature model to suggest a considerably lower equivalent local temperature of the flexural phonons than those of other phonon polarizations. The finding reveals weak coupling between the flexural modes with hot electrons and optical phonons. Since the ultrahigh intrinsic thermal conductivity of graphene has been largely attributed to contributions from the flexural phonons, the observed local non-equilibrium phenomena have important implications for understanding energy dissipation processes in graphene-based electronic and optoelectronic devices, as well as in Raman measurements of thermal transport in graphene and other two-dimensional materials., Comment: 10 pages, 5 figures

Equilibrium molecular dynamics (EMD) simulations along with the Green-Kubo formula have been widely used to calculate lattice thermal conductivities. Previous studies, however, focused primarily on the calculated thermal conductivities, with the uncertainty of the thermal conductivities remaining poorly understood. In this paper, we study the quantification of the uncertainty by using solid argon, silicon, and germanium as model material systems, and examine the origin of the observed uncertainty. We find that the uncertainty increases with the upper limit of the correlation time, $t_{\text{corre, UL}}$, and decreases with the total simulation time, $t_{\text{total}}$, whereas the velocity initialization seed, simulation domain size, temperature, and type of material have minimal effects. The relative uncertainties of the thermal conductivities for solid argon, silicon, and germanium under different simulation conditions all follow a similar trend, which can be fit with a "universal" square-root relation, as $\sigma_{k_x}/k_{x, \text{ave}} = 2(t_{\text{total}}/t_{\text{corre, UL}})^{-0.5}$. We have also conducted statistical analysis of the EMD-predicted thermal conductivities and derived a formula that correlates the relative error bound ($Q$), confidence level ($P$), $t_{\text{corre, UL}}$, $t_{\text{total}}$, and number of independent simulations ($N$). We recommend choosing $t_{\text{corre, UL}}$ to be 5-10 times the effective phonon relaxation time, $\tau_{\text{eff}}$, and choosing $t_{\text{total}}$ and $N$ based on the desired relative error bound and confidence level. This study provides new insights into understanding the uncertainty of EMD-predicted thermal conductivities. It also provides a guideline for running EMD simulations to achieve a desired relative error bound with a desired confidence level and for reporting EMD-predicted thermal conductivities., Comment: Main article: 14 pages, 11 figures; Supplemental information: 4 pages, 3 figures