Phonon Thermal Conductivity Research Articles

Atomistic insights into mechanical and thermal properties of stanene with defects

Stanene, two-dimensional, graphene-like buckled honeycomb structure, has been deemed as a potential material for the next generation nano-electronics application. In electronic applications, the materials are subjected to both thermal and mechanical loadings. In addition, structural defects are inevitable during synthesis of nanomaterials. Therefore, it is essential to study the mechanical and thermal properties of stanene with various structural defects. We investigated the effects of point vacancy, bivacancy and Stone-Wales defects on tensile response and thermal transport of single-layer bulk stanene sheets using classical molecular dynamics (MD) simulations. MEAM potential is used to describe the inter-atomic forces in order to predict the properties of the stanene adequately. We probed the deformation process of defective bulk stanene by applying uniaxial tensile loading. Our study suggests that tensile strength and elastic modulus of stanene decrease with the increment of defect concentrations. Moreover, stanene sheet with Stone-Wales defect shows less in-plane stiffness to the loading. Using non-equilibrium molecular dynamics (NEMD) method, we found that, the phonon thermal conductivity of stanene is highly sensitive to defect concentrations. Only 0.1% of defect concentrations result in about 40% reduction in thermal conductivity. To elucidate the underlying mechanism responsible for this reduction, vibrational density of states (vDOS) are calculated. Overall, our reported results provide an insight into the effect of defects in mechanical and thermal properties of defective bulk stanene and will facilitate further tailoring of the design of stanene based nanoelectronics device.

Low cross-plane thermal conductivity of sub-1 µm polycrystalline silicon thin films for thermoelectric applications

Silicon thin films with sub-1 µm thickness are of technological significance in many electronic and energy conversion devices. While a number of previous works have investigated the in-plane thermal conductivity of silicon films, less reported is their cross-plane thermal conductivity, particularly at sub-1 µm thickness. Here, we report on the cross-plane thermal conductivity of sub-1 µm, undoped, polycrystalline silicon films (75 and 246 nm) with columnar grain structure at room temperature. Using an optical pump-probe thermoreflectance metrology and a semi-classical phonon transport model, we find the cross-plane thermal conductivity to be 4.5 ± 0.8 and 12.5 ± 2.3 W m−1 K−1 for the 75 and 246 nm films, respectively. To the best of our knowledge, the cross-plane thermal conductivities we report here are the lowest ever reported for undoped polycrystalline silicon films with columnar grain structure, which can be ascribed to the impact of increased phonon scattering by a higher density of defects as compared to previous data. Given that a significant reduction in phonon thermal conductivity is required to enhance the thermoelectric energy conversion efficiency, our findings may be promising particularly for thermoelectric energy conversion applications.

Simulating stress-tunable phonon and thermal properties in heterostructured AlN/GaN/AlN-nanofilms

The acoustic phonon and thermal properties of GaN-based heterostructured nanofilms are investigated theoretically considering the effects of quantum confinement and prestress fields. The continuum elastic model is utilized to derive the acoustic phonon dispersion relations of GaN-based nanofilms in which the prestress fields are taken into account. The numerical results demonstrate that prestress fields can alter acoustic phonon properties significantly, such as dispersion relation and phonon group velocities. The trend of variation turns to be opposite as the direction of prestress fields reverses. The change of phonon properties under various prestress fields is sensitive to the thickness of core layer in heterostructured nanofilms. Moreover, the modification of acoustic phonon properties in heterostructured nanofilms under prestress fields gives rise to the change of phonon thermal conductivities for different phonon modes. Moreover, prestress fields can modify the influence of temperature-dependent phonon thermal conductivity of GaN-based heterostructured nanofilms. The results in this work could be helpful for the thermal management and rational design of high-performance in nano/microelectronic devices.

Enhanced Thermoelectric Properties of Armchair Graphene Nanoribbons with Pore Passivation

There is a need to discover efficient thermoelectric materials that can generate electricity from waste heat and could play an important role in a global sustainable energy solution. Graphene Nanoribbons have been explored for a range of pore dimensions in order to achieve better thermoelectric performance. In this paper, we investigate the thermoelectric properties of porous armchair graphene nanoribbons by introducing hydrogen atoms as passivators at the pore surfaces. The aim of this work is to study the influence of pore passivation on the thermoelectric parameters as a function of pore geometry so as to open the possibility for an optimal pore engineering which can significantly improve the thermoelectric efficiency. The results show that the phonon thermal conductivity has a very little dependence on the pore edge passivation. An improvement in thermoelectric figure of merit is achieved due to the increased values of the power factor with consistent values of thermalconductivity. The unique thermoelectric properties of graphene nanoribbons with pore passivation suggest their great potentials for nanoscale thermoelectric applications. Within ballistic transport regime, semi-empirical extended Huckel method has been used for electrical properties while Tersoff potential has been employed for phononic calculations.

Characteristics of acoustic phonon transport and thermal conductance in multi-frame graphene nanoribbons

Using non-equilibrium Green’s function method and maintaining the zigzag carbon chains unchanged, we investigate the transmission rate of acoustic phonon and the reduced thermal conductance through multi-frame graphene nanoribbons (GNRs). The results show that the reduced thermal conductance approaches [Formula: see text] in the limit [Formula: see text]. Due to the fact that only long wavelength acoustic phonons with zero cutoff frequency are excited at such low temperatures, the scattering influence on the long wavelength acoustic phonons by the multi-frame in GNRs can be ignored and these phonons can go through the scattering region perfectly. As the temperature goes up, the reduced thermal conductance decreases. This is because the high-frequency phonons are excited and these high-frequency phonons are scattered easily by the scattering structures. With the further rise in temperature, acoustic phonon modes with the cutoff frequency greater than zero are excited, which leads to a rapid increase of the reduced thermal conductance. This study shows that changing the frame structure by a small length can lead to a significant change of transmission probability. In the higher frequency region, the transmission spectra display complex peak-dip structures, which results from the fact that in higher frequency region more phonon modes are excited and scattered in the middle scattering region with multi-frames, and the scattering phonons are coupled with the incident phonons, with the increase of the length of frame structure, the scattering of the phonon is also enhanced, which leads to the decrease in the phonon transmission; by changing the frame structure, the parameters can effectively adjust the position of low-frequency phonon transmission valley. The frame structure can induce high-frequency phonon blocking effect and the blocking effect depending on the structure parameter of the frame. When the single frame and double frame GNRs are narrowest, the scattering from low-frequency phonons by the scattering structure is largest, which leads to the fact that the reduced thermal conductance is smallest at low temperatures; however, at high temperature, the reduced thermal conductance is biggest when the single frame and double frame GNRs are narrowest. This is because the scattering from high-frequency phonons by the scattering structure is the smallest. When the length of the frame structure is unchanged, a graphite chain is inserted in which the reduced thermal conductance is always reduced. These results provide an effective theoretical basis for designing the thermal transport quantum devices based on GNRs.

Oxygen‐vacancy‐mediated microstructure and thermophysical properties in Zr3Ln4O12 for high‐temperature applications

AbstractYttria‐stabilized zirconia (YSZ) has been considered as state‐of‐the‐art material for high‐temperature thermal barrier coatings, which provide thermal insulation to the superalloy components in gas turbines and jet engines. Oxygen vacancies induced by yttria substitutions are believed to be mainly responsible for the low thermal conductivity of YSZ due to their phonon scattering effect. However, high mobility of oxygen vacancies in YSZ leads to a rapid oxygen diffusion at high temperatures, therefore accelerates the failure of coatings by grain coarsening, sintering, and simultaneous oxidation of the underlying metallic bondcoat. In the present research, we further explored in the ZrO2–Ln2O3 binary phase diagram and synthesized a series of ceramic materials with the chemical formula of Zr3Ln4O12 (Ln = La, Gd, Y, Er, and Yb), in which more oxygen vacancies were involved and extremely low phonon thermal conductivities (1.3‐1.6 W/m·K) were obtained, even approaching to the theoretical minimum. In addition, the mobility of these oxygen vacancies was remarkably suppressed by the lattice ordering with the decrease of Ln3+ radius, as confirmed by X‐ray diffraction, Raman and transmission electron microscopy. Thus, the oxygen barrier property and sintering resistance were significantly enhanced accordingly, which makes Zr3Ln4O12 compounds promising thermal barrier coating materials for next generation gas turbines and jet engines.

Photon‐Mediated Phonon Heat Current Between Distant Graphene Sheets Inserted Into a Cavity

In this work, a mechanism of achieving phonon heat current between distant graphene sheets inserted into a cavity with two reflectors at different temperatures are presented. The photon‐mediated pseudospin interaction between two graphene sheets and electron–phonon interaction in each graphene sheet lead to the generation of this phonon heat current. We calculate the phonon heat current, thermal conductivity, and current–current correlation functions between distant graphene sheets. This phonon heat current can be manipulated by the energy flow density and frequency of photons. The giant heat current and thermal conductivity of phonons induced by intense photon field indicate that this mechanism has potential applications on the chip cooling, and far‐range heat transfer.

The thermoelectric performance of dumbbell silicene nanoribbons

ABSTRACTDumbbell silicene, a stable allotrope of low-buckled (LB) silicene containing both sp2 and sp3 hybridized states, is a new topic in current graphene-derived material research community. In this paper, we performed a comprehensive study on the thermoelectric property of dumbbell silicene nanoribbons (DB-SNRs) via utilizing nonequilibrium Green's function (NEGF) method as implemented in the density functional based tight-binding (DFTB) framework. Our results show that DB-SNRs present superb electronic transport properties, e.g., the room temperature Seebeck coefficient could approach 2.11 mV/K (about 80% larger than that of LB silicene). A unique step-like width dependence of phononic thermal conductance is also observed in Z-DB-SNRs, which mainly attributes to localized phonon modes raised from the edged sp3 Si atoms. Based on the electronic and phononic transport coefficient, the thermoelectric performance of DB-SNRs is predicted and the stable ZT value at room temperature is found to be about 0.7(0.3) and 0.6(0.2) for A-DN-SNRs and Z-DB-SNRs with p(n)-type doping. Such thermoelectric performance could be further improved by increasing the temperature. The findings presented in this work shed light on the thermoelectric property of DB-SNRs and could provide helpful guideline for designing and fabricating of future Si-based thermoelectric devices.

Edge-oxidation effects on the thermoelectric properties in graphene nanoribbons

The thermal, electrical and thermoelectric properties in edge modified zigzag graphene nanoribbon are analyzed carefully by nonequilibrium Green's function formalism combined with first principles calculation. Epoxy (-O-) and hydroxyl groups (-OH) are considered for the ZGNR edge modification (ZGNR-O and ZGNR-OH). The results show that ZGNR-O and ZGNR-OH both can suppress obviously the phonon transport, leading to low phonon thermal conductance. While ZGNR-O and ZGNR-OH hardly suppress electron transport within the positive energy, which induces one conductance quantum plateau can be observed in ZGNR-O and ZGNR-OH. At the negative energies, ZGNR-O can suppress obviously the electron transport, which induces violent fluctuation of electronic transmissions, leading to high Seebeck coefficient and enhanced thermopower.

Control of oxygen content of n-type Bi2Te3 based compounds by sintering process and their thermoelectric properties

Oxygen content in n-type Bi2Te3-based alloys plays a crucial role in determining the thermoelectric properties. We aimed to control the residual oxygen that originated from the ball milling process; for this, sintering processes such as spark plasma sintering (SPS) and plasma activated sintering (PAS) were utilized. The reduction of oxygen content was successfully achieved with PAS, leading to improved electrical properties. With the removal of residual oxygen, the carrier concentration increased, resulting in reduced electrical resistivity. The phonon thermal conductivity was reduced due to the grain size of this sample, which was smaller than that of the hot-pressed (HP) samples. An enhanced value of the dimensionless figure of merit (ZT) of 0.83 at 473 K, an increase of 25.2% compared with that of the HP samples, was achieved. The selection of the appropriate sintering process should be considered to remove oxygen content, as well as to minimize grain growth.

(Invited) Isotopically Programmed Group IV Semiconductors: A Versatile Platform for Quantum Technologies

The introduction of stable isotopes as an additional degree of freedom in the growth of semiconductor films and quantum structures provides a wealth of opportunities to manipulate their basic properties, design an entirely new class of devices, and highlight subtle but important nanoscale and quantum phenomena. In this presentation, I will describe the historical context and outline the recent progress in the area of isotopically engineering group IV semiconductors with focus on nanoscale and quantum structures and devices. This ability to isotopically program semiconductor structures has been a powerful paradigm to investigate and manipulate some of the important physical properties of semiconductors and exploit them in innovative device structures [1-13]. Isotopes of an element differ in the number of neutrons in the nucleus. This creates differences between the isotopes in their lattice dynamics and nuclear properties. For instance, the slight difference in zero-point motion leads to a difference in atomic volume between the isotope atoms, which influences the lattice constant [3]. Also, the difference in electron-phonon coupling between crystals of different isotopic composition was found to affect the electronic band gap [4]. The nuclear spin is another significant difference between stable isotopes. For instance, natural silicon (Si) has three stable isotopes: 28Si, 29Si, and 30Si, with isotopic abundances of 92.23%, 4.67%, and 3.10%, respectively. Among these three isotopes, only 29Si has a nuclear spin of ½, whereas 28Si and 30Si are nuclear spin-free. This property has been crucial in the realization of Si-based quantum information devices [5-8]. One of the most drastic isotope related effect in semiconductors is found in phonon properties [9-13]. Mass fluctuation induced by isotope disorder acts as a substitutional defect in a crystal thus affecting the phonon mean free path and consequently the phononic thermal conductivity. Measurements on isotopically pure Ge [9] and Si [10] crystals showed an enhanced thermal conductivity as compared to their natural counterparts. Also, lower thermal conductivity was recently demonstrated in Si isotope superlattices [11]. All the properties of semiconductor stable isotopes have been investigated and exploited in bulk materials or thin films. Herein, we will describe the new opportunities emerging from the combinations of the isotope effects with size-related effects in nanoscale materials [14-18]. More specifically, we will discuss phonon engineering in metal catalyzed silicon nanowires with tailor-made isotopic compositions grown using isotopically enriched silane and german precursors 28SiH4, 29SiH4, 30SiH4, 74GeH4 and 76GeH4, with purity better than 99.9%. Isotopically mixed nanowires 28Six 30Si1-x with a composition close to the highest mass disorder (x ~ 0.5) were used as a playground to elucidate the interplay between nanoscale interface phenomena and heat transport [16]. We will show how isotopically engineered nanowire homo-junctions can be introduced to realize innovative phononic devices such as thermal diodes and thermal transistors. Additionally, we will also discuss the use of nuclear spin-full 29Si to engineer novel quantum devices in nuclear spin-free SiGe nanostructures. Finally, atomistic-level investigations of isotopically programmed nanoscale materials will be presented based on laser-assisted atom probe tomography [15,17].

Thermoelectric Characteristics of N-type Bi-Te Materials by Powder-Based Sintering Process

Thermal technology is one by using the Seebeck and the Peltier effect of converting thermal energy and electrical energy to each other reversibly by utilizing the semiconductor material used in power generation and cooling technology. The technology has been attracting attention as one eco-friendly energy technology that can improve energy conversion efficiency. The energy conversion efficiency of thermoelectric materials are presented by ZT, which is the dimensionless figure of merit, ZT = [(σα2)T]/κ where σ is electrical conductivity, α is Seebeck coefficient, T is absolute temperature, and κ is electronic and phonon thermal conductivity, respectively. Bismuth-telluride-based alloys are widely used as thermoelectric materials because of its high thermoelectric performance ZT near the room temperature in 273~473K As thermoelectric systems are constructed by connecting pairs of p-type and n-type materials in series, it is necessary to improve the performance of both p- and n-type materials to increase the value of ZT. For the Bismuth-telluride based alloys materials, research on improving the performance of n-type material is necessary because it is lower than that of p-type material. To improve the thermoelectric performance, materials with a high electrical conductivity (σ) and low thermal conductivity (κ) are required. Research on adding dopants to improve the electrical conductivity or on material nanostructuring, dispersed. In this study, In order to improve the performance of the n-type materials, the improvement of the characteristics was carried out by using the powder-based sintering process Considering the anisotropy of the synthesized thermoelectric materials, their physical properties were measured in both the vertical and horizontal directions with respect to the pressure direction. XRD (D/Max 2500, Rigaku) was used to analyze the phase characteristics of the sintered bodies, and the microstructural characteristics of the fracture surfaces of the sintered bodies were analyzed using a field-emission scanning electron microscope (FESEM, JSM- JEOL). To measure the electrical characteristics of the thermoelectric materials, the Seebeck coefficient and electrical conductivity were measured at temperatures ranging from room temperature to 423 K using the four-probe method (ZEM-3, Ulvac-Riko). The thermal conductivity was obtained by multiplying the thermal diffusivity, the specific heat of a sample, and its density after taking samples from the sintered bodies and measuring the thermal diffusivity using the laser flash method (LFA-467, Netzsch Co.). In this case, the average value of the specific heats of the samples of 0.167 was used, which was obtained by measuring the specific heats of multiple specimens using DSC (Pyris-1, Perkin Elmer). In addition, samples were taken from the sintered bodies, and their carrier concentrations and mobilities were measured through the Hall effect using the van der Pauw method (HMS-3000, Ecopia). Keyword : Bi2Te3, Thermoelectric materials, Powder, Sintering

Point defect effects on the thermal conductivity of [formula omitted]-SiC by molecular dynamics simulations

The point defect effects on phonon thermal conductivity of bulk crystalline β-SiC at 750 K and 1098 K are calculated with reverse non-equilibrium molecular dynamics method. Quantum correction is used to correct the corresponding temperatures. By extrapolation and quantum correction, the results of thermal conductivity of bulk β-SiC with point defects are achieved and corrected. For the eight types of point defects studied in this work, the thermal conductivity of SiC decreases with the increase of the concentration of certain point defects. The thermal conductivity drops rapidly at low concentration condition and gradually reaches certain value at high concentration condition. At high defect concentration condition, the temperature does not affect the thermal conductivity too much. The additional thermal resistivity is proportional to the concentration of all types of the point defects we studied. In these point defects, the interstitial SiTC decreases the thermal conductivity of β-SiC the most. On the other hand, the interstitial CTSi affects the thermal conductivity the least.

Simulation and prediction on phonon thermal conductivity of Al/Cu interface

Based on the non-equilibrium molecular dynamics (NEMD) method, phonon thermal conductivity of Al/Cu interfaces is systematically studied by considering the temperature dependence and size effect of thickness under different temperatures, for which an approximate mathematical model is also proposed. In this model, phonon thermal conductivity can be described by the thermal conductivities of Al and Cu thin materials according to the electrical thermal transport and the free electron approximation theories. Meanwhile, the thermal conductivities of each thin films can be described using the thermal conductivities of each bulk materials due to the Wiedemann-Franz Law under the thin thickness (less than the mean free path) and below the recrystallization temperature. The results show that the contribution of Al and Cu is inversely proportional to the interface thermal conductivity. This investigation based on the thermal and electronic conductivity of bulk materials, is helpful for understanding the interface heat transfer mechanism of interface structures, which also implies a potential method for the analysis of thermal performance of interfaces and design of interface structures.

Electronic and thermoelectric properties of zigzag and armchair boron nitride nanotubes in the presence of C island

Electronic and thermoelectric properties of zigzag and armchair single wall Boron Nitride Nanotubes (SWBNNTs) are investigated with and without one hexagonal carbon island by using first density functional theory (DFT), which is carried out in the Quantum Espresso packages. The ZSWBNNTs and ASWBNNTs show semiconductor and insulator behaviors, respectively along with a direct bandgap at the Γ point in the pristine cases. The obtained results display that this island is affected and altered to the electronic and thermoelectric properties of all systems. The behaviors of all systems are turning to semiconductor and the electronic band gaps are reduced with the C island which enables to use these doped materials in various applications. Meanwhile, the thermoelectric parameters, such as Seebeck coefficient (S), thermoelectric figure of Merit (ZT), phonon thermal conductance (Kph), electrons thermal conductance (Ke), and thermal conductivity of all systems are calculated and studied with and without the C island. The results show that all these thermoelectric properties are related directly to the diameter of the ZSWBNNTs and ASWBNNTs.

Phonon-kink scattering effect on the low-temperature thermal transport in solids

We consider contribution to the phonon scattering, in the temperature range of 1K, by the dislocation kinks pinned in the random stress fields in a crystal. The effect of electron-kink scattering on the thermal transport in the normal metals was considered much earlier \cite{Muk86}. The phonon thermal transport anomaly at low temperature was demonstrated by experiments in the deformed (bent) superconducting lead samples \cite{Mez79} and in helium-4 crystals \cite{Mez82, Mez84} and was ascribed to the dislocation dynamics. Previously, we had discussed semi-qualitatively the phonon-kink scattering effects on the thermal conductivity of insulating crystals in a series of papers \cite{mezmuk, ostmukmez}. In this work it is demonstrated explicitly that exponent of the power low in the temperature dependence of the phonon thermal conductivity depends, due to kinks, on the distribution of the random elastic stresses in the crystal, that pin the kinks motion along the dislocation lines. We found that one of the random matrix distributions of the well known Wigner-Dyson theory is most suitable to fit the lead samples experimental data \cite{Mez79}. We also demonstrate that depending on the distribution function of the oscillation frequencies of the kinks, the power low temperature dependences of the phonon thermal conductivity, in principle, may possess exponents in the range of $2\div 5$.

Thermoelectric Charge and Spin Current Generation in Magnetic Single-Molecule Junctions: First-Principles Calculations

We apply first-principles approaches to investigate the spin (charge) Seebeck effects [Ss(c)] and spin (charge) thermoelectric figure of merits [ZTs(c)] of manganese-phthalocyanine spin-polarized scanning tunneling microscopy (MnPc SP-STM) junctions. The magnetic tunneling junctions are N-type junctions because their Sc values are negative. Their Ss and Sc values are sufficiently large for the efficient generation of measurable spin and charge currents. ZTs(c) values strongly depend on the competition between electron and phonon thermal conductances: ZTs(c) ∝ Ss(c)2 for κph ≪ κel, and ZTs(c) ∝ Ss(c)2κel for κel ≪ κph. Ss changes signs when the spin-valve junction rotates its magnetic structure from the antiparallel (AP) to the parallel (P) configuration. This behavior indicates that spin-current direction can be reversed by alternating magnetic configurations between AP and P states. Spin-current dissipation in the junctions is minimized because the sizes of the junctions are considerably smaller than the lengths of spin-flip scattering and spin dephasing. The low spin-current dissipation of the junctions suggests that they have potential applications in spintronics and renewable energy. The present finding provides a new approach to spin-current generation through the use of SP-STM based on temperature difference and to controlling spin-current direction through magnetic configurations. The integration of numerous single-molecule magnetic junctions as building blocks into a high-density device is a promising strategy for generating a considerable net spin current for applications in molecular spin caloritronics.

Heat conduction tuning by hyperbranched nanophononic metamaterials

Phonon dispersion and thermal conduction properties of hyperbranched nanostructures with unique topological complexity are theoretically and numerically investigated in this research. We present analytical cantilever-in-mass models to analyze and control the inherent resonance hybridization in hyperbranched nanomembranes containing different configurations and cross sections. We show that these local resonances hosted by hyperbranched nanopillars can generate numerous flat bands in the phonon dispersion relation and dramatically lower the group velocities, consequently resulting in a significant reduction of the thermal conductivity. The applicability of the proposed analytical models in thermal conductivity tuning is demonstrated, and a superior performance in reducing the heat flux in nano-structured membranes is exhibited, which can potentially lead to improved thermoelectric energy conversion devices.

Thermoelectric performance of Te doped with As and alloyed with Se

Recently, it was found that element semiconductor tellurium (Te) behaved a high thermoelectric (TE) performance. Further enhancement of its TE performance was expected in decreasing phonon thermal conductivity. In this paper, element semiconductor Te doped with arsenic (As) and alloyed with selenium (Se) was prepared by one-step high-pressure method. Trace amounts of As doping could increase the carrier concentration of Te effectively and thereby optimize its power factor. The phonon thermal conductivity of Te was depressed sharply, due to the effect of high-pressure compression (introducing dislocations, lattice curvatures and nanograins) and Se alloying (introducing point defects and crystal dislocation). The beneficial effect of As doping on the power factor, high-pressure compression and Se alloying on thermal conductivity led to a peak ZT of 0.81 at 540 K for Te doped with 0.5 mol% As and alloyed with 10 mol% Se.

Thermal conductivity of hexagonal Si, Ge, and Si1-xGex alloys from first-principles

Hexagonal Si and Ge with a lonsdaleite crystal structure are allotropes of silicon and germanium that have recently been synthesized. These materials as well as their alloys are promising candidates for novel applications in optoelectronics. In this paper, we systematically study the phonon transport and thermal conductivity of hexagonal Si, Ge, and their alloys by using the first-principle-based Peierls-Boltzmann transport equation approach. Both three-phonon and four-phonon scatterings are taken into account in the calculations as the phonon scattering mechanisms. The thermal conductivity anisotropy of these materials is identified. While the thermal conductivity parallel to the hexagonal plane for hexagonal Si and Ge is found to be larger than that perpendicular to the hexagonal plane, alloying effectively tunes the thermal conductivity anisotropy by suppressing the thermal conductivity contributions from the middle-frequency phonons. The importance of four-phonon scatterings is assessed by comparing the results with the calculations without including four-phonon scatterings. We find that four-phonon scatterings cannot be ignored in hexagonal Si and Ge as the thermal conductivity would be overestimated by around 10% (40%) at 300 K (900) K. In addition, the phonon mean free path distribution of hexagonal Si, Ge, and their alloys is also discussed.