Phonon Mean Free Path Research Articles

Solubility limit and annealing effects on the microstructure & thermoelectric properties of [formula omitted] Heusler compounds

Full-Heusler compounds with the composition Fe2V1−xTaxAl1−ySiy have recently shown to exhibit some of the highest thermoelectric power factors reported so far among bulk materials due to the band convergence and band gap opening caused by the V/Ta substitution. Therefore, the solubility limit of Ta and Si regarding the stability of the L21 phase is investigated in this study. The crystal structure and microstructure of a large number of samples is probed by X-ray diffraction as well as scanning electron microscopy and energy dispersive X-ray analysis. The results show that the Al/Si substitution significantly hampers the solubility of Ta within the Heusler structure. Furthermore, Fe2V0.9Ta0.1Al and Fe2V0.95Ta0.05Al0.9Si0.1 reveal nanoscale impurity precipitates in the microstructure, together with diffuse contrasts that indicate a non-equilibrium metastable state. For that reason, different annealing conditions, varying temperature and time, have been applied to the latter and the effect on the microstructure and thermoelectric properties is investigated. It is found that additional annealing leads to further phase segregation and grain growth of the impurity precipitates, which have a detrimental effect on the Seebeck coefficient due to their metallic-like nature. They can, however, effectively reduce the lattice thermal conductivity if their average size remains below the phonon mean free path. The thermoelectric efficiency in terms of the dimensionless figure of merit ZT is increased up to ZT=0.3–0.34 at 300 K which is beyond the values previously reported for Fe2VAl-based bulk materials.

Density Functional Theory Investigation of Thermal Conductivity in α-CN and α-CP Monolayers: Implications for Thermal Management of Electronic Devices

This work presents the density functional theory based investigations of two-dimensional carbon pnictides α-CX (X = N and P). Despite being from the group of the pnictide family, there are significant differences in the trends of the electronic and vibrational properties of both systems. The calculated electronic band gaps are 3.77 eV and 1.79 eV for α-CN and α-CP, respectively. The direct nature and moderate gap magnitude of α-CP indicate its applicability in the field of optoelectronic and photovoltaic device applications, which is confirmed by the calculated absorption spectra of the system. Distinguished phonon dispersion curves of both systems show a highly anisotropic trend. The diverse and steep nature of the acoustic phonon modes together with high phonon group velocity, low phonon anharmonicity, and high phonon mean free path (MFP) leads to a pronounced magnitude of thermal conductivity in the case of α-CN. In contrast to α-CN, α-CP owing to the lower gap between the optoacoustic phonon modes, lower MFP, and high anharmonicity possesses a remarkably lower thermal conductivity of 292 W m–1 K–1. The thermoelectric performance of the system is assessed by calculating the figure-of-merit ZT in the case of α-CP, which is 0.36 at 300 K that further attains > 0.7 at higher temperatures; whereas, for α-CN, the ZT value remains < 0.1 due to its ultra-high thermal conductivity. The present study paves the pathway toward exploration of carbon-based low-dimensional materials for high mobility and high thermal conductivity-based nanoelectronic device applications.

Defect, temperature, and strain effects on lattice heat conductivity of egg-tray graphene

Micro and nano devices generally have the characteristics of high performance and compact size, so their own heat transfer and heat dissipation problems are becoming more and more serious. Therefore, it is necessary to clarify the heat transport mechanism in the micro–nano structure by analyzing the heat transport properties of nanomaterials, and then control the thermal conductivity of nanodevices. We have investigated the lattice heat transfer of egg-tray graphene using non-equilibrium molecular dynamics simulations. Three structures (I, II and III) are studied according to the number of hexagons as 10, 16, and 56 respectively. The increases of lattice thermal conductivity with an increase of length in sub-microns implies the large mean free path of phonons in egg-tray graphene, similar as that of graphene. The large-size-limit thermal conductivity is 43, 45, and 60 W m−1 K−1 for I, II, and III respectively, much smaller than that of graphene (393 W m−1 K−1) in our model. The thermal conductivity decreases with an increase of strain, as well as temperature. The heat transfer performance of structure-II is sensitive to both phonon modes and phonon quantities in compression, while in tension it is determined only by the phonon modes. Our results may be useful in thermal conductivity engineering and heat transfer management in egg-tray graphene.

Approach to Phonon Relaxation Time and Mean Free Path in Nonlinear LatticesSupported by the National Natural Science Foundation of China (Grant Nos. 12075199 and 11675133).

Based on the self-consistent phonon theory, the spectral energy density is calculated by the canonical transformation and the Fourier transformation. Through fitting the spectral energy density by the Lorentzian profile, the phonon frequency as well as the phonon relaxation time is obtained in one-dimensional nonlinear lattices, which is validated in the Fermi–Pasta–Ulam-β (FPU-β) and ϕ 4 lattices at different temperatures. The phonon mean free path is then evaluated in terms of the phonon relaxation time and phonon group velocity. The results show that, in the FPU-β lattice, the phonon mean free path as well as the phonon relaxation time displays divergent power-law behavior. The divergent exponent coincides well with that derived from the Peierls–Boltzmann theory at weak anharmonic nonlinearity. The value of the divergent exponent expects a power-law divergent heat conductivity with system size, which violates Fourier’s law. For the ϕ 4 lattice, both the phonon relaxation time and mean free path are finite, which ensures normal heat conduction.

Dimension-dependent thermal conductivity of graphene nanoribbons on silicon carbide

Acoustic phonons are defined as the quantum of crystal lattice vibrational energy. The physics of phonon transport within graphene is potentially important and practical. This study relates to the heat conduction properties of graphene nanoribbons deposited on a silicon carbide substrate. The graphene nanoribbons have dimensions comparable to or smaller than the phonon mean free path. The effect of nanoscale grain dimensions on the thermal conductivity of the graphene nanoribbons was investigated experimentally and theoretically to better understand the applied physics of thermal transport at the nanoscale. The characteristics of ballistic and diffusive heat conduction in the graphene nanoribbons were investigated. The edge-scattering effects arising from the crystallographic disorder of the edges of the graphene nanoribbons were determined in order to reduce phonon scattering and enhance phonon transport. The results indicated that the transport mode of phonons depends upon the length scales of the graphene nanoribbons. As the dimensions of the graphene nanoribbons decrease, there is a transition from the diffusive transport mode to the ballistic transport mode. The method of structural and dimensional design is effective to reduce phonon scattering and enhance phonon transport, thereby allowing the thermal conductivity approaching as closely as possible the theoretical limit.

Thermal conductivity ofCaF2at high pressure

We study the thermal transport properties of three CaF$_{2}$ polymorphs up to a pressure of 30 GPa using first-principle calculations and an interatomic potential based on machine learning. The lattice thermal conductivity $\kappa$ is computed by iteratively solving the linearized Boltzmann transport equation (BTE) and by taking into account three-phonon scattering. Overall, $\kappa$ increases nearly linearly with pressure, and we show that the recently discovered $\delta$-phase with $P\bar{6}2m$ symmetry and the previously known $\gamma$-CaF$_{2}$ high-pressure phase have significantly lower lattice thermal conductivities than the ambient-thermodynamic cubic fluorite ($Fm\bar{3}m$) structure. We argue that the lower $\kappa$ of these two high-pressure phases stems mainly due to a lower contribution of acoustic modes to $\kappa$ as a result of their small group velocities. We further show that the phonon mean free paths are very short for the $P\bar{6}2m$ and $Pnma$ structures at high temperatures, and resort to the Cahill-Pohl model to assess the lower limit of thermal conductivity in these domains.

Structure Domain Size of Carbon Fibers

The internal micro-structure is an important factor affecting the thermal conductivity of materials. In this work, the relationship between micro-structure, thermal conductivity, and temperature variation for carbon fibers (CF) are systematically studied by using the transient electrothermal technique. When the temperature is below the critical temperature (about 110 K), the internal structure of carbon fiber deteriorates, resulting in a very different behavior of thermal conductivity variation with temperature. By introducing the thermal reffusivity theory, the structure domain size of CF can be represented by the phonon mean free path at 0 K. The thermal reffusivity change of two temperature ranges is studied, and the mean free path of phonons in CF before and after deterioration can be calculated as 317 nm and 234 nm, respectively. The results are in good agreement with the crystallite grain size of 288 nm determined by Raman study. The thermal reffusivity provides another feasible method to study the relationship between structure domain size and thermophysical properties of materials.

Thermal conductivity of the quasi-one-dimensional materials TaSe3 and ZrTe3

The high breakdown current densities and resilience to scaling of the metallic transition metal trichalcogenides TaSe3 and ZrTe3 make them of interest for possible interconnect applications, and it motivates this study of their thermal conductivities and phonon properties. These crystals consist of planes of strongly bonded one-dimensional chains more weakly bonded to neighboring chains. Phonon dispersions and the thermal conductivity tensors are calculated using density functional theory combined with an iterative solution of the phonon Boltzmann transport equation. The phonon velocities and the thermal conductivities of TaSe3 are considerably more anisotropic than those of ZrTe3. The maximum LA velocity in ZrTe3 occurs in the cross-chain direction, and this is consistent with the strong cross-chain bonding that gives rise to large Fermi velocities in that direction. The thermal conductivities are similar to those of other metallic two-dimensional transition metal dichalcogenides. At room temperature, a significant portion of the heat is carried by the optical modes. In the low frequency range, the phonon lifetimes and mean free paths in TaSe3 are considerably shorter than those in ZrTe3. The shorter lifetimes in TaSe3 are consistent with the presence of lower frequency optical branches and zone-folding features in the acoustic branches that arise due to the doubling of the TaSe3 unit cell within the plane.

Phonon drag thermopower and energy loss rate in single and bilayer graphene due to piezoelectric surface acoustic phonons in Bloch-Gruneisen regime

In this report, we have both numerically and analytically calculated the phonon drag thermopower, Spz and, energy loss rate, Fpz due to piezoelectric surface acoustic phonons present in the underlying piezoelectric substrate at a distance, d apart from single and bilayer graphene as a function of carrier's temperature, concentration and phonon mean free path. The numerical results are then reduced to analytical results in the Bloch-Gruneisen regime and the corresponding power dependency of the quantities described above are obtained. We have also included the effect of Thomas-Fermi and Random Phase Approximation screening into account in these calculations. The obtained unscreened results are further reduced in much simpler form for a particular case having no distance between the graphene samples and the underlying substrate or at larger values of distances. The temperature dependency in Spz and Fpz for both SLG and BLG systems is found to be one order less than the in-plane acoustic phonons dependency, which is directly related to the matrix element of electron-in plane acoustic phonon interaction having a linear dependence on the phonon wave vector, q. Furthermore, a comparison of these calculations is made between the in-plane and piezoelectric surface acoustic phonon modes. One finds a crossover between these phonons modes depicting these are important in providing effective scattering channels for energy relaxation in typical experimental situations at different temperatures.

The Effect of Hydroxylated Multi-Walled Carbon Nanotubes on the Properties of Peg-Cacl2 Form-Stable Phase Change Materials

Calcium ions can react with polyethylene glycol (PEG) to form a form-stable phase change material, but the low thermal conductivity hinders its practical application. In this paper, hydroxylated multi-walled carbon nanotubes (MWCNTs) with different mass are introduced into PEG1500·CaCl2 form-stable phase change material to prepare a new type of energy storage material. Carbon nanotubes increased the mean free path (MFP) of phonons and effectively reduced the interfacial thermal resistance between pure PEG and PEG1500·CaCl2 3D skeleton structure. Thermal conductivity was significant improved after increasing MWCNTs mass, while the latent heat decreases. At 1.5 wt%, composite material shows the highest phase change temperature of 42 °C, and its thermal conductivity is 291.30% higher than pure PEG1500·CaCl2. This article can provide some suggestions for the preparation and application of high thermal conductivity form-stable phase change materials.

Characteristics of quasi-ballistic heat conduction in a multiple materials system based on the solution of the Boltzmann transport equation

Phonons will exhibit quasi-ballistic heat transport when the mean free path is longer than the dimension of the medium through which the phonons travel. Such a transport regime can yield information about the phonon mean free path. The primary focus of this study is on numerically solving the one-dimensional transient Boltzmann transport equation to investigate how the phonon mean free path can be determined in accordance with the characteristics of quasi-ballistic heat conduction in a multiple materials system. The Boltzmann transport equation is solved for heat conduction within an aluminum film with a double-layered structure based on the discrete ordinates method. The metal film is deposited onto a silicon substrate. Frequency-dependent boundary conditions are used to define the difference in phonon dispersion between the metal film and the substrate. The frequency-dependent Boltzmann transport equation is used to determine how the thermal conductivity changes with the modulation frequency when phonons travel quasi-ballistically. The distribution of the phonon mean free path is discussed, and comparisons are made between theoretical results at different modulation frequencies. The results indicated that the effective thermal conductivity of the multiple materials system does not depend upon the modulation frequency. Phonons with mean free paths longer than the penetration depth do not contribute to the effective thermal conductivity. The effect of quasi-ballistic heat conduction is noticeable in semiconductor alloys even at room temperature.

Computational method for studying the thermal conductivity of molecular crystals in the course of condensed matter physics

This paper presents a computational method for studying the thermal conductivity of molecular crystals that can be used in the educational course of condensed matter physics. This method is based on the Debye model of thermal conductivity in the approximation of the corresponding relaxation times and allows studying the heat transfer processes features in simple molecular crystals at temperatures close to or above Debye temperature. The thermal conductivity is analysed in the framework of modified Debye model in which heat is transferred by low-frequency phonons and above the phonon mobility edge by “diffusive” modes migrating randomly from site to site. The mobility edge ω0 is found from the condition that the phonon mean-free path cannot become smaller than half the phonon wavelength. The contributions of phonon-phonon, one-, and two-phonon scattering to the total thermal resistance of molecular crystals are calculated under the assumption that the different scattering mechanisms contribute additively. The presented computational method will be useful in pedagogical activities for teaching students of physical faculties.

Effect of diffuse phonon boundary scattering on heat flow

We propose a model for the thermal conductivity of 2D-samples when the mean free paths due to the phonon–phonon interactions exceed the sample dimensions. The physical mechanisms that ensure the stationary heat flux and the stationary nonequilibrium temperature distribution are examined. A recursive equation is derived to quantify the contribution of phonon scattering to the net heat flux in the pure elastic isotropic diffusive regime, as a function of the number of scattering at the boundaries. As the length to width ratio L/W increases above unity, our model shows an increase in the phonon mean free path compared to that predicted by the Casimir model in which the lateral walls are assumed to be black bodies. The present model also reveals that the multiple phonon interactions with the lateral walls lead to a stationary, but non-linear temperature distribution. The dependence of the heat flux and the thermal conductivity on the sample dimensions is then shown to be non-monotonic. This infers that the location of the thermometers on the sample influences experimental measurements of the thermal conductivity.

Lattice thermal conductivity of zigzag and armchair black phosphorus: Role of normal phonons

Theoretical investigations of size and temperature dependent normal phonon effects on lattice thermal conductivity of zigzag and armchair black phosphorus are carried out employing Boltzmann transport formalism. The phonons – heat carriers, are assumed to be scattered by resistive processes and conservative normal processes. The effects of normal phonons on scattering rates due to longitudinal and transverse phonons show significant contributions along zigzag and armchair black phosphorus. The transition of resistive scattering regime to combined resistive-normal scattering regime and its demarcation for zigzag and armchair black phosphorus is investigated at practically relevant temperatures. This transition in zigzag and armchair direction shifts towards higher phonon mean free path with decrease in temperature. The size dependent thermal conductivity investigations show considerable contributions of normal phonons in higher dimension samples. Significant reduction in thermal conductivity due to normal phonons is reported and results are compared with recent available experimental data.

Atomic-Scale Visualization and Quantification of Configurational Entropy in Relation to Thermal Conductivity: A Proof-of-Principle Study in t-GeSb2Te4.

It remains a daunting task to quantify the configurational entropy of a material from atom‐revolved electron microscopy images and correlate the results with the material's lattice thermal conductivity, which strides across statics, dynamics, and thermal transport of crystal lattice over orders of magnitudes in length and time. Here, a proof‐of‐principle study of atomic‐scale visualization and quantification of configurational entropy in relation to thermal conductivity in single crystalline trigonal GeSb2Te4 (aka t‐GeSb2Te4) with native atomic site disorder is reported. A concerted effort of large t‐GeSb2Te4 single crystal growth, in‐lab developed analysis procedure of atomic column intensity, the visualization and quantification of configurational entropy including corresponding modulation, and thermal transport measurements enable an entropic “bottom‐up” perspective to the lattice thermal conductivity of t‐GeSb2Te4. It is uncovered that the configurational entropy increases phonon scattering and reduces phonon mean free path as well as promotes anharmonicity, thereby giving rise to low lattice thermal conductivity and promising thermoelectric performance. The current study sheds lights on an atomic scale bottom‐up configurational entropy design in diverse regimes of structural and functional materials research and applications.

Probing the phonon mean free paths in dislocation core by molecular dynamics simulation

Thermal management is extremely important for designing high-performance devices. The lattice thermal conductivity of materials is strongly dependent on detailed structural defects at different length scales, particularly point defects like vacancies, line defects like dislocations, and planar defects such as grain boundaries. Traditionally, the McKelvey–Shockley phonon Boltzmann’s transport equation (BTE) method, combined with molecular dynamics simulations, has been widely used to evaluate the phonon mean free paths (MFPs) in defective systems. However, this method can only provide the aggregate MFPs of the whole sample, as it is challenging to extract the MFPs in different regions with varying thermal conductivities. In this study, the 1D McKelvey–Shockley phonon BTE method was extended to model inhomogeneous materials, where the contributions of defects to the phonon MFPs are explicitly obtained. Then, the method was used to study the phonon scattering with the core structure of an edge dislocation. The phonon MFPs in the dislocation core were obtained and were found to be consistent with the analytical model in a way that high frequency phonons are likely to be scattered in this area. This method not only advances the knowledge of phonon–dislocation scattering but also shows the potential to investigate phonon transport behaviors in more complicated materials.

Anisotropic lattice thermal conductivity in topological semimetal ZrGeX (X = S, Se, Te): a first-principles study

Topological semimetals have attracted significant attentions owing to their potential applications in numerous fields such as low-power electron devices and quantum computation, which are closely related to their thermal transport properties. In this work, the phonon transport properties of topological Dirac nodal-line semimetals ZrGeX (X = S, Se, Te) with the PbClF-type structures are systematically studied using the first-principles calculations combined with the Boltzmann transport theory. The obtained lattice thermal conductivities show an obvious anisotropy, which is caused by the layer structures of ZrGeX (X = S, Se, Te). The room-temperature lattice conductivity of ZrGeTe along c direction is found to be as low as 0.24 W m−1 K−1, indicating that it could be of great significance in the fields of thermal coating materials and solar cell absorber. In addition, we extract each phonon branch from group velocities, phonon scattering rates, Grüneisen parameters, and phase space volumes to investigate the mechanism underlying the low thermal conductivity. It is concluded that the difference of thermal conductivities of three materials may be caused by the number of scattering channels and the effect of anharmonic. Furthermore, the phonon mean free path along a direction is relatively longer. Nanostructures or polycrystalline structures may be effective to reduce the thermal conductivity and improve the thermoelectric properties.

Small-Nanostructure-Size-Limited Phonon Transport within Composite Films Made of Single-Wall Carbon Nanotubes and Reduced Graphene Oxides.

Nanocarbon materials have been widely used for nanoelectronics and energy-related applications. In this work, composite films consisting of reduced graphene oxides (rGOs) and single-wall carbon nanotubes (SWCNTs) are synthesized and studied for their in-plane thermal conductivities. Different from pristine carbon nanotubes or graphene with decreased thermal conductivities above 300 K, the in-plane thermal conductivities of these composite films are found to follow the trend of the specific heat of graphene from 100 to 400 K, i.e., monotonously increasing at elevated temperatures. Such a trend can often be found within amorphous solids but has seldom been observed for nanocarbon. This unique temperature dependence of thermal conductivities is attributed to the largely restricted phonon mean free paths within the graphene sheets that mainly contribute to the in-plane thermal transport. The highest in-plane thermal conductivity among samples with different synthesis conditions is 62.8 W/(m·K) at 300 K. Such a high thermal conductivity, combined with its unique temperature dependency, can be ideal for applications such as flexible film-like thermal diodes based on the junction between two materials with a large contrast for their temperature dependence of the thermal conductivity.

Phonon vortex dynamics in graphene ribbon by solving Boltzmann transport equation with ab initio scattering rates

In this work, we study thermal phonon vortex in graphene ribbon by a discrete-ordinate solution of phonon Boltzmann equation under Callaway's dual relaxation model. The phonon scattering rates of normal and resistive processes are acquired from ab initio calculation without need of any empirical input parameters. The temperature, size and isotope effects on transition from phonon vortex transport to conventional Fourier's heat conduction in both simple and complex geometries are investigated. The physical mechanism for the evolution of phonon vortex is declared by wide phonon mean free path distribution of resistive processes. A hierarchical vortex series is obtained with primary, secondary and terniary vortexes in a complicated geometry. The present work provides an accurate and efficient multi-scale numerical framework for modeling hydrodynamic phonon transport in high-thermal-conductivity materials and also sheds light on the heat dissipation applications.

Thermal rectification in asymmetric two-phase nanowires

Thermal rectification based on a new strategy of nanostructuration has been assessed with nonequilibrium molecular dynamics and wave-packet propagation simulations. The use of asymmetric crystalline-core/amorphous-conical-shell nanowires creates a direction-dependent thermal conductivity due to variable axial and radial phonon propagation/confinement. The origin of this effect is related to the combination of a crystalline/amorphous interface parallel to the heat flux, together with the variable amount of amorphous coating due to the conical shell of the nanowire. Physical insights of the rectification are given by the mean free path of phonons, the axial and radial energy transfer, the energy diffusivity, and the vibrational density of states restricted to different constitutive elements of the nanowire.