Average Phonon Mean Free Path Research Articles

Research of the impact of uniaxial tension on the thermoelectric properties of NbCoX (X=Ge, Sn, Pb) compounds

Half-Heusler materials have been confirmed as excellent thermoelectric materials. To simulate the stress conditions in engineering applications, we adopt uniaxial tensile strain to assess the impact of lattice changes on NbCoX (X=Ge, Sn, Pb) compound's thermoelectric performance. The research reveals that when NbCoX compounds are stretched by 1.5 %, the material almost does not decrease the power factor but significantly reduces thermal conductivity, thereby enhancing the ZT value. At a carrier concentration of 1E22 cm−3 and a temperature of 873 K, the predicted ZT values for p-type NbCoSn compound reach 0.359 and 0.354 after stretching by 1.5 % in the x-y and z directions, respectively. Compared to the previous original values, this improvement is approximately 1.5 times, highlighting the significant role of tensile strain in enhancing thermoelectric performance. This may be attributed to changes in compound lattice symmetry induced by strain, leading to increased defects and interfaces, which complicate phonon transport paths, resulting in a decrease in the average phonon mean free path and consequently lowering thermal conductivity. Additionally, with the increase in atomic number of Ge, Sn, and Pb, their thermoelectric figure of merit also increases continuously, with ZT values remaining higher under stretching than compression. Such research provides a new avenue for designing and optimizing high-performance thermoelectric materials and offers insights into strain engineering for future exploration of thermoelectric materials.

Thickness-Dependent Cross-Plane Thermal Conductivity Measurements of Exfoliated Hexagonal Boron Nitride.

Submicrometer-thick layers of hexagonal boron nitride (hBN) exhibit high in-plane thermal conductivity and useful optical properties, and serve as dielectric encapsulation layers with low electrostatic inhomogeneity for graphene devices. Despite the promising applications of hBN as a heat spreader, the thickness dependence of its cross-plane thermal conductivity is not known, and the cross-plane phonon mean free paths (MFPs) have not been measured. We measure the cross-plane thermal conductivity of hBN flakes exfoliated from bulk crystals. We find that submicrometer thick flakes exhibit thermal conductivities up to 8.1 ± 0.5 W m-1 K-1 at 295 K, which exceeds previously reported bulk values by more than 60%. Surprisingly, the average phonon mean free path is found to be several hundred nanometers at room temperature, a factor of 5 larger than previous predictions. When planar twist interfaces are introduced into the crystal by mechanically stacking multiple thin flakes, the cross-plane thermal conductivity of the stack is found to be a factor of 7 below that of individual flakes with similar total thickness, thus providing strong evidence that phonon scattering at twist boundaries limits the maximum phonon MFPs. These results have important implications for hBN integration in nanoelectronics and improve our understanding of thermal transport in two-dimensional materials.

Теплофизические свойства мультиферроиков Bi-=SUB=-1-x-=/SUB=-Tm-=SUB=-x-=/SUB=-FeO-=SUB=-3-=/SUB=-

Investigations of the heat capacity, thermal diffusivity, and thermal conductivity of multiferroics Bi1-xTmxFeO3 (x = 0, 0.05, 0.10, 0.20) have been carried out in the high temperature range of 300-1200 K. and thermal conductivity in the region of phase transitions. The temperature dependences of the specific heat for compositions with x = 0.10 and 0.20 exhibit an additional anomaly characteristic of the phase transition at T = 580 K. The dominant mechanisms of phonon heat transfer in the region of ferroelectric and antiferromagnetic phase transitions are considered. The temperature dependence of the average phonon mean free path is determined.

Thermophysical properties of multiferroics Bi-=SUB=-1-x-=/SUB=-Tm-=SUB=-x-=/SUB=-FeO-=SUB=-3-=/SUB=-

Investigations of the heat capacity, thermal diffusivity, and thermal conductivity of multiferroics Bi1-xTmxFeO3 (x=0, 0.05, 0.10, 0.20) have been carried out in the high temperature range of 300-1200 K. and thermal conductivity in the region of phase transitions. The temperature dependences of the specific heat for compositions with x=0.10 and 0.20 exhibit an additional anomaly characteristic of the phase transition at T=580 K. The dominant mechanisms of phonon heat transfer in the region of ferroelectric and antiferromagnetic phase transitions are considered. The temperature dependence of the average phonon mean free path is determined. Keywords: multiferroics, heat capacity, thermal diffusivity, thermal conductivity.

Thermoelectric properties of holey silicon at elevated temperatures

Compatibility to the semiconductor industry makes silicon thin-film devices attractive for thermoelectric applications. Silicon has a competitive thermoelectric power factor but a large thermal conductivity, which results in an overall small thermoelectric figure of merit, ZT. By patterning arrays of nano-sized holes with spacing less than the average phonon mean free path into the Si thin films, their thermal conductivity can be greatly suppressed, whereas their electronic properties are less affected. We fabricated and measured the electronic and thermal transport properties of such holey Si devices from 300 K to 650 K. Heat diffusion imaging, a hybrid approach that combines thermoreflectance imaging and the heat spreader method was used for the in-plane thermal conductivity measurement and gives a value of 6.00 ± 1.83 W/mK at room temperature. The power factor times temperature is about 0.52 ± 0.04 W/mK at 300 K and 1.10 ± 0.09 W/mK at 650 K. Therefore, ZT of the holey Si device is approximately 0.09 at room temperature and is at least 0.29 at 650 K. Further improvement is possible by optimizing the feature sizes and using surface doping.

Ultralow lattice thermal conductivity of chalcogenide perovskite CaZrSe3 contributes to high thermoelectric figure of merit

An emerging chalcogenide perovskite, CaZrSe3, holds promise for energy conversion applications given its notable optical and electrical properties. However, knowledge of its thermal properties is extremely important, e.g. for potential thermoelectric applications, and has not been previously reported in detail. In this work, we examine and explain the lattice thermal transport mechanisms in CaZrSe3 using density functional theory and Boltzmann transport calculations. We find the mean relaxation time to be extremely short corroborating an enhanced phonon–phonon scattering that annihilates phonon modes, and lowers thermal conductivity. In addition, strong anharmonicity in the perovskite crystal represented by the Grüneisen parameter predictions, and low phonon number density for the acoustic modes, results in the lattice thermal conductivity to be limited to 1.17 W m−1 K−1. The average phonon mean free path in the bulk CaZrSe3 sample (N → ∞) is 138.1 nm and nanostructuring CaZrSe3 sample to ~10 nm diminishes the thermal conductivity to 0.23 W m−1 K−1. We also find that p-type doping yields higher predictions of thermoelectric figure of merit than n-type doping, and values of ZT ~0.95–1 are found for hole concentrations in the range 1016–1017 cm−3 and temperature between 600 and 700 K.

Monte Carlo phonon transport simulations in hierarchically disordered silicon nanostructures

Hierarchical material nanostructuring is considered to be a very promising direction for high performance thermoelectric materials. In this work we investigate thermal transport in hierarchically nanostructured silicon. We consider the combined presence of nanocrystallinity and nanopores, arranged under both ordered and randomized positions and sizes, by solving the Boltzmann transport equation using the Monte Carlo method. We show that nanocrystalline boundaries degrade the thermal conductivity more drastically when the average grain size becomes smaller than the average phonon mean free path. The introduction of pores degrades the thermal conductivity even further. Its effect, however, is significantly more severe when the pore sizes and positions are randomized, as randomization results in regions of higher porosity along the phonon transport direction, which introduce significant thermal resistance. We show that randomization acts as a large increase in the overall effective porosity. Using our simulations, we show that existing compact nanocrystalline and nanoporous theoretical models describe thermal conductivity accurately under uniform nanostructured conditions, but overestimate it in randomized geometries. We propose extensions to these models that accurately predict the thermal conductivity of randomized nanoporous materials based solely on a few geometrical features. Finally, we show that the new compact models introduced can be used within Matthiessens rule to combine scattering from different geometrical features within approximately 10 per cent accuracy.

Thermal conductivity of thermoelectric material β-Cu2Se: Implications on phonon thermal transport

Thermal transport properties associated with the thermal structure evolution of β-Cu2Se are studied using density functional theory (DFT) and molecular dynamics (MD) simulations. Thermal conductivity of β-Cu2Se is calculated over a temperature range of 400–1000 K using reverse non-equilibrium molecular dynamics simulations. The thermal conductivity found through MD simulations decreases monotonically with increasing temperature, which is in line with the reported experimental data and our calculated DFT data. The average phonon mean free path evaluated using the kinetic theory, found to be within the range of 1.0–1.5 Å, decreases with increasing temperature. Furthermore, we have investigated the temperature-dependent heat transport phenomena using phonon density of states, calculated using MD simulations. The phonon modes are found to shift towards the low frequency numbers with increasing temperature, indicating lower heat carrying capacity of the material and in agreement with the computed thermal conductivity.

Temperature-Dependent Mean Free Path Spectra of Thermal Phonons Along the c-Axis of Graphite.

Heat conduction in graphite has been studied for decades because of its exceptionally large thermal anisotropy. While the bulk thermal conductivities along the in-plane and cross-plane directions are well-known, less understood are the microscopic properties of the thermal phonons responsible for heat conduction. In particular, recent experimental and computational works indicate that the average phonon mean free path (MFP) along the c-axis is considerably larger than that estimated by kinetic theory, but the distribution of MFPs remains unknown. Here, we report the first quantitative measurements of c-axis phonon MFP spectra in graphite at a variety of temperatures using time-domain thermoreflectance measurements of graphite flakes with variable thickness. Our results indicate that c-axis phonon MFPs have values of a few hundred nanometers at room temperature and a much narrower distribution than in isotropic crystals. At low temperatures, phonon scattering is dominated by grain boundaries separating crystalline regions of different rotational orientation. Our study provides important new insights into heat transport and phonon scattering mechanisms in graphite and other anisotropic van der Waals solids.

Steady state and modulated heat conduction in layered systems predicted by the analytical solution of the phonon Boltzmann transport equation

Based on the phonon Boltzmann transport equation under the relaxation time approximation, analytical expressions for the temperature profiles of both the steady state and modulated heat conduction inside a thin film deposited on a substrate are derived and analyzed. It is shown that these components of the temperature depend strongly on the ratio between the film thickness and the average phonon mean free path (MFP), and they exhibit the diffusive behavior as predicted by the Fourier's law of heat conduction when this ratio is much larger than unity. In contrast, in the ballistic regime when this ratio is comparable to or smaller than unity, the steady-state temperature tends to be independent of position, while the amplitude and the phase of the modulated temperature appear to be lower than those determined by the Fourier's law. Furthermore, we derive an invariant of heat conduction and a simple formula for the cross-plane thermal conductivity of dielectric thin films, which could be a useful guide for understanding and optimizing the thermal performance of the layered systems. This work represents the Boltzmann transport equation-based extension of the Rosencwaig and Gersho work [J. Appl. Phys. 47, 64 (1976)], which is based on the Fourier's law and has widely been used as the theoretical framework for the development of photoacoustic and photothermal techniques. This work might shed some light on developing a theoretical basis for the determination of the phonon MFP and relaxation time using ultrafast laser-based transient heating techniques.

Experimental evidence of very long intrinsic phonon mean free path along the c-axis of graphite

We report on experimental studies of the average phonon mean free path in the c-axis direction of graphite. Through systematically measuring the cross-plane thermal conductivity of thin graphite flakes with thickness ranging from 24 nm to 714 nm via a differential three omega method, we demonstrate that the average phonon mean free path in the c-axis direction of graphite is around 200 nm at room temperature, much larger than the commonly believed value of just a few nanometers. This study provides direct experimental evidence for the recently projected very long phonon mean free path along the c-axis of graphite.

Equilibrium limit of thermal conduction and boundary scattering in nanostructures.

Determining the lattice thermal conductivity (κ) of nanostructures is especially challenging in that, aside from the phonon-phonon scattering present in large systems, the scattering of phonons from the system boundary greatly influences heat transport, particularly when system length (L) is less than the average phonon mean free path (MFP). One possible route to modeling κ in these systems is through molecular dynamics (MD) simulations, inherently including both phonon-phonon and phonon-boundary scattering effects in the classical limit. Here, we compare current MD methods for computing κ in nanostructures with both L ⩽ MFP and L ≫ MFP, referred to as mean free path constrained (cMFP) and unconstrained (uMFP), respectively. Using a (10,0) CNT (carbon nanotube) as a benchmark case, we find that while the uMFP limit of κ is well-defined through the use of equilibrium MD and the time-correlation formalism, the standard equilibrium procedure for κ is not appropriate for the treatment of the cMFP limit because of the large influence of boundary scattering. To address this issue, we define an appropriate equilibrium procedure for cMFP systems that, through comparison to high-fidelity non-equilibrium methods, is shown to be the low thermal gradient limit to non-equilibrium results. Further, as a means of predicting κ in systems having L ≫ MFP from cMFP results, we employ an extrapolation procedure based on the phenomenological, boundary scattering inclusive expression of Callaway [Phys. Rev. 113, 1046 (1959)]. Using κ from systems with L ⩽ 3 μm in the extrapolation, we find that the equilibrium uMFP κ of a (10,0) CNT can be predicted within 5%. The equilibrium procedure is then applied to a variety of carbon-based nanostructures, such as graphene flakes (GF), graphene nanoribbons (GNRs), CNTs, and icosahedral fullerenes, to determine the influence of size and environment (suspended versus supported) on κ. Concerning the GF and GNR systems, we find that the supported samples yield consistently lower values of κ and that the phonon-boundary scattering remains dominant at large lengths, with L = 0.4 μm structures exhibiting a third of the periodic result. We finally characterize the effect of shape in CNTs and fullerenes on κ, showing the angular components of conductivity in CNTs and icosahedral fullerenes are similar for a given circumference.

Length-dependent thermal conductivity in suspended single-layer graphene.

Graphene exhibits extraordinary electronic and mechanical properties, and extremely high thermal conductivity. Being a very stable atomically thick membrane that can be suspended between two leads, graphene provides a perfect test platform for studying thermal conductivity in two-dimensional systems, which is of primary importance for phonon transport in low-dimensional materials. Here we report experimental measurements and non-equilibrium molecular dynamics simulations of thermal conduction in suspended single-layer graphene as a function of both temperature and sample length. Interestingly and in contrast to bulk materials, at 300 K, thermal conductivity keeps increasing and remains logarithmically divergent with sample length even for sample lengths much larger than the average phonon mean free path. This result is a consequence of the two-dimensional nature of phonons in graphene, and provides fundamental understanding of thermal transport in two-dimensional materials.

Effect of electrostatics techniques on the estimation of thermal conductivity via equilibrium molecular dynamics simulation: application to methane hydrate

Equilibrium molecular dynamics (MD) simulations for three system sizes of fully occupied methane hydrate have been performed at around 265 K to estimate the thermal conductivity using the Ewald, Lekner, reaction field, shifted-force and undamped Fennell–Gezelter methods. The TIP4P water model was used in conjunction with a fully atomistic methane potential with which it had been parameterized from quantum simulation. The thermal conductivity was evaluated by integration of the heat flux autocorrelation function (ACF) derived from the Green–Kubo formalism; this approach vas validated by estimation of the average phonon mean free path. The thermal conductivities predicted by non-periodic techniques were in reasonable agreement with the experimental results of 0.62 and 0.68 W/m K, although it was found that the estimates by the non-periodic techniques were up to 25% larger than those of Lekner and Ewald estimates, particularly for larger systems. The results for the Lekner method exhibited the least variation with respect to system size. A decomposition of the heat flux vector into its respective contributions revealed the importance of electrostatic interactions, and how different electrostatic treatments affect the contribution to the thermal conductivity.

Influence of the Grain Boundaries on the Heat Transfer in Laser Ceramics

Grain boundaries play a key role in determining several key properties of polycrystalline laser ceramics. Heat transfer measurements at low temperature constitute a good tool to probe grain boundaries. We review the results of heat transfer measurements in polycrystalline Y3Al5O12 garnets as well as Y2O3 and Lu2O3 sesquioxide materials obtained by self-energy-driven sintering of nano-particles. The average phonon mean free path in Y3Al5O12 was found to be significantly larger than the average grain size and to scale with temperature as T−2 at low temperature. Existing models describing the interaction between phonons and grain boundaries are reviewed. Correct temperature dependence of the mean free path and order of magnitude of scattering rates were found by assuming the existence of a grain boundary layer having acoustic properties different from those of the bulk. A different temperature dependence of phonon mean free path was found for the sesquioxides and was ascribed to the stronger elastic anisotropy of these materials. The thermal resistance associated to the grain boundaries of laser ceramics was found to be lower than in other dense polycrystalline ceramic materials reported in the literature.

Lattice thermal conductivity of minerals at high temperatures

Simple perturbation theory predicts that the lattice thermal conductivity should be inversely proportional to the absolute temperature. It is shown that the lattice thermal conductivity of minerals should not depart markedly from that variation, even when the average phonon mean free path is comparable to the lattice spacing.