Anisotropic Nature of Thermal Transport in Nanoscale Materials

2005 ◽  
Author(s):  
Xinwei Wang
Keyword(s):  
Thermal Conductivity ◽  
Thermal Transport ◽  
Axial Direction ◽  
Mean Free Path ◽  
Characteristic Size ◽  
Appreciable Effect ◽  
Temperature Differential ◽  
Energy Carriers ◽  
Different Shapes ◽  
The Mean

In this work, an equilibrium technique is developed to study the thermal transport in nanomaterials. By directly tracking the relaxation behavior of energy carriers, the developed technique is able to determine the effect of boundary scattering on thermal transport. Since no temperature differential across the material is required to determine its thermal conductivity, the developed technique is applicable to nanomaterials of different shapes and capable of capturing the anisotropic nature of the thermal transport inside. Applying this technique, the thermal transport in several typical nanomaterials—nanofilms, square and round nanowires, and spherical and cubic nanoparticles are studied in detail. A strong anisotropic nature of thermal transport in nanomaterials is observed. For nanofilms and nanowires, the thermal conductivity in the restricted directions (thickness and radial) is smaller than that in the unrestricted direction. This anisotropic nature is more obvious and important when the characteristic size of nanomaterials becomes comparable to or smaller than the mean free path of energy carriers. Our results comparison shows that with the same characteristic size, the shape of the cross section of nanowires has appreciable effect on the thermal transport in the axial direction. For spherical and cubic nanoparticles, little difference is observed between their thermal conductivities.

scholarly journals Tuning the Anisotropic Thermal Transport in {110}-Silicon Membranes with Surface Resonances

Nanomaterials ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 123
Author(s):  
Keqiang Li ◽  
Yajuan Cheng ◽  
Maofeng Dou ◽  
Wang Zeng ◽  
Sebastian Volz ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Thermal Transport ◽  
Heat Dissipation ◽  
Mean Free Path ◽  
Dynamic Simulations ◽  
Resonant Structures ◽  
Thermoelectric Energy ◽  
Thin Membranes ◽  
The Mean ◽  
Equilibrium Molecular Dynamic

Understanding the thermal transport in nanostructures has important applications in fields such as thermoelectric energy conversion, novel computing and heat dissipation. Using non-homogeneous equilibrium molecular dynamic simulations, we studied the thermal transport in pristine and resonant Si membranes bounded with {110} facets. The break of symmetry by surfaces led to the anisotropic thermal transport with the thermal conductivity along the [110]-direction to be 1.78 times larger than that along the [100]-direction in the pristine structure. In the pristine membranes, the mean free path of phonons along both the [100]- and [110]-directions could reach up to ∼100 µm. Such modes with ultra-long MFP could be effectively hindered by surface resonant pillars. As a result, the thermal conductivity was significantly reduced in resonant structures, with 87.0% and 80.8% reductions along the [110]- and [100]-directions, respectively. The thermal transport anisotropy was also reduced, with the ratio κ110/κ100 decreasing to 1.23. For both the pristine and resonant membranes, the thermal transport was mainly conducted by the in-plane modes. The current work could provide further insights in understanding the thermal transport in thin membranes and resonant structures.

scholarly journals Ballistic Heat Transport in Nanocomposite: The Role of the Shape and Interconnection of Nanoinclusions

Nanomaterials ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 1982
Author(s):  
Paul Desmarchelier ◽  
Alice Carré ◽  
Konstantinos Termentzidis ◽  
Anne Tanguy
Keyword(s):  
Thermal Conductivity ◽  
Molecular Dynamics ◽  
Molecular Dynamics Simulations ◽  
Free Path ◽  
Mean Free Path ◽  
Strong Increase ◽  
Moderate Increase ◽  
Energy Propagation ◽  
The Mean ◽  
Dynamics Simulations

In this article, the effect on the vibrational and thermal properties of gradually interconnected nanoinclusions embedded in an amorphous silicon matrix is studied using molecular dynamics simulations. The nanoinclusion arrangement ranges from an aligned sphere array to an interconnected mesh of nanowires. Wave-packet simulations scanning different polarizations and frequencies reveal that the interconnection of the nanoinclusions at constant volume fraction induces a strong increase of the mean free path of high frequency phonons, but does not affect the energy diffusivity. The mean free path and energy diffusivity are then used to estimate the thermal conductivity, showing an enhancement of the effective thermal conductivity due to the existence of crystalline structural interconnections. This enhancement is dominated by the ballistic transport of phonons. Equilibrium molecular dynamics simulations confirm the tendency, although less markedly. This leads to the observation that coherent energy propagation with a moderate increase of the thermal conductivity is possible. These findings could be useful for energy harvesting applications, thermal management or for mechanical information processing.

Experiments on the flow of heat in liquid helium below 0.7 °K

1958 ◽  
Vol 246 (1246) ◽  
pp. 390-405 ◽  
Keyword(s):  
Thermal Conductivity ◽  
Liquid Helium ◽  
Free Path ◽  
Empirical Relation ◽  
Mean Free Path ◽  
Series Of Experiments ◽  
The Mean ◽  
Set Up ◽  
Low Pressures ◽  
Measured Thermal Conductivity

A series of experiments has been performed to study the steady flow of heat in liquid helium in tubes of diameter 0.05 to 1.0 cm at temperatures between 0.25 and 0.7 °K. The results are interpreted in terms of the flow of a gas of phonons, in which the mean free path λ varies with temperature, and may be either greater or less than the diameter of the tube d . When λ ≫ d the flow is limited by the scattering of the phonons at the walls, and the effect of the surface has been studied, but when λ ≪ d viscous flow is set up in which the measured thermal conductivity is increased above that for wall scattering. This behaviour is very similar to that observed in the flow of gases at low pressures, and by applying kinetic theory to the problem it can be shown that the mean free path of the phonons characterizing viscosity can be expressed by the empirical relation λ = 3.8 x 10 -3 T -4.3 cm. This result is inconsistent with the temperature dependence of λ as T -9 predicted theoretically by Landau & Khalatnikov (1949).

scholarly journals The thermal conductivity of carbon dioxide

1927 ◽  
Vol 114 (767) ◽  
pp. 354-366 ◽  
Keyword(s):  
Thermal Conductivity ◽  
Free Path ◽  
Critical Pressure ◽  
Mean Free Path ◽  
Double System ◽  
Wire Method ◽  
The Mean ◽  
The Absolute ◽  
The Many

Of the many experimental determinations of the thermal conductivity of Co 2 which have been made, the absolute values given by the various observers vary from 3·07 × 10 -5 cal. sec. -1 cm. -1 deg. -1 (Winkelman, 1), to 3·39 × 10 -5 cal. sec. -1 cm. -1 deg. -1 (Weber, 2), and generally speaking the experiments were modifications of two principal methods, namely, the electrically heated wire of Schleimacher (3) and the cooling thermometer method. In both of these methods convection losses were present to a degree depending on the dimensions and disposition of the apparatus, and on the pressure of the gas; therefore, in the author’s opinion, the discrepancies amongst various observers are due to the practice of attempting to eliminate these convective losses by diminishing the pressure. Such a procedure is justifiable only if the reduction of pressure is not carried beyond the point at which the mean free path of the molecules becomes comparable with the dimensions of the containing vessel. This is a critical point in the determination of the conductivity of a gas, as the authors’ experiments on Co 2 indicate that the convection becomes negligible only at pressures for which the mean Free Path Effect is such that the significance imposed on the conductivity by Fourier’s law loses its meaning, and below this critical pressure the conductivity varies with the pressure in a manner depending on the dimensions of the vessel containing the gas. In the experiments of Gregory and Archer (4), on the thermal conductivities of air and hydrogen, the use of a double system of electrically-heated wires enabled the authors accurately to identify the critical pressure at which convective losses became negligible. This is an extremely important point in all applications of the hot-wire method to the absolute determination of the conductivities of gases, and alone justifies the procedure of lowering the pressure to eliminate convective losses. Above this critical pressure it is necessary to disentangle the conduction and convection losses, and below, the meaning of conduction loses its ordinary significance.

Ballistic Heat Transfer Modelling in Semiconductor Electronic Devices: A Modified Fourier-Based Approach

2010 ◽  
Author(s):  
Aydin Nabovati ◽  
Daniel P. Sellan ◽  
Cristina H. Amon
Keyword(s):  
Electronic Devices ◽  
Mean Free Path ◽  
Characteristic Size ◽  
Fourier Law ◽  
Transport Models ◽  
Size Dependent ◽  
Semiconductor Electronic ◽  
Ballistic Heat Transfer ◽  
The Mean ◽  
Boltzmann Method

It is well known that continuum-based thermal transport models, such as the Fourier law, fail when the characteristic size of a system becomes comparable to the mean free path of carriers that transport thermal energy. The current work uses the lattice Boltzmann method to develop two modifications to the Fourier heat equation so that it can capture sub-continuum effects. The two modifications are: (i) a size-dependent thermal conductivity and (ii) a size-dependent temperature jump at the system boundaries.

Thermal Conductivity of α-Tetragonal Boron Nanoribbons

2009 ◽  
Author(s):  
Scott W. Waltermire ◽  
Juekuan Yang ◽  
Deyu Li ◽  
Terry T. Xu
Keyword(s):  
Thermal Conductivity ◽  
Thermal Transport ◽  
Room Temperature ◽  
High Hardness ◽  
Mean Free Path ◽  
Good Oxidation Resistance ◽  
Elemental Boron ◽  
Past Half Century ◽  
Materials Research ◽  
Low Dimensional

Elemental boron has many interesting properties, such as high melting point, low density, high hardness, high Young’s modulus, good oxidation resistance, resulting from its complex crystalline structure from its electron-deficient nature. Boron forms complex crystalline structures according to the various arrangements of B12 icosahedra in the lattice, such as α (B12)- and β (B105)-rhombohedral and α (B50)- and β (B196)-tetragonal boron polymorphs, among others. Even though considerable materials research has been conducted over the past half century on boron and boron-based compounds, investigating their unique structures and corresponding properties, our understanding of this complex class of materials is still poor, compared to some other well-studied materials with much simpler structures such as silicon. Thermal transport studies through bulk boron have been performed mainly on β-rhombohedral and amorphous boron, because of the difficulty to grow high quality bulk α-rhombohedral boron samples [1–3]. Some efforts have been made to measure B12As2, B12P2, AlB12 samples that have an α-rhombohedral form [2,3]. There is almost no information available on α-tetragonal boron. However, Slack predicted the thermal conductivity of α-boron should be ∼200 W/m-K at room temperature, which is 1/2 that of copper. Large phonon mean free path has been predicted for α-boron (from ∼200 nm at room temperature to 6 nm at the Debye temperature), which could lead to interesting thermal transport properties for low dimensional boron structures.

Lattice Boltzmann Modeling of Phonon Heat Conduction in Superlattice Structures

2010 ◽  
Author(s):  
Cristian J. San Marti´n ◽  
Amador M. Guzma´n ◽  
Rodrigo A. Escobar
Keyword(s):  
Thermal Conductivity ◽  
Free Path ◽  
Lattice Boltzmann ◽  
Phonon Dispersion ◽  
Effective Conductivity ◽  
Mean Free Path ◽  
One Dimension ◽  
The Mean ◽  
Superlattice Structures ◽  
Boltzmann Method

The results of temperature prediction and determination of effective thermal conductivity in periodic Si-Ge superlattice in one dimension, at length scale comparable to the mean free path are presented. Classical heat transfer models such as Fourier’s law do not represent what actually happens within electronic devices at these length scales. Phonon-border and phonon-interface scattering effects provide discontinuous jumps in temperature distribution when the mean free path is comparable with the device’s characteristic length, a relation given by the Knudsen number (Kn). For predicting the temperature within the periodic Si-Ge superlattice use is made of the lattice Boltzmann method in one dimension, using Debye’s model in the phonon dispersion relation. The predictions show that as Kn increases, so do the jumps at the borders, the same as at the interfaces. The prediction also shows that the effective conductivity of the Si-Ge superlattice decreases as Kn and the number of layers of material increase, and that keff decreases as the magnitude of p increases, a factor that allows heat flow between one layer and another. Use of gray LBM leads to good approximations of the actual temperature field and thermal conductivity values for the superlattice materials model when the physics of phonons established by Debye’s model is used.

Thermal transport of small systems

2017 ◽  
Author(s):  
Takahiro Yamamoto ◽  
Kazuyuki Watanabe ◽  
Satoshi Watanabe
Keyword(s):  
Thermal Transport ◽  
Thermal Conductance ◽  
Transmission Function ◽  
Mean Free Path ◽  
Phonon Transport ◽  
Fourier Law ◽  
Small Systems ◽  
One Dimensional ◽  
Sample Dimension ◽  
The Mean

This article focuses on the phonon transport or thermal transport of small systems, including quasi-one-dimensional systems such as carbon nanotubes. The Fourier law well describes the thermal transport phenomena in normal bulk materials. However, it is no longer valid when the sample dimension reduces down to below the mean-free path of phonons. In such a small system, the phonons propagate coherently without interference with other phonons. The article first considers the Boltzmann–Peierls formula of diffusive phonon transport before discussing coherent phonon transport, with emphasis on the Landauer formulation of phonon transport, ballistic phonon transport and quantized thermal conductance, numerical calculation of the phonon-transmission function, and length dependence of the thermal conductance.

The Effects of Diameter and Chirality in the Thermal Transport in Free-Standing and Supported Carbon-Nanotubes

2012 ◽  
Author(s):  
Bo Qiu ◽  
Yan Wang ◽  
Qing Zhao ◽  
Xiulin Ruan
Keyword(s):  
Thermal Conductivity ◽  
Molecular Dynamics ◽  
Thermal Transport ◽  
Lattice Thermal Conductivity ◽  
Axial Direction ◽  
Md Simulations ◽  
Phonon Transport ◽  
Free Standing ◽  
Effective Boundary ◽  
Phonon Lifetime

We use molecular dynamics (MD) simulations to explore the lattice thermal transport in freestanding and supported single-wall carbon-nanotube (SWCNT) in comparison to that in graphene nanoribbon (GNR) and graphene sheet. We find the lattice thermal conductivity of freestanding SWCNT and GNR increases with diameter/width and approaches that of graphene. This is partly attributed to the curvature that shortens phonon lifetime in SWCNT. In contrast to GNR, there is only weak chirality dependence in the thermal conductivity of freestanding SWCNT. When SWCNT is put on substrate, an effective boundary along the SWCNT axial direction at the SWCNT-substrate interface is created, rendering resemblance between the phonon transport in supported SWCNT and that in freestanding GNR. As a result, the thermal conductivity of supported SWCNTs differ by around 10%, depending on chirality. The thermal conductivity of SWCNT decreases by about 34–41% when supported, which is less than that of the reduction seen in supported graphene.

scholarly journals Impact of the Regularization Parameter in the Mean Free Path Reconstruction Method: Nanoscale Heat Transport and Beyond

Nanomaterials ◽  
2019 ◽  
Vol 9 (3) ◽  
pp. 414 ◽  
Author(s):  
Miguel-Ángel Sanchez-Martinez ◽  
Francesc Alzina ◽  
Juan Oyarzo ◽  
Clivia Sotomayor Torres ◽  
Emigdio Chavez-Angel
Keyword(s):  
Heat Transport ◽  
Free Path ◽  
Regularization Parameter ◽  
Physical Nature ◽  
Mean Free Path ◽  
Reconstruction Technique ◽  
Reconstruction Method ◽  
Energy Carriers ◽  
The Mean ◽  
The Impact

The understanding of the mean free path (MFP) distribution of the energy carriers in materials (e.g., electrons, phonons, magnons, etc.) provides a key physical insight into their transport properties. In this context, MFP spectroscopy has become an important tool to describe the contribution of carriers with different MFP to the total transport phenomenon. In this work, we revise the MFP reconstruction technique and present a study on the impact of the regularization parameter on the MFP distribution of the energy carriers. By using the L-curve criterion, we calculate the optimal mathematical value of the regularization parameter. The effect of the change from the optimal value in the MFP distribution is analyzed in three case studies of heat transport by phonons. These results demonstrate that the choice of the regularization parameter has a large impact on the physical information obtained from the reconstructed accumulation function, and thus cannot be chosen arbitrarily. The approach can be applied to various transport phenomena at the nanoscale involving carriers of different physical nature and behavior.

Sign in / Sign up

Export Citation Format

Share Document