Transient, Sub-Continuum, Heat Conduction in Irregular Geometries

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Saad Bin Mansoor ◽  
Bekir S. Yilbas
Keyword(s):  
Intensity Distribution ◽  
Mean Free Path ◽  
Phonon Transport ◽  
Geometric Feature ◽  
Shape Effect ◽  
Film Material ◽  
Irregular Shapes ◽  
Frequency Independent ◽  
Order Of Magnitude ◽  
The Mean

Abstract Phonon transfer in irregular shapes is important for assessing the influence of shape effect on thermal transport characteristics of low-scale films. It becomes critical for evaluating the contribution of the scattering phonons to the phonon intensity distribution inside the film. Hence, the sub-continuum ballistic-diffusive model is incorporated to formulate the phonon transport in an irregular geometry of low-size film adopting the transient, frequency-independent, equation of phonon radiative transfer. The discrete ordinate method is used in the numerical discretization of the governing transport equation. It is demonstrated that the geometric feature of the film influences the phonon intensity distribution within the film material. The transport characteristics obtained from the Fourier and the ballistic-diffusive models are markedly different in their spatial and temporal behavior. This is true when the device sizes are of the same order of magnitude as the mean-free path of the heat carriers.

scholarly journals III. Alkali films with the properties of the normal metal

1938 ◽  
Vol 166 (925) ◽  
pp. 270-277 ◽  
Keyword(s):  
Free Path ◽  
Alkali Metals ◽  
Lattice Strain ◽  
Mean Free Path ◽  
Film Material ◽  
Residual Resistance ◽  
Bulk Metal ◽  
Conduction Electrons ◽  
Considerable Excess ◽  
The Mean

In the present work the measurements of the resistivity of evaporated films of the alkali metals (Lovell 1936 a, b ; Appleyard and Lovell 1937) have been extended to a thickness of several thousand angstroms. The previous results were limited to films of less than a few hundred angstroms in thick­ness; and it appeared that thin creased resistivity of these thin films com­pared with that of the bulk metal was due merely to the shortening of the mean free path of the conduction electrons by collision with the boundaries of the film. It was therefore to be expected that at thicknesses much in excess of the mean free path the resistivity of the film material should closely approximate to that of the bulk metal. The present results confirm this expectation only in the case of caesium, where the resistivity approaches within a few per cent that of the bulk metal. Potassium and rubidium films, on the other hand, show a considerable excess of resistivity above that of the bulk metal, but it is shown that this excess is a residual resistance due to lattice strain, and that it may be partially removed by suitable annealing.

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.

scholarly journals Observation of a transition to a localized ultrasonic phase in soft matter

2022 ◽  
Vol 5 (1) ◽  
Author(s):  
Bernard R. Matis ◽  
Steven W. Liskey ◽  
Nicholas T. Gangemi ◽  
Aaron D. Edmunds ◽  
William B. Wilson ◽  
...  
Keyword(s):  
Phase Transition ◽  
Free Path ◽  
Soft Matter ◽  
Volume Fraction ◽  
Localization Length ◽  
Mean Free Path ◽  
Sound Waves ◽  
Classical Waves ◽  
Order Of Magnitude ◽  
The Mean

AbstractAnderson localization arises from the interference of multiple scattering paths in a disordered medium, and applies to both quantum and classical waves. Soft matter provides a unique potential platform to observe localization of non-interacting classical waves because of the order of magnitude difference in speed between fast and slow waves in conjunction with the possibility to achieve strong scattering over broad frequency bands while minimizing dissipation. Here, we provide long sought evidence of a localized phase spanning up to 246 kHz for fast (sound) waves in a soft elastic medium doped with resonant encapsulated microbubbles. We find the transition into the localized phase is accompanied by an anomalous decrease of the mean free path, which provides an experimental signature of the phase transition. At the transition, the decrease in the mean free path with changing frequency (i.e., disorder strength) follows a power law with a critical exponent near unity. Within the localized phase the mean free path is in the range 0.4–1.0 times the wavelength, the transmitted intensity at late times is well-described by the self-consistent localization theory, and the localization length decreases with increasing microbubble volume fraction. Our work sets the foundation for broadband control of localization and the associated phase transition in soft matter, and affords a comparison of theory to experiment.

Perpendicular Resistance of Co/Cu Multilayers Prepared by Molecular Beam Epitaxy

1995 ◽  
Vol 384 ◽  
Author(s):  
N.J. List ◽  
W.P. Pratt ◽  
M.A. Howson ◽  
J. Xu ◽  
M.J. Walker ◽  
...  
Keyword(s):  
Free Path ◽  
Spin Diffusion ◽  
Mean Free Path ◽  
Ferromagnetic Structure ◽  
Order Of Magnitude ◽  
The Mean ◽  
Electron Mean Free Path ◽  
Determining Factor ◽  
Second Peak ◽  
Key Parameter

ABSTRACTResults are presented of the magnetoresistance of MBE-grown (111) Co/Cu multilayers measured with the current perpendicular to the plane of the layers (CPP). Although for measurements made with the more common geometry of current in the plane of the layers (CIP) there are large differences between the results on samples made by sputtering and those prepared by MBE, for these new CPP data the results on samples made by the two techniques are very much alike. For copper layers with thicknesses between 0.9nm to 6nm the magnetoresistance shows oscillations with copper thickness that were almost non-existent in the earlier CIP data. At the second peak the magnetoresistance in the CPP geometry is an order of magnitude greater than that in the CIP configuration. Although the interfaces in these samples have been shown to be very sharp, they appear to form a mosaic structure with the antiferromagnetic regions embedded in a ferromagnetic structure. It is argued that for CIP measurements the GMR is greatly reduced by these ferromagnetic correlations over lengthscales long compared to the electron mean free path. For CPP measurements, on the other hand, it is the spin diffusion length that is the determining factor with the mean free path no longer a key parameter and with values of the GMR virtually independent of the growth process.

scholarly journals The resistance of liquid metals

1934 ◽  
Vol 146 (857) ◽  
pp. 465-472 ◽  
Keyword(s):  
Melting Point ◽  
Liquid Metals ◽  
Mean Free Path ◽  
Quantitative Agreement ◽  
Liquid Lead ◽  
Modern Theory ◽  
Wave Mechanics ◽  
Normal Metals ◽  
Order Of Magnitude ◽  
The Mean

The electrical resistance of most normal metals in the liquid state just above the melting point is about twice as great as that of the solid metal just below the melting point. Certain abnormal metals, however, such as bismuth, gallium and antimony, which are rather poor conductors in the solid state, increase their conductivity on melting. The purpose of this paper is to discuss this change of resistance from the point of view of the modern theory of electronic conduction which is based on the wave mechanics, and to obtain a formula for the change of resistance which is in quantitative agreement with experiment for normal metals. No quantitative theory can as yet be given for the abnormal metals, but we shall show that their behaviour is explicable in a qualitative way. In a solid the atoms vibrate about mean positions which are fixed in the solids in a liquid at temperatures near the melting point, it is now generally recognized that the atoms vibrate about mean positions which, though not fixed, move slowly compared with the velocity, of order of magnitude √( k T/M), with which the atoms vibrate. The most direct evidence for this is afforded by the specific heats of monatomic metals, which have, within the limits of experimental error (~7%), the same values (in the neighbourhood of 3R) for a given metal in the solid and liquid states near the melting point. Further evidence is given by the rates of diffusion of gold in mercury (0·72 sq cm/day) or of thorium B (Pb) in non-radioactive liquid lead (2·2 sq cm/day). If one compares these numbers with the formula for the diffusion coefficient in gases, D = 1/3 lc , where l is the mean free path, and c the mean molecular velocity, one finds, on setting c equal to a quantity of the order of magnitude of √( k T/M), that l must be taken to be about one-hundredth of the interatomic distance.

scholarly journals Temperature Distribution through a Nanofilm by Means of a Ballistic-Diffusive Approach

Inventions ◽  
2019 ◽  
Vol 4 (1) ◽  
pp. 2 ◽  
Author(s):  
Hatim Machrafi
Keyword(s):  
Heat Transport ◽  
Temperature Jump ◽  
Mean Free Path ◽  
Phonon Transport ◽  
Behavior Changes ◽  
Heat Management ◽  
Qualitative Comparison ◽  
Microelectronic Devices ◽  
Order Of Magnitude ◽  
Non Local

As microelectronic devices are important in many applications, their heat management needs to be improved, in order to prolong their lifetime, and to reduce the risk of damage. In nanomaterials, heat transport shows different behaviors than what can be observed at macroscopic sizes. Studying heat transport through nanofilms is a necessary tool for nanodevice thermal management. This work proposes a thermodynamic model incorporating both ballistic, introduced by non-local effects, and diffusive phonon transport. Extended thermodynamics principles are used in order to develop a constitutive equation for the ballistic behavior of heat conduction at small-length scales. Being an irreversible process, the present two-temperature model contains a one-way transition of ballistic to diffusive phonons as time proceeds. The model is compared to the classical Fourier and Cattaneo laws. These laws were not able to present the non-locality that our model shows, which is present in cases when the length scale of the material is of the same order of magnitude or smaller than the phonon mean free path, i.e., when the Knudsen number K n ≤ O ( 1 ) . Moreover, for small K n numbers, our model predicted behaviors close to that of the classical laws, with a weak temperature jump at both sides of the nanofilm. However, as K n increases, the behavior changes completely, the ballistic component becomes more important, and the temperature jump at both sides of the nanofilms becomes more pronounced. For comparison, a model using Fourier’s and Cattaneo’s laws with an effective thermal conductivity has shown, with reasonable qualitative comparison for small Knudsen numbers and large times.

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.

scholarly journals Relaxation Times in Strictly Disk Systems

1971 ◽  
Vol 10 ◽  
pp. 15-19
Author(s):  
George B. Rybicki
Keyword(s):  
Numerical Experiments ◽  
Relaxation Times ◽  
Galactic Structure ◽  
Large Numbers ◽  
Order Of Magnitude ◽  
Vlasov Limit ◽  
The Mean ◽  
Gravitating Systems

AbstractIt is shown that the time of relaxation by particle encounters of self-gravitating systems in the plane interacting by 1/r2 forces is of the same order of magnitude as the mean orbit time. Therefore such a system does not have a Vlasov limit for large numbers of particles, unless appeal is made to some non-zero thickness of the disk. The relevance of this result to numerical experiments on galactic structure is discussed.

Sputtering pressure dependence of hydrogen-sensing effect of palladium films

2009 ◽  
Vol 24 (6) ◽  
pp. 1919-1927 ◽  
Author(s):  
Chung Wo Ong ◽  
Yu Ming Tang
Keyword(s):  
Electrical Resistivity ◽  
Magnetron Sputtering ◽  
Mean Free Path ◽  
Induced Response ◽  
Resistivity Ratio ◽  
Hydrogen Sensing ◽  
The Mean ◽  
Sputtering Pressure ◽  
Specific Volumes ◽  
Hydride Phases

The electrical resistivity ρ of palladium (Pd) films prepared by using magnetron sputtering at different pressures φ ranging from 2 to 15 mTorr showed very different hydrogen (H)-induced response. This reaction is because the mean free path of the particles in vacuum changes substantially with φ, such that the structure of the deposits is altered accordingly. A film prepared at a moderate φ value of 6 mTorr has a moderate strength. After a few hydrogenation-dehydrogenation cycles, some cracks are generated because of the great difference in the specific volumes of the metal and hydride phases. Breathing of the cracks in subsequent switching cycles occurred, which led to the response gain of ρ, defined as the resistivity ratio of the dehydrogenated-to-hydrogenated states during a cycle, to increase to 17. This result demonstrates the attractiveness of using the Pd films in H2 detection application. The H-induced resistive response of the films prepared at other φ values was found to be much smaller.

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