Current progress on heat conduction in one-dimensional gas channels

We give a brief review of the past development of model studies on one-dimensional heat conduction. Particularly, we describe recent achievements on the study of heat conduction in one-dimensional gas models including the hard-point gas model and billiard gas channel. For a one-dimensional gas of elastically colliding particles of unequal masses, heat conduction is anomalous due to momentum conservation, and the divergence exponent of heat conductivity is estimated as α≈0.33 in k ∼ L ^α . Moreover, in billiard gas models, it is found that exponent instability is not necessary for normal heat conduction. The connection between heat conductivity and diffusion is investigated. Some new progress is reported. A recently proposed model with a quantized degree of freedom to study the heat transport in quasi-one dimensional systems is illustrated in which three distinct temperature regimes of heat conductivity are manifested. The establishment of local thermal equilibrium (LTE) in homogeneous and heterogeneous systems is also discussed. Finally, we give a summary with an outlook for further study about the problem of heat conduction.     

Anomalous heat conduction and anomalous diffusion in nonlinear lattices, single walled nanotubes, and billiard gas channels

We study anomalous heat conduction and anomalous diffusion in low-dimensional systems ranging from nonlinear lattices, single walled carbon nanotubes, to billiard gas channels. We find that in all discussed systems, the anomalous heat conductivity can be connected with the anomalous diffusion, namely, if energy diffusion is sigma(2)(t)=2Dt(alpha) (01) implies an anomalous heat conduction with a divergent thermal conductivity (beta>0), and more interestingly, a subdiffusion (alpha<1) implies an anomalous heat conduction with a convergent thermal conductivity (beta<0), consequently, the system is a thermal insulator in the thermodynamic limit. Existing numerical data support our theoretical prediction.     

Anomalous heat conduction and anomalous diffusion in one-dimensional systems

We establish a connection between anomalous heat conduction and anomalous diffusion in one-dimensional systems. It is shown that if the mean square of the displacement of the particle is =2Dt(alpha)(01) implies anomalous heat conduction with a divergent thermal conductivity (beta>0). More interestingly, subdiffusion (alpha<1) implies anomalous heat conduction with a convergent thermal conductivity (beta<0), and, consequently, the system is a thermal insulator in the thermodynamic limit. Existing numerical data support our results.     

Influence of fluctuations on thermal conductivity of high-Tc YBa2Cu3O7−δ superconductor

To study a behavior of the thermal conductivity near T_c specific heat and thermal diffusivity of the YBa₂Cu₃O_7−δ high-T_c ceramics were simultaneously measured. Close to T_c = 92.30 K the thermal diffusivity and the thermal conductivity discovered minima and the specific heat – maximum. Quantitative analysis of the influence of thermodynamical fluctuations showed the same power laws with Gaussian exponent equal to 0.5 and existing of crossover from the 3D Gaussian to 3D XY critical behavior in the specific heat and thermal conductivity at the approach to T_c. To explain the minimum in thermal conductivity at T_c we propose a mechanism of scattering of phonons on the superconducting fluctuations.     

Computer Simulation Study of Thermal Conduction in 1D Chains of Anharmonic Oscillators

In this work thermal conduction in one-dimensional(1D) chains of anharmonic oscillators are studied using computer simulation.The temperature profile,heat flux and thermal conductivity are investigated for chain length N = 100,200,400,800 and 1600.In the computer simulation anharmonicity is introduced due to Fermi-Pasta-Ulam-β(FPU-β) model.For substrate interaction,an onsite potential due to Frenkel-Kontorova(FK) model has been used.Numerical simulations demonstrate that temperature gradient scales behave as N-1 linearly with the relation J = 0.1765/N.For the thermal conductivity K,KN to N obey the linear relation of the type KN = 0.8805N.It is shown that thermal transport is dependent on phonon-phonon interaction as well as phonon-lattice interaction.The thermal conductivity increases linearly with increase inanharmonicity and predicts relation κ = 0.133 + 0.804β.It is also concluded that for higher value of the strength of the onsite potential system tends to a thermal insulator.     

Direct absorption of gas-phase atomic hydrogen by si(100): A narrow temperature window

We discuss the thermal conductivity of a chain of coupled rotators, showing that it is the first example of a 1D nonlinear lattice exhibiting normal transport properties in the absence of an on-site potential. Numerical estimates obtained by simulating a chain in contact with two thermal baths at different temperatures are found to be consistent with those based on linear response theory. The dynamics of the Fourier modes provides direct evidence of energy diffusion. The finiteness of the conductivity is traced back to the occurrence of phase jumps. Our conclusions are confirmed by the analysis of two variants of this model.     

Thermal rectification and thermal resistive phase cross over in exponential mass graded materials

Concept of the functional graded materials (FGMs) has been explored by consideringexponential mass variation along the chain of anharmonic oscillators in the study of heattransport at low dimensions. This exponential distribution of mass along the space invokesthe diffusion of phonons transport which results to temperature gradient, asymmetric heatflow, thermal rectification and cross over between positive differential thermalresistance (PDTR) and negative differential thermal resistance (NDTR) in one-dimensional(1D) exponential mass graded chain. The temperature dependence thermal rectificationachieved is 4?74% and also predicted that the thermal rectification can be controlled bytuning the higher and lower average temperature limits of two thermal reservoirs. It isalso seen that in FGMs, the thermal conductivity does not change drastically against theaverage temperature of two heat baths. The cross over between PDTR and NDTR can be tunedeither by mass ratio of one dimensional (1D) exponential mass graded anharmonic chainand/or by temperature difference between two heat baths. The figure of merit of the 1Dstructure can also be tuned by mass gradient, the higher mass gradient material will workas the potential candidate for better thermoelectric material.     

Thermal properties of carbon nanotubes and nanotube-based materials

The thermal properties of carbon nanotubes are directly related to their unique structure and small size. Because of these properties, nanotubes may prove to be an ideal material for the study of low-dimensional phonon physics, and for thermal management, both on the macro- and the micro-scale. We have begun to explore the thermal properties of nanotubes by measuring the specific heat and thermal conductivity of bulk SWNT samples. In addition, we have synthesized nanotube-based composite materials and measured their thermal conductivity. The measured specific heat of single-walled nanotubes differs from that of both 2D graphene and 3D graphite, especially at low temperatures, where 1D quantization of the phonon bandstructure is observed. The measured specific heat shows only weak effects of intertube coupling in nanotube bundling, suggesting that this coupling is weaker than expected. The thermal conductivity of nanotubes is large, even in bulk samples: aligned bundles of SWNTs show a thermal conductivity of >200 W/m K at room temperature. A linear K(T) up to approximately 40 K may be due to 1D quantization; measurement of K(T) of samples with different average nanotube diameters supports this interpretation. Nanotube–epoxy blends show significantly enhanced thermal conductivity, showing that nanotube-based composites may be useful not only for their potentially high strength, but also for their potentially high thermal conductivity. Received: 17 October 2001 / Accepted: 3 December 2001 / Published online: 4 March 2002     

Thermal Conductivity of the Toda Lattice with Conservative Noise

We study the thermal conductivity of the one dimensional Toda lattice perturbed by a stochastic dynamics preserving energy and momentum. The strength of the stochastic noise is controlled by a parameter γ. We show that heat transport is anomalous, and that the thermal conductivity diverges with the length n of the chain according to κ(n)∼n ^α , with 0<α≤1/2. In particular, the ballistic heat conduction of the unperturbed Toda chain is destroyed. Besides, the exponent α of the divergence depends on γ.     

From compact point defects to extended structures in silicon

We show that in contrast to the 1d Frenkel-Kontorova (FK) chain known to obey the Fourier law of heat conduction and several 2d models which show logarithmic dependence of conductivity on system size, a scalar 2d FK lattice with commensurate structure exhibits anomalous heat conduction, whose thermal conductivity displays a power law behavior. The dependence of thermal gradient on bulk temperature and noise correlation is critically analyzed. A dynamical contribution to conductivity when the system attains a nonequilibrium steady state of thermal conduction has been identified.     

MEASUREMENTS OF THERMAL CONDUCTIVITY AND OPTICAL PROPERTIES OF POROUS PARTIALLY STABILIZED ZIRCONIA

Experimental measurements of the high-temperature (300 < T < 800 K) thermal conductivity of highly porous (porosity greater than 80%), partially stabilized zirconia (PSZ) were performed. A method of simultaneously inverting conductivity and extinction coefficient from the experimental data is presented. The effect of natural convection within the porous plates with heating from below was found to be negligible. The thermal conductivity integral (TCI) method was incorporated into the inversion of conductivity and radiative properties from the diffusion approximation of the combined radiation and conduction heat flux measurement. The measured conductivity decreased slightly as the pore size of the PSZ increased. The extinction coefficient decreased with increased pore size, and for pore size greater than 0.6 mm the trend had good agreement with the geometric optics limit prediction.     

Molecular dynamics study for the thermal conductivity of diatomic liquid

The thermal conductivity of diatomic liquids was analyzed using a nonequilibrium molecular dynamics (NEMD) method. Five liquids, namely, O₂, CO, CS₂, Cl₂ and Br₂, were assumed. The two-center Lennard-Jones (2CLJ) model was used to express the intermolecular potential acting on liquid molecules. First, the equation of state of each liquid was obtained using MD simulation, and the critical temperature, density and pressure of each liquid were determined. Heat conduction of each liquid at various liquid states [metastable (ρ=1.9ρ_cr), saturated (ρ=2.1ρ_cr), and stable (ρ=2.3ρ_cr)] at T=0.7T_cr was simulated and the thermal conductivity was estimated. These values were compared with experimental results and it was confirmed that the simulated results were consistent with the experimental data within 10%. Obtained thermal conductivities at saturated state were reduced by the critical temperature, density and mass of molecules and these values were compared with each other. It was found that the reduced thermal conductivity increased with the increase in the molecular elongation. Detailed analysis of the molecular contribution to the thermal conductivity revealed that the contribution of the heat flux caused by energy transport and by translational energy transfer to the thermal conductivity is independent of the molecular elongation while the contribution of the heat flux caused by rotational energy transfer to the thermal conductivity increases with the increase in the molecular elongation. Moreover, by comparing the reduced thermal conductivity at various states, it was found that the increase of thermal conductivity with the increase in the density, or pressure, was caused by the increase of the contribution of energy transfer due to molecular interaction.     

Thermal properties of amorphous materials at low temperatures

Recent investigations of X-ray diffraction and electron micrograph studies reveal high density clusters separated by density deficient regions (voids) in amorphous materials. The low temperature specific heat and the thermal conductivity anomalies are explained on the basis of such a structure for amorphous materials. It is a generalisation of Debye's theory applied to most of the amorphous solids in the temperature range from 0 to 10 K. The anharmonic effects lead to the observed temperature dependence of the sound velocity. The thermal conductivity between 0 and 2 K is due to thermal diffusion, the plateau observed between 2 and 20 K is a consequence of the decrease in thermal conductivity due to three phonon processes compensated by intercluster diffusion, while beyond this range it is due to excitations within a cluster limited by the size of a cluster. Further the model predicts the coefficient of expansion about 100 times that found in the corresponding crystalline solids. An experimental verification of this result can be a good test for the model.     

Energy diffusion in hard-point systems

We investigate the diffusive properties of energy fluctuations in a one-dimensional diatomic chain of hard-point particles interacting through a square-well potential. The evolution of initially localized infinitesimal and finite perturbations is numerically investigated for different density values. All cases belong to the same universality class which can be also interpreted as a Levy walk of the energy with scaling exponent γ=3/5. The zero-pressure limit is nevertheless exceptional in that normal diffusion is found in tangent space and yet anomalous diffusion with a different rate for perturbations of finite amplitude. The different behaviour of the two classes of perturbations is traced back to the “stable chaos" type of dynamics exhibited by this model. Finally, the effect of an additional internal degree of freedom is investigated, finding that it does not modify the overall scenario.     

Spin thermal conductivity of the haldane chain compound Y(2)BaNiO(5)

We have measured the thermal conductivity of the spin S=1 chain compound Y(2)BaNiO(5). Analyzing the anisotropy of the thermal transport allows us to identify a definite spin-mediated thermal conductivity kappa(s) along the chain direction. The calculated spin-related energy diffusion constant D(E)(T) shows a broad peak around 120 K. Close to room temperature, D(E)(T) approaches the theoretically predicted high-temperature value, while scattering of spin excitations by magnetic impurities seems to be the major limiting factor of kappa(s) at low temperature.     

Study of thermal conductivity and thermal rectification in exponential mass graded lattices

Concept of exponential mass variation of oscillators along the chain length of N oscillators is proposed in the present Letter. The temperature profile and thermal conductivity of one-dimensional (1D) exponential mass graded harmonic and anharmonic lattices are studied on the basis of Fermi-Pasta-Ulam (FPU) β model. Present findings conclude that the exponential mass graded chain provide higher conductivity than that of linear mass graded chain. The exponential mass graded anharmonic chain generates the thermal rectification of 70-75% which is better than linear mass graded materials, so far. Thus instead of using linear mass graded material, the use of exponential mass graded material will be a better and genuine choice for controlling the heat flow at nano-scale.     

Thermal Conductivity of Complex Plasmas Using Novel Evan-Gillan Approach

The thermal conductivity of complex fluid materials(dusty plasmas) has been explored through novel Evan-Gillan homogeneous non-equilibrium molecular dynamic(HNEMD) algorithm. The thermal conductivity coefficient obtained from HNEMD is dependent on various plasma parameters(Γ, κ). The proposed algorithm gives accurate results with fast convergence and small size effect over a wide range of plasma parameters. The cross microscopic heat energy current is discussed in association with variation of temperature(1/Γ) and external perturbations(P_z). The thermal conductivity obtained from HNEMD simulations is found to be very good agreement and more reliable than previously known numerical techniques of equilibrium molecular dynamic, nonequilibrium molecular dynamic simulations. Our new investigations point to an effective conclusion that the thermal conductivity of complex dusty plasmas is dependent on an extensive range of plasma coupling(Γ) and screening parameter(κ) and it varies by the alteration in these parameters.It is also shown that a different approach is used for computations of thermal conductivity in 2D complex plasmas and can be appropriate method for behaviors of complex systems.     

Vortex sink under conditions of a thermal choking with regard to the real properties of gases

Changes in the formulation of the problem for a vortex source and a vortex sink upon taking into account the change in the heat capacity and the adiabatic exponent for a diatomic gas (for the example of air) in response to an increase in the temperature from 300 K to a few thousands of Kelvin are discussed. A thermal choking is studied for a vortex sink, and critical values of the energy parameter are calculated. It is shown that the minimal radius of the vortex sink decreases upon a heat release. Similarity parameters including the dimensionless circulation (or mass flow), the energy parameter, and the position and thickness of the heat-release region are varied. Errors of the gas model that assumes constant heat capacities and a constant adiabatic exponent are estimated.     

Anomalous energy diffusion and heat conduction in one-dimensional system

We propose a new concept, the centre of energy, to study energy diffusion and heat conduction in one-dimensional hard-point model. For diatom model, we find an anomalous energy diffusion as $\langle x^2 \rangle\sim t^\beta$ with $\beta=1.33$, which is independent of initial condition and mass rate. The present model can be viewed as the model composed by independent quasi-particles, the centre of energy. In this way, heat current can be calculated. Based on theory of dynamic billiard, the divergent exponent of heat conductivity is estimated to be $\alpha=0.33$, which is confirmed by a simple numerical calculation.     

SiNx薄膜热物性参数实验测量与分析研究

采用一种新的实验测量方案，将金属加热单元与温度探测单元合二为一，间接获得了在半导体和微电子学MEMS领域内有重要用途的SiN_x薄膜的导热系数、发射率、比热容和热扩散系数，并对实验结果进行了不确定度分析，为微电子电路设计和掩模成型工艺等提供了可靠的热物性数据. 实验结果表明，薄膜的导热系数、发射率、热扩散系数远比相应体材质低，而且还与温度、厚度有关，尺寸效应显著，而比热容则与体材质相差不大. 关键词： 微尺度传热 热物性参数 x薄膜')" href="#">SiN_x薄膜 测量技术