Local thermal property analysis by scanning thermal microscope of ultrafine-grained surface layer in copper and in titanium produced by surface mechanical attrition treatment

Ultrafine-grained surface layers were obtained by surface mechanical attrition treatment (SMAT) in copper and titanium samples. The thermal properties of the deformed layers were characterized using a scanning thermal microscope (SThM) that allows thermal conductivity to be mapped down to the submicrometer scale. A theoretical approach, based on this investigation, was used to calculate the heat flow from the probe tip to the sample and then estimate the thermal conductivities at different scanning positions. Experimental results and theoretical calculation demonstrate that scanning thermal microscope can be used as a powerful tool for the thermal property and microstructural characterization of ultrafine-grained microstructures.     

An effective thermal conductivity model of nanofluids with a cubical arrangement of spherical particles

The theoretical investigation of the effective thermal conductivities of nanofluids, a new class of solid-liquid suspensions, is important in both predicting and designing nanofluids with effective thermal conductivities. We have developed a new thermal conductivity model for nanofluids that is based on the assumption that monosized spherical particles are uniformly dispersed in the liquid and are located at the vertexes of a simple cubic lattice, with each particle surrounded by a liquid layer having a thermal conductivity that differs from that of the bulk liquid. This model nanofluid with a cubical arrangement of nanoparticles gives a more practical upper limit of thermal conduction than a model nanofluid with a parallel arrangement of nanoparticles. The new model unexpectedly shows a nonlinear relationship of thermal conductivity with particle concentration, whereas the conductivity-concentration curve changes from convex upward to concave upward with increasing volume concentration. The effects of particle and layer parameters on the effective thermal conductivities are also analyzed. A comparison of predicted thermal conductivity values and experimental data shows that the predicted values are much higher than the experimental data, a finding that indicates that there is a potential to further improve the effective thermal conductivities of nanofluids with more uniformly dispersed particles.     

Electrical and thermal conduction in atomic layer deposition nanobridges down to 7 nm thickness

While the literature is rich with data for the electrical behavior of nanotransistors based on semiconductor nanowires and carbon nanotubes, few data are available for ultrascaled metal interconnects that will be demanded by these devices. Atomic layer deposition (ALD), which uses a sequence of self-limiting surface reactions to achieve high-quality nanolayers, provides an unique opportunity to study the limits of electrical and thermal conduction in metal interconnects. This work measures and interprets the electrical and thermal conductivities of free-standing platinum films of thickness 7.3, 9.8, and 12.1 nm in the temperature range from 50 to 320 K. Conductivity data for the 7.3 nm bridge are reduced by 77.8% (electrical) and 66.3% (thermal) compared to bulk values due to electron scattering at material and grain boundaries. The measurement results indicate that the contribution of phonon conduction is significant in the total thermal conductivity of the ALD films.     

A two-scale homogenization framework for nonlinear effective thermal conductivity of laminated composites

In this study, we formulate the effective temperature-dependent thermal conductivity of laminated composites. The studied laminated composites consist of laminas (plies) made of unidirectional fiber-reinforced matrix with various fiber orientations. The effective thermal conductivity is obtained through a two-scale homogenization scheme. A simplified micromechanical model of a unidirectional fiber-reinforced lamina is formulated at the lower scale. Thermal conductivities of fiber and matrix constituents are allowed to change with temperature. The upper scale uses a sublaminate model to homogenize temperature-dependent thermal conductivities of only a representative lamina stacking sequence in laminated composites. The effective thermal conductivity of each lamina, in the sublaminate model, is obtained using the simplified micromechanical model. The thermal conductivities from the micromechanical and sublaminate models represent average nonlinear properties of fictitiously homogeneous composite media. Interface conditions between fiber and matrix constituents and within laminas are assumed to be perfect. Experimental data available in the literature are used to verify the proposed multi-scale framework. We then analyze transient heat conduction in the homogenized composites. Temperature profiles, during transient heat conduction, in the homogenized composites are compared to the ones in heterogeneous composites. The heterogeneous composites, having different fiber arrangements and sizes, are modeled using finite element (FE) method.     

The importance of water migration in the measurement of the thermal conductivity of unsaturated frozen soils

The transport of heat in frozen soil may occur by conduction and by the convective transport of sensible and latent heat arising from the flow of water in the vapor, liquid and solid states. Theory describing the coupled flow of heat and of water in the liquid and vapor states is used to derive a definition of apparent thermal conductivity (the convective transport of heat in the movement of ice in unstaturated soils is assumed to be negligible). Calculations suggest that, at temperatures close to 0°C, the transport of latent heat may exceed the contribution of heat flow by conduction. Under these conditions, the apparent thermal conductivity will be much greater than the thermal conductivity calculated from the thermal conductivities and volume fractions of the components.Insufficient published data prevent a rigorous evaluation of the theory. However the functional dependence on temperature of both thermal conductivity and the apparent thermal conductivity are calculated for a Tomakomai soil at different subzero temperatures. These values are compared to the apparent thermal conductivities of this soil which were measured at a water content in the unfrozen state of 0.48 cm³ cm^?3 and at temperatures ranging from ?0.7°C to ?10°C using the line heat source technique. The dependence of apparent thermal conductivity on subzero temperature, as calculated from theory, compares favourably to the dependence which was observed for this soil.     

Thermal conductivity of crystalline particulate materials

In order to explore the relationship between effective thermal conductivity of an evacuated powder and the bulk thermal conductivity of the same material, the effective thermal diffusivities of particulate NaCl and Dianin's inclusion compound with ethanol guests (abbrev. ED) with effective porosities 0.5 were measured and used to determine their effective thermal conductivities below 300 K. Calculations showed that contact heat conduction is the predominant mechanism, i.e., heat transfer by radiation and by conduction through the gas phase are negligible in the measurement conditions. The effective thermal conductivity of particulate as-synthesised ED powder was found to be proportional to the bulk thermal conductivity for three different samples. On the other hand, the effective thermal conductivity of NaCl powder was found to have a softer temperature dependence than the bulk thermal conductivities reported for measurements of NaCl single crystals. This was related to increased concentration of structural defects formed during mechanical grinding of the NaCl sample.     

Quantitative Thermal Microscopy Measurement with Thermal Probe Driven by dc+ac Current

Quantitative thermal measurements with spatial resolution allowing the examination of objects of submicron dimensions are still a challenging task. The quantity of methods providing spatial resolution better than 100 nm is very limited. One of them is scanning thermal microscopy (SThM). This method is a variant of atomic force microscopy which uses a probe equipped with a temperature sensor near the apex. Depending on the sensor current, either the temperature or the thermal conductivity distribution at the sample surface can be measured. However, like all microscopy methods, the SThM gives only qualitative information. Quantitative measuring methods using SThM equipment are still under development. In this paper, a method based on simultaneous registration of the static and the dynamic electrical resistances of the probe driven by the sum of dc and ac currents, and examples of its applications are described. Special attention is paid to the investigation of thin films deposited on thick substrates. The influence of substrate thermal properties on the measured signal and its dependence on thin film thermal conductivity and film thickness are analyzed. It is shown that in the case where layer thicknesses are comparable or smaller than the probe–sample contact diameter, a correction procedure is required to obtain actual thermal conductivity of the layer. Experimental results obtained for thin SiO\(_{\mathrm {2}}\) and BaTiO\(_{\mathrm {3 }}\)layers with thicknesses in the range from 11 nm to 100 nm are correctly confirmed with this approach.     

A theoretical model for effective thermal conductivity (ETC) of particulate beds under compression

Thermal conductivity of particulate beds is an important property for many industrial handling processes as well as for storage of particulate materials. This paper presents a new theoretical model that is based on heat transfer between particles in three modes: heat conduction through contact area, heat conduction through voids and radiation through voids. The model is further adjusted in order to obtain effective thermal conductivity of a particulate bed by using empirical augmentation factors for the heat transfer coefficient of each one of the heat transfer mechanisms. Comparison of the results predicted by the semi-empirical model to our experimental results show good agreement. The theoretical model was investigated to examine the effect of various parameters (such as: particle elasticity and surface roughness, particle and gas thermal conductivity and particle diameter), on the effective thermal conductivity of various particulate beds. Our results show the significant effect of the contact area (that is a clear function of the compression load) between particles on the effective thermal conductivity.     

Measurement of Thermal Conductivity of Anisotropic SiC Crystal

Silicon carbide (SiC) crystals with excellent heat conduction and thermal stability can be widely used in microelectronic devices and integrated circuits. It is important for the study of a functional type SiC material to have accurate thermal-conductivity and thermal-diffusivity values of SiC crystal. A 3ω technique is employed to determine the anisotropic thermal conductivity of SiC crystal. Three micrometal probes with different widths are deposited by chemical-vapor deposition on the surface of SiC crystal. Each micrometal probe is used as a heater, and also as a thermometer. The temperature fluctuation signals of a micrometal probe represent heat conduction in different directions in the specimen. Thermal conductivities both in the cross-plane and in-plane directions of SiC crystal are achieved through fitted values. The results indicate that thermal conductivities in three different directions of SiC crystal can be characterized using the metal heater construction.     

Realizing the Accurate Measurements of Thermal Conductivity over a Wide Range by Scanning Thermal Microscopy Combined with Quantitative Prediction of Thermal Contact Resistance

Quantitative thermal performance measurements and thermal management at the micro-/nano scale are becoming increasingly important as the size of electronic components shrinks. Scanning thermal microscopy (SThM) is an emerging method with high spatial resolution that accurately reflects changes in local thermal signals based on a thermally sensitive probe. However, because of the unclear thermal resistance at the probe-sample interface, quantitative characterization of thermal conductivity for different kinds of materials still remains limited. In this paper, the heat transfer process considering the thermal contact resistance between the probe and sample surface is analyzed using finite element simulation and thermal resistance network model. On this basis, a mathematical empirical function is developed applicable to a variety of material systems, which depicts the relationship between the thermal conductivity of the sample and the probe temperature. The proposed model is verified by measuring ten materials with a wide thermal conductivity range, and then further validated by two materials with unknown thermal conductivity. In conclusion, this work provides the prospect of achieving quantitative characterization of thermal conductivity over a wide range and further enables the mapping of local thermal conductivity to microstructures or phases of materials.     

Simultaneous measurements of thermal expansion and thermal conductivity of FRPs by employing a hybrid measuring head on a GM refrigerator

This paper describes a setup for the simultaneous measurements of thermal expansion and thermal conductivity at temperatures down to 20 K. The sample holder is an integrated compartment of two cells--one for the measurement of thermal expansion coefficient and another for that of thermal conductivity. The sample holder is thermally isolated from all modes of heat inleak using 130 μPa vacuum and sufficient number of aluminized mylar layer. Linear thermal expansion coefficient and thermal conductivity are measured by 3-terminal capacitance technique and double-specimen guarded-hot-plate method respectively. Experiments are carried out under steady state condition with a set of stability criteria. The effect of addendum, stray capacitance and frequencies, non-uniformity of electric flux on the measurement of capacitance, the effects on heat inleak by gaseous conduction, radiation, copper lead wires and contact resistance on this measurement are made to minimum. The setup is calibrated with standard teflon as sample. The experimental values of teflon show the deviation of about −9% for thermal expansion and about −8% for thermal conductivity from the published values.     

预报纤维增强复合材料有效热导率的随机微结构胞元模型

发展了能预报复合材料有效性质的随机微结构胞元模型以预测单向纤维增强复合材料横向热导率。研究了能反映宏观有效性质的模型最小化问题, 探讨了微结构影响宏观有效热传导性能的机制。结果表明: 通过对模型指定周期边界条件并且以多个合适的小规模模型计算的平均值取代大模型计算, 可大大改进收敛性并提高计算效率, 从10×10个到30×30个子胞的模型, 所得有效热导率计算结果的最大相对变化量仅为0.6%。不同纤维排列引起热流穿过热阻大的基体的路径长度改变, 造成有效热导率不同; 纤维热导率远大于基体热导率时, 纤维随机分布造成纤维偏聚, 部分纤维接触形成"热流通道", 使得有效热导率增大, 揭示了某一体积分数下有效热导率急剧增加是由"热流通道"贯通引起。与实验结果的比较说明了微结构随机性研究的必要性和本文工作的实用价值。     

Effective thermal conductivity of loose particulate systems

The effective thermal conductivity for several loose particulate insulation systems has been measured in the temperature range from 273 K–900 K and the results compared to those predicted from three different models. The measured thermal conductivities increase with temperature. This is accounted for in terms of increased conduction by the fluid (air) and the radiative heat transfer through the media although the latter mode of heat transfer is relatively suppressed in materials containing finer particles. The model due to Zumbrunnen et al. [1] was found to predict values that closely agreed with the experimental values.     

Effect of thermal coarsening on the thermal conductivity of nanoporous gold

The thermal conductivities of nanoporous gold (NPG) microwires annealed at different temperatures have been measured in the temperature range from 100 to 320 K. Considering the electron-surface scattering, the thermal conductivity is expected to increase with the increase of ligament diameter. However, the thermal conductivity of NPG microwire is found to decrease after thermal coarsening, and has a maximum value at around 250 K for the as-dealloyed sample. We suggest that the defects accumulating at a relatively high temperature and the reduction in defect spacing may cause these temperature behaviors of thermal conductivity. Taking into account the electron scattering on ligament surfaces and defects, a modified theoretical model for the thermal conductivity of nanoporous metal is proposed to agree with our experimental results.     

Estimation of thermal conductivity of magneto-optic media

We describe a method to estimate the thermal conductivity of the substrate, the dielectric layer, and the magneto-optic (MO) layer of MO recording media. The method relies on the disappearance of the polar Kerr rotation above the Curie temperature of the MO layer. We obtain the thermal conductivities by taking into account the differences in the heat diffusion behavior under different sized focused spots. The results are reliable to better than 5% accuracy.     

Effect of coating on the microstructure and thermal conductivities of diamond-Cu composites prepared by powder metallurgy

Diamond-Cu composites from the direct combination of diamond and Cu show low thermal conductivities due to weak interface and high thermal resistance as a result of chemical incompatibility. In this paper, a new method is proposed to strengthen interfacial binding between diamond and Cu by coating strong carbide-forming elements, e.g., Ti or Cr on the surface of the diamond through vacuum micro-deposition. Interfacial thermal resistance of diamond-Cu composites is greatly decreased when diamond particles are coated by a Cr or Ti layer of a certain thickness before combining with Cu. Thermal conductivity is also increased several times. Cr coating can reduce more effectively interface thermal resistance between diamond and Cu than Ti coating. Moreover, it has a smaller negative impact on the thermal conductivity of the Cu matrix, resulting in higher thermal conductivity of Cr-coated diamond-Cu composites. Through the vacuum micro-deposition technology, Cr on the diamond particle surface is present in the form Cr₇C₃ near diamond and a pure Cr outer layer at 2:1. The optimum thickness is within 0.6-0.9 μm; at this depth, the thermal conductivities of 70 vol% diamond-Cu composites can be increased four times and reach as high as 657 W/m K. In this work, an original theoretical model is proposed to estimate the thermal conductivities of composite materials with an interlayer of a certain thickness. The predicted values from this model are in good agreement with the experimental values.     

Imaging of Thermal Conductivity with Sub-Micrometer Resolution Using Scanning Thermal Microscopy

With the development of new emerging technologies, many objects in scientific research and engineering are of sub-micrometer and nanometer size, such as microelectronics, micro-electro-mechanical systems (MEMS), biomedicines, etc. Therefore, thermal conductivity measurements with sub-micrometer resolution are indispensable. This paper reports on the imaging of various micrometer and sub-micrometer size surface variations using a scanning thermal microscope (SThM). The thermal images show the contrasts indicating the differences of the local thermal conductivity in the sample. Thermal resistance circuits for the thermal tip temperature are developed to explain the heat transfer mechanism between the thermal tip and the sample and to explain the coupling between the local thermal conductivity and the topography in the test results.     

镧掺杂Sr0.4Ba0.6TiO3材料的导热性能

研究了不同镧掺杂浓度下Sr0.4Ba0.6TiO3材料的导热性能,研究镧元素对其导热性能的影响,得到了不同掺杂量下钛酸锶钡材料的热导率,材料密度随烧结温度与成型压力的增加而增大;同时发现少量镧元素的掺杂,可以增加钛酸锶钡材料的热导率;当镧元素掺杂量较大时,降低了材料的热导率.钛酸锶钡材料的电子热导率随材料烧结温度的升高基本不变,声子热导率随材料烧结温度的升高而增加.     

The effect of Fe3O4 nanoparticles on the thermal conductivities of various base fluids

Conventional heat transfer fluids have intrinsically poor heat transfer properties compared to solids. Enhancing the efficiency of heat transfer is of great interest for various industrial applications. Suspending solid particles in a fluid increases the thermal conductivity of the resulting suspension and enhances the heat transfer properties. In this work, changes in thermal conductivities of fluids upon the addition of magnetic nanoparticles have been investigated. Fe(3)O(4) nanoparticles are synthesized using different synthesis methods and are suspended in various oils. The effect of the base fluid and the type of magnetic particle on the thermal conductivity is investigated in detail. Up to 28% increase in the thermal conductivity is obtained with 2.5 wt% magnetic particles in hexane. The thermal conductivity enhancement is found to depend on the particle concentration, method of preparation and base fluid. The enhancements obtained are higher than those estimated using any theoretical model present in the literature.     

Radiative heat exchange method for thermal conductivity measurement applying a perpendicular heat flow to a thin-plate sample: Principle and apparatus

To measure thermal conductivity of materials of low conductivity (0.1 to 1 W·m^–1·K^–1), a method using a specimen of small size (2×25×25 mm) has been developed. This method applies a well-defined, steady, and uniform heat flux perpendicular to the surface of a small plate sample of polymers or ceramics jointly by means of radiative heat exchange as well as by an areal heater on the sample surface and allows a reasonably rapid (5-min) measurement of thermal conductivity. This method of measuring conductivity is an absolute and direct measurement method which does not need any standard reference materials or information about heat capacity. The principle of the method has been demonstrated by constructing a measurement apparatus and measuring thermal conductivity of a few materials. The thermal conductivities of silicone rubber and Pyrex (Corning 7740) glass measured by the present method between 30 and 90°C are compared with recommended values.