Measurement Of Thermal Expansion Coefficient Research Articles

Measurement of Thermal Expansion Coefficient of MgZnY Alloys with Synchronized Long-Period Stacking Ordered Phase

We measured the thermal expansion coefficients of 18R-LPSO phase and α-Mg phase in a Mg97Zn1Y2 alloy polycrystal. This was achieved by using a Gandolfi camera, which was attached on a high precision diffractometer at SPring-8 BL40XU beamline. By using this system, fine diffraction data were obtained from a Mg97Zn1Y2 polycrystal at 6 different temperatures between 90 and 450 K. We succeeded to determine cell parameters of 18R-LPSO phase and α-Mg phase separately in the Mg97Zn1Y2 alloy polycrystal. The thermal expansion coefficients were determined from the refined cell parameters. The differences of the thermal expansion coefficients of 18R-LPSO phase and α-Mg phase in the Mg97Zn1Y2 alloy were much smaller than those of single-phase 18R-LPSO and α-Mg polycrystals.

Heat-capacity measurements of sandstone at high temperatures

To evaluate geothermal energy generation systems, we must predict the amount of heat present and the rate at which it can be extracted. These two factors—amount of heat and recovery rate—in turn depend on the basic physical properties of the reservoir rocks. The amount of heat present in a reservoir depends on the heat capacity CP of the rocks. The heat capacity of the rocks is needed to evaluate energy storage, Q = (1 − ϕ)ρCP(T)T, where ϕ is the porosity, ρ is the density, CP is the heat capacity, and T is the temperature. For global heat balances, the mean specific heat between two extreme temperatures T1 and T2, can be defined as \(Q = \frac{1}{{T_{2} - T_{1} }}\int\nolimits_{{T_{1} }}^{{T_{2} }} {C_{P} \left( T \right)dT}\), where CP(T) is the temperature-dependence of the heat capacity. For dynamic processes, the value of heat-capacity at each given temperature is needed. The area under a CP(T) curve between any two temperature limits yields an enthalpy change as \(\Delta H = \int\nolimits_{{T_{1} }}^{{T_{2} }} {C_{P} \left( T \right)dT}\). In the present work we have detailed study of the temperature dependence of the heat capacity (CP) of sandstone over the temperature range from 308 to 763 K using a differential scanning calorimeter model of 204 F1. The combined expanded uncertainty of the heat capacity measurements at the 95% confidence level with a coverage factor of k = 2 is estimated to be 1%. A rapid increase (from 1.06 to 1.85 kJ kg−1 K−1) of the measured heat capacities above the classical value (3R) in the high-temperature range above 575 K was observed. This increase at high temperatures can be explained as being due to microstructural changes during heating of the sample (the microstructural effect), which was confirmed by thermal expansion coefficient measurements. The effect of microstructural changes (“thermal cracking”) on the temperature behavior of heat-capacity of sandstone was studied. Theoretically-based correlations for the heat capacity were adopted to accurately represent the measured data. The measured CP(T) data for sandstone were used to check the accuracy, predictive capability, and applicability of various correlation models proposed in the literature. The proposed correlation equations for the heat capacity are based on the present experimental data that have been critically assessed for consistency with other measured properties and for agreement with theory whenever possible.

Thermal Global Expansion Coefficient Measurement for a Harmonic Trapped Gas Across Bose-Einstein Condensation

We report the measurement of the global thermal expansion coefficient of a confined Bose gas of $^{87}\rm Rb$ in a harmonic potential around the Bose-Einstein condensation transition temperature. We use the concept of global thermodynamic variables, previously introduced and appropriated for a non-homogeneous system. We observe the behavior of the thermal expansion coefficient above and below the critical temperature showing the lambda-like shape present in superfluid helium. The study demonstrates the potentiality of global thermodynamic variables for the investigation of properties across the critical temperature and a new way to study the thermodynamic properties of the quantum systems.

Thermal expansion/shrinkage measurement of battery separators using a dynamic mechanical analyzer

Polymer separators for lithium ion batteries are thin, porous membranes of 20–30 μm thickness. At elevated temperatures, some separators can shrink considerably. To predict the deformation and stresses in the separator in battery cells, it is necessary to measure the expansion/shrinkage property of a separator as expressed by the coefficient of thermal expansion (CTE). The reported CTE measurement techniques for thin films have their limitations. This paper examines the use of a dynamic mechanical analyzer (DMA) for the measurement of the thermal expansion/shrinkage property of polymer separators. The effect of the dimensional change of the testing fixture was considered. The influences of the preloading levels and heating rates were investigated. The measurements were carried out for three common types of polymer based separator. The CTE as a function of temperature was determined from the DMA data. DMA offers continuous measurements in an automatic fashion, which is an efficient and convenient method to characterize the thermal expansion/shrinkage behavior of thin polymer films.

Reduction of Thermal Stress in Copper TSV due to Annealing by Low TEC Copper

Introduction Copper through-silicon via (TSV) is the key technology used in 3D packaging. However, the large mismatch in thermal expansion coefficient (TEC) between copper and silicon generates the thermomechanical stress inside and surround the TSV during fabrication process. This thermomechanical stress changes the carrier mobility1 and causes extrusion of copper2. In this study, thermomechanical stress in copper TSV, as well as copper extrusion were reduced using low TEC copper. Moreover, conventional copper TSV was also studied as a comparison. Results and Discussion Fig. 1 shows TEC measurement results of conventional copper and copper electrodeposited with different concentrations of 2M5S leveler. The expansion length of conventional copper (line a) is linear with temperature. Copper pipes electrodeposited with 2M5S leveler (line b, c, and d) start to shrink at 120oC. The reason for the shrinkage of copper is the diffusion of carbon out of copper lattices3. Furthermore, at a 2M5S leveler concentration of 1 ppm, the expansion length of electrodeposited copper is lowest. Therefore, 1 ppm of 2M5S leveler is used for TSV filling for the next experiments.Fig. 2 illustrates the cross-sectional views of copper TSVs after annealing at 500oC. Fig. 2a and 2b are conventional copper TSV. Fig. 2c is low TEC copper TSV (TSV filled with 1 ppm of 2M5S leveler). In Fig. 2a, cracks occur at the vias bottom. Wang found that the stress at the via bottom was very high by simulation using ANSYS4. That large stress is the cause of the cracks at the bottom of the TSV. In Fig. 2b, the extrusion height of conventional copper is about 1.5 µm. In Fig. 2c of low TEC copper TSV, no cracks are observed at the vias bottom. Moreover, the copper extrusion height is only 0.3 µm. Therefore, the stress as well as the extrusion of copper in TSV have been reduced by using low TEC copper. References S. E. Thompson, G. Sun, Y. S. Choi, and T. Nishida, IEEE Trans. Electron Devices, 53, 1010–1020 (2006).A. Heryanto et al., J. Electron. Mater., 41, 2533–2542 (2012).V. Q. Dinh and K. Kondo, ECS J. Solid State Sci. Technol., 6, P566–P569 (2017).J.-S. Hwang, S.-H. Seo, and W.-J. Lee, J. Electron. Packag., 138, 31006 (2016). Figure 1

Thermal expansion coefficient measurement from electron diffraction of amorphous films in a TEM

We measured the linear thermal expansion coefficients of amorphous 5–30 nm thick SiN and 17 nm thick Formvar/Carbon (F/C) films using electron diffraction in a transmission electron microscope. Positive thermal expansion coefficient (TEC) was observed in SiN but negative coefficients in the F/C films. In case of amorphous carbon (aC) films, we could not measure TEC because the diffraction radii required several hours to stabilize at a fixed temperature.

Reducing the Coefficient of Thermal Expansion of Polyimide Films in Microelectronics Processing Using ZnS Particles at Low Concentrations

We report a reduction in the coefficient of thermal expansion (CTE) of polyimide (PI) film in microelectronics processing by using ZnS particles as nanofillers. To prevent agglomeration of ZnS particles, the surfaces of ZnS particles were modified with the (3-mercaptopropyl)trimethoxysilane, creating surface hydroxyl groups. For means of comparison, SiO2 and ZrW2O8 particles that have widely been studied as fillers for various polymer films were also synthesized. The CTE measurements showed that the ZnS particles produced PI nanocomposite film with a much lower CTE than either SiO2 or ZrW2O8 particles at the same concentration. In particular, the surface-modified ZnS particles showed the lowest CTE (13 ppm/K) at 15 wt %, which is comparable to the largest percentage decrease (70%) in CTE from the bare-PI film to date at a much lower particle concentration. To rationalize the significant reduction in CTE with the surface-modified ZnS particles, we considered the intrinsic CTE and thermal conductivity, ther...

Measurement of the Thermal Expansion Coefficient for Ultra-High Temperatures up to 3000 K

The paper is devoted to a new high-temperature dilatometer, a part of the State Primary Standard of the thermal expansion coefficient (TEC) unit. The dilatometer is designed for investigation and certification of materials for TEC standards in the range of extremely high temperatures. The critical review of existing methods of TEC measurements is given. Also, the design, principles of operation and metrological parameters of the new device are described. The main attention is paid to the system of machine vision that allows accurate measurement of elongation at high temperatures. The results of TEC measurements for graphite GIP-4, single crystal $$\hbox {Al}_{2}\hbox {O}_{3}$$ , and some other materials are also presented.

Evaluation of thermal expansion coefficient of carbon fiber reinforced composites using electronic speckle interferometry.

An optical system for measuring the coefficient of thermal expansion (CTE) of materials has been developed based on electronic speckle interferometry. In this system, the temperature can be varied from -60°C to 180°C with a Peltier device. A specific specimen geometry and an optical arrangement based on the Michelson interferometer are proposed to measure the deformation along two orthogonal axes due to temperature changes. The advantages of the system include its high sensitivity and stability over the whole range of measurement. The experimental setup and approach for estimating the CTE was validated using an Aluminum alloy. Following this validation, the system was applied for characterizing the CTE of carbon fiber reinforced composite (CFRP) laminates. For the unidirectional fiber reinforced composites, the CTE varied with fiber orientation and exhibits anisotropic behavior. By stacking the plies with specific angles and order, the CTE of a specific CFRP was constrained to a low level with minimum variation temperature. The optical system developed in this study can be applied to CTE measurement for engineering and natural materials with high accuracy.

Dilatrometric sintering study and characterization of alumina-nickel composites

Alumina-nickel composite samples (with 0, 10 and 20 vol.% of Ni) are prepared via slip casting method. Nickel and aluminium oxide powders were used as precursors and diammonium hydrocitrate and citric acid were used as dispersants. The obtained materials were analysed by dilatometry, X-ray diffraction and SEM. The densities were measured by Archimedes method and the hardness and fracture toughness were determined by using Vickers hardness tester. Special attention was paid to the linear shrinkage and the effective coefficient of thermal expansion measurements. The shrinkage curves were obtained by dilatometry test in a heating mode. It was shown that the increased amount of Ni particles in Al2O3-Ni composite structure causes reduction of starting densification temperature, increasing temperature of maximum densification and decreasing total shrinkage of the sample during sintering.

Anisotropic thermomechanical behavior of AA6082 aluminum alloy Al–Mg–Si–Mn

Abstract Hot rolled aluminum alloy 6082 was subjected to tensile tests and coefficient of thermal expansion measurements. These tests were realized in order to investigate the effect of direction on its anisotropic behavior. Specimens for both tests were cut in three directions (long transverse, longitudinal rolling and short transverse) with respect to rolling direction. Results showed that the longitudinal rolling and long transverse directions had limited effect on thermomechanical properties as compared to the short transverse direction. It was found that the short transverse direction exhibited higher values of stress hardening capacity and thermal expansion coefficient, lower ductility and dilatation, than the longitudinal rolling and long transverse directions. Thermomechanical anisotropy was attributed to the microstructure and precipitation behavior. It was assessed by means of tensile tests, coefficient of thermal expansion measurements, optical microscopy, X-ray diffraction and differential scanning calorimetry techniques.

High‐throughput, high‐accuracy determination of coefficient of thermal expansion of carbon fibre–epoxy composites using digital image correlation

AbstractHigh‐throughput, high‐accuracy determination of thermal deformation and coefficient of thermal expansion (CTE) of carbon fibre–epoxy composites using 2D‐digital image correlation (2D‐DIC) is described. With the aid of a specially designed ultra‐stable and high fidelity imaging system, which integrates a high‐quality bilateral telecentric lens with monochromatic blue light illumination, surface images of multiple samples heated by a heating furnace can be captured simultaneously. The images of these samples at different temperatures are processed by advanced DIC algorithm to extract the thermal strains and the CTE of isotropic Al alloy, anisotropic unidirectional, and bidirectional carbon fibre–epoxy composites. Pure thermal expansions of these samples obtained after removing the small rigid‐body rotations clearly indicate the isotropic and anisotropic expansions of these samples. The well‐agreed results with literature values demonstrate the effectiveness and practicality of the proposed method for high‐throughput and high‐accuracy CTE measurements.

Determination on the Coefficient of Thermal Expansion in High-Power InGaN-based Light-emitting Diodes by Optical Coherence Tomography

The coefficient of thermal expansion (CTE) is a physical quantity that indicates the thermal expansion value of a material upon heating. For advanced thermal management, the accurate and immediate determination of the CTE of packaging materials is gaining importance because the demand for high-power lighting-emitting diodes (LEDs) is currently increasing. In this study, we used optical coherence tomography (OCT) to measure the CTE of an InGaN-based (λ = 450 nm) high-power LED encapsulated in polystyrene resin. The distances between individual interfaces of the OCT images were observed and recorded to derive the instantaneous CTE of the packaged LED under different injected currents. The LED junction temperature at different injected currents was established with the forward voltage method. Accordingly, the measured instantaneous CTE of polystyrene resin varied from 5.86 × 10−5 °C−1 to 14.10 × 10−5 °C−1 in the junction temperature range 25–225 °C and exhibited a uniform distribution in an OCT scanning area of 200 × 200 μm. Most importantly, this work validates the hypothesis that OCT can provide an alternative way to directly and nondestructively determine the spatially resolved CTE of the packaged LED device, which offers significant advantages over traditional CTE measurement techniques.

Measurement of cryogenic thermal expansion coefficient and accuracy analysis

In order to realize the high-precision measurement of the thermal expansion coefficient of the infrared material under the cryogenic vacuum environment, a measurement scheme of solid material is proposed. Based on the self-collimation principle, this scheme designs a microstructure, establishes the relationship between structural deformation and angle, and deduces the formula of thermal expansion coefficient measurement. Using the measurement formula, this article analyzes the relationship between the measurement error transfer function of the scheme, and also uses the error sensitivity function to analyze the design accuracy of cryogenic thermal expansion coefficient measuring device for infrared materials, and finally the relative error of the scheme is calculated. The thermal expansion coefficient of the scheme is measured to be only 0.76%, which satisfies the nanometer measurement requirement.

Tailorable Thermal Expansion of Lightweight and Robust Dual-Constituent Triangular Lattice Material

Current studies on tailoring the coefficient of thermal expansion (CTE) of materials focused on either exploring the composition of the bulk material or the design of composites which strongly depend on a few negative CTE materials or fibers. In this work, an approach to achieve a wide range of tailorable CTEs through a dual-constituent triangular lattice material is studied. Theoretical analyses explicitly reveal that through rational arrangement of commonly available positive CTE constituents, tailorable CTEs, including negative, zero, and large positive CTEs can be easily achieved. We experimentally demonstrate this approach through CTE measurements of the specimens, which were exclusively fabricated from common alloys. The triangular lattice material fabricated from positive CTE alloys is shown to yield large positive (41.6 ppm/°C), near-zero (1.9 ppm/°C), and negative (−32.9 ppm/°C) CTEs. An analysis of the collapse strength and stiffness ensures the robust mechanical properties. Moreover, hierarchal triangular lattice material is proposed, and with certain constituents, wide range of tailorable CTEs can be easily obtained through the rationally hierarchal structure design. The triangular lattice material presented here integrates tailorable CTEs, lightweight characteristic, and robust mechanical properties, and is very promising for engineering applications where precise control of thermally induced expansion is in urgently needed.

Single-spot two-dimensional displacement measurement based on self-mixing interferometry

The simultaneous and independent measurements of in-plane and out-of-plane displacements are significant issues to be solved in research. Here a novel system to realize single-spot two-dimensional (2D) displacement measurement of a noncooperative target is reported. The performance of the system is tested in the displacement measurement of an aluminum target with a rough surface. 2D random movement and 2D movement with different parameters of Lissajous figures are measured by the system. The ranges of the 2D displacement measurement reach 500 μm and the accuracies reach the submicron scale. The resolutions of the two dimensions are all better than 5 nm. The measurement system is based on laser heterodyne self-mixing interferometry with frequency multiplexing, which has advantages such as noncontact, nondestruction, nanometer-scale resolution and high sensitivity. The method is promising to be applied in 2D deformation tests of materials, 2D rotor vibration measurement, 2D positioning of particles, thermal expansion coefficient measurement, and other applications.

Evaluation of the Specimen Saturation Criterion for the AASHTO T336 Test Method

Abstract Realizing the importance of coefficient of thermal expansion (CTE) in concrete pavement design, the Federal Highway Administration conducted a ruggedness study for the AASHTO T336 test method in 2012. Of the seven variables that were evaluated as part of the ruggedness study, specimen saturation criterion was found to be one of the significant variables that warranted further investigation. This paper documents a follow-up study performed to specifically evaluate the effect of specimen saturation criterion on the measurement of CTE using the AASHTO T336 test method. CTE tests were conducted on multiple specimens from five concrete mixtures (two field and three laboratory prepared) at different levels of saturation in water: T336 criterion, 4 days, 7 days, 14 days, 28 days, and vacuum saturation. Data analysis from this study indicated that there is no statistical difference in CTE measurement after 28 days of water saturation versus T336 criterion, 4 days, 7 days, 14 days, and vacuum saturation. Based on this limited study, it appears that the current saturation criterion outlined in AASHTO T336 is adequate.

Effect of CuO addition on crystallization and thermal expansion properties of Li2O–ZnO–SiO2 glass-ceramics

A Li2O-ZnO-SiO2 (LZS) glass system was modified with CuO, and its phase development, microstructure evolution, crystallization kinetics and thermal expansion properties were investigated as a function of heat treatment temperature. As a result of the X-ray diffraction study and microstructure observation, lithium zinc silicate formed as the first crystalline phase with increasing heat treatment temperature. Silica polymorph developed as minor crystalline phase at higher temperatures. From the X-ray diffraction patterns, CuO addition led to a decrease in both the crystallization temperature of lithium zinc silicate phase and the volume fraction of quartz phase. According to the crystallization kinetics, the crystallization activation energy for lithium zinc silicates is almost equal to the diffusion activation energy of Zn2+ in glass, it suggests that the diffusion of network modifier Zn2+ dominates the crystallization of lithium zinc silicates. Additionally, CuO addition caused the transition of Zn2+ from network modifiers to network formers. From the thermal expansion coefficient measurements, two abrupt changes in slope of the thermal expansion curves were observed and attributed to the phase transitions of cristobalite and lithium zinc silicate, respectively. Comparison of the thermal expansion coefficient of two types of glass-ceramics revealed that CuO addition in the LZS system can partly inhibit the formation of cristobalite at high temperatures.

Simultaneous measurement of thermo-optic and thermal expansion coefficients with a single arm double interferometer.

A low-cost single arm double interferometer was developed for the concurrent measurement of linear thermal expansion (α) and thermo-optic (dn/dT) coefficients of transparent samples with plane and parallel surfaces. Owing to its common-path optical arrangement, the device is compact and stable, and allows the simultaneous measurement of interferences arising from a low-finesse Fabry-Perot etalon and from a Mach-Zehnder-type interferometer. The method was demonstrated with measurements of solid (silica, BK7, SF6) and liquid (water, ethanol and acetone) samples.

Investigation of the residual stress in reaction-bonded SiC under irradiation

The development of reaction-bonded SiC (RB-SiC) for an application in nuclear reactor environments has been suspended for many years because of the possible swelling mismatch between SiC and Si under irradiation. Therefore, we studied the residual stresses in RB-SiC due to the irradiation-induced swelling mismatch and the mismatch between the coefficients of thermal expansion. The maximum irradiation-induced swelling stress for the amorphous state was obtained by irradiation with 2MeV Au2+ ions (1×1016ions/cm2) at room temperature. Utilizing Raman piezo-spectroscopy, nanoindentation tests and thermal expansion coefficient measurements, we demonstrate that the irradiation-induced swelling stress is remarkably high at low temperatures, whereas the thermal stress becomes the dominant residual stress at medium (415°C<T<700°C) or higher temperatures. By optimizing the residual Si content in the RB-SiC, the thermal stress and the irradiation-induced swelling stress can be adjusted and the initiation of cracks can be prevented.