Coefficient Of The Thermal Expansion Research Articles

Analysis of thermal strain of metallized silicon nitride substrate under cyclic thermal loading by digital image correlation

AbstractIn this research, a digital image correlation method was employed to measure the thermal strain of a metallized silicon nitride substrate subjected to multiple successive thermal cycles from −40 to 250°C. In all the thermal strain curves observed during the 1000 thermal cycles, consistent hysteresis loops were detected. At the beginning of the heating or cooling process, the curves display slopes nearly identical to the theoretical coefficient of the thermal expansion (CTE) of the metallized composite. Subsequently, the slope gradually decreased until the completion of heating or cooling and eventually reached the CTE of the plain silicon nitride substrate. However, as the number of thermal cycles increased, the deviation temperature from the theoretical CTE during heating increased, whereas the temperature decreased during cooling, but it did so to a lower temperature. The maximum expansion and contraction observed during each cycle increased equally between the initial thermal cycle and the 100th cycle, after which a saturation point was reached. The relationship between the increase, saturation, and cyclic hardening of copper plates on a metallized silicon nitride substrate is further discussed in this study, shedding light on the overall strain range over thermal cycles.

Origin and Evolution of Cracks in the Glaze Surface of a Ceramic during the Cooling Process.

Because of the significant difference between the thermal expansion coefficients of ceramic blank and glaze, the glaze typically undergoes more pronounced shrinkage than the blank during ceramic cooling, which results in high stress concentrations and cracking. In this study, the mechanical mechanism of glaze cracking is studied, based on the statistical strength theory, damage mechanics, and continuum mechanics. Furthermore, the influence of the glaze layer thickness, heat transfer coefficient, expansion coefficient, and temperature difference on the creation and propagation of inner microcracks is systematically investigated, and the final discrete fracture network of ceramics is discussed at the specific crack saturation state. The results show that (1) a higher heat transfer coefficient will lead to a more uniform distribution of the surface temperature and a faster cooling process of the ceramics, reducing the number of microcracks when the ambient temperature is reached; (2) the thinner glaze layer is less prone to cracking when its thickness is smaller than that of the blank. However, when the thickness of the glaze layer is similar to that of the blank, the increased thickness of the glaze layer will increase the number of cracks on its surface; and (3) when the expansion coefficient of the glaze layer is smaller than that of the blank, cracks will not occur inside the glaze layer. However, as the coefficient of the thermal expansion of the glaze layer continuously rises, the number of cracks on its surface will first increase and then decrease.

Pressure effect on the physical, mechanical, and thermal properties of ternary halide perovskite AgCaCl3: a first-principles study.

As an inorganic halide perovskite material, AgCaCl3, characterized by its high stability and environmental friendliness, is considered a potential candidate for major applications in optoelectronics and lens manufacturing. This work aimed to determine the electronic properties such as density of state (DOS) and band structure (BS) of AgCaCl3. The results showed that the material has an indirect band gap almost invariably at 1.5eV in the pressure range studied. The dielectric function [Formula: see text], absorption coefficient [Formula: see text], optical conductivity [Formula: see text], reflectivity [Formula: see text], and the refractive index [Formula: see text] showed clearly that the perovskite AgCaCl3 preserved its optical characteristics within the chosen pressure range investigated. The calculated elastic constants C11, C12, and C14 as dynamic stability criteria for the elastic moduli such as bulk modulus (B), shear modulus (G), Young's modulus (Y), Poisson's ratio ([Formula: see text]), and anisotropy factor (A) showed that the material is a ductile plastic. Debye temperature ([Formula: see text]), isobaric and isochoric heat capacities (CP, CV), coefficient of the thermal expansion (α), Gibbs free energy (G), and entropy (S) were also studied. The results obtained provide a theoretical basis for experimental work and offer the possibility of future industrial applications of AgCaCl3. Density functional theory (DFT) calculations as implemented in the Wien2K code were used to study the mechanical and thermal properties of AgCaCl3 perovskite over a pressure range. Lattice parameters, electronic, and optical properties are optimized with the approximation of the generalized gradient of the Perdew-Burke-Ernzerhof function (PBE-GGA) function. The mechanical and thermodynamic properties were calculated using ElaStic and Gibbs2 codes, and the properties of AgCaCl3 over the pressure range investigated were predicted.

Effect of thermal shock induced dislocation multiplication on the thermal conductivity of 60 vol% SiCp/Al–7Si composites

Dislocation affects the thermal conductivity and coefficient of the thermal expansion of high-volume fraction SiCp/Al composites. However, it still remains unclear to what extent the dislocation density in the composite would be increased by thermal shock. Herein, the as-cast 60 vol% SiCp/Al–7Si composites produced via the gas-infiltration technique possess a relatively low porosity but significant lattice misfit at the interfaces. The aqueous- and liquid nitrogen-quenching exerted on the as-cast samples can produce fractures at the SiCp/Al interfaces at different extent. The neutron diffraction technique is carried out to investigate the effect of thermal shock treatments on volume-averaged dislocation densities in the composites. Results show that the dislocation configuration of the composites with as-cast and aqueous-quenching states are similar, but different from that of the sample with a liquid nitrogen-quenching state. Compared with the as-cast composite, the aqueous-quenching and liquid nitrogen-quenching treatments cause the significant increase of dislocation density. However, it only results in a relatively slight reduction of the thermal conductivity of the aluminum matrix. This work provides some references for the dislocation density determination in the high-volume fraction metal matrix composites.

Chemical models of molybdenum-calcium phosphate glasses

The influence of molybdenum at varying phosphate network was studied. Three series of MoO3CaO-P2O5 glasses starting with calcium metaphosphate and ending with chemical compositions formally corresponding to molybdenyl metaphosphate(2+), molybdenyl pyrophosphate(2+) and their equimolar mixture were prepared. Molybdenum is incorporated as molybdenyls, which to a significantly predominant extent form the divalent colorless two-oxygen diamagnetic cation MoVIO22+ accompanied in low concentration by colored paramagnetic MoVO2+. Molybdenyls are bound in the structure by four donor-acceptor bonds with non-bridging phosphate oxygens and form a distiorted tetragonal bipyramid. A chemical model of glasses describing their actual chemical compositions and compositional dependencies was created. It has been shown that the actual chemical composition of glasses is a complicated mixture of chemical compounds. The chemical model also made it possible to have an explanation of the compositional dependences of the glass transition temperature and the coefficient of the thermal expansion of glasses.

Influence of Vanadium and Niobium Carbide Particles on the Mechanical, Microstructural, and Physical Properties of AA6061 Aluminum-Based Mono- and Hybrid Composite Using FSP

The ceramic particle reinforcement process is one of the most utilized techniques to enhance the metal surface. The current investigation uses vanadium and niobium carbides to reinforce the AA6061 alloy using the friction stir process (FSP). The mechanical properties are evaluated using ultrasound and conventional compressive tests; furthermore, the microstructure and physical properties are carried out to show the effect of single and hybrid additives of ceramic particles on the surface composites of aluminum alloy. Scanning electron microscopy (SEM) is utilized to examine the presence and distribution of the reinforcement VC and NbC particles inside the composite matrix. The microstructure examination revealed a good dispersion and homogenized distribution of the reinforcement particles. The results indicated that reinforcement particles significantly enhanced the mechanical and physical properties. The VC and NbC particles play an important role in improving the surface hardening behavior and grain refinement by restricting grain growth during the dynamic recrystallization process in the FSP action. The hybrid composited AA6061/NbC + VC recorded an increase in the compressive stress, yield stress, and hardness of 25%, 20%, and 50%, respectively, relative to the base metal, in addition to a 55% decrease in the coefficient of the thermal expansion (CTE) was reported. Moreover, the hybrid composite AA6061/NbC + VC significantly affected the corrosion rate with a reduction of 45%.

Effect of Thermal Properties of Aggregates on the Mechanical Properties of High Strength Concrete under Loading and High Temperature Conditions.

The effect of the thermal properties of aggregates on the mechanical properties of high-strength concrete was evaluated under loading and high-temperature conditions. For the concrete, granite was selected as a natural aggregate, and ash-clay and clay as lightweight aggregates. The mechanical properties of the concrete (stress–strain, compressive strength, elastic modulus, thermal strain, and transient creep) were evaluated experimentally under uniform heating from 20 to 700 °C while maintaining the load at 0, 20, and 40% of the compressive strength at room temperature. Experimental results showed that the concrete containing lightweight aggregates had better mechanical properties, such as compressive strength and elastic modulus, than that of the concrete with a granite aggregate at high temperature. In particular, the concrete containing lightweight aggregates exhibited high compressive strength (60–80% of that at room temperature) even at 700 °C. Moreover, the concrete containing granite exhibited a higher thermal strain than that containing lightweight aggregates. The influence of the binding force under loaded conditions, however, was found to be larger for the latter type. The transient creep caused by the loading was constant regardless of the aggregate type below 500 °C but increased more rapidly when the coefficient of the thermal expansion of the aggregate was above 500 °C.

Soft computing paradigm for Ferrofluid by exponentially stretched surface in the presence of magnetic dipole and heat transfer

In the presented research article, the intelligence based numerical computation of artificial neural network backpropagated with Levenberg-Marquardt algorithm has been developed to analyze the novel ferrofluid flow model in the presence of magnetic dipole. Heat transfer effects are also incorporated along the horizontal. The designed fluid flow model initially represented by system of partial differential equations are converted into system of non-linear ordinary differential equations through suitable similarity transformations. The reference dataset of the possible outcomes is obtained from Adam numerical solver for the different scenarios of flow model by variation of co-efficient of the thermal expansion, Eckert number, suction parameter, magnetization and radiation parameter. The approximated solutions are interpreted for designed model by testing, training and validation process of backpropagated neural networks. Furthermore, the comparative studies and performance analysis of used algorithm is validated through regression analysis, histogram studies, correlation index and results of mean square error.

Ultra-low dielectric constant polyimides: Combined efforts of fluorination and micro-branched crosslink structure

In the previous work, a micro-branched crosslink structure was constructed to molecular chain in the polyimide (PI) film of the 3,3′4,4′-biphenyltetracarboxylic dianhydride/1,4-phenylenediamine (BPDA/PDA) system by introducing a trifunctional monomer 1,3,5-tri(4-aminophenoxy) benzene (TAPOB). It was found that the micro-branched structure is instrumental in reducing the dielectric constant via increasing the free fraction volume (FFV) while the crosslink can lower the coefficient of the thermal expansion (CTE) through confining the chain movement. This helps to break the design contradiction between low dielectric and CTE, thereby realizing the synchronous optimization of the two. To further reduce the dielectric constant to meet the application requirements of modified PI (MPI) in 5G equipment, PI films were designed and prepared using pyromellitic anhydride (PMDA), 4,4′-(hexafluoroisopropyl) phthalic anhydride (6FDA), 4,4′-diaminobiphenyl ether (ODA), and 2,2′-bis(trifluoromethyl)-4,4′-diaminobipheyl (TFMB) as the monomers while TAPOB as the crosslinking agent, which involved four systems of PMDA/ODA/TAPOB, PMDA/TFMB/TAPOB, 6FDA/ODA/TAPOB, and 6FDA/TFMB/TAPOB. The influence of molecular chain stiffness and flexibility on the micro-branched crosslink structure was studied by means of experiment and molecular dynamic simulation, and PI films with lowered dielectric constant, which are expectably applicable in the electronics industry, were obtained.

Joining of SiC ceramics using CaO-Al2O3-SiO2 (CAS) glass ceramics

CaO-Al2O3-SiO2(CAS) glass ceramics were designed and prepared using a melt-quench approach. The coefficient of the thermal expansion (CTE) of the synthesized CAS (4.12 × 10−6 K−1) matched perfectly with that of the SiC ceramic (4.01 × 10−6 K−1). Thermal analysis of the CAS was conducted. Then the joining of the SiC ceramics by the CAS glass ceramics under various process parameters were conducted. The bonding temperature affects the fluidity of the CAS glass and the oxidation of the SiC substrate. The holding duration decides the infiltration of the CAS glass into the SiC substrate. The optimal bonding parameter is 1400 ℃/10 min and the corresponding highest shear strength of the SiC/CAS/SiC bonded joints in average was 56 MPa. Fracture observation was also conducted to help analyze the relationship between the interfacial microstructure and the joint strength. Finally, the formation mechanism of the SiC/CAS/SiC bonded joints was proposed.

Probabilistic Reliability Analysis of Carbon/Carbon Composite Nozzle Cones with Uncertain Parameters

A methodology to perform the probabilistic and reliability-based design of a novel carbon/carbon rocket nozzle subjected to operational thermal and mechanical loads is described in this paper. In this methodology, the nozzle is represented by a multiphysics finite element model capable of predicting the temperature and stress fields of the exit cone. The analysis shows that the most likely failure modes of the exit cone are related to compressive stress along the axial and hoop directions, as well as interlaminar shear. The probabilistic models used in this methodology account for the uncertainty of the material properties by using uniform and normal distributions and different variances. The reliability analysis is performed by using surface response methods. A global sensitivity analysis is also carried out using polynomial expansion chaos surface response models. A particular novelty of the analysis is the use of Sobol indices to rank the importance of the single uncertain parameters in the models. The methodology provides a high level of confidence and robustness in determining that the axial thermal conductivity of the carbon/carbon material is the most critical material property to affect the three main failure modes, whereas the coefficient of the thermal expansion and the heat capacity play a very marginal role.

Pressure-induced phase transitions in Na2B12H12, structural investigation on a candidate for solid-state electrolyte

closo-Borates, such as Na2B12H12, are an emerging class of ionic conductors that show promising chemical, electrochemical and mechanical properties as electrolytes in all-solid-state batteries. Motivated by theoretical predictions, high-pressure in situ powder X-ray diffraction on Na2B12H12 was performed and two high-pressure phases are discovered. The first phase transition occurs at 0.5 GPa and it is persistent to ambient pressure, whereas the second transition takes place between 5.7 and 8.1 GPa and it is fully reversible. The mechanisms of the transitions by means of group theoretical analysis are unveiled. The primary-order parameters are identified and the stability at ambient pressure of the first polymorph is explained by density functional theory calculations. Finally, the parameters relevant to engineer and build an all-solid-state battery, namely, the bulk modulus and the coefficient of the thermal expansion are reported. The relatively low value of the bulk modulus for the first polymorph (14 GPa) indicates a soft material which allows accommodation of the volume change of the cathode during cycling.

Ba2BiSbO6: A novel microwave dielectric ceramic with monoclinic structure

A novel Ba2BiSbO6 microwave dielectric ceramic was prepared via the traditional solid-state method, and the microwave dielectric properties of Ba2BiSbO6 were investigated for the first time. The analysis of X-ray diffraction patterns indicated that the pure monoclinic Ba2BiSbO6 phase could be formed in the temperature range of 950–1150 °C. Rietveld refinement results further confirmed that Ba2BiSbO6 belonged to a monoclinic system with space group I2/m (12). Dense and homogeneous microstructures of Ba2BiSbO6 ceramics sintered at 1100–1150 °C could be revealed from the scanning electric microscope. The bond ionicity, lattice energy and coefficient of the thermal expansion were initially calculated based on the complex chemical bond theory. The complex dielectric constant and loss were gained from the fitting data of far infrared spectra, which were in good agreement with the measured values. The optimum microwave dielectric properties of εr = 26.61, Q·f = 13,764 GHz (at 5.95 GHz) and τf = −26.6 ppm/°C were achieved in Ba2BiSbO6 ceramic sintered at 1100 °C.

Mixed Rigid and Flexible Component Design for High-Performance Polyimide Films.

To develop the polyimide (PI) which is closely matched to the coefficient of the thermal expansion (CTE) of copper, a series of PIs are prepared from 5,4′-diamino-2-phenyl benzimidazole (DAPBI), 4,4′-diaminodiphenyl ether (ODA), and 3,3′,4,4′-benzophenonetetracarboxylic dianhydride (BTDA) using a sequential copolymerization, blade coating, and thermal imidization process. The physical properties of the PIs are effectively regulated and optimized by adjusting the ratio of the rigid DAPBI and flexible ODA components. By increasing the DAPBI content, thermal stability, dimensional stability, and mechanical properties, the resultant polymer is enhanced. PI-80 exhibits an excellent comprehensive performance, a glass transition temperature of 370 °C, and a tensile strength of 210 MPa. Furthermore, the CTE as calculated in the range 50–250 °C is ca. 19 ppm/K, which is equal to that of copper. A highly dimensionally stable, curl-free, and high T-style peel strength (6.4 N/cm) of copper/PI laminate was obtained by casting the polyamic acid onto copper foil (13 μm) and thermally curing at 360 °C, which indicates that it has the potential to be applied as an electronic film for flexible displays and flexible printed circuit boards. A structural rationalization for these remarkable properties is also presented.

Thermal expansion behaviour of squeeze-cast aluminium matrix composites reinforced with PAN- and Pitch-based carbon fibres

Aluminium composites reinforced with the PAN- and pitch-based short carbon fibres were fabricated by squeeze casting, then the thermal expansion behaviour of the composites was investigated. Optical microscopy revealed that the fibres were in a random arrangement on the plane parallel to the pressed plane during the melt infiltration process. TEM observation and hardness test revealed that the PAN-based fibre bonds strongly with the aluminium matrix while the pitch-based fibre bonds poorly. The difference in the bonding strength affected the thermal strain response; the heating and cooling curve approximately traced the same paths during the heating-cooling cycles for the PAN-based fibre composite, while the curve did not trace the same path for the pitch-based fibre composite. The fibre-reinforcement decreased the coefficient of the thermal expansion (CTE) of matrices in the direction parallel to the pressed plane. For example, the CTE of the pure aluminium and its composite at 333 K were 23.0 and 19.0 × 10−6/K, respectively.

Investigation and characterization on crystal structure of ixiolite structure ATiNb2O8 (A = Mg, Zn) ceramics at microwave frequency based on the complex chemical bond theory

Ixiolite structure ATiNb2O8 (A = Mg, Zn) microwave dielectric materials were prepared via the conventional solid state reaction method. The crystal structure was researched by X-ray diffraction. Rietveld refinement was used to analyze the crystal structure and the lattice parameters were obtained. Based on the complex chemical bond theory and lattice parameters, intrinsic factors such as the bond ionicity, lattice energy, bond energy and coefficient of thermal expansion were calculated. The relationships between structures and properties of ATiNb2O8 (A = Mg, Zn) ceramics were researched. The microwave properties were strongly dependent on intrinsic factors. The dielectric constant (εr) was strongly dependent on the bond ionicity of NbO bonds. The quality factor (Q·f) was mainly affected by the lattice energy of NbO bonds. The temperature coefficient of resonant frequency (τf) could be mainly influenced by the bond energy and coefficient of the thermal expansion of NbO bonds.

The role of kyanite in the improvement in the crystallization and densification of the high strength mullite matrix

Fine particles of kyanite were used as reinforcement in mullite matrix composite. Mix of metakaolin and meta-alumina (calcined bauxite) received different fraction of fine kyanite particles: 37.5, 42.5 and 50 mass%. The objectives were to improve the crystallization of kaolin-based mullite matrix reducing the amorphous content and the grain growth. Packing process and densification were enhanced, leading to the action of kyanite at low temperature ( 1350 °C), the kyanite particles are decomposed to mullite still without glassy phase and the metastable alumina presented in the mix reacts with amorphous silica to produce additional mullite. The sintering behaviour, the thermal expansion behaviour of ~0.5 % between 200 and 1000 °C and the coefficient of the thermal expansion of 5.92, 5.15 and 6.92 × 10−6/°C for KY3, KY4 and KY5, respectively, between 200 and 1000 °C, and their decrease at higher temperature demonstrated the optimum refractoriness of the mullite matrix composites developed.

A first-principles study on the negative thermal expansion material: Mn3(A0.5B0.5)N (A=Cu, Zn, Ag, or Cd; B=Si, Ge, or Sn)

In this paper, using the first-principles calculations, we systemically study the magnetic and the negative thermal expansion (NTE) properties of Mn3(A0.5B0.5)N (A = Cu, Zn, Ag, or Cd; B = Si, Ge, or Sn). From the calculated results, except Mn3(Cu0.5Si0.5)N, all the doped compounds considered would exhibit the NTE. For the dopants at B sites, the working temperature of the NTE shifts to higher temperature range from Si to Sn, and among the compounds with these dopants, Mn3(A0.5Ge0.5)N has the largest amplitude of the NTE coefficient. As to the dopants at A sites, compared to Mn3(Cu0.5B0.5)N, Mn3(A0.5B0.5)N (A = Ag or Cd) exhibit the NTE with higher temperature ranges and lower coefficient of the thermal expansion. In a word, these compounds would have different working temperatures and coefficients of the NTE, which is important for the applications in different conditions.

1 Hz linewidth Ti:sapphire laser as local oscillator for (40)Ca(+) optical clocks.

A Ti:sapphire laser at 729 nm is frequency stabilized to an ultra-stable ultra-low thermal expansion coefficient (ULE) cavity by means of Pound-Drever-Hall method. An acousto-optic modulator is used as the fast frequency feedback component. 1 Hz linewidth and 2 × 10(-15) frequency stability at 1-100 s are characterized by optical beating with a separated Fabry-Perot cavity stabilized diode laser. Compared to the universal method that the error signal feedback to inject current of a diode laser, this scheme is demonstrated to be simple and also effective for linewidth narrowing. The temperature of zero coefficient of the thermal expansion of the ULE cavity is measured with the help of a femto-second frequency comb. And the performance of the laser is well defined by locking it to the unperturbed clock transition line-center of 4 S1/2-3 D5/2 clock transition of a single laser cooled (40)Ca(+) ion. A Fourier-transform limited resonance of 6 Hz (Δv/v = 1.5 × 10(-14)) is observed. This laser is also used as the local oscillator for the comparison experiment of two (40)Ca(+) ion optical clocks and improves the stability of comparison for an order of magnitude better than the previous results.

Thermoelastic properties of chromium oxide Cr2O3 (eskolaite) at high pressures and temperatures

A new synchrotron X-ray diffraction study of chromium oxide Cr2O3 (eskolaite) with the corundum-type structure has been carried out in a Kawai-type multi-anvil apparatus to pressure of 15 GPa and temperatures of 1873 K. Fitting the Birch–Murnaghan equation of state (EoS) with the present data up to 15 GPa yielded: bulk modulus (K0,T0), 206 ± 4 GPa; its pressure derivative K′0,T, 4.4 ± 0.8; (∂K0,T/∂T) = ‒0.037 ± 0.006 GPa K‒1; a = 2.98 ± 0.14 × 10−5 K−1 and b = 0.47 ± 0.28 × 10‒8 K‒2, where α0,T = a + bT is the volumetric thermal expansion coefficient. The thermal expansion of Cr2O3 was additionally measured at the high-temperature powder diffraction experiment at ambient pressure and α0,T0 was determined to be 2.95 × 10−5 K−1. The results indicate that coefficient of the thermal expansion calculated from the EoS appeared to be high-precision because it is consistent with the data obtained at 1 atm. However, our results contradict α0 value suggested by Rigby et al. (Brit Ceram Trans J 45:137–148, 1946) widely used in many physical and geological databases. Fitting the Mie–Gruneisen–Debye EoS with the present ambient and high-pressure data yielded the following parameters: K0,T0 = 205 ± 3 GPa, K′0,T = 4.0, Gruneisen parameter (γ0) = 1.42 ± 0.80, q = 1.82 ± 0.56. The thermoelastic parameters indicate that Cr2O3 undergoes near isotropic compression at room and high temperatures up to 15 GPa. Cr2O3 is shown to be stable in this pressure range and adopts the corundum-type structure. Using obtained thermoelastic parameters, we calculated the reaction boundary of knorringite formation from enstatite and eskolaite. The Clapeyron slope (with \({\text{d}}P/{\text{d}}T = - 0.014\) GPa/K) was found to be consistent with experimental data.