Expansion Coefficient Research Articles

Tailoring the coefficient of thermal expansion in a functionally graded material: Al alloyed with Ti-6Al-4V using additive manufacturing

Functionally graded materials enable the spatial tailoring of properties through controlling compositions and phases that appear as a function of position within a component. The present study investigates the ability to reduce the coefficient of thermal expansion (CTE) of an aluminum alloy, Al 2219, through additions of Ti-6Al-4V. Thermodynamic simulations were used for phase predictions, and homogenization methods were used for CTE predictions of the bulk CTE of samples spanning compositions between 100 wt% Al 2219 and 70 wt% Al 2219 (balance Ti-6Al-4V) in 10 wt% increments. The samples were fabricated using directed energy deposition (DED) additive manufacturing (AM). Al2Cu and fcc phases were experimentally identified in all samples, and aluminides were shown to form in the samples containing Ti-6Al-4V. Thermomechanical analysis was used to measure the CTE of the samples, which agreed with the predicted CTE values from homogenization methods. The present study demonstrates the ability to tailor the CTEs of samples through compositional modification, thermodynamic calculations, and homogenization methods for property predictions.

3D bi-directional auxetic square metastructure with programmable thermal expansion and Poisson's ratio

Multifunctional integration research on metastructures has become the current development trend and hotspot, especially satellite platforms and hypersonic aircraft in the aerospace field. A 3D bi-directional auxetic square metastructure (BASM) with the programmable coefficient of thermal expansion (CTE) and Poisson's ratio (PR) is designed through the combination of re-entrant hexagonal structures and bi-material triangles. Specimens in the form of the 1*2 array are designed and fabricated through 3D printing. The correctness of the results of finite element analysis (FEA) of the BASM is verified by uniaxial compression experiments. Additionally, FEA is adopted to investigate the effective mechanical properties of the BASM with the form of the 2*3 array, and deformation mechanisms are further explored. Results indicate that the CTE, PR, and stiffness of the BASM depend on material combinations and geometric parameters. Under thermal and mechanical loads, the BASM achieves bi-directional regulation of the CTE and PR, encompassing both axial and circumferential deformations. Notably, the deformation mechanisms and critical conditions of the BASM are explored under the thermo-mechanical load. A novel strategy for programming the PR of the BASM is proposed in addition to changing the geometric parameters and the material combinations.

Negative Thermal Expansion Realized by an Incomplete Bimaterial Ring

Incomplete bimaterial ring (a circular ring with a gap) capable of producing negative macroscopic thermal expansion is proposed and its behavior is analyzed. The ring exhibits negative thermal expansion (NTE) (in the plane of the ring) when the outer ring has higher thermal expansion coefficient than the inner one. When the thermal expansion coefficients are equal (monomaterial incomplete ring), the effective (macroscopic) planar thermal expansion becomes zero. (The complete thermal expansion will be positive but small.) It is the presence of the gap which is the basis of this thermal behavior. Similar effect can be achieved by spring or spiral structures where the role of the gap is played by the open ends. These structures will have higher stiffness than the incomplete bimaterial ring. The thermal expansion of the ring is characterized by the effective (macroscopic) coefficient of linear thermal expansion. The effective coefficient of linear thermal expansion depends on the temperature increase, making the thermal expansion nonlinear. Planar and 3D NTE structures are considered.

Preparation of high transparency, thermal stability, flame retardant polymethyl methacrylate nanocomposite via gamma-radiation polymerization

Achieving flame retardancy and thermal stability in poly(methyl methacrylate) (PMMA) while maintaining its inherent high transparency presents a significant challenge. In this work, we successfully fabricated an exceptional composite (P-SiO2-PMMA) with high transparency, flame retardancy, and thermal stability using 60Co γ-ray irradiation-induced copolymerization of methyl methacrylate (MMA), 2-hydroxyethyl 2-methyl-2-propenoate phosphate (HEMAP), and nano-silica (SiO2). The impact of the HEMAP on the crystal, optical, thermal stability, and combustion behavior properties of P-SiO2-PMMA has been investigated. P-SiO2/PMMA forms a three-dimensional network cross-linked molecular chain structure, enhancing the thermal decomposition temperature (Tdi), maximum thermal decomposition temperature (Tmax), glass transition temperature (Tg), and reducing the coefficient of thermal expansion (CTE). HEMAP and SiO2 significantly enhance the flame retardancy of the material. The limiting oxygen index (LOI) value of transparent flame-retardant 20-P-SiO2/PMMA composite material increased from 17.5% for PMMA to 23.2%, with a 47.3% decrease in peak heat release rate (PHRR). The flame retardant mechanism was also investigated. This study offers a novel approach for the industrial application of high transparency, thermal stability, and halogen-free flame-retardant PMMA composite.

Glass-based encapsulant enabling SiC power devices to long-term operate at 300 °C

The high-temperature applications of Silicon Carbide (SiC) power devices are constrained by traditional epoxy molding compound (EMC). A significant challenge arises from the mismatch between the thermal expansion coefficients (CTE) of the encapsulant and the SiC chip, generating thermal and mechanical stresses during prolonged high-temperature operation. While glass encapsulants offer stability above 300 °C, these stresses can lead to mechanical degradation and eventual failure of SiC power devices. We design a glass-based encapsulation material to adjust the CTE of the glass to match that of the SiC chip (3–9 ppm/℃), enabling encapsulation of the device for long-term operation at 300 °C. Finite element analysis (FEA) confirms that the CTE adjustment effectively reducs internal thermal stresses. The glass composite with 10 wt% PbTiO3demonstrates a Tg of 310 °C and a CTE of 8.48 ppm/℃, successfully encapsulating a SiC schottky barrier diode in TO-247 package form. The encapsulated device exhibits low leakage current, a reverse breakdown voltage of 1,700 V, and a thermal resistance of 0.45 °C/W. Notably, the device maintains excellent performance even after 1,176 h of high-temperature aging, including 336 h at 300 °C and exhibits minimal change during thermal cycling between −50 and 150 °C for 100 cycles. Long-term performance analysis demonstrates superior stability compared to EMC encapsulation. These results highlight the potential of glass-based encapsulants for wide band gap power devices, offering reliability and performance under extreme conditions.

Spontaneous imbibition of unsaturated sandstone under different vertical temperature gradients: neutron radiography experiments and dynamic models

To elucidate the imbibition behavior of water in complex temperature and stress environments, spontaneous imbibition experiments were conducted on unsaturated matrix sandstones at different vertical temperature gradients by neutron radiography technology. Additionally, corresponding dynamic models of water imbibition in porous media were established. The research results reveal the phased characteristics of sandstone spontaneous imbibition and the influence of vertical temperature gradient on the evolution of wetting front. Specifically, the initial development speed of the wetting front increases with an increase in the vertical temperature gradient, indicating a direct relationship. However, the growth rate of the wetting front gradually slows down with increasing time, eventually reaching a saturated state. Model validation demonstrates that the traditional Washburn's law is still valid in isothermal conditions without temperature gradient (G=0). Further analysis indicates that the imbibition rate has a direct correlation with linear thermal expansion coefficient (α) and viscosity temperature coefficient (β) across various vertical temperature gradients, and an inverse correlation with surface tension temperature coefficient (γ). Furthermore, when the values of α, β, and γ fall below 0.001, their impact on the imbibition rate becomes negligible. The sensitivity of the imbibition rate to parameters γ, β, and α decreases in that order, with γ being the most sensitive, followed by β, and α being the least sensitive. Moreover, the relative importance of α, β, and γ dictates their specific influence on the imbibition rate, and a synergistic effect exists among these parameters, which collectively influence the water absorption behavior of sandstone.

Thermomechanical behavior of alumina–magnesia castables and numerical modeling of the steel ladle thermal process

AbstractBy experimental characterization and numerical modeling, the dependence of thermophysical properties on time and temperature as well as its influence on the thermomechanical behavior of alumina–magnesia castables has been studied in this work. The thermal conductivity, thermal expansion coefficient, and Young's modulus are the most important parameters, which evolve with temperature and piecewise change with the thermal processes of drying, preheating, and service. It is mainly related to the sintering degree and amount of formed calcium aluminate and spinel phases. The sensitivity analysis of parallel simulations for multilayer steel ladle with different numbers of temperature‐dependent thermophysical parameters demonstrates that the thermal conductivity is the most influential parameter, as it dominates the temperature distribution and affects the succeeding thermal expansion as well as deformation. The increase of thermal expansion coefficient and decrease of Young's modulus with temperature counterbalance the deformation of linings under thermal process. Meanwhile, compared with the simulation using temperature‐independent parameters, the model with temperature‐dependent thermophysical parameters exhibits more severe damage in outer surface of both the working lining and the permanent lining. This gives new insight into the adoption of temperature‐dependent parameters for actual thermomechanical behavior evaluation of refractories.

Convenient synthesis of phthalonitrile‐containing mono‐benzoxazines with exceptional thermal stability and improved curing activity

AbstractSimple synthesis and high performance are eternal pursuit for polymers. To lower the curing temperature, lower the melt viscosity and improve the processability of high performance phthalonitrile resins, a solvent‐free method was applied to synthesize three from different phenols. Their chemical structure was confirmed by FTIR and NMR spectra, the curing behavior was investigated by DSC and rheology. It was found that the polymerization of phthalonitrile groups could be effectively promoted by benzoxazine moieties and the curing temperature of phthalonitrile groups dropped to around 240°C. Consequently, owing to the high curing reactivity, polymers obtained at relatively low curing temperature possessed high crosslinking density and extremely high thermal stability. P‐apn‐200, which was cured at 200°C, showed 5 wt% weightloss temperature (Td5) of 472°C and char yield (Yc) of 75.77% at 800°C. Moreover, the polymers obtained after curing at 280°C showed superior dimensional stability, CN‐apn‐280 showed extremely low linear expansion coefficient (CTE) of 10.7 ppm/°C. And mP‐apn‐280 showed HR capacity of 3.99 J/g‧K, peak HRR of 4.0 W/K and total HR of 0.8 kJ/g.

Renormalization flow of nonlinear electrodynamics

We study the renormalization flow of generic actions that depend on the invariants of the field strength tensor of an Abelian gauge field. While the Maxwell action defines a Gaussian fixed point, we search for further non-Gaussian fixed points or rather fixed functions, i.e., globally existing Lagrangians of the invariants. Using standard small-field expansion techniques for the resulting functional flow equation, a large number of fixed points is obtained, which—in analogy to recent findings for a shift-symmetric scalar field—we consider as approximation artifacts. For the construction of a globally existing fixed function, we pay attention to the use of proper initial conditions. Parametrizing the latter by the photon anomalous dimension, both the coefficients of the weak-field expansion are fully determined and those of the large-field expansion can be matched such that a global fixed function can be constructed for magnetic fields. The anomalous dimension also governs the strong-field limit. Our results provide evidence for the existence of a continuum of non-Gaussian fixed points parametrized by a small positive anomalous dimension below a critical value. We discuss the implications of this result within various scenarios with and without additional matter. For the strong-field limit of the 1PI QED effective action, where the anomalous dimension is determined by electronic fluctuations, our result suggests the existence of a singularity free strong-field limit, circumventing the standard conclusions connected to the perturbative Landau pole. Published by the American Physical Society 2024

Resolving the Role of Configurational Entropy in the Optimization of Mechanical, Thermal, and Microwave Dielectric Properties of SrLa(Al0.50-xGaxZn0.125Mg0.125Ti0.25)O4 Ceramics.

The demand for high-performance microwave dielectric ceramics has surged with the proliferation of fifth-generation (5G) communication networks. In this work, SrLa(Al0.50-xGaxZn0.125Mg0.125Ti0.25)O4 (x = 0-0.20) ceramics were designed by leveraging the unique properties of SrLaAlO4 ceramics and high-entropy engineering. The effects of configurational entropy (Sconf = 1.23R - 1.54R) on the mechanical, thermal, and microwave dielectric properties of SrLa(Al0.50-xGaxZn0.125Mg0.125Ti0.25)O4 ceramics were investigated. X-ray diffractometer and transmission electron microscope analyses confirmed that each composition belonged to the tetragonal structure with a space group of I4/mmm. Significant improvements in Vickers hardness were observed with increasing Sconf, reaching 8.05 GPa at Sconf = 1.54R compared to 5.64 GPa in SrLaAlO4 ceramics. Additionally, the increasing entropy showed great potential in reducing the thermal expansion coefficient (CTE) from 12.32 to 11.49 ppm/°C. The optimal quality factor (Q × f) of 98,000 GHz was achieved at Sconf = 1.37R, attributed to the optimization of intrinsic lattice energy and infrared-damped modes. The temperature coefficient of resonant frequency (τf) was successfully modified toward zero due to entropy-driven CTE and structural modifications. Excellent microwave dielectric properties with εr = 22.5, Q × f = 98,000 GHz, and τf = -2.0 ppm/°C were obtained at Sconf = 1.37R. This work highlights the potential of entropy-engineering in developing high-performance microwave dielectric ceramics, offering a promising pathway for the advancement of 5G communication components.

Analysis on scattering and inner near-field characteristics of a uniaxial anisotropic sphere by an off-axis high-order Bessel (vortex) beam

Based on the generalized Lorenz–Mie theory (GLMT) and the Fourier transform method, a theoretical approach is introduced to study the scattering of a uniaxial anisotropic sphere illuminated by an off-axis high-order Bessel (vortex) beam (HOBVB). According to the orthogonality of the associated Legendre function and exponential function, a concise expression of the expansion coefficients of the off-axis HOBVB in terms of the spherical vector wave functions (SVWFs) is derived that can effectively reconstruct the HOBVB with all conical angles. The differences of scattering characteristics of a uniaxial anisotropic sphere illuminated by an on-axis and off-axis HOBVB and a plane wave are exhibited. Influences of the topological charge, conical angle, particle size, and off-axis distance on the angle distributions of the radar cross-section (RCS), scattering and extinction efficiencies, and asymmetric factor are analyzed in detail. The unique internal and near-field distributions of a uniaxial anisotropic spherical particle illuminated by an on-axis and off-axis HOBVB are demonstrated. The results provide insights into the scattering and Bessel beam–matter interactions and may find important applications in optical propagation and optical micromanipulation, microwave engineering, target shielding, and near-field measurement.

High-temperature structure, elasticity, and thermal expansion of ε-ZrH1.8

Zirconium hydride is a promising candidate material for nuclear microreactor applications as a solid-state moderator component, owing to its favorable neutronics properties and good thermal stability over other metal hydrides. In the present work, the crystal structure, thermal expansion, and elastic properties of the hydrogen-rich ε phase hydride were measured at elevated temperatures in the range 300–900 K. Samples were prepared by direct hydriding Zircaloy-4 metal – a nuclear-grade zirconium alloy. Room-temperature lattice parameters agree well with those reported from literature for unalloyed zirconium hydride and fall within an observed quadratic H-content dependence. The coefficients of thermal expansion, determined from lattice expansion and dilatometry, agree well within our work but were about 30 % lower than those reported by others for unalloyed hydrides. Density functional theory-based molecular dynamics simulations were used to compare with thermal expansion and elasticity measurements. Results showed lattice parameter temperature dependence and slope of thermal expansion align with those from measurements. Based on diffraction scans at select temperatures, ε phase remained stable in air up to at least 770 K. Likewise, dilatometry showed smooth thermal expansion up to the thermal decomposition temperature around 950 K. The precise decomposition temperature was not determined via diffraction due to sparse scanning. The complete elastic property measurements were gathered for ε-phase Ziracloy-4 hydride for the first time. Young's modulus was lower compared to the metal and δ hydride phases. High-temperature elasticity measurements were limited to <350 K due to acoustic dissipation effects.

Tensile Properties and Coefficient of Thermal Expansion of Laser Powder Bed Fusion Fabricated IN718‐YSZ Compositionally Graded Composite

The microstructure, tensile properties, and thermal expansion characteristics of a laser powder bed fusion (LPBF) manufactured compositionally graded composite with 0.5–8 wt% yttria‐stabilized zirconia (YSZ) reinforced Inconel 718 are investigated. Along the composition gradient, which is perpendicular to the build direction, in all cross sections, the YSZ segregates at the melt‐pool boundaries and the IN718 matrix has randomly oriented equiaxed grains. Cross sections with &gt;2 wt% YSZ contain significant porosity (&gt;2%) and solidification cracks, which reduces their strength and ductility significantly. In the section with 1.5 wt% YSZ, the YS, UTS, and ductility are 819 ± 30, 1008 ± 40, and 7.4 ± 0.4 MPa, which matches well with that of LPBF fabricated YSZ‐free IN718. Dilatometry measurements on sections with 0.5–1.5 wt% YSZ in the temperature range of 25–1200 °C indicate that their coefficient of thermal expansion (CTE) is intermediate to that of IN718 and YSZ. Finally, the variations in CTE with temperature are discussed in detail by considering the microstructural evolution in the composite with changes in temperature.

Dimensional change and springback of spherical shell in cryogenic forming

Cryogenic forming has been developed to manufacture thin-walled curved aluminum alloy components, whose final dimensions are affected by cryogenic shrinkage and springback. Therefore, dimensional changes of spherical shell in cryogenic forming were studied theoretically and experimentally. The cryogenic forming process was discussed to elucidate the factors affecting the dimensional change. The stress distribution was analyzed to qualitatively reveal the springback behavior. Cryogenic dimensional measurement devices were built to quantitatively evaluate the dimensional changes in the forming processes of punch cooling, springback, and specimen restoration to room temperature. The temperature dependencies of the elastic modulus and expansion coefficient were modeled to quantitatively calculate the effect of thermal expansion and contraction on the dimensions of specimen and punch. The theoretical analysis results indicate that depth reduction and opening expansion are produced by cryogenic springback, determined by the radial stress, hoop stress, and bending moment in different deformation regions. The cryogenic springback in the biaxial tensile stress zone was reduced by 37.8 % owing to the increasing radial deformation and decreasing bending deformation. In contrast, cryogenic springback in the tensile-compressive stress zone increased by 30.8 %. The punch cooling shrinkage and specimen warming expansion in depth direction can reduce for the dimensional deviation caused by springback but cause the opposite effect in hoop direction. Expansion and shrinkage were effectively predicted using the proposed model, with an error of less than 16 %. The deformation region of the biaxial tensile stress can be enlarged by the significantly improved hardening ability at cryogenic temperature, which benefits enhancing deformation uniformity and further reduces springback. Therefore, cryogenic forming offers considerable potential for the precision manufacturing of aluminum alloy deep-cavity thin-walled components.

Utilizing porous dielectric material to enhance the performance of capacitive MEMS accelerometers for shaft monitoring

This research investigates the optimization of the performance of a capacitive-based microelectromechanical systems (MEMS) shaft monitoring accelerometer using a porous soft dielectric material with high polarization capability and low Young’s modulus. The nonlinear governing equations of a microbeam with a proof mass coupled with the squeeze motion equation of the polymeric dielectric material excited by shaft vibrations are extracted and solved in both the spatial and temporal domains. The studied model considers the stiffness, dissipative, and inertial effects of the polymeric material and incorporates porosity as a displacement-dependent variable, which introduces an additional nonlinearity. After discretizing the coupled nonlinear differential equations using the Galerkin method, the response in the frequency domain is obtained by applying an energy balance method, where the coefficients of the Fourier expansion of the response are found by arc-length continuation through a physical gradient descent learning-based approach method. The occurrence of secondary and primary resonances in different harmonic responses is studied for different harmonic acceleration inputs. The equivalent rigidity of the design is investigated for different shaft frequency magnitudes and different proof mass geometries. The effect of the initial porosity volume fraction of the elastomeric dielectric material on the dynamic response of the accelerometer is also examined. The sensor’s sensitivity is dependent on its geometry and properties and can vary based on the structure’s material parameters. Consequently, the selection of different geometries and materials may result in either an improvement or a deterioration of the sensor’s performance.

The Role of Alkyl Chains in the Thermoresponse of Supramolecular Network.

Supramolecular materials provide a pathway for achieving precise, highly ordered structures while exhibiting remarkable response to external stimuli, a characteristic not commonly found in covalently bonded materials. The design of self-assembled materials, where properties could be predicted/design from chemical nature of the individual building blocks, hinges upon ourability to relate macroscopic properties to individual building blocks - a feat which has thus far remained elusive. Here, a design approach is demonstrated to chemically engineer the thermal expansion coefficient of 2D supramolecular networks by over an order of magnitude (\boldmath 120 to \boldmath 1000 × 10-6K-1). This systematic study provides a clear pathway on how to carefully design the thermal expansion coefficient of a 2D molecular assembly. Specifically, a linear relation has been identified between the length of decorating alkyl chains and the thermal expansion coefficient. Counter-intuitively, the shorter the chains the larger is the thermal expansion coefficient. This precise control over thermo-mechanical properties marks a significant leap forward in the de-novo design of advanced 2D materials. The possibility to chemically engineer their thermo-mechanical properties holds promise for innovations in sensors, actuators, and responsive materials across diversefields.

Exploring the effects of finite size and indenter shape on the contact behavior of functionally graded thermoelectric materials

The performance enhancement of functionally graded thermoelectric (FGTE) devices is significantly influenced by contact studies of the FGTE materials. It is unclear how the finite thickness and the punch geometry influence the FGTE materials’ contact behaviors. This paper investigates the frictionless contact problem between three types of rigid punches (flat, triangular, and cylindrical) and the FGTE strip with finite thickness. The electric-thermo-elastic parameters of the FGTE strip vary in the thickness direction according to an exponential function. Based on the Fourier integral transform and the transformation matrix method, the problem is transformed into the numerical solution of three sets of singular integral equations. The presence of singular features on either side of the punch demands the adoption of specific collocation strategies. The distribution of the normal current density, the normal energy flux, and the normal contact stress is obtained by adjusting multiple electric-thermo-elastic parameters. The contact stresses in the case of punches with varying shapes can be effectively controlled by modulating the coefficient of thermal expansion and the strip thickness, whereas the effect of the electrical conductivity, the shear modulus, and the thermoelectric load on these stresses depends on whether they are increased or decreased.

Spectral expansion methods for prediction uncertainty quantification in systems biology

Uncertainty is ubiquitous in biological systems. For example, since gene expression is intrinsically governed by noise, nature shows a fascinating degree of variability. If we want to use a model to predict the behaviour of such an intrinsically stochastic system, we have to cope with the fact that the model parameters are never exactly known, but vary according to some distribution. A key question is then to determine how the uncertainties in the parameters affect the model outcome. Knowing the latter uncertainties is crucial when a model is used for, e.g., experimental design, optimisation, or decision-making. To establish how parameter and model prediction uncertainties are related, Monte Carlo approaches could be used. Then, the model is evaluated for a huge number of parameters sets, drawn from the multivariate parameter distribution. However, when model solutions are computationally expensive this approach is intractable. To overcome this problem, so-called spectral expansion (SE) methods have been developed to quantify prediction uncertainty within a probabilistic framework. Such SE methods have a basis in, e.g., computational mathematics, engineering, physics, and fluid dynamics, and, to a lesser extent, systems biology. The computational costs of SE schemes mainly stem from the calculation of the expansion coefficients. Furthermore, SE effectively leads to a surrogate model which captures the dependence of the model on the uncertainty parameters, but is much simpler to execute compared to the original model. In this paper, we present an innovative scheme for the calculation of the expansion coefficients. It guarantees that the model has to be evaluated only a restricted number of times. Especially for models of high complexity this may be a huge computational advantage. By applying the scheme to a variety of examples we show its power, especially in challenging situations where solutions slowly converge due to high computational costs, bifurcations, and discontinuities.

Internal radiation effect on semiconductor β-Ga2O3 crystals grown by the VB Method and anisotropic thermal stress

Gallium oxide crystals are semitransparent semiconductors with good optical and electrical properties, which allow their use for several technological applications. During the growth process of β-Ga2O3 crystals, internal radiation plays a crucial role that affects the growth process and then the crystal quality. In this work, the effect of the melt and the crystal transparency on the vertical Bridgman growth of β-Ga2O3 oxide is thoroughly studied. Using a global 2D/3D finite element model, temperature, melt flow, melt-crystal interface, and three-dimensional anisotropic thermal stress are computed at different growth stages. At each stage, four cases are considered, namely, opaque melt and crystal, semi-transparent melt and opaque crystal, semitransparent crystal and opaque melt, and finally semitransparent melt and crystal. The role of internal radiation in each case at different growth stages is then highlighted separately and then coupled together. It was found that the melt-crystal interface is shifted from a convex shape at the early stage to a nearly plane and then to a concave shape at the last stage. The melt flow is then changed from two rolls pattern at the beginning to a single-roll structure at the last stage. Thermal stress of the as-grown ingot is decreased during the growth due to the decrease of temperature non-linearities. Internal radiation inside the crystal acts to increase the melt-crystal interface convexity at the early and middle stages of the growth process and leads to a decrease in its concavity at the final stage. However, the melt transparency leads to the opposite effects, i.e., it decreases the interface convexity at the early stage and increases the interface concavity at the final stage. As a result, for semitransparent crystal and melt, the interface is between the two previous cases. The calculated thermal stresses are found to be more affected by the transparency of the crystal than the melt as the absorption coefficient of β-Ga2O3 crystal is smaller than that of the melt. At all stages, the thermal stresses are found to be larger for the opaque case due to the increase of temperature non-linearities in the crystal. Large values are found at the bottom and the lower part of the periphery. Furthermore, internal radiation inside the melt plays a major role during the early growth stage due to the large liquid volume. It reduces the melt flow intensity close to the free surface where the shear stress is combined with the buoyant force and leads to the flattening of the interface decreasing then the radial temperature gradients, which leads to small attenuation of the thermal stress. At the final stage, the transparency of the melt plays the opposite role due to the increase of the interface concavity which leads to an increase in both of the temperature gradients and the thermal stress inside the crystal. Due to the crystal anisotropy, and especially to the large thermal expansion coefficient in the [010] direction, the 3D thermal stress values are found to be larger in this direction, especially in the bottom part of the ingot. Comparisons with available experimental and numerical works are provided in this paper.

Effect of filer content on the thermal characteristics of underfill materials for Ball-Grid-Array component package

High-density integration and fast processing speed in the semiconductor industry have increased heat generation in electronic devices. Underfill materials, known for their high thermal conductivity and low coefficient of thermal expansion (CTE), offer a potential solution to dissipate heat and improve device reliability. In this study, we investigate the effect of filler content on the thermal reliability of underfill materials for ball grid array (BGA) component packaging. Mainly, we investigate the thermal conductivity, CTE, and mechanical properties of different filler contents of Al2O3 and Al2O3–BN hybrid underfills to facilitate heat dissipation and improve device reliability. The thermal conductivity of the underfill materials was evaluated by measuring the surface temperatures of underfill molded flip-chip light-emitting diodes (FCLEDs). The mechanical properties and thermo-mechanical reliability of the underfill materials were evaluated via a three-point bending test of the underfill packaged BGA components after the thermal shock test. The results showed that optimizing underfill properties based on specific application environments is crucial for obtaining enhanced thermal reliability and mechanical properties of underfill packaged BGA components.