In-plane Coefficient Of Thermal Expansion Research Articles

Glass fiber strengthened BNNS/ST/polyolefin composites with high dielectric constant and high thermal conductivity

The present research presents an examination of the consequential effects brought about by the introduction of short-cut E-glass fibers (GF) on the properties of high-dielectric constant, high-thermal conductivity microwave composite systems (xGF/(8-x)BNNS/78 wt%ST/polyolefin, x = 0-8 wt%, BNNS: hexagonal boron nitride nanosheets). The GF is modified using KH550, with the success of the surface modification definitively confirmed by X-ray Photoelectron Spectroscopy (XPS) and Fourier Transform infrared spectroscopy (FTIR). All components are found to exhibit consistently ultra-high and stable dielectric constants within the 8–12 GHz frequency range (Dk = 17.7–18.08). Based on thermogravimetry analysis (TGA) and dynamic mechanical analysis (DMA) results, the incorporation of modified GF improve the thermal stability of the composite materials, enhancing thermal decomposition temperature, residual carbon content and glass transition temperature. Furthermore, replacing BNNS with GF significantly amplifies the mechanical properties of the composite substrate. This substitution leads to a notable reduction in the coefficient of thermal expansion (CTE) in all directions while simultaneously increasing the bending and tensile strength. At the same time, the composites can maintain reasonably high thermal conductivity values. Overall, with a GF concentration of 4 wt%, the composite showcases an appreciable increase in dielectric constants (17.81), a high thermal conductivity (1.3 W/m·K) and enhances mechanical properties (cross-plane CTE: 15.44 μm/(m·°C), in-plane CTE: 26.06 μm/(m·°C), bending strength: 65.6 MPa, tensile strength: 17.42 MPa). Considering its superior performance metrics, the composite can be identified as an optimal choice for microwave composite dielectric substrate material.

Strain accumulation and relaxation on crack formation in epitaxial AlN film on Si (111) substrate

The formation of cracks is often observed in the epitaxial growth of ultrawide-bandgap aluminum nitride (AlN) semiconductor films on economical and versatile silicon (Si) substrates due to the significant differences in in-plane lattice parameters and thermal expansion coefficients between the film and the substrate, which hampers the development of template, buffer layer, and device structure with a relatively thick AlN layer for devices. The present study aims to elucidate the conditions of crack formation through a simple but comprehensive estimation of strain energy accumulation and relaxation by lattice strain, misfit dislocation density, and crack formation. Strain energy in the epitaxial film from lattice and thermal mismatches is evaluated by an elastic strain equation tailored to the epitaxy of the hexagonal crystal structure. The effects of temperature, thickness, and dislocation density on the lattice and dislocation strain energies of the film are also considered. Finally, the comparison in the changes in the total strain energy and cleavage energy with decreasing temperature shows that cleavage energy is higher than strain energy if the film is thinner than 400 nm but becomes lower than the strain energy if the film is thicker than 400 nm during cooldown, suggesting the crack formation, which matches well with experimental observations.

Anisotropic thermo-mechanical response of layered hexagonal boron nitride and black phosphorus: application as a simultaneous pressure and temperature sensor.

Hexagonal boron nitride (hBN) and black phosphorus (bP) are crystalline materials that can be seen as ordered stackings of two-dimensional layers, which lead to outstanding anisotropic physical properties. Knowledge of the thermal equations of state of hBN and bP is of great interest in the field of 2D materials for a better understanding of their anisotropic thermo-mechanical properties and exfoliation mechanism towards the preparation of important single-layer materials like hexagonal boron nitride nanosheets and phosphorene. Despite several theoretical and experimental studies, important uncertainties remain in the determination of the thermoelastic parameters of hBN and bP. Here, we report accurate thermal expansion and compressibility measurements along the individual crystallographic axes, using in situ high-temperature and high-pressure high-resolution synchrotron X-ray diffraction. In particular, we have quantitatively determined the subtle variations of the in-plane and volumetric thermal expansion coefficients and compressibility parameters by subjecting these materials to hydrostatic conditions and by collecting a large number of data points in small pressure and temperature increments. In addition, based on the anisotropic behavior of bP, we propose the use of this material as a sensor for the simultaneous determination of pressure and temperature in the range of 0-5 GPa and 298-1700 K, respectively.

In-plane thermal expansion behavior of M55J carbon fiber reinforced SiC matrix composite

With the rapid development of high-precision ultra-stable spacecraft, the absolute values of coefficients of thermal expansion (CTE) of carbon fiber reinforced SiC matrix composite (C/SiC) are required to be closer to 10−7 K−1 or even lower. In this work, high-modulus and low-expansion M55J carbon fiber was selected to replace T300 carbon fiber as the reinforcement to decrease the CTE of C/SiC. The interfacial region, pore distribution and microstructure evolution during the densification process were investigated. With the replacement of T300 carbon fiber by M55J carbon fiber as the reinforcement, axial thermal residual stress in SiC matrix can increase to 378 ± 26 MPa, resulting in the generation of matrix microcracks. This can reduce the constraint of matrix to carbon fiber and provide expansion space for M55J-C/SiC. Therefore, the average in-plane technical CTE of C/SiC in the range of −20 to 50 °C can be reduced from 1.09 × 10−6 to 0.34 × 10−6 K−1.

Analysis of warpage of a flip-chip BGA package under thermal loading: Finite element modelling and experimental validation

The objective of this study is to investigate warpage of a Flip-Chip Ball Grid Array (FCBGA) package experimentally and numerically. Projection Moiré technique was used to measure full-field warpage during heating experiment from room temperature up to 250 °C. As temperature changes within the FCBGA package, different thermal strains are generated in the package resulting from the mismatch in the Coefficient of Thermal Expansion (CTE) between the constituent material layers. A finite element model and analytical equations based on the classical bending theory were used to analyze the thermally induced deformations of package under test. The results show that a maximum warpage value of 67 μm with a concave or smiling shape occurred at the neighborhood of 70 °C during heating and 87 μm warpage with a convex crying shape at 250 °C by assuming a stress-free temperature at 175 °C. Warpage analysis showed that the studied FCBGA package exhibits a different curvature in the die region at the center of the package compared to the region outside the die. At temperatures higher than 175 °C, a concave or smiling warpage shape was shown in the die region while a convex or crying shape in the region outside the die. In contrast, at room temperature, the die area has a convex shape warpage, while outside this area presented a concave shape.Furthermore, the good agreement between warpage of the studied package from finite element simulation and measurements was achieved thanks to the use of the measured material's thermal-mechanical properties of the substrate and Molding Compound (MC) rather than using datasheet data. In-plane CTE and Young's modulus of the substrate were measured using stereo-digital image correlation. Moreover, temperature dependent Young's modulus of the MC was measured by nanoindentation.

Smart sandwich structures with dynamically switchable in-plane thermal expansion coefficients from positive to negative

Capacity to autonomously respond to external stimuli with some switchable structural shapes/properties/functions is highly desirable in many occasions where either system service environments or functional requirements are dynamically changing over time. In this paper, we conceptually propose a new type of smart sandwich structure with the ability to dynamically switch in-plane coefficients of thermal expansion (CTEs) from initially positive to negative or even zero value through internal microstructural transformation triggered solely by a certain temperature stimulus. To this end, a thermally driven snap-through action is purposely added into the design of the microstructure of periodic face-sheets by introducing an active spherical shell component constituted by two materials with different positive CTEs. The lattice core is connected to the upper and lower face-sheets for preventing the overall transverse deformation of face-sheet during temperature variation. Numerical simulations are subsequently carried out to demonstrate the completely reversible snap-through behavior, and the designed function of dynamically switchable in-plane CTE is also validated. Numerical results also reveal that the increasing thickness ratio of high CTE layer to low ones causes a decreased tendency for effective in-plane CTE before snapping, but the influence on after-snapping CTE is negligible. Similarly, the larger shell span brings an obvious increase in effective after-snapping in-plane CTE but without influence on before-snapping CTE. These significant results are beneficial to be summarized as practical design skills for simultaneously designing customized snap-through temperature and effective before or after-snapping in-plane CTE, all of which enable the proposed smart sandwich structure to be flexible to satisfy various requirements in more potential applications.

Concurrent enhancement of dimensional stability and thermal conductivity of thermoplastic polyamide 12T/Boron nitride composites by constructing oriented structure

Excellent thermal management property and high-temperature dimensional stability are very important for the materials applied in the electronic devices. In this study, high temperature resistant PA12T was applied as the matrix, and PA12T/BN composites with oriented structure were fabricated by the injection molding method. Morphology, thermal conductivity, thermal expansion property and mechanical properties of the composite were systematically investigated. Results demonstrate that when the content of BN is 40 wt%, the in-plane thermal conductivity and thermal expansion coefficient of the composites are 6.5 W/(m·K) and 36 ppm/°C, respectively, which are 4 times higher and 80% lower than those along the through-plane direction. Meanwhile, the thermal expansion behavior and mechanism of the composite with oriented filler structure are well revealed by finite element analysis, and the simulated results will provide important guidance for the design and application of the composite. Furthermore, by using the PA12T/BN composite with oriented structure as the substrate of printed circuit board, temperature gradient as well as thermal stress inside the device can be well controlled. Therefore, the PA12T/BN composite has great potential in the application as the substrate or packaging materials of electronic devices.

Thermomechanical Behavior of Poly(3-hexylthiophene) Thin Films on the Water Surface

The thermomechanical behavior of a conjugated polymer (CP) in a thin film state has rarely been studied despite the importance of understanding the polymer morphologies and optimizing the thermal processes of organic semiconductors. Moreover, the seamless integration of multilayers without mechanical failures in CP-based electronic devices is crucial for determining their operational stability. Large differences in the coefficients of thermal expansion (CTEs) between the multilayers can cause serious degradation of devices under thermal stress. In this study, we measure the intrinsic thermomechanical properties of poly(3-hexylthiophene) (P3HT) thin films in a pseudo-freestanding state on the water surface. The as-cast P3HT thin films exhibited a large thermal shrinkage (−1001 ppm K–1) during heating on the water surface. Morphological analyses revealed that the thermal shrinkage of the polymer films was caused by the rearrangement of the polymer chain networks accompanied by crystallization, thus indicating that preheating the polymer films is essential for estimating their intrinsic CTE values. Moreover, the rigidity of the substrate significantly influences the thermomechanical behavior of the polymer films. The polymer films that were preheated on the glass substrate showed nonlinear thermal expansion due to the substrate constraint inhibiting sufficient relaxation of the polymer chains. In comparison, a linear expansion behavior is observed after preheating the films on the water surface, exhibiting a consistent CTE value (185 ppm K–1) regardless of the number of thermal strain measurements. Thus, this work provides a direct method for measuring in-plane CTE values and an in-depth understanding of the thermomechanical behaviors of CP thin films to design thermomechanically reliable organic semiconductors.

Effect of simultaneously introduced bulky pendent group and amide unit on optical transparency and dimensional stability of polyimide film

Monomers of 4,4′-((4-(trifluoromethyl)phenyl)methylene)bis(2,6-dimethylaniline) (3FTMDT) and N,N'-(2,2′-bis(trifluoromethyl)-[1,1′-biphenyl]-4,4′-diyl)bis(1,3-dioxo-1,3-dihydroisobenzofuran-5-carboxamide) (TA-TFMB) were synthesized and designed to fabricate polyimide film with simultaneously designed bulky pendent group and amide unit in polymer chains and their effects on the optical transparency and dimensional stability of films were investigated in detail. The prepared polyimide (3FTMDT/TA-TFMB) film possesses highly optical transparency (λcutoff = 384 nm, T450 nm = 81%, Haze = 0.86) and lighter color (L*=95.09, a*=-2.14, b*=6.44) with the in-plane coefficient of linear thermal expansion of 45 ppm/oC. Meanwhile, the film presents good thermal stability and mechanical properties, with a glass transition temperature (Tg) of 337 °C and 5 wt% decomposition temperature of 459 °C under N2, the fracture strength and tensile modulus of the film are 105 MPa and 2.2 GPa, respectively. The film also exhibits low dielectric performances with intrinsic dielectric constant of 2.29 and dielectric loss of 8 × 10-3 at 10 KHz, and which could keep stable up to 280 °C. In addition, the film shows good solubility in common solvents and is easy to be processed. The highly transparent polyimide film with reduced coefficient of linear thermal expansion is expected to be used as substrate material for flexible display or other photoelectric fields.

Measurement of the in-plane coefficient of thermal expansion of ceramic protective coatings from room temperature to 1400 °C

A technique for measuring the coefficient of thermal expansion (CTE) of ceramic protective coatings from 25 °C to 1400 °C is proposed. The surface of a self-standing mullite coating heated in a furnace was observed by a scanning laser microscope which detects only the blue laser light reflected from the sample surface as an image source and thereby eliminates the effect of thermal radiation. Images with constant contrast independent of temperature without halation by thermal radiation were obtained. The series of images from 25 °C to 1400 °C was used for the digital image correlation and the thermal strain was measured for each temperature; the CTE was calculated from the data as a function of temperature. The reliability of the measurement was confirmed through the CTE measurement of a c-plane sapphire plate and practically applied to the measurement of a mullite coating. For cases in which a self-standing coating cannot be obtained, we also proposed a method of CTE measurement for a coating adhered to a substrate, with consideration for the effect of substrate constraint.

Low Thermal Expansion Machine Frame Designs Using Lattice Structures

In this work, we investigated tessellating cellular (or lattice) structures for use in a low thermal expansion machine frame. We proposed a concept for a lattice structure with tailorable effective coefficient of thermal expansion (CTE). The design is an assembly of two parts: a lattice outer part and a cylindrical inner part, which are made of homogenous materials with different positive CTEs. Several lattice design variations were investigated and their thermal and mechanical performance analysed using a finite element method. Our numerical models showed that a lattice design using Nylon 12 and ultra-high molecular weight polyethylene could yield an effective in-plane CTE of 1 × 10−9 K−1 (cf. 109 × 10−6 K−1 for solid Nylon 12). This paper showed that the combination of design optimisation and additive manufacturing can be used to achieve low CTE structures and, therefore, low thermal expansion machine frames of a few tens of centimetres in height.

Tailoring thermal expansion of shape memory alloys through designed reorientation deformation

Manipulating macroscopic linear thermal expansion (TE) through microstructure engineering is emerging as a new research topic of shape memory alloys (SMAs). Here, we perform a modelling-and-experiment combined study to design and tune the coefficient of TE (CTE) of polycrystalline martensitic SMAs based on reorientation deformation. Using Landau thermodynamic theory of first-order phase transition, we prove that the martensite lattices of most SMAs possess intrinsic negative (positive) TE along the directions of transformation elongation (contraction). As a combined result of such intrinsic lattice-level TE and the extrinsic reorientation-deformation texture, the overall linear CTEs of martensite polycrystals decrease (increase) with the amount of reorientation stretching (contraction). The deformation paths and strain magnitudes are designed to obtain zero linear TE in 17 types of bulk SMAs and are verified by the available experimental data. Furthermore, through designed cross-rolling on martensitic NiTi sheets, we obtain ultralow in-plane CTEs (+0.13 × 10−6 K−1 ∼ +1.4 × 10−6 K−1), which are smaller than the reported values of SMAs and are even smaller than the commercial FeNi Invar alloy (+2.0 × 10−6 K−1). Our work provides a theoretical base to design SMAs with desired linear CTEs for many applications.

Microstructural topology optimization for patch-based sandwich panel with desired in-plane thermal expansion and structural stiffness

Apart from the lightweight and excellent mechanical properties, sandwich panels can be endowed with tailorable in-plane coefficient of thermal expansion (CTE) through an elaborate design of periodic face-sheets. However, albeit that the microstructural topology of their periodic face-sheets promises unique thermal expansion behaviors, it may also bring significant influences to the structural stiffness of sandwich panels. In this study, we apply the topology optimization method to design face-sheet microstructures to enable the sandwich panels to possess desired in-plane CTEs, lightweight and benign mechanical properties, simultaneously. By introducing the patch-based cell as initial configuration, the existing thermally bending adjustment mechanism for thermal deformation control is integrated to the process of topology optimization. The entire topology optimization process including the equivalent mechanical properties prediction and the sensitivity computation is performed within an in-house program coupled with commercial finite element analysis software. To this end, a matching numerical sensitivity analysis method to extract sensitivities straightforwardly from software’s output is also developed on the basis of asymptotic homogenization method. Three types of specific optimization problems in terms of different objective functions and constraint conditions are proposed, solved, and studied, namely, in-plane zero thermal expansion combining with maximum stiffness, the other for in-plane zero thermal expansion optimal specific stiffness, and minimizing in-plane isotropic thermal expansion. Some specific resulting topologies, microstructural features, and design details are subsequently obtained. In particular, the current strategy of integrating effective mechanism and topological technology can be extended to design more microstructures for simultaneously tailorable CTE and high mechanical performance by replacing present thermal deformation control mechanism with others.

Thermal stresses in composite cylindrical lattices

Deployable spacecraft technology should be both lightweight and compact for storage while also being rigid and expansive once deployed. A new type of structure that can meet both of these requirements is the morphing cylindrical lattice. This multi-stable structure can morph from a compact stowed state, to a long and slender deployed beam. It comprises narrow strips of carbon fibre composite material, making it particularly suitable for deployable booms, solar arrays and antennae. While existing modelling techniques focus on predicting the stability of lattices using symmetrical laminates, current work extends upon state-of-the-art by including the effects of thermal strains and curvatures that arise in non-symmetrical laminates when cured at elevated temperatures. As non-symmetrical laminates cool during post-cure, thermal stresses increasingly develop due to the variation of in-plane thermal expansion coefficient through the thickness. The model developed in this work, includes thermal stress effects, allowing for the design of thermally actuating lattices. This model is verified through comparison with finite element analysis and experimental data, both of which show excellent agreement.

Improving dimensional stability at high temperature and toughness of polyimide films via adjustable entanglement density

Polyimide (PI) films with ultralow coefficient of thermal expansion (CTE) and high glass transition temperature (Tg) are in great demand for applications as substrates in flexible displays. Furthermore, trade-off between CTE and toughness is highly concerned due to strategies for reducing CTE always result in weakness of toughness. In this work, we developed a facile method to improve dimension stability and toughness of PI containing benzimidazole units via regulating entanglement density based on controlling molecular weight and solid content of precursor polyamic acid (PAA) solution. As a result, the Tg of PI films increased from 394.3 to 441.4 °C and the in-plane CTE (40–350 °C) decreased from 65.7 to 3.9 ppm/K with entanglement density increasing from 253.3 to 2868.6 mol/m3. Moreover, mechanical properties especially toughness of PI films were enhanced significantly (from 7% to 18%) as entanglement density increased. In short, we delineated the effects of entanglement on the properties of PI films and found that the decrease of CTE mainly arises from the increase of entanglement density. Our studies provide new insights into the future design of flexible PI substrates with low CTE.

In-plane low thermal expansion of NiTi via controlled cross rolling

Shape memory alloy (SMA) sheets processed via unidirectional rolling (UniR) exhibit macroscopic low thermal expansion (TE) over a wide temperature span but only along a certain direction. Here, we use controlled cross rolling (CroR) to achieve in-plane low coefficients of TE (CTEs) of polycrystalline NiTi sheets. It is shown that the in-plane CTEs of a CroRed NiTi sheet with the three-step rolling path (RD-15%, TD-10% and RD-5%) can be reduced close to zero within a very narrow range (-2.7 × 10−6 K−1 to +3.0 × 10−6 K−1) over a large temperature span of 223 K. The obtained in-plane CTEs are an order of magnitude smaller than those of UniRed NiTi sheets and are comparable to that of commercial FeNi Invar alloy (+2.0 × 10−6 K−1). The physical origin of such in-plane low TE is explored through in situ neutron diffraction from 2.3 K to 300 K and a rule-of-mixture theoretical model. It is found that in the CroRed nanostructured NiTi, the in-plane positive TEs of textured B2 and B19’ aggregates are compensated by the in-plane negative TE caused by the continuous formation (vanishing) of {102}〈UVW〉 fiber-textured B19’ variants in cooling (heating), thereby leading to the overall in-plane low TE. Such compensation mechanism in CroR can also be used to achieve in-plane low TE of other SMAs.

Effects of chirality and stacking on the thermal expansion effects of graphene

Graphene has huge application potential in the field of micro-nano devices, and due to the micro/nano-level application size, the thermal expansion coefficient of graphene has a certain impact on device performance. In this paper, a comprehensive study was carried out by molecular dynamics on the in-plane and through-plane thermal expansion effect of graphene. First of all, the in-plane thermal expansion coefficients of zigzag and armchair graphene were analyzed; they were similar and relatively close to the experiment value in the temperature range of 223–428 K. Secondly, the through-plane thermal expansion effect of double-layered graphene was investigated; the thermal expansion coefficient of through-plane was an order of magnitude larger than that of in-plane. Finally, the influence of graphene stacking on the thermal expansion effect was studied; Order-stacked graphene has a greater thermal expansion effect than that of AB- and ABC-stacked graphene. These discoveries in this article are of great significance to the development and application of graphene-based micro-nano devices.

Material properties and structure of natural graphite sheet

Natural graphite sheet (NGS) is compressible, porous, electrically and thermally conductive material that shows a potential to be used in fuel cells, flow batteries, electronics cooling systems, supercapacitors, adsorption air conditioning, and heat exchangers. We report the results of an extensive material characterization study that focuses on thermal conductivity, thermal diffusivity, electrical conductivity, coefficient of thermal expansion (CTE), compression strain, and emissivity. All the properties are density-dependent and highly anisotropic. Increasing the compression from 100 to 1080 kPa causes the through-plane thermal and electrical conductivities to increase by up to 116% and 263%, respectively. The properties are independent of the sheet thickness. Thermal and electrical contact resistance between stacked NGS is negligible at pressures 100 to 1080 kPa. In the in-plane direction, NGS follows the Wiedemann-Franz law with Lorenz number 6.6 times 10^{-6} W Omega K^{-2}. The in-plane CTE is low and negative (shrinkage with increasing temperature), while the through-plane CTE is high, increases with density, and reaches 33 times 10^{-6} K^{-1}. Microscope images are used to study the structure and relate it to material properties. An easy-to-use graphical summary of the forming process and NGS properties are provided in Appendices A and B.

Improved semi-analytical and numerical methods on prediction of in-plane coefficients of thermal expansion of woven ceramic matrix composite considering defects

The in-plane coefficients of thermal expansion (CTEs) are important parameters of woven ceramic matrix composite (CMC) in the processes of design, manufacture and utilization. In this paper, five-harness satin woven C/C composites with different volume fractions of matrix fabricated by precursor infiltration and pyrolysis (PIP) method are used for microstructure observation and in-plane CTEs tests. The morphological features and evolution process of defects are studied via analysis of scanning electron microscope (SEM) figures. The improved semi-analytical method and the improved finite element method (FEM) on prediction of the equivalent in-plane CTE of woven CMC considering the effects of defects are established. The improved methods are validated by the results of experiments. Therein the improved semi-analytical method is more efficient in calculation. The improved FEM needs to establish complicated finite element models, but it can reveal the structural details and the deformation mechanism after heating.

How free-edge effects impede CTE determination for composite laminates

The determination of in-plane coefficients of thermal expansion (CTEs) of full-stack composite laminates by means of thermo-mechanical analysis (TMA) is affected by free-edge effects. A numerical study has been performed, which is focussed on the quantification of the effects of TMA sample size, laminate layup and the presence of discrete interleaf layers on the determined laminate CTEs. Fine finite-element (FE) meshes have been used to visualize and to examine free-edge effects. The study results call for carefulness when CTEs of full multi-angle laminates shall be determined by means of TMA. When the typical sample dimensions of a few millimeter are used CTEs will likely be overestimated.