In-plane Thermal Expansion Research Articles

Measurement of in-plane thermal expansion of ceramic coating by an optical method

Measurement of in-plane thermal expansion of ceramic coating by an optical method

Design and analysis of dual-constituent lattice sandwich panel with in-plane zero thermal expansion and high structural stiffness

The lattice sandwich panel may achieve in-plane zero thermal expansion (ZTE) property through a special design of upper and lower face sheets, both of which are attached with an additional layer of patch with high coefficient of thermal expansion (CTE). This type of sandwich panels with ZTE property is highly demanded for aerospace vehicles, where often suffer from large variations of temperature. The design of curved surface for the face sheet cells is necessary to achieve in-plane ZTE attribute, however, it will also result in structural stiffness reduction significantly. In this study, a novel dual-constituent lattice sandwich panel with in-plane ZTE and high structural stiffness properties is proposed, designed and analyzed. Six different kinds of cell configurations through two types of curved surface and three different patches are compared to obtain the optimal design. A further parametric study is carried out by numerical simulations to show the influences of curved surface, patch covering form, patch shape, size and thickness on cell equivalent stiffness as well as the control effectiveness of thermal deformation. Optimal cell designs that enable the sandwich panels to achieve the in-plane ZTE and high in-plane stiffness properties are also presented. The stiffness reduction for achieving in-plane ZTE is acceptable. Sufficient residual stiffness ensures the load carrying capacity of dual-constituent lattice sandwich panels.

Thermal expansion behavior of thin films expanding freely on water surface

Coefficient of thermal expansion (CTE) for thin film has been measured only from change in thickness because thin film has to be constrained on a solid substrate. However, thin film CTE shows different values depending on the supporting solid substrate. Here, a novel measurement method is suggested to quantitatively measure the in-plane thermal expansion of thin films floating on a water surface. In-plane thermal expansion of thin films on water surface is achieved by heating the water. The CTE is measured through a digital image correlation (DIC) technique. The DIC tracks displacement marks deposited on the film surface, and the in-plane thermal strain is defined as the change in distance between the patterns. The method can be applied to measure the CTE of polymer, metal, and graphene with a thickness ranging from a micrometer to one-atom-thickness. The in-plane thermal expansion of the polystyrene (PS) thin film decreased as the film thickness decreased. The negative CTE of graphene is also successfully explored without any substrate effects or complicated calculations. The CTE measurement method can provide understanding of the intrinsic thermal expansion behavior of thin films including emerging two-dimensional materials.

A new design concept of dual-constituent sandwich panel with in-plane zero thermal expansion

The lattice metamaterials with zero, large positive or negative coefficients of thermal expansions (CTEs) have attracted much attention because of urgent demands in practical engineering structure. Due to the porosity of the above lattice metamaterials, most of structures made of them are also porous and are unsuitable to the outermost need to seal, for example, the skin of supersonic vehicles. In this paper, a new design concept of dual-constituent sandwich panel with in-plane zero thermal expansion is proposed. Different from the structures made of porous metamaterial with zero CTE, the upper and lower face-sheets of sandwich panels are all solid and not porous. The counterintuitive properties come from the special design of face-sheets, which are comprised of bi-layer materials with different positive CTEs. The difference of CTEs of two bonded layers leads to transverse bending of face-sheet during temperature increase, which results in the in-plane contraction and thereby compensates the in-plane thermal expansion deformation. The core is connected to the special locations on face-sheets to ensure the desired thermal transverse deformation occurs. In order to verify the validity of the design concept, two kinds of specific examples of corrugated and lattice sandwich panels are separately presented. The results indicate they can separately achieve in-plane unidirectional and bidirectional zero thermal expansion if the appropriate structure parameters and materials are selected.

Phase Instability and Thermal Properties of Multilayered Vanadium Diselenide: DAC-Based High Pressure Studies

Two-dimensional layered trichalcogenides are of current research interest because of their robust opto-electronics, and thermal properties. Mechanical and phonon vibrational properties of these materials are of significant importance in the field of stress and thermal management. Here we report the pressure dependence of structural and phonon behaviors of high quality few-layers vanadium diselenide nano-sheets grown by hydrothermal method employing synchrotron x-rays and micro-Raman scattering techniques. The high crystalline nature of the nanosheets was examined using transmission electron microscopy. Synchrotron x-ray studies at high pressure (up to 22 GPa) using a diamond-anvil cell identify a displacive type phase transition to a low symmetry monoclinic phase (C2/m) around 7 GPa corroborated with the P-dependent Raman scattering results. Raman spectroscopic studies at high pressure (up to 34 GPa) identify two prominent Raman bands with symmetry Eg and A1g. Eg band at 207 cm-1 shows normal hardening and A1g band at 236 cm-1 softens. The first order pressure derivatives of these phonons at ambient phase (P-3m1) are found to be -3.547(2) and 0.388(6) cm-1/ GPa, respectively. Using the experimental mode Grüneisen parameter of Eg Raman mode, the in-plane thermal expansion coefficient of the titular compound at the ambient phase is estimated. The observed results are expected to be useful in calibration and performance of next generation nano-electronics and optical devices under extreme stress conditions. These experimental results corroborated with our ab-initio calculations will be presented in the ECS meeting.

Development of a machine learning potential for graphene

We present an accurate interatomic potential for graphene, constructed using the Gaussian Approximation Potential (GAP) machine learning methodology. This GAP model obtains a faithful representation of a density functional theory (DFT) potential energy surface, facilitating highly accurate (approaching the accuracy of ab initio methods) molecular dynamics simulations. This is achieved at a computational cost which is orders of magnitude lower than that of comparable calculations which directly invoke electronic structure methods. We evaluate the accuracy of our machine learning model alongside that of a number of popular empirical and bond-order potentials, using both experimental and ab initio data as references. We find that whilst significant discrepancies exist between the empirical interatomic potentials and the reference data - and amongst the empirical potentials themselves - the machine learning model introduced here provides exemplary performance in all of the tested areas. The calculated properties include: graphene phonon dispersion curves at 0 K (which we predict with sub-meV accuracy), phonon spectra at finite temperature, in-plane thermal expansion up to 2500 K as compared to NPT ab initio molecular dynamics simulations and a comparison of the thermally induced dispersion of graphene Raman bands to experimental observations. We have made our potential freely available online at [http://www.libatoms.org].

Temperature dependence of the energy bandgap of multi-layer hexagonal boron nitride

The temperature dependence of the energy bandgap of hexagonal boron nitride (h-BN) has been probed via photoluminescence emission characteristics of a donor-to-acceptor pair transition in a 20-layer h-BN epilayer. The results indicate that the universal behavior of bandgap decreasing with temperature is absent in multi-layer h-BN. Below 100 K, the bandgap energy variation with temperature, Eg vs. T, is dominated by the electron-phonon coupling and conforms to the common behavior of redshift with an increase in temperature. At T > 100 K, the bandgap shows an unusual blueshift with temperature, which can be attributed to the unique behavior of the in-plane thermal expansion coefficient of h-BN that becomes negative above around 60 K. Although both graphite and h-BN have negative thermal expansion coefficients in a broad temperature range, graphite has a zero energy bandgap, which makes h-BN a unique semiconductor to exhibit this unusual temperature dependence of the energy bandgap.

Control of Head/Tail Isomeric Structure in Polyimide and Isomerism-Derived Difference in Molecular Packing and Properties.

Two sequence isomeric poly(amic acid)s (PAAs) are successfully synthesized from 3,3',4,4'-biphenyltetracarboxylic dianhydride and unsymmetrical 5(6)-amino-2-(4-aminobenzene) benzimidazole (PABZ). The syntheses are based on the site-selective reactivity of head/tail amino groups of PABZ and solubility differences of PABZ in good solvent (dimethyl sulfoxide, DMSO) and poor solvent (N-methyl-2-pyrrolidone, NMP). The proton nuclear magnetic resonance (1 H-NMR) results reveal that the content of head tail-head tail (HTHT) bonding units in PAA-DMSO (PAA synthesized in DMSO) is 37%, while this content increases to 54% in PAA-NMP (PAA synthesized in NMP). The wide-angle X-ray diffraction (WAXD) results indicate polyimide (PI)-NMP film with high HTHT content exhibits a semicrystalline structure, while PI-DMSO film is amorphous. Moreover, PI-NMP also shows higher in-plane orientation than PI-DMSO. The ordered molecular packing and higher in-plane orientation of PI-NMP lead to an increase in mechanical properties and a decrease in in-plane thermal expansion coefficient.

Fundamental properties of Ti6Si2B—a new ternary phase in the Ti–Si–B system

Density functional theory studies combined with the method of quasi-harmonic phonons have been undertaken to describe structural, bonding, elastic, vibrational and thermal properties of Ti6Si2B, which is a new ternary phase in the Ti–Si–B system. Analysis of the results is performed in relation to selected compounds from the Ti–Si and Ti–B systems as well as available experimental data. Titanium borosilicide exhibits covalent-type bonds of different strength as indicated by the calculated electron localization functions and the Bader charges. Its elastic and thermal properties are anisotropic due to higher out-of-plane than in-plane lattice compressibility and thermal expansivity. Polycrystalline Ti6Si2B is predicted to be a brittle material with quite high Vicker’s hardness. It is shown that on one hand Ti6Si2B shares many common features with titanium silicides and borides, but on the other hand its mechanical, vibrational and thermal properties are distinct from those of compounds forming the Ti–Si and Ti–B systems. Theoretical phonon and Raman spectra, which are simulated at conditions close to experimental ones, may serve as a guide for interpretation and refinement of experimental spectra as well as symmetry mode assignment. The present work can be considered as a prediction study, still awaiting an experimental verification.

Effect of ripples on the finite temperature elastic properties of hexagonal boron nitride using strain-fluctuation method

This work intents to put forth the results of a classical molecular dynamics study to investigate the temperature dependent elastic constants of monolayer hexagonal boron nitride (h-BN) between 100 and 1000 K for the first time using strain fluctuation method. The temperature dependence of out-of-plane fluctuations (ripples) is quantified and is explained using continuum theory of membranes. At low temperatures, negative in-plane thermal expansion is observed and at high temperatures, a transition to positive thermal expansion has been observed due to the presence of thermally excited ripples. The decrease of Young's modulus, bulk modulus, shear modulus and Poisson's ratio with increase in temperature has been analyzed. The thermal rippling in h-BN leads to strong anharmonic behaviour that causes large deviation from the isotropic elasticity. A detailed study shows that the strong thermal rippling in large systems is also responsible for the softening of elastic constants in h-BN. From the determined values of elastic constants and elastic moduli, it has been elucidated that 2D h-BN sheets meet the Born's mechanical stability criterion in the investigated temperature range. The variation of longitudinal and shear velocities with temperature is also calculated from the computed values of elastic constants and elastic moduli.

Cross laminated timber properties including effects of non-glued edges and additional cracks

Cross laminated timber (CLT) is usually comprised of multiple timber layers having alternating grain directions. Because individual boards are glued on their faces between layers, but usually not glued on their edges within layers, those edges define “precracks” in the composite. When exposed to differential thermal and moisture expansion after installation, CLT, like all cross-laminated composites, is prone to formation of “additional cracks”. Confidant CLT design must be able to account for changes in CLT properties during life of a structure caused by such additional cracks. By extending variational mechanics methods for aerospace composites, this paper provides analytical solutions for all in-plane mechanical, thermal expansion, and moisture expansion properties of a three-layer CLT panel. By using the three-layer solution to evaluate effective layer properties as a function of the number of cracks, the analysis can be extended to in-plane mechanical, out-of-plane bending, and expansion properties for CLT panels with any number or arrangement of layers. Some sample calculations are provided along with comments on limitations of the approximations and needs for future work.

Zero in-Plane Thermal Expansion in Guest-Tunable 2D Coordination Polymers

Zero in-plane thermal expansion (TE) in a two-dimensional (2D) coordination polymer is demonstrated. The combination of components that expand and those that shrink into zigzag layers results in no net area change in the 2D materials with temperature. Single crystals of [Mn(salen)]2[Mn(N)(CN)4(guest)] (salen = N,N'-ethylenebis(salicylideneaminato), guest = MeOH and MeCN) were prepared, and variable-temperature single-crystal X-ray structural analyses demonstrated that these compounds exhibited both anisotropic positive and negative thermal expansion depending on the guest species. The TE behavior results from distortions of the octahedral coordination geometry of [Mn(salen)]+ units in the zigzag layers. When both guests MeOH and MeCN were incorporated into one material, [Mn(salen)]2[Mn(N)(CN)4(MeOH)0.25(MeCN)0.75], zero in-plane TE resulted in a range of temperature between 380 and 440 K.

Anisotropic Thermal Expansion of α-YbAlB4

Thermal expansion measurements were performed for α-YbAlB4 using powder X-ray diffraction and our high resolution capacitance dilatometry. Highly anisotropic thermal expansion, which is much larger along the c-axis compared to the a- and b-axes, was observed. In addition, high resolution capacitance dilatometry revealed negative thermal expansion appears below 90 K only along the a-axis, not along the c-axis. The observation is consistent with anisotropic hybridization stronger in the ab-plane, suggesting the formation of anisotripic heavy fermion well below the valence fluctuation temperature scale of 200 ∼ 300 K. Furthermore, linear thermal expansion coefficient along the a-axis starts to decrease below 115 K. The characteristic temperature scale of 90 - 115 K may correspond to the crystal electric field excited level. The in-plane negative thermal expansion can be regarded as a development of anisotropic hybridization due to |Jz = ±5/2 > crystal electric field ground states which becomes dominant on cooling below the excited states.

Origin of zero and negative thermal expansion in severely-deformed superelastic NiTi alloy

We have investigated the physical origin of anomalous in-plane thermal expansion (TE) anisotropy leading to invar-like behavior and negative TE in nanostructured NiTi sheets manufactured via severe cold-rolling. The roles of grain size (GS), crystallographic texture, thermally-induced phase transformation, and intrinsic (lattice level) TE of austenite (B2) and martensite (B19′) phases on the macroscopic TE behavior are addressed. It is shown that by controlling the cold-rolling thickness reduction and heat-treatment temperature the coefficient of thermal expansion (CTE) can be controlled in a wide range from positive (α ∼ 2.1 × 10−5 K−1) to negative (α ∼ −1.1 × 10−5 K−1) via in-plane anisotropy of TE. A very small CTE of α ∼ −5.3 × 10−7 K−1 (invar-like behavior) in a wide temperature window of 230 K (353–123 K) is obtained at an angle of 33.5° to the rolling direction (RD) of the severely cold-rolled sheet. TEM and XRD studies show that the microstructure underlying such anomalous TE behavior consists of a mixture of B2 nano-grains and retained/residual deformation-induced martensite and that the observed anomalous TE anisotropy is due to the intrinsic anisotropic TE of residual martensite. The invar-like behavior is the result of the cancellation of the positive TE of austenite phase with the negative TE of residual martensite along 33.5° to the RD. A simple rule of mixture model incorporating the intrinsic TE of B2 and B19′ lattices and the texture coefficients of the sample is proposed which successfully captures the anomalous in-plane TE anisotropy. The discovery of high dimensional stability over a wide temperature window along with temperature insensitive non-hysteretic linear superelasticity of the severely-deformed NiTi opens up a new route for designing stable SMAs for applications in ragged environments.

Rigid unit modes insp−sp2hybridized carbon systems: Origin of negative thermal expansion

Using density functional theory combined with quasi-harmonic approximation, we investigate the thermal expansion behaviors of three different types ({\alpha}, {\beta}, and {\gamma}) of graphyne which is a two-dimensional carbon allotrope composed of sp and $sp^2$ bonds. For each type of graphyne, we obtain the temperature dependent area variation by minimizing its free energy as a function of temperature, which is calculated by considering all the phonon modes in the whole Brillouin zone. We find that all three types of graphyne exhibit negative in-plane thermal expansion up to $T\lesssim1000$ K. The observed in-plane thermal contraction can be attributed partially to the ripple effect, similarly in graphene. The ripple effect itself, however, is not sufficient to explain anomalously larger thermal contraction found in graphyne than in graphene. Our deliberate analysis on the phonon modes observed in graphyne enables us to discover another source causing such thermal expansion anomaly. We find that there are particular phonon modes with frequencies around a few hundreds of cm$^{-1}$ existing exclusively in graphyne that may fill empty spaces resulting in area reduction. These modes are identified as "rigid unit modes" corresponding to the libration of each rigid unit composed of $sp^2$ bonds.

How does solvent annealing influence stress-driven surface undulations in polymer composite films with immobilized film-spanning nanoparticles?

Our study on poly(methyl methacrylate) (PMMA) films with fixed nanoparticles (NPs) on the supporting substrate, where the nanoparticles span the film thickness, reveal a three-stage evolution of wavelike undulations on the film surface: early stage, intermediate stage and late stage. The wavelike height undulations are induced by the compressive stresses, which are enhanced by introducing fix constrians (NPs) that resist the in-plane thermal expansion of the polymer film. We quantified the evolution of surface undulations, in an effort to understand the effect of solvent annealing on the undulations. The polymer chains in PMMA films prepared by spin coating are not fully equilibrated due to the rapid solvent evaporation during drying. Solvent annealing increases the molecular mobility and enables relaxation of the polymer network. This solvent treatment could perhaps give rise to an increase in entanglement density and associated film modulus. The surface undulations increase with the solvent annealing time before they reach the equilibrium values. The wavelike surface undulations might be associated with the entanglement density of polymer chains.

Thermo-mechanical response of superalloy honeycomb sandwich panels subjected to non-steady thermal loading

This paper investigates heat-shielding performance and 3D thermal deformation behavior of two superalloy honeycomb-core sandwich panels in time-varying thermal environment by using a self-developed transient aerodynamic heating simulation system and a novel active imaging stereo-digital image correlation (stereo-DIC) technique. To facilitate deformation measurement of large objects using stereo-DIC, a simple but practical technique is adopted for fabricating high-temperature speckle patterns on large measuring areas. The results indicate that the sandwich panels provide good thermal shielding performance under 900°C with the thermal insulation effect stabilizing at around 30%. The measured high-temperature deformation fields of the test sandwich panels reveal that an in-plane homogeneous thermal expansion occurs as expected, while the out-of-plane deformation shows evident axisymmetric distributions with the maximum deflections dependent on the temperature differences between the back and front facets. The results provide a foundational understanding on the thermal–mechanical characteristics of superalloy honeycomb-core sandwich panels, which is essential to the structural design of a superalloy honeycomb sandwich thermal protection system.

3D thermal deformation measurement of superalloy honeycomb panels in time-varying thermal radiation environment

Superalloy honeycomb panels with the advantages of light weight,high strength and excellent heat-shielding properties have been widely used in the field of aeronautics and astronautics. Deformation measurement of superalloy honeycomb panels due to transient thermal loading is essential for the design of heatshielding structures. Firstly,a self-developed infrared radiation transient aerodynamic heating simulation system was used to simulate conditions similar to transient aerodynamics service conditions and a novel active imaging three-dimensional digital image correlation( 3D-DIC) method was used to measure 3D thermal deformation of a superalloy honeycomb panel sample with a size of 210 mm × 210 mm at different times in time-varying thermal radiation environment. Secondly,to ensure the reliability of measurement by using 3D-DIC,a new technique for making large-area high-temperature speckle pattern on a test sample was proposed. The hightemperature speckle pattern stayed stable throughout the experiment and could be used as an effective carrier of thermal deformation. Finally,the largest warping displacement was also calculated by Hoff's equivalent stiffness theory. Study results indicate that in-plane thermal expansion is homogeneous when the panel is heated one-side by radiation heating,while the out-plane displacements show evident axisymmetric warp deformation with the largest warping displacement of approximate 1. 6 mm at a temperature of 900℃. The experimental results agree well with theoretical predictions made by Hoff's equivalent stiffness theory.

Solder–Graphite Network Composite Sheets as High-Performance Thermal Interface Materials

Low-cost solder–graphite composite sheets (‡55 vol.% solder), with solder and graphite forming interpenetrating networks to a degree, are excellent thermal interface materials (TIMs). Solders 63Sn-37Pb and 95.5Sn-4Ag-0.5Cu are separately used, with the latter performing better. In composite fabrication, a mixture of micrometer-size solder powder and ozone-treated exfoliated graphite is compressed to form a graphite network, followed by fluxless solder reflow and subsequent hot pressing to form the solder network. The network connectivity (enhanced by ozone treatment) is lower in the through-thickness direction. The electrical conductivity obeys the rule of mixtures (parallel model in-plane and series model through-thickness), with anisotropy 7. Thermal contact conductance £26 9 10 4 W/(m 2 K) (with 15-lm-roughness copper sandwiching surfaces), through-thickness thermal conductivity £52 W/ (m K), and in-plane thermal expansion coefficient 1 9 10 � 5 /� C are obtained. The contact conductance exceeds or is comparable to that of all other TIMs, provided that solder reflow has occurred and the composite thickness is £100 lm. Upon decreasing the thickness below 100 lm, the sandwich thermal resistivity decreases abruptly, the composite through-thickness thermal conductivity increases abruptly to values comparable to the calculated values based on the rule of mixtures (parallel model), and the composite–copper interfacial thermal resistivity (rather than the composite resistivity) becomes dominant.

Secondary effects in wide frequency range measurements of the pyroelectric coefficient ofBa0.6Sr0.4TiO3andPbZr0.2Ti0.8O3epitaxial layers

We describe measurements of the pyroelectric coefficient of epitaxial layers of ${\mathrm{Ba}}_{0.6}{\mathrm{Sr}}_{0.4}{\mathrm{TiO}}_{3}$ (BST) and ${\mathrm{PbZr}}_{0.2}{\mathrm{Ti}}_{0.8}{\mathrm{O}}_{3}$ (PZT) using a modulated laser as the heat source in the frequency range 1 Hz to 10 MHz. The pyroelectric coefficient is also measured as a function of applied static electric field and for films grown on ${\mathrm{SrTiO}}_{3}$, ${\mathrm{DyScO}}_{3}$, and ${\mathrm{GdScO}}_{3}$ substrates. The heat diffusion equation is solved in cylindrical coordinates for the temperature field in a multilayer sample heated by a Gaussian-shaped laser beam. The secondary contribution to the pyroelectric effect caused by piezoelectric effects and in-plane thermal expansion is revealed by the difference between the pyroelectric coefficients at high and low frequencies. The secondary pyroelectric effect has the same dependence on applied field as the pyroelectric coefficient. The magnitude of the secondary effect changes with heating frequency because of changing mechanical conditions, but the pyroelectric coefficient has no other frequency dependence between 1 Hz and 10 MHz. The secondary effect is approximately 15% and 20% of the total pyroelectric response for PZT and BST films, respectively.