Temperature Dependence Of Thermal Expansion Coefficient Research Articles

Bridge decks under cold waves: Implications of concrete’s temperature-dependent CTE

Temperature fluctuations within a bridge deck during a cold wave event can cause severe continuity stresses in structures where movement is restrained. Thermal loads are accounted for using thermal gradients that vary depending on bridge location and cross-sectional geometry. However, the effect of temperature change on material properties, particularly on the coefficient of thermal expansion (CTE) is rarely accounted for in the analysis and design. A review of the literature indicates that the CTE of concrete materials can vary significantly with changes in temperature, especially under freezing conditions, whereas saturated or partly saturated concrete exhibits nonlinear expansion at temperatures below freezing, resulting from effective reversal of the CTE sign. This effect has not been considered in the literature, when investigating thermal actions on bridge decks in cold temperatures. The aim of this study is to analyze, using an advanced nonlinear F.E. platform, the structural response of a prestressed concrete box bridge structure subjected to cold wave events, when considering the effect of temperature on the nonlinearity, the magnitude and the sign of the CTE of concrete. Meteorological data from three historical cold events of different intensity is input in the thermal models to simulate the temperature distribution in the bridge deck; the estimated temperature field was then used in a structural model to determine the resulting thermal stresses. The temperature-dependence and nonlinearity of the CTE is modeled after calibration of the mathematical relationships against published data. The results indicate that this behavior has a significant influence on structural response, highlighting the need for pertinent consideration of its effect in the relevant sections of the bridge codes.

Coupled thermal-mechanical analysis of power electronic modules with finite element method and parametric model order reduction

This work presents a new approach for performing a parametric study and examining nonlinear material behaviours of a coupled thermal-mechanical model of a Power Electronics Module (PEM) by integrating the Finite Element Method (ANSYS-FEM) with Parametric Model Order Reduction (pMOR). The considered coupling method solves the thermal and structural models concurrently compared to the widely practised sequential coupling method. Instead of constant parameter values, which are generally regarded for pMOR studies, the temperature-dependent material properties of the wire material have been parametrised in the work using the pMOR method. A generalised 2D model has been regarded here for thermal-mechanical analysis with the pMOR approach, parametrising temperature-dependent coefficient of thermal expansion (CTE) and Young’s modulus (E) of the wire material to explore their impact on wire bonds. The matrix interpolation method has been applied here for the pMOR study, and PRIMA, a Krylov subspace-based model order reduction (MOR) technique, has been exercised for local model order reductions. A new efficient process of matrix interpolation, based on the Lagrange interpolation technique, has been developed to implement matrix interpolation in the parametric reduced order model (pROM). The local reduced order models (ROMs) have a degree of freedom (DOF) of just 8, compared to the full-order models’ (FOMs) of 50,602. The pROM provides an excellent solution and reduces computational time by 84% for the presented case.

Investigation of the anisotropic thermal expansion of PbIn6Te10 crystal by high temperature x-ray diffraction measurements

The PbIn6Te10 crystal, an IR laser frequency conversion material, grown via the Bridgman method with dimensions ϕ35 mm × 90 mm in a four-zone furnace, was subject to the investigation of its thermal expansion behavior using high-temperature x-ray diffraction in the range of 25–450 °C. Based on the obtained data, the average thermal expansion coefficients of 15.21 × 10−6 K−1 for α a and 6.44 × 10−6 K−1 for α c were determined utilizing the least square method. The study revealed that the linear and volume thermal expansion coefficients of PbIn6Te10 crystals satisfy the relationships α a > α c > 0, α V = 2α a + α c , and α a increased while α c decreased with increasing temperature, accentuating a substantial anisotropy in thermal expansion between the crystal’s principal axes. A detailed exploration pinpointed that the variations in the PbTe6 octahedron primarily governed the changes in the PbIn6Te10 unit cells, with further investigation uncovering its association with variations in the nearest neighboring bonds, which is mainly related to Pb-Te4 and Pb-Te2 bonds. Additionally, the determination of temperature-dependent anisotropic thermal expansion coefficient α was complemented by calculating Grüneisen parameter γ using Quasi-harmonic Debye model. Remarkably, these parameters also exhibited anisotropic behaviors ( γ⊥ increases with temperature whereas γ// decreases, α ⊥ > α ∥), contributing additional insights into the crystal thermal characteristics.

Anharmonic phonon scattering study in wide bandgap semiconductor β -Ga2O3 by Raman spectroscopy

The low thermal conductivity of β-Ga2O3 single crystal imposes limitations on its device performance under high-temperature and high-power conditions. Phonons are widely recognized to play the main role in heat transport, while the anharmonic scattering among these quasi-particles significantly diminishes thermal conductivity. Therefore, investigating the anharmonic phonon scattering within β-Ga2O3 single crystal holds paramount significance. In this study, we mainly employed temperature-dependent Raman spectroscopy and first-principles calculation to give a quantitative analysis on the anharmonic phonon scattering. The mode Grüneisen parameters and temperature-dependent thermal expansion coefficient were studied. Strong anharmonic phonon scattering was also confirmed, which was mainly caused by cubic scattering, but quartic scattering is also nonnegligible and causes nonlinear linewidth broadening. Moreover, high wavenumber peaks are more likely to undergo asymmetric phonon scattering by comparing the symmetric and asymmetric scattering models. In all, this study provides a profound understanding of the anharmonic phonon scattering properties within the β-Ga2O3 single crystal. It enriches our understanding of quasi-particle interaction dynamics and offers theoretical pathways for expanding the applications of β-Ga2O3 single crystal and optimizing its device performance.

The Evolution of Microwave-Induced Thermoacoustic Signals Generated During Pulsed Microwave Ablation in Bovine Liver

The temperature dependence of microwave-induced thermoacoustic signals generated in tissue may be exploited to monitor microwave ablation in real-time. We present an experimental study investigating the evolution of microwave-induced thermoacoustic signals that are generated within an ablation zone during microwave ablation in bovine liver tissue. An X-band interstitial coaxial ablation antenna is used to simultaneously heat liver tissue to temperatures up to 90 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{\circ }$</tex-math></inline-formula> C and excite thermoacoustic signals via the absorption of pulsed microwave energy. Thermoacoustic signals are detected using a single-element ultrasound transducer located at the surface of the tissue. Both fresh and boiled liver tissue samples are used in experiments to decouple the influence of temperature and tissue coagulation on thermoacoustic signal characteristics. We identify two thermoacoustic signal characteristics of interest: arrival time of the pulse at the ultrasound receiver and the energy in the pulse. We find that the time difference of arrival over the course of microwave ablation grows in magnitude due to temperature-dependent speed of sound and tissue shrinkage. Thermoacoustic signal energy generally increases throughout microwave ablation, implying an increasing temperature-dependent thermal expansion coefficient of liver tissue. Of the two characteristics, time difference of arrival shows the most promise as a trackable feature for monitoring microwave ablation in real time.

Thermally Induced Pore Pressure Build Up in Saturated Porous Low Permeable Formation

Heating a saturated low permeable geological formation induces pore pressure build-up, so-called thermal pressurization, due to the difference in thermal dilation of the solid skeleton and the pore water. The excess pore pressure generally leads to a decrease in the effective stress and can provoke thermally hydraulic fracturing or shear failure. This paper aims at deriving an explicit solution of the pore pressure increase as a linear function of the temperature variation and total mean stress variation in the framework of linear poroelasticity under undrained conditions. The thermal pressurization coefficient is deduced and then under the condition o constant total stress, which is a function of the difference between the thermal expansion coefficients of the pore water and the porous medium, porosity, bulk moduli of water, porous medium and solid phase. The finite element solution is used to show the accuracy of mathematical development. The presence of this solution allows evaluation the effect of temperature dependent thermal expansion coefficient and temperature and pressure dependent bulk modulus of water. An equivalence between thermo-poro-elastic and thermo-elastic problems are established. This equivalence allows determining the pore pressure from a thermo-mechanical simulation. Moreover, the undrained dilation coefficient and undrained bulk modulus are also derived from this analysis.

Calculation of Temperature-Dependent Thermal Expansion Coefficient of Metal Crystals Based on Anharmonic Correlated Debye Model

This study aims to calculate the anharmonic thermal expansion (TE) coefficient of metal crystals in the temperature dependence. The calculation model is derived from the anharmonic correlated Debye (ACD) model that is developed using the many-body perturbation approach and correlated Debye model based on the anharmonic effective potential. This potential has taken into account the influence on the absorbing and backscattering atoms of all their nearest neighbors in the crystal lattice. The numerical results for the crystalline zinc (Zn) and crystalline copper (Cu) are in agreement with those obtained by the other theoretical model and experiments at several temperatures. The analytical results show that the ACD model is useful and efficient in analyzing the TE of coefficient of metal crystals.

Exceptional strength-ductility combination of additively manufactured high-entropy alloy matrix composites reinforced with TiC nanoparticles at room and cryogenic temperatures

The cryogenic mechanical properties and deformation behaviour of additively manufactured (AM) medium/high-entropy alloys (MEA/HEA) and their composites are seldom studied. This work fills this gap by systematically studying the mechanical properties, deformation behaviour and strengthening mechanism of the additively manufactured CoCrFeMnNi high-entropy alloy (HEA) and 2 wt% TiC/CoCrFeMnNi composite (HEC) at room (293 K) and cryogenic (93 K) temperatures. The TiC nanoparticles promote the densification behaviour, and they are uniformly distributed around and in interior of the cellular substructures of the HEC sample. The tensile tests reveal that the strength and ductility can be simultaneously increased in both HEA and HEC samples when the temperature decreases from 293 K to 93 K. The TiC nanoparticles significantly promote a remarkable combination of strength and ductility in the HEC at both 293 K and 93 K, and the cryogenic tensile strength of HEC (1506 ± 6.6 MPa) is the highest value reported for AM-fabricated MEA/HEAs. For the HEA sample, the significant increase in strength and ductility is attributed to an additional hardening contribution induced by multiple twin systems at 93 K, which results in a steady and even increased strain hardening rate. When the temperature decreases from 293 K to 93 K, a remarkable yield strength increment (344.4 MP) is found in the HEC sample, which is significantly higher than that of HEA (229.0 MPa). The difference in the increase in yield strength between HEA and HEC sample is ascribed to the difference in dislocation strengthening and Orowan strengthening, which are related to the temperature-dependent thermal expansion coefficient and elastic modulus, respectively. However, the HEC sample has a smaller ductility increase (10.3%) than the HEA sample (26.4%), since no additional hardening mechanism is generated during the cryogenic deformation in the HEC sample. This research provides a new route to design materials with a good combination of strength and ductility for cryogenic applications.

Thermophysical properties of balsa wood used as core of sandwich composite bridge decks exposed to external fire

The load-bearing performance of sandwich bridge decks comprising a balsa core and fiber-reinforced polymer composite face sheets exposed to fire is a main concern regarding the application of these deck systems. In order to obtain the thermal responses of the balsa core exposed to fire, the temperature-dependent values of thermal conductivity and specific heat capacity are required. Furthermore, information about the char depth and charring rate and the temperature-dependent coefficient of thermal expansion is also needed for the subsequent thermomechanical modeling. In the current study, the effective thermal conductivity and specific heat capacity of balsa up to 850 °C were obtained from one-dimensional transient heat transfer models and experimental data using an inverse heat transfer analysis. The results showed that both properties depend significantly on the stages of combustion, direction of heat flow (in the tracheid or transverse direction) and density. Moreover, charring temperatures and rates were obtained, again as a function of direction and density. Finally, the coefficient of thermal expansion was measured in the transverse direction during evaporation and pyrolysis.

Electron-phonon coupling, thermal expansion coefficient, resonance effect, and phonon dynamics in high-quality CVD-grown monolayer and bilayer MoSe2

Probing phonons, quasiparticle excitations, and their coupling has enriched our understanding of two-dimensional (2D) materials and proved to be crucial for developing their potential applications. Here, we report comprehensive temperature 4--330 K and polarization-dependent Raman measurements on monolayer (1L) and bilayer (2L) ${\mathrm{MoSe}}_{2}$. Phonon modes up to the fourth order are observed, including forbidden Raman and infrared modes, and understood considering the Fr\"ohlich mechanism of exciton-phonon coupling. Most notably, anomalous variations in the phonon linewidths with temperature point at the significant role of electron-phonon coupling in these systems, especially for the out-of-plane (${A}_{1g}$) and shear modes (${E}_{2g}^{2}$), which is found to be more prominent in the narrow-gapped 2L than the large gapped 1L. We deciphered the ambiguity in symmetry assignments, especially to the peaks \ensuremath{\sim}170 and $\ensuremath{\sim}350\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{--1}$ via polarization-dependent measurements. Temperature-dependent thermal expansion coefficient, an important parameter for device performance, is carefully extracted for both 1L and 2L by monitoring the temperature dependence of the real part of the phonon self-energy parameter. Our temperature-dependent in-depth Raman studies pave a way for uncovering the deeper role of phonons in these 2D layered materials from a fundamental as well as application point of view.

Investigation of Temperature-Dependent Magnetic Properties and Coefficient of Thermal Expansion in Invar Alloys.

Invar Fe–Ni alloy is a prominent Ni steel alloy with a low coefficient of thermal expansion around room temperature. We investigate the correlation between magnetic properties and thermal expansion in cold-drawn Fe–36Ni wires with different heat treatment conditions, where the annealing parameters with furnace cooling (cooling from the annealing temperature of 300, 400, 500, 600, 700, 800, 900, and 1000 °C) are used. The variation trend of magnetic properties is consistent with that of thermal expansion for all samples, where the maximum appears at 600 °C -treated sample and 400 °C shows the minimum. The domain size and the area of domain walls determine the total energy of the domain wall, and the total energy directly determines the size of magnetostriction, which is closely related to the coefficient of thermal expansion. Also, the differential thermal analysis (DTA) shows endothermic and exothermic reactions represent crystalline transitions, which could possibly cause the abrupt change of magnetic properties and thermal expansion coefficient of materials. The results indicate that there is a certain relation between thermal expansion and magnetic properties. Besides the fundamental significance, our work provides an Invar alloy with a low coefficient of thermal expansion for practical use.

Determination of temperature dependent static Young's modulus of refractory ceramics using RUL tests

AbstractRefractory linings are, in addition to loads due to corrosion and creep processes, particularly affected by thermomechanical stresses caused by the restricted thermal expansion of the lining. These stresses can occur within individual components as well as in bricks and can lead to plastic deformation, cracks, and material failure. Thus, comprehensive knowledge about thermomechanical behavior is mandatory for an accurate prediction of occurring stresses to design load‐optimized linings. This paper presents a method for utilizing refractoriness under load (RUL) tests to determine a temperature dependent static Young's modulus for refractories. In a first step, RUL tests with a negligible load are carried out in order to determine the materials temperature dependent thermal expansion coefficient. Afterwards, several RUL tests with higher loads are carried out. The measured data of change in temperature and length are then corrected by the thermal expansion and used to construct elastic lines for several temperatures, where the elastic slope is determined using the change in length and the respective load. Thus, Young's modulus for several temperatures can be determined. The obtained values for the Young's modulus are then compared to resonant frequency damping analysis measurements and validated using a finite element (FE) model of the RUL test.

A methodology for predicting processing induced thermal residual stress in thermoplastic composite at the microscale

A computational finite element (FE) model of thermal residual stress was developed for carbon fiber/thermoplastic composites at the microscale and implemented via user material subroutine (UMAT) in ABAQUS. This model accounts for cooling-rate effects on crystallinity and stress-free temperature, temperature-dependent elastic modulus, temperature-dependent coefficient of thermal expansion (CTE) of the matrix, and the temperature-independent transversely isotropic properties of the carbon fiber. Results are generated for a model composite, consisting of a single carbon fiber embedded in a polypropylene thin film. Single filaments are pre-tensioned in the polymer melt to induce different levels of residual axial strain as well as maintain straight fibers during cool-down. Three different preload conditions (1g, 4g, and 8g) were experimentally fabricated and modeled. The residual strain along the length of the fiber is quantified and validated including the shear lag region that develops at the free edge of the sample. Experimentally measured residual strain shows a good correlation with the FE predictions for the applied fiber preloading conditions.

A multi-material topology optimization with temperature-dependent thermoelastic properties

This is a study on the development of a novel multi-material topology optimization scheme considering temperature-dependent thermoelastic properties for engineering structure design. Two cases, a three-point-bending beam under a uniform temperature field and a cantilever beam under a non-uniform temperature field, are investigated for the effects of thermoelastic properties on topology optimization. The proposed optimization scheme is compared with two existing topology optimization approaches: conventional topology optimization and thermoelastic topology optimization. The results show that the temperature-dependent elastic modulus dominantly influences the design optimization outcomes, in terms of material distribution, structural shape and compliance, while the temperature-dependent thermal expansion coefficient has a much more crucial impact on determining the material distribution and structural geometry than on compliance. Taken together, the findings demonstrate that the developed topology optimization scheme can be used to design thermally sensitive multi-materials in industrial applications, e.g. aerospace structures under high temperature and polymers in additive manufacturing.

The Features of Martensitic Transformation in 12% Chromium Ferritic-Martensitic Steels.

An anomaly in martensitic transformation (the effect of martensitic two-peak splitting in the temperature-dependent thermal expansion coefficient) in complex alloyed 12% chromium steels Fe-12%Cr-Ni-Mo-W-Nb-V-B (ChS-139), Fe-12%Cr-Mo-W-Si-Nb-V (EP-823) and Fe-12%Cr-2%W-V-Ta-B (EK-181) was investigated in this study. This effect is manifested in steels with a higher degree of alloying (ChS-139). During varying temperature regimes in dilatometric analysis, it was found that the splitting of the martensitic peak was associated with the superposition of two martensitic transformations of austenite depleted and enriched with alloying elements. The anomaly was subsequently eliminated by homogenization of the steel composition due to high-temperature aging in the γ-region. It was shown that if steel is heated to 900 °C, which lies in the (α + γ) phase region or slightly higher during cooling, then the decomposition of austenite proceeds in two stages: during the first stage, austenite is diffused into ferrite with carbides; during the second stage, shear transformation of austenite to martensite occurs.

Thermo-elastic properties of bcc Mn-rich high-entropy alloy

We report a chemically disordered solid solution, Al0.6Cr0.2MnFe0.5Co0.3Ni0.5, based on a body-centered cubic underlying lattice with the measured Curie temperature of ∼380 K. First-principles alloy theory is employed to investigate the temperature-dependent free energy, elastic constants, and coefficient of thermal expansion at the ferromagnetic and paramagnetic states. Theory and experiment are found to strengthen each other, and the results indicate that the magnetic state has a strong impact on the thermo-elastic properties of the considered alloy. The present advance in the thermo-magneto-elasticity enhances the understanding required for controlling the magnetic and mechanical response of multi-component systems.

Temperature-dependent Raman spectroscopy studies of 1–5-layer WSe2

In this work, Raman measurements of 1–5-layer WSe2 supported on SiO2/Si in the temperature range of 133 to 533 K are reported. A physical model including both volume effect and temperature effect is used to quantitatively understand the nonlinear temperature dependence of $$\rm{E}_{2g}^1$$ Raman mode. It is found this nonlinear dependence of Raman mode mainly originates from thermal expansion effect and three-phonon scattering. The former effect increases with an increase in number of layers, which is inverse for the latter effect. The temperature-dependent thermal expansion coefficients of 1–5-layer WSe2 are also obtained from Raman spectra. The full width at half maximum (FWHM) of $$\rm{E}_{2g}^1$$ mode is also systematically studied both experimentally and theoretically in the temperature range of 133 to 413 K. It is found that the increase in FWHM of $$\rm{E}_{2g}^1$$ mode originates from decaying of E2g1 phonon. This work will promote the understanding of anharmonic behaviors of phonons in WSe2 flakes with different thicknesses.

Synchrotron Based Measurement of the Temperature Dependent Thermal Expansion Coefficient of Ammonium Perchlorate

AbstractAmmonium perchlorate is commonly used as an oxidizer in solid rocket propellant. Having a knowledge of its thermal expansion properties is essential for its application in different environments. Knowledge of thermal expansion properties is also useful for the prediction of propellant mechanical properties and response of propellant slow cook off applications. X‐ray diffraction analysis was performed on ammonium perchlorate at temperatures ranging from 260 K to 500 K. From there, Bragg peaks were indexed by fitting theoretical values of 2θ to the 2θ values of peaks obtained from the experiment. The Miller indices along with the 2θ values were then used to solve for the lattice parameters at each temperature. The lattice parameters, in nanometers, range from 0.9201 to 0.9373, 0.5805 to 0.5865, and 0.7439 to 0.7535 for a, b, and c, respectively. The measurement of the lattice parameter expansion leads to the determination of the temperature dependent thermal expansion coefficients within the temperature range. The lattice parameter values also lead to the determination of strain and stress on the ammonium perchlorate crystal. Direct measurement of the strain within the crystal lattice provides a more accurate measurement method over traditional optical‐based techniques.

Dominant ZA phonons and thermal carriers in HfS2

Through a systematic study of HfS2 based on density functional theory calculations using the quasiharmonic approximation, we show that out-of-plane ZA phonons alone are responsible for 80% of the thermal transport—both in-plane and out-of-plane. The calculations determine the temperature-dependent structural, phonon, and thermal properties in HfS2. The cause is the uncommonly strong interlayer van der Waals interaction relative to its in-plane interaction. The highly anisotropic interactions also give rise to a combination of effects including anisotropic phonon group velocities, a large ZA-optical phonon gap, and a vanishing Grüneisen parameter in ZA modes that leads to large phonon lifetimes. In turn, these enable other unusual properties. HfS2 can have either a negative (T&amp;lt;40 K) or positive (T&amp;gt;40 K) temperature-dependent thermal expansion coefficient and an exceptionally large LO-TO splitting.

Thermodynamics of solid Sn and Pb[sbnd]Sn liquid mixtures using molecular dynamics simulations

We present a new set of modified embedded-atom method parameters for the PbSn system that describes many 0 K and high temperature properties including melting point, elastic constants, and enthalpy of mixing for solid and liquid PbSn alloys in agreement with experiments. Then, we calculate the phase diagram of the Sn-rich side of PbSn alloys utilizing a hybrid Molecular Dynamics/Monte Carlo simulation that agrees with experimental solidus and liquidus curves as well as stability of α-Sn and β-Sn. In addition, we present structure factors of PbSn liquid alloys as well as temperature-dependent thermal expansion coefficients and heat capacity. Our simulations show that the ratios of the heights of the second and third peaks over the first peak for PbSn liquid mixtures are maximum at Pb-0.6Sn concentration.