Temperature Dependence Of Thermal Expansion Research Articles

Crystal structure, oxygen nonstoichiometry and properties of Pr1-xSrxCoO3-δ

The crystal structure, oxygen content and homogeneity range of Pr1-xSrxCoO3-õ solid solutions from room temperature (RT) up to 1100 °C in air were studied. It has been shown that an increase in temperature and Sr content causes an Orthorhombic → Rhombohedral → Cubic transformation of the crystal structure. The heterovalent substitution of Sr2+ for Pr3+ is compensated by an increase in the mean oxidation state of Co ions (zCo) and the formation of oxygen vacancies. The temperature dependences of thermal expansion and conductivity of Pr1-xSrxCoO3-õ solid solutions are explained from the point of view of crystal and defect structure. The diagram of phase relation in the PrCoO3 – “SrCoOz” cross section has been constructed.

Anisotropic thermal expansion tensor of β -Ga2O3 and its critical role in casting-grown crystal cracking

Thermal expansion tensor represents a key parameter for the numerical modeling of the crystal growth process. However, the modeling of β-Ga2O3 commonly utilizes one single thermal expansion constant that misses its anisotropic nature and temperature-dependent characteristics. Herein, we addressed this limitation by calibrating an anisotropic, temperature-dependent thermal expansion tensor using the experimental lattice parameters of β-Ga2O3 up to 1200 K. We found that COMSOL Multiphysics simulations employing the calibrated tensor yield stress distribution remarkably distinct from those relying on the commonly assumed constants. Specifically, our simulations predict a von Mises stress concentration near the crystal bottom, which explains the experimentally observed crack formation at corresponding locations. This contrasts with the simulations using the single-value thermal expansion constant, which fails to predict such stress concentration. The physical origin of crystal cracking is found to be rooted in the compressive force exerted by the iridium crucible during the cooling process. Our findings suggest that the physical anisotropy of β-Ga2O3 should be carefully considered in modeling and simulation. With the calibrated thermal expansion tensor, we provide a validated set of thermomechanical parameters for reliable β-Ga2O3 crystal growth simulations.

Influence of Thermally Aged Underfill on Flip-Chip Packages

Underfill material plays a crucial role in flip-chip package reliability, thus it necessary to accurately understand the mechanical properties. The material itself is nonlinear and is dependent on degree of cure, temperature, strain rate and thermal aging, among others. In this work, two underfill materials were characterized for thermal expansion and viscoelastic properties over a wide temperature range. A second set of each material was thermally aged through flip-chip processing steps and 250 thermal cycles and then characterized. Temperature dependent thermal expansion and timetemperature dependent moduli curves were generated to represent each material type. These material models were then implemented into a nonlinear finite element model of a flip-chip package to evaluate package stress interaction through processing steps and thermal cycling. The influence that each underfill material had with and without thermal aging was analyzed with respect to typical package failure mechanisms.

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.

Asymmetrical LaO9 polyhedron inducing anisotropic positive thermal expansion and moderate lattice thermal conductivity in LaBO3 with isolated planar [BO3] group

Thermal physical properties of inorganic borates are important in application of optical device working under high temperature. Herein, we investigate the temperature-dependent thermoelasticity, thermal expansion(α), and lattice thermal conductivity(κ) of simple orthohomibic LaBO3 with a two dimension like crystal structure though first principles for the first time. The calculated rate of temperature-dependent second elastic constant C11 is significantly larger than that of C22 and C33, and the theoretical slopes of corresponding bulk, shear, and Young's moduli in the range of 300–900 K are −0.0289 GPa•K−1, −0.0156 GPa•K−1, and −0.0398 GPa•K−1, respectively. The predicted α is positive and increases with the rise of temperature. The anisotropic ratio αc/αa or αc/αb is approximately 2 at 300 K, which might be attributed to the difference of elastic compliance S12 and S13. Besides, the anisotropic lattice thermal conductivity κa, κb and κc of LaBO3 is predicted to be 1.43, 1.40 and 0.80 W/m-K at 300 K via Debye-Callaway model. Most importantly, the atomic projected Grüneisen parameters γ reveal that asymmetrical LaO9 polyhedra in the crystal lattice dominate the thermal expansion and lattice thermal conductivity. Our results indicate that LaBO3 has good thermal physical properties working under high temperature.

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.

The Temperature-Dependent Phase Transformation and Microstructural Characterisation in In-Sn Solder Alloys

Indium-based solder alloys are considered candidates for the next generation of low-temperature solder materials, especially for superconducting joints because of the properties of the β-In3Sn phase. The temperature-dependent phase transformation and thermal expansion behaviour of two different solder compositions including In-35Sn (in wt.%) and In-25.6Sn have been characterised using an in situ synchrotron powder X-ray diffraction method. The c-axis of the β-In3Sn unit cell in the In-35Sn alloy exhibited a complex relationship with increasing temperature compared to the positive increasing trend in In-25.6Sn due to the temperature-dependent solubility of Sn in β-In3Sn and change in the volume fraction of phases commencing at 80°C. In situ heating scanning electron microscopy recorded a real-time melting-solidification microstructure variation and phase transition during annealing at 90°C that was further analysed using energy dispersive X-ray spectroscopy. The observations are discussed with respect to the lattice parameters of the γ-InSn4 and β-In3Sn phases and the proportions and composition of both phases present within the alloys.

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 solid solutions of lead zirconate titanate obtained in various solid state states

Phase transitions in PbZrO3 (PZ), PbTiO3 (PT), and solid solutions of Pb(Zr1-xTix)O3 system were studied by dilatometric method. The temperature dependence of thermal expansion and linear coefficient of thermal expansion for both single crystals and ceramic samples exhibit several anomalies corresponding to phase transitions of different origin and correlate to the results of X-ray diffraction studies. The obtained results should be taken into account for development of materials and devices based on the studied solid solutions of Pb(Zr1-xTix)O3 system.

Novel approach in analyzing phase transitions in Na0.5Bi0.5TiO3—Comparison with 0.95Na0.5Bi0.5TiO3–0.05CaTiO3

Recently, Na0.5Bi0.5TiO3 and its solid solutions are receiving intensive study as one of the most perspective lead-free ferroelectrics. Not only physical properties, but also the structure and nature of phase transitions of these compositions are of great interest, as their previous studies contain many uncertainties. In the present research, Na0.5Bi0.5TiO3 and 0.95Na0.5Bi0.5TiO3–0.05CaTiO3 solid solutions were thoroughly studied focusing on the elastic and thermal expansion characteristics, accompanying the obtained results by x-ray diffraction, scanning electron microscopy, differential calorimetry, and second harmonic generation measurements. Temperature-frequency dependences of dielectric permittivity were observed to be similar for both compositions. In spite of this, the experimentally obtained temperature dependences of thermal expansion and Young's modulus in Na0.5Bi0.5TiO3 and 0.95Na0.5Bi0.5TiO3–0.05CaTiO3 reveal unambiguous differences in the temperature range of the observed or expected (as in the case of Na0.5Bi0.5TiO3) phase transitions. X-ray diffraction patterns are fitted using Pnma symmetry. This allows us to distinguish the temperature regions with different behaviors of lattice parameters, which correlate with the observed behavior of thermal expansion and Young's modulus. A reduction in the intensity of second optical harmonic was observed upon increasing the temperature in the whole studied temperature range. This encourages us to reconsider the mechanism responsible for the temperature dependence of dielectric permittivity.

Numerical Study of Heat Transfer in a Gun Barrel Made of Selected Steels

The results of numerical simulations of transient heat transfer in the barrel wall of a 35 mm caliber cannon for a single shot and the sequences of seven shots and sixty shots for chosen barrel steels are presented. It was assumed that the cannon barrel was made of one of the three types of steel: 38HMJ (1.8509), 30HN2MFA and DUPLEX (1.4462). To model the thermal phenomena in the barrel, the barrel wall material was assumed to be homogeneous and the inner surface of the barrel had no protective chromium or nitride layer. The calculations were made for temperature-dependent thermophysical parameters, i.e., thermal conductivity, specific heat and thermal expansion (in the range from RT up to 1000 °C) of the selected barrel steels. A barrel with a total length of 3150 mm was divided into 6 zones (i = 1, …, 6) and in each of them, the heat flux density was calculated as a function of time q˙i(t) on the inner surface of the barrel. Using lumped parameter methods, an internal ballistic code was developed to compute in each zone the heat transfer coefficient as a function of time hi(t) and bore gas temperature as a function of time Tg(t) to the cannon barrel for given ammunition parameters. A calculation time equaling 100 ms per single shot was assumed. The results of the calculations were obtained using FEM implemented in COMSOL Multiphysics ver. 5.6 software.

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.

Thermal expansivity of NaCl and KCl at high temperatures

A new mathematical equation for temperature dependence of thermal expansivity of Alkali halides (NaCl and KCl) has been developed for high temperatures. This relation is used to calculate thermal expansivity of NaCl and KCl for temperature range 350K to 750K along with available values of melting temperature. The results obtained are compared with available data. A good agreement between calculated and available data verifies the validity of obtained relation

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 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.

Impact of three-body interactions in a ReaxFF force field for Ni and Cr transition metals and their alloys on the prediction of thermal and mechanical properties

In this work, we discuss the temperature-dependent elastic constants, thermal expansion and melting temperature of Ni and Cr transition metals using a ReaxFF reactive force field. While the ReaxFF force field has been successfully applied to various chemistries on these transition metals, it cannot replicate the experimentally observed relationship between C12 and C44. In addition, ReaxFF predicts the negative stacking-fault energy for fcc Ni, accelerating the fcc → hcp phase transformation. We show that by introducing three-body interaction parameters to the metal force field, which have not been included previously for transition metals, ReaxFF can successfully predict experimental elastic constants of fcc Ni and bcc Cr at finite temperatures.We then evaluate the thermal lattice expansion at T = 0 – 1700 K and compare to experimental data available in the literature – the higher thermal expansion coefficient corresponds to Ni, which is known to have a lower melting temperature than Cr. To estimate the melting temperature of Ni and Cr using the ReaxFF force field, we performed molecular dynamics (MD) simulations by adopting the hysteresis method. With a sufficiently large system size and void concentration, the melting temperature is predicted to be 1698 K for Ni (agreeing within 1.7%) and 2410 K for Cr (within 10%). Furthermore, we develop a Ni/Cr alloy force field by combining Ni and Cr force fields and optimizing their cross-interaction parameters. It is shown in both ReaxFF and DFT that fcc-based Ni3Cr is the most stable phase with a negative heat of formation while all bcc alloys have positive heats of formation, indicating a possible phase separation for Ni and Cr. The elastic constants at 0 K calculated by ReaxFF agree with DFT values within 5–10%, except for the large deviation in C33.