Temperature Dependence Of Thermal Expansion Research Articles

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.

Numerical simulation and experimental validation of bending and curling behaviors of liquid crystal elastomer beams under thermal actuation

The exceptional actuation properties of liquid crystal elastomers (LCEs) have made these materials highly attractive for various emerging applications such as soft robotics and artificial muscles. The large strain gradients occurring under thermal stimuli induce bending and curling of initially flat LCE films. Due to the complex physics behind the spontaneous deformation in nematic liquid crystal elastomers, there is no single universal finite element-based method for the simulation of the behaviors of LCE actuators. In this work, we developed a simple layered 2D model for modeling and simulation of the bending and curling characteristics of LCE beams based on the gradient of the temperature-dependent equivalent thermal expansion. The appropriate parameters were derived by measuring the radius of curvature of the LCE film aligned unidirectionally at one surface produced on a rubbed Kapton film. It was found that in a large range of thicknesses (12–134 μm) of the LCE beams, the equivalent thermal expansion coefficients tend to approach a similar value. It was demonstrated and experimentally validated that the thermal expansion model is very effective in predicting the nonlinear curling behavior of LCE beams of various thicknesses. Remarkably, the model is also capable of simulating the rolling behavior of LCE beams with tapered thickness variation. The proposed method offers good flexibility in terms of the geometric shape and expansion parameters, computational efficiency, and accuracy.

Temperature dependence of thermal expansion of solids: A new approach in the terms of the Lambert function

The new equation for the temperature dependence of the thermal expansion of solids is explicitly presented in terms of the Lambert function. The resulting expression is suitable for a wide class of solids in the entire temperature range of the solid phase, in which, upon heating, there are no other phenomena causing changes in atomic volume, such as phase or glass transitions and the formation of vacancies. At temperatures well below the Debye temperature, the new equation provides a linear correlation between thermal expansivity and specific heat in accordance with Grüneisen's law. Whereas at intermediate temperatures not exceeding half the melting point, the [1/1] and [1/2] Padé approximants of the present equation reduce to the Grüneisen expressions in the second and third order of approximation. Unlike the previous ones, the new equation predicts a sharp increase in expansivity at high temperatures in accordance with experiment.

Brucite (Mg(OH)2) under small perturbation: A combined first principles and synchrotron X-ray diffraction study

In this work, we discuss the discrepancy observed in previous experimental and theoretical studies in determining hydrogen's position in brucite (Mg(OH)2) at ambient conditions with the aid of temperature dependent synchrotron x-ray powder diffraction (XRPD) and first-principles calculation based on density functional theory. To date, the literature reports two competing descriptions of brucite's ground state structural configuration based on P-3m1 and P-3 symmetry without a conclusive choice for the best solution. Our study confirms that Mg(OH)2 exists in P-3m1 structure at 0 GPa and 0 K from its lattice dynamical and mechanical stability. Transition from P-3m1 to P-3 symmetry occurs under small structural perturbation causing a volume compression. We show with the aid of temperature dependent XRPD that perturbations causing a small volume compression can lead to a transition in brucite from hydrogen ordered (P-3m1 symmetry) to hydrogen disordered (P-3 symmetry) structure. DFT calculations with different exchange-correlation potentials show that the contradicting results among previous static calculations can be resolved by the use of a van der Waals density functional. Further, we report temperature dependent thermal expansion of brucite in the temperature range 110–400 K.

Factors Influencing Ultrasonic Wave Propagation in Tourmaline

P-wave propagation velocity in tourmaline is related to its microstructure, chemical composition, temperature, and other factors. The effects of tourmaline density, FeO contents, and temperature on P-wave propagation were studied in this paper. The results show that the temperature affects P-wave velocity due to the temperature dependence of thermal expansion, and elastic and dielectric constants of tourmaline. The propagation velocity of P-wave decreases with increasing porosity or FeO content. The content of FeO in tourmaline can be used as the basis for the determination of different species of tourmaline, which provides an important experimental basis for ultrasonic waves to be used as a nondestructive testing technology to distinguish different types of tourmaline.

Deformational and magnetic effects in Cu–Al–Mn alloys

A comparative analysis of the magnetic, size and deformation effects of martensitic transformation in aged Cu–Al–Mn alloys with a minimum width of the temperature hysteresis was performed. According to the experimental studies of the behavior of alloys during martensitic transformations, the changes in temperature dependences of thermal expansion, magnetic susceptibility and electrical resistance, depending on preliminary thermomagnetic treatment of alloys, were found. The thermomagnetic treatment contributes to a change in the magnitude of volume effect of martensitic transformation. Using magnetic analysis, the state and distribution of precipitated particles, affecting both the magnetic characteristics and the volume effects of martensitic transformation in the alloys, were determined.

Temperature dependent elastic constants and thermodynamic properties of BAs: An ab initio investigation

We present an ab initio study of the temperature dependent elastic constants of boron arsenide, a semiconductor that exhibits ultra-high thermal conductivity and is under investigation for thermal management in electronics. We test the consistency of our predictions by computing the temperature dependent sound velocity of the longitudinal acoustic mode along the [111] direction and comparing with experiments. Furthermore, as a by-product, we present the room temperature phonon dispersions and the temperature dependent thermal expansion, isobaric heat capacity, and average Grüneisen parameter compared with the most updated experiments and previous calculations when available. Finally, we present the theoretical estimate of the temperature dependent mean square atomic displacements.

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.

Analysis of equations of state as applied to thermoelastic properties of C60 crystalline solid

In the present paper, an attempt has been made for the comparative study of different equations of state and investigated the thermodynamic and thermoelastic properties for C60 crystalline solid. We have fitted the experimental compression curve to the modified Tait’s equation of state. Using the best fit values of B0 and B0′, we have computed the compression behavior of C60 crystalline solid in the face-centered-cubic structure in the pressure range of 0–11 GPa at room temperature. Tait’s EOS has further extended to analyze the temperature dependence of thermal expansivity and bulk modulus for C60 crystalline solid. We have attempted for theoretical prediction of pressure-dependent Gruneisen parameter and isothermal bulk modulus for C60 crystalline solid at reference temperature. The calculated values of thermal expansion are in good agreement with the available theoretical and experimental results, which reveals the validity of present work. The results of the coefficient of thermal expansion achieved in the present study are found to display good agreement with other available results. The present relationship of thermal expansivity may be used to understand the temperature behavior of nanomaterials.

The Effect of a Uniform Stationary Temperature Field on the Stress-Strain State of Elastomers under Static Large Deformations

The formulation of the problems of thermoelasticity is demonstrated, taking into account the nonlinear temperature dependence of thermal expansion at finite strains. In the framework of this formulation, a significant effect of the thermal expansion of elastomers on the stress-strain state is shown. As an example, the isothermal deformation of a round elastomeric cylindrical sleeve with the potential energy of the Mooney—Rivlin strain subjected to longitudinal shear forces on the inner and outer side surfaces is considered. Further, the deformed sleeve is placed in a uniform temperature field in which it expands freely.

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<40 K) or positive (T>40 K) temperature-dependent thermal expansion coefficient and an exceptionally large LO-TO splitting.

Electrical resistivity under pressure and thermal expansion of LaPt2Si2 single crystal

We have performed electrical transport under pressure and thermal expansion measurements on a LaPt2Si2 single crystal. The charge density wave (CDW) transition temperature TCDW decreases, while the superconducting transition temperature TC increases with the application of pressure, which confirms the competing nature of the two phases. We present an attempt to understand the pressure (P) dependence of TCDW within the framework of the mean field theory. A well defined anomaly in temperature-dependent relative thermal expansion (ΔL/L0) and the linear thermal expansion coefficient (αa) has been observed around TCDW associated with the structural transformation accompanied by a CDW transition.

A Comment on the Paper Entitled “Temperature Dependence of Interatomic Separation and Bulk Modulus for Alkali Halides” Published in Int. J. Thermophys (2016) 37.65 DOI 10.1007/s10765-016-2069-6

It is emphasized that the formulation developed by Liu by taking into account the variation of the Anderson–Gruneisen parameter with volume for the temperature dependence of thermal expansivity is not consistent with the earlier studies performed by Anderson and coworkers. The results obtained from the Liu formulation do not present any improvement over the Anderson model which is based on the constant value of the Anderson–Gruneisen parameter independent of temperature for a given material.

Thermal-induced irreversible straining of ultrathin boron nitride nanosheets

We investigate the thermal-induced mechanical deformations in mono- and few-layer hexagonal boron nitride nanosheets (BNNSs) on flat silicon dioxide substrates by using atomic force microscopy and Raman spectroscopy techniques. The measurements reveal that the deformation of thin BNNS follows the reversible expansion/contraction of the substrate at relatively low temperatures. Irreversible deformations in BNNS are observed at elevated temperatures, which are attributed to interfacial sliding on the BNNS-substrate interface that is caused by the temperature-dependent thermal expansion mismatch of BN and substrate materials. Monolayer BNNS is found to possess the highest onset temperature of irreversible straining, which decreases with an increase in the BNNS thickness. The interfacial load transfer characteristics of the BNNS-substrate interface are quantitatively investigated using a micromechanics model. The analysis reveals that monolayer BNNS possesses a maximum interfacial shear strength of about 28.38 MPa on its binding interface with substrates at about 525 °C. The findings are useful to better understand the fundamental structural and mechanical properties of BNNS and in pursuit of its applications, in particular, those involved with high temperature processing and/or working environments.

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.

The Zero Point Position in Morse’s potential and accurate prediction of thermal expansion in metals

The analytical expression for the matrix elements between Morse’s wavefunctions is shown and a modified temperature-dependent Morse potential was developed and validated. The developed formulae indicate that anharmonicity is responsible for a non-null displacement with respect to the equilibrium position at 0K, that we call Zero Point Position. With their advantage of being computationally inexpensive and fast, the present model can be used to provide highly accurate theoretical estimation in the internuclear distance at vibrational ground state as well as their temperature dependence for not only diatomic but also polyatomic molecules. The present theoretical model was implemented to the development of a simple atomic-level model for the estimation of temperature-dependent thermal expansion coefficients of bulk metals, and was proved to be an efficient and rapid way for the evaluation of material mechanic properties. These models are analytical and are successfully tested on a series of metals.

Elastic properties of Mn-rich α intermetallic phase in engineering aluminum alloys: An ab initio study

The α intermetallic phase can be found in almost all aluminum alloys used in engineering, primarily because of the presence of unwanted but unavoidable impurities from primary production or recycling. There are ample examples showing that α intermetallic particles act as damage nucleation sites during forming operations. To achieve an in-depth understanding of these particles as damage nucleation sites, it is important to know their thermomechanical behavior, as well as their interactions with the matrix during production and service. Despite their importance, however, the mechanical properties of the α intermetallic phase, such as the elastic modulus and the thermal expansion, have not been very well studied. Here, we apply ab initio methods to study the mechanical properties of the α intermetallic phase, with the focus on two polymorphs of the Mn-rich α phase: Al114Mn24 and Al108Mn24Si6. Besides the ground-state elastic properties, the temperature-dependent thermal expansion coefficient and bulk modulus are also calculated. As a case study, these calculated properties are used as input to an Eshelby-type eigenstrain model to evaluate the thermal residual stress of a spherical α-phase particle in an aluminum matrix during a cooling process.

Temperature-dependent thermal expansion of graphene

In this paper the coefficient of thermal expansion of graphene is calculated by a new method based on the thermodynamics parameters. First, the graphene is investigated at zero temperature and then the changes made by temperature are studied. The Brenner many-body potential and harmonic oscillator model are employed to describe the interactions between carbon atoms in the graphene. The results show that the coefficient of thermal expansion of graphene is negative and tends toward zero by increasing the temperature which is in good agreement with reported experimental results. The approach presented in this paper can be used to predict theoretically the CTE of other structures of carbon such as nanotubes and composites.