Thermoelastic Properties Research Articles

Thermodynamic and thermoelastic properties of wurtzite-ZnS by density functional theory

AbstractIn the present paper, we provide a detailed theoretical investigation on fundamental thermodynamic, thermomechanical, and electronic properties of wurtzite ZnS between 0–20 GPa and 0–2000 K, obtained by ab initio density functional theory and the B3LYP functional. Several properties, such as phonon dispersion relations, elastic and piezoelectric constants, and thermodynamic and thermoelastic behaviors were calculated and reported. The analysis of the data via volume-integrated third-order Birch-Murnaghan fitting resulted in K0 = 72.17(4) GPa, K′ = 3.87(1), and V0 = 85.781(1) Å3 at T = 0 K. The Born criteria for the mechanical stability of the mineral phase showed that wurtzite is unstable above about 19 GPa in static conditions. We calculated a direct bandgap for wz-ZnS of 4.86 eV at zero compression, which became an indirect one by increasing pressure above 17 GPa. The results are in good agreement with the experimental and theoretical ones reported in the literature, and further extend the knowledge of an important zinc sulfide phase, for both geological and industrial applications.

Progress in Bulk 4H SiC Crystal Growth for 150 mm Wafer Production

The thermoelastic stress, mechanical properties and defect content of bulk 4H n-type SiC crystals were investigated following adjustments to the PVT growth cell configuration that led to a 40% increase in growth rate. The resulting 150 mm wafers were compared with wafers produced from a control process in terms of wafer bow and warp, and dislocation density. Wafer shape was found to be comparable among the processes, indicating minimal impact on internal stress. Threading edge and threading screw dislocation densities increased and decreased, respectively, while basal plane dislocation densities were unaffected by the increase in growth rate. Loss of wafer planar stability was observed in certain cases. The elastic modulus was measured to be in the range of approximately 420-450 GPa for selected stable and unstable wafers, and was found to correspond to resistivity.

A Method for the Parametrization of the Pairwise Interatomic Potential

Drawbacks of some methods known from the literature for determining four parameters of the Mie–Lennard-Jones pairwise interatomic potential as applied to crystals are pointed out. A new method for parametrization of the potential by thermoelastic properties of the crystal is proposed. The method determines the parameters by the best agreement of the calculated values with experimental data such as (1) the sublimation energy of the crystal at the zero values of the temperature (T = 0 K) and pressure (P = 0), (2) the thermal expansion coefficient and the isothermal modulus of elasticity measured at P = 0 and T = 300 K, and (3) the dependence of the isotherm curve T = 300 K of the equation of state on the volume P(300 K, V). The method was verified for iron and gold and showed good results. Further, the proposed method was applied to determine the parameters of the interatomic potential for refractory metals, viz., Nb, Ta, Mo, and W. The results obtained also allowed for more accurate determination of the sublimation energy, the Debye temperature, and the surface energy of the above metals.

Micromechanics-based modeling of elastic modulus and coefficient of thermal expansion for CNT-metal nanocomposites: effects of waviness, clustering and aluminum carbide layer

A micromechanical model is analytically developed to estimate the elastic modulus and the coefficient of thermal expansion (CTE) of the carbon nanotube (CNT)-reinforced metal matrix nanocomposites (MMNCs). The effects of two important microstructural features, including the CNT clusters and the waviness on the thermo-elastic response are investigated. The formation of aluminum carbide (Al4C3) layer due to the interaction between the CNT and the metal matrix is considered. A good agreement is found between the available experimental data and the simulation results considering the waviness, clustering, and Al4C3 interphase. The influences of volume fraction, and dispersion type of CNTs and Al4C3 layer thickness on the elastic modulus and the CTE of the CNT-metal nanocomposites are examined. The non-straight shape and the clustering of CNTs are two critical factors that can significantly degrade the thermo-elastic properties. From the mechanical viewpoint on designing the CNT-metal nanocomposites, producing the homogeneous microstructure without the CNT clusters and using the straight CNTs are necessary factors to obtain the maximum level of the thermomechanical performances. The numerical results show that the formation of the Al4C3 interphase may improve the MMNC macroscopic engineering constants. It is observed that aligning the CNTs into the metal matrixes leads to a significant improvement in the MMNC thermo-elastic properties. The proposed micromechanical approach can be a suitable model to predict the elastic modulus and the CTE of the CNT-reinforced MMNCs considering the important microstructural features.

Peter Chadwick. 23 March 1931—12 August 2018

Peter Chadwick studied mathematics as an undergraduate at the University of Manchester, graduating with first-class honours in 1952, from where he moved to Cambridge and completed a PhD on the thermal history of the Earth in the Department of Geodesy and Geophysics under the supervision of Dr Robert Stoneley. His research then developed to focus primarily on the propagation of waves, and he made a major contribution to the mathematical theory of elastic wave propagation and became a world-leading authority in this area. He also made fundamental advances in the modelling of the thermo-elastic properties of rubberlike materials. At the University of East Anglia, where he was a professor for 26 years, he was the driving force behind the development of a research group in theoretical mechanics in the School of Mathematics and Physics, leading by example and supporting and encouraging fellow faculty members, especially the younger staff, academic visitors and students. He gave considerable service to the University of East Anglia in a number of capacities, including a period as Dean of the School, and to the scientific community, through substantial journal editorial activities and as a member of several national and international committees.

Robust topology optimization of thermoelastic metamaterials considering hybrid uncertainties of material property

Metamaterials with extreme thermoelastic properties (i.e. thermal expansion and stress) offer significant value in applications that require maintaining thermal geometric stability, e.g., aerospace equipment. However, material uncertainty has a great impact on the thermoelastic properties of such multiphase composites. Thus, a robust topology optimization design for the thermoelastic composites under hybrid uncertainties of material property is investigated. The distribution of base materials in the periodic unit cell is achieved by multi-phase solid isotropic material with penalization method and the equivalent properties of composites are evaluated by the numerical homogenization method. To obtain a clear material interfaces in the unit cell, a filtering method named the element perimeter control method is proposed. Considering the uncertainties of material property, the linear thermal expansion coefficients of two constituent materials are assumed to be a random variable and an interval variable, respectively. A robust topology optimization model based on Polynomial-Chaos-Chebyshev-Interval method is proposed, where the Polynomial chaos and Chebyshev interval functions are integrated to perform uncertainty analysis. The robust objective function is formulated by a combination of average mean, average and bandwidth of standard deviation of the objective value. The effectiveness of the proposed robust topology optimization methodology is illustrated with several numerical examples.

Effect of the hyperbolic two-temperature model without energy dissipation on photo-thermal interaction in a semi-conducting medium

In this article, the generalized model for photo-thermoelastic waves under a hyperbolic two-temperature model without energy dissipation is used to calculate the conductive and thermodynamic temperatures, carrier density, displacement and stress in a semi-infinite semi-conducting medium. Thermo-elastic properties are considered in presence of the coupling of thermoelastic and plasma waves. The analytic solutions for all physical variables are obtained by applying Laplace transform and eigenvalues approach. The results are illustrated graphically to show the difference between the hyperbolic two-temperature model and the classical two-temperature model upon without energy dissipation. We believe that the present study will help to understand the basic features of the new model for heat conduction.

The seismically fastest chemical heterogeneity in the Earth's deep upper mantle—implications from the single-crystal thermoelastic properties of jadeite

Jadeite is a major mineral phase (up to 50 vol%) in the subducted sediments/crust with continental origin, which are one of the major heterogeneities and important enriched geochemical reservoirs (such as EM-1 and EM-2) for incompatible elements in the Earth's interior. Identifying and locating the enriched geochemical heterogeneities requires knowledge of the elastic properties of relevant mineral phases at high pressure-temperature conditions. Unfortunately, the single-crystal elastic properties of jadeite have never been measured at high-pressure conditions, partially due to its low crystal symmetry. In this study, we have experimentally determined the single-crystal elastic moduli of jadeite at high pressures for the first time up to 18 GPa at the ambient temperature condition using Brillouin spectroscopy. Fitting the third-order finite strain equation of state to the velocity-pressure data yields KS0′=3.9(1), G0′=1.09(4) with ρ0=3.302(5) g/cm3, KS0=138(3) GPa, and G0=84(2) GPa. In addition, we have also conducted synchrotron single-crystal X-ray diffraction experiments up to 25 GPa and 700 K. The fitting of a Holland-Powell type thermal-pressure Birch-Murnaghan equation of state yields KT0′=3.8(2) and α0=3.4(5) ×10−5 K−1. Based on the obtained thermoelastic parameters of jadeite, the density and seismic velocities of continent-derived sediments/crust are modeled at the depth range from 200 to 500 km. The seismic velocities of the subducted continental sediments/crust become extremely fast at depths greater than ∼300 km, up to 11.8% and 14.7% faster than the Vp and Vs of the ambient mantle, and 5.6% and 7.3% faster than the Vp and Vs of the subducted oceanic crust. The existence of even a small amount of the subducted continental sediments/crust can result in strong seismic anomalies in the Earth's interior.

Compressibility and thermoelasticity of CrN

ABSTRACT We report experimental determination of compressibility and thermoelasticity for CrN based on in situ high pressure/high temperature synchrotron x-ray diffraction measurements. The pressure-induced cubic-to-orthorhombic phase transition is observed at ∼ 5 GPa in high-quality CrN samples synthesized using a high pressure reaction route. Equation of state, bulk modulus and axial compressibility of this material are obtained by analysis of high pressure x-ray diffraction data collected at room temperature. Both cubic and orthorhombic phases have a similar bulk modulus value of 257 (5) and 262 (6) GPa, respectively. For orthorhombic CrN, the b-axis has the most axial incompressibility, which should be associated with magnetic properties. In addition, the isothermal equation of states is also determined at different temperatures of 300, 400, 600, 800, 1000, and 1200 K, respectively. Some of the important thermoelastic properties of cubic CrN are thus derived, including temperature derivative of bulk modulus and volumetric thermal expansivity where a 0 = 1.95 (16) × 10−5 K−1 and a 1 = 4.39 (3) × 10−9 K−1.

Simultaneous measurement of coefficient of thermal expansion and biaxial modulus of enamel thick films deposited on glass substrates by curvature technique

AbstractThe measurement of the thermoelastic properties of enamel thick films deposited onto soda‐lime silicate glass is challenging. The film properties can be modified by the interdiffusion between the glass substrate and the enamel and by the crystallization that occur during the sintering. The average biaxial modulus and coefficient of thermal expansion of several enamel thick films deposited onto 700 µm glass substrates have been simultaneously measured using the curvature method. The value of the coefficient of thermal expansion measured with a dilatometer on enamel bulk samples is significantly higher, associated with the absence of diffusion and a different enamel structure. The interdiffusion of elements between the enamel film and the glass substrate has been demonstrated with Time‐of‐Flight Secondary Ion Mass Spectrometry (TOF‐SIMS). The amount of porosity ratio presents in the enamel film, evaluated via Scanning electron microscopy(SEM), has a great influence on the biaxial modulus. The amount of compressive stress in the enamel, calculated from the film thermoelastic properties, is strongly correlated with the mechanical performance of enameled glasses, investigated by Ring On Ring methods. Therefore, a high Young's modulus for the enamel and a mismatch of the coefficient of thermal expansion between the enamel film and substrate, the film having the lowest value, has been found to increase significantly the mechanical performance of the stack.

Thermoelastic analysis of FGM hollow cylinder for variable parameters and temperature distributions using FEM

AbstractThis paper presents, numerical study of stress field in functionally graded material (FGM) hollow cylinder by using finite element method (FEM). The FGM cylinder is subjected to internal pressure and uniform heat generation. Thermoelastic material properties of FGM cylinder are assumed to vary along radius of cylinder as an exponential function of radius. The governing differential equation is solved numerically by FEM for isotropic and anistropic hollow cylinder. Additionally, the effect of material gradient index (β) on normalized radial stresses, normalized circumferential stress and normalized axial stress are evaluated and shown graphically. The behaviour of stress versus normalized radius of cylinder is plotted for different values of Poisson’s ratio and temperature. The graphical results shown that stress field in FGM cylinder is influenced by some of above mentioned parameters.

A new domain-independent interaction integral for three-dimensional non-homogeneous thermoelastic materials

This work establishes a new domain-independent interaction integral for the evaluation of mixed-mode stress intensity factors (SIFs) in three-dimensional non-homogeneous materials with complex thermo-mechanical interfaces subjected to thermo-mechanical loadings. A new auxiliary field called Zero-Mean stress field is developed to deal with the mismatch of thermoelastic properties across the material interfaces. An area integral along with the material interfaces, which is indispensable to keep domain-independence of the conventional interaction integral using Williams’ auxiliary fields, is eliminated by using this new auxiliary. A crack-face integral is added to maintain the domain-independence of this new method. The expression of this new domain-independent interaction integral contains no thermal property parameters. Because of this feature, the new interaction integral holds domain-independent for both discontinuous mechanical properties and discontinuous thermal properties. Since tracking crack-planes is much easier than tracking a material interface in numerical implementations, it brings convenience to the practical applications to analyze three-dimensional non-homogeneous materials with discontinuous thermoelastic material properties. The new interaction integral, combined with the finite element method, is applied to investigate several representative examples, which demonstrates that the new interaction integral has good accuracy and domain-independence for thermo-mechanical interfaces.

Thermoelastic homogenization of periodic composites using an eigenstrain-based micromechanical model

This paper presents a study on effective thermoelastic properties of composite materials with periodic microstructures. The overall elastic moduli and coefficients of thermal expansion of such materials are evaluated by a micromechanical model based on the Eshelby equivalent inclusion approach. The model employs Fourier series in the representation of the periodic strain and displacement fields involved in the homogenization procedures and uses the Levin's formula for determining the effective coefficients of thermal expansion. Two main objectives can be highlighted in the work. The first of them is the implementation and application of an efficient strategy for computation of the average eigenstrain vector which represents a crucial task required by the thermoelastic homogenization model. The second objective consists in a detailed investigation on the behavior of the model, considering the convergence of results and efficiency of the strategy used to obtain the approximate solution of the elastic homogenization problem. Analyses on the complexity of the eigenstrain fields in function of the inclusion volume fractions and contrasts between the elastic moduli of the constituent phases are also included in the investigation. Comparisons with results provided by other micromechanical methods and experimental data demonstrate the very good performance of the presented model.

Inverse scattering problem for identification buried object in a thermoelastic layer

This work is devoted to studying a direct and inverse scattering problem by an elliptical void in a thermoelastic layer subjected to a dynamic load. In the context of the linear theory of thermoelasticity, coupled boundary integral equations, in terms of the displacement field and temperature over the contour of the void, are formulated. By measuring the surface oscillations, over a finite-length interval on the upper surface layer, the inverse problem in one mode-frequency range is constructed. So, we have developed an efficient numerical algorithm to identify the size and position of the void in the layer. A series of numerical examples, to check the influence of the thermoelastic properties on the algorithm of detection, has been presented at different noise levels.

Mean-field homogenization of thermoelastic material properties of a long fiber-reinforced thermoset and experimental investigation

Fiber-reinforced polymers contribute significantly to weight-reducing components for various industrial applications. A discontinuous glass fiber-reinforced thermoset resin is considered which is produced by the sheet molding compound (SMC) process. Related to the production process, the samples considered in this work exhibit an anisotropic fiber orientation distribution which highly affects the thermomechanical properties. The thermoviscoelastic material behavior of three selected samples is characterized by means of dynamic mechanical analysis. These tests show the temperature-dependent elastic modulus and the glass transition of the composite. Measurements of the thermal expansion of the SMC composite provide data on the coefficient of thermal expansion (CTE). These experimental investigations provide data for the thermoelastic material modeling. Aiming at the prediction of the effective thermal and mechanical properties, a Hashin–Shtrikman-based homogenization method is presented. Based on an eigenstrain formulation, the effective Young’s modulus and CTE are computed in two steps. Moreover, the mean-field method is given in dependence of a variable reference stiffness allowing to tailor the approach to the material system. The influence of this variable reference stiffness on the effective quantities as well as the predicted behavior is analyzed with respect to the experiments. The presented numerical results are in good agreement with the experimental data.

Thermoelastic properties of MgSiO3-majorite at high temperatures and pressures: A first principles study

As the major component of garnet, the second most abundant phase in Earth's transition zone, MgSiO3-majorite plays a fundamental role in controlling the state and dynamics of Earth's mantle. However, due to challenges of experiments and simulations, there are still very limited data on the elastic properties of MgSiO3-majorite at simultaneously high temperatures and pressures. In this study, we have carried out extensive first principles calculations to determine the thermoelastic properties of MgSiO3-majorite up to 2000 K and 40 GPa. We find that the elastic constants of MgSiO3-majorite change significantly over the temperature and pressure range studied, with noticeable non-linearities in their pressure dependences. The seismic anisotropy of MgSiO3-majorite is high and generally increases with pressure. It is much higher than that of the other end-members of garnet and ringwoodite, which makes it the most anisotropic mineral in assemblages expected in the lower transition zone. Based on our calculated elastic moduli and with careful elimination of systematic errors, we establish a third-order Birch-Murnaghan-Mie-Grüneisen model for MgSiO3-majorite with the parameters: V0 = 114.1 cm3/mol, K0 = 163.6 GPa, G0 = 86.4 GPa, K0′ = 4.44, G0′ = 1.16, γ0 = 1.08, q0 = 0.48, ηS0 = 0.76, and θ0 = 822.5 K. Integrating our results into a thermodynamic model able to predict the properties of mantle assemblages, we find that a pyrolite composition produces velocities that agree with the seismic model AK135 in the upper transition zone. In the lower transition zone, a pyrolite composition fits well with some specific local observations, but a mechanical mixture with 18% basalt and 82% harzburgite is in better agreement with the global seismic model PREM. The much larger abundance of MgSiO3-majorite in the garnet phase of harzburgite suggests that the anisotropy in the lower transition zone may not be negligible and would be observable at least in the heterogeneous zones near subducting slabs.

Optically-excited simultaneous photoacoustic and ultrasound imaging based on a flexible gold-PDMS film

We constructed a flexible gold-polydimethylsiloxane (gold-PDMS) nanocomposites film with controllable thickness and light transmittance, to realize optically-excited simultaneous photoacoustic (PA) and ultrasound (US) imaging under a single laser pulse irradiation. Benefiting from the excellent thermoelastic properties, the gold-PDMS film absorbs part of the incident laser energy and produces a high-intensity US, which is used to realize US imaging. Meanwhile, the partly transmitted light is used to excite samples for PA imaging. By controlling the thickness of the gold-PDMS, we can control the center frequency in the US imaging. We experimentally analyzed the frequency of the produced US signal by the gold-PDMS film and compared it with the finite element analysis (FEA) method, where the experiments agree with the FEA results. This method is demonstrated by the experiments on phantoms and a mouse model. Our work provides a cost-effective methodology for simultaneous PA and US imaging.

Three-dimensional braided composites with zero, negative and isotropic thermal expansion behavior

Three-dimensional braided composites with zero, negative and isotropic coefficient of thermal expansion are presented based on an analytical homogenization technique. The configuration of the braided composites is worked out considering the exact jamming condition leading to higher fiber volume fraction. A total of four configurations of three-dimensional-braided composite representative unit cells were analyzed. Among these, two arrangements are 4-axes and the other two are 5-axes. Special emphasis is given on the detailed description of the representative unit cells. Analysis reveals that a three-dimensional-braided composite configuration with thermoelastic isotropic properties having same coefficient of thermal expansion along x-, y-, and z-axes is achievable. As a special case, the homogenization model is used to predict, for the first time, a configuration of braided architecture and material leading to zero coefficient of thermal expansion along x-, y- and z-directions.

Temperature expansions in the square-shoulder fluid. II. Thermodynamics.

In Paper I [O. Coquand and M. Sperl, J. Chem. Phys. 152, 124112 (2020)], we derived analytical expressions for the structure factor of the square-shoulder potential in a perturbative way around the high- and low-temperature regimes. Here, various physical properties of these solutions are derived. In particular, we investigate the large wave number sector and relate it to the contact values of the pair-correlation function. Then, the thermoelastic properties of the square-shoulder fluids are discussed.

Thermoelastic Properties of K0.7Na0.3AlSi3O8 Hollandite and NaAlSi2O6 Jadeite: Implication for the Fate of the Subducted Continental Crust in the Deep Mantle

The thermoelastic properties of K0.7Na0.3AlSi3O8 hollandite and NaAlSi2O6 jadeite, synthesized from a (K, Na)-felspar (microcline), were investigated by a combination of in situ energy dispersive synchrotron X-ray radiation and multi-anvil techniques at high pressure (P) and temperature (T) up to 21 GPa and 1700 K. The second-order phase transformation was found to occur in hollandite at ~16 GPa from tetragonal I/4m (hollandite-I) to monoclinic I2/m (hollandite-II), which confirms the previous report that the incorporation of Na in the hollandite structure decreases the transformation pressure. Fitting the pressure–volume–temperature data to the Birch–Murnaghan equation of state yielded estimates of the thermoelastic parameters for jadeite as well as the K0.7Na0.3AlSi3O8 hollandite-I and -II phases, which indicate that the incorporation of Na is likely to decrease the bulk moduli of both hollandite phases. The obtained thermoelastic parameters were combined with those of other mantle minerals reported previously to estimate the density of continental materials along an average mantle geotherm. Based on our results, continental crust and sediment become, respectively, 11% and 15% denser than the pyrolitic mantle at pressure >10 GPa, suggesting that once pulled down to the critical depth of ~300 km, the continental portions of the slab can subduct further into the deep mantle, down to the lowermost part of the mantle transition region.