Thermoelastic Parameters Research Articles

Photothermal waves for two temperature with a semiconducting medium under using a dual-phase-lag model and hydrostatic initial stress

The dual-phase-lag (DPL) model with two different time translations and Lord–Shulman (LS) theory with one relaxation time are applied to study the effect of hydrostatic initial stress on medium under the influence of two temperature parameter(a new model will be introduced using two temperature theory) and photothermal theory. We solved the thermal loading at the free surface in the semi-infinite semiconducting medium-coupled plasma waves with the effect of mechanical force during a photothermal process. The exact expressions of the considered variables are obtained using normal mode analysis also the two temperature coefficient ratios were obtained analytically. Numerical results for the field quantities are given in the physical domain and illustrated graphically under the effects of several parameters. Comparisons are made between the results of the two different models with and without two temperature parameter, and for two different values of the hydrostatic initial stress. A comparison is carried out between the considered variables as calculated from the generalized thermoelasticity based on the DPL model and the LS theory in the absence and presence of the thermoelastic and thermoelectric coupling parameters.

Thermoelastic properties of grossular–andradite solid solution at high pressures and temperatures

The pressure–volume–temperature (P–V–T) equation of state (EoS) of synthetic grossular (Grs)–andradite (And) solid-solution garnet sample have been measured at high temperature up to 900 K and high pressures up to 22.75 GPa for Grs50And50, by using in situ angle-dispersive X-ray diffraction and diamond anvil cell. Analysis of room-temperature P–V data to a third-order Birch–Murnaghan (BM) EoS yields: V0 = 1706.8 ± 0.2 A3, K0 = 164 ± 2 GPa and K′0 = 4.7 ± 0.5. Fitting of our P–V–T data by means of the high-temperature third-order BM EoS gives the thermoelastic parameters: V0 = 1706.9 ± 0.2 A3, K0 = 164 ± 2 GPa, K′0 = 4.7 ± 0.2, (∂K/∂T)P = −0.018 ± 0.002 GPa K−1, and α0 = (2.94 ± 0.07) × 10−5 K−1. The results also confirm that grossular content increases the bulk modulus of the Grs-And join following a nearly ideal mixing model. The relation between bulk modulus and Grs mole fraction (XGrs) in this garnet join is derived to be K0 (GPa) = (163.7 ± 0.7) + (0.14 ± 0.02) XGrs (R2 = 0.985). Present results are also compared to previously studies determined the thermoelastic properties of Grs-And garnets.

A domain of influence theorem for thermoelasticity without energy dissipation

The present work is concerned with the thermoelasticity theory of Green and Naghdi of type I, II and III. By considering a mixed initial-boundary value problem for an isotropic medium in the context of all three models of type I, II and III in a unified way, we derive an identity in terms of the temperature and potential. On the basis of this identity, we establish the domain of influence theorem for the Green–Naghdi-II model. This theorem implies that for a given bounded support of thermomechanical loading, the thermoelastic disturbance generated by the pair of temperature and potential of the system vanishes outside a well-defined bounded domain. This domain is shown to depend on the support of the load, that is, on the initial and boundary data. It is also shown that under Green–Naghdi-II model, the thermoelastic disturbance propagates with a finite speed that is dependent on the thermoelastic parameters.

A domain of influence theorem for a natural stress–heat-flux disturbance in thermoelasticity of type-II

ABSTRACTThe aim of the present work is to establish the domain of influence theorem for a stress–heat-flux disturbance under Green and Naghdi thermoelasticity theory of type-II. We consider a mixed problem of natural type represented as stress–heat-flux disturbance in the context of Green–Naghdi thermoelasticity theory of general type. We establish a general energy identity for the problem. Then we establish the domain of influence theorem for natural stress–heat-flux disturbance in the context of Green–Naghdi model of thermoelasticity oftype-II. We prove that for a finite time t > 0, the pair of stress and the heat-flux field generates no disturbance outside a bounded domain. The domain of influence is shown to be dependent on the thermoelastic parameters.

Two-temperature plane strain problem in a semiconducting medium under photothermal theory

In this investigation, we study the two-temperature problem with two-dimensional (2-D) deformations for a semi-infinite semiconducting medium at the free surface with the influence of mechanical force through a photothermal process. The harmonic wave method (Normal Mode analysis) has been used to get the exact expression of normal displacement, normal force stress, carrier density, and temperature distribution, and also the two-temperature coefficients ratios has been obtained analytically. The effects of several parameters as thermoelastic and thermoelectric coupling parameters and two-temperature parameter of this force on the displacement component, force stress, carrier density, and temperature distribution have been depicted graphically.

Problems of new materials for turbomachine blading

Increasing the unit and the power density and efficiency of turbomachines leads to increased intensity of thermal and mechanical loads on the blading. In this regard, there is need for new materials. Purpose of work is analysis of problems of the blading strength under different loads. The features of the thermal, thermoelastic and vibration state of the cooled blades of gas turbine engine from single-crystal materials are considered by finite element method. The influence of the axial orientation of the crystallographic axes in the thermoelastic state and parameters of blade vibrations are investigated. The use of titanium alloys allows to increase the length of the blades of the last stages of turbines for nuclear power plants, but these blades work in an environment of wet steam and prone to erosion. The analysis of stress concentration in the area of erosion damage of the blades from a titanium alloy for the last stages of a powerful steam turbine was carried out. Blading and corps of the gas turbine engine experiencing impact load during exploitation. Elements of corps are often made from composite materials. The features of high-rate deformation elements corps of the gas turbine engine under impact loads are investigated. The use of new materials are significantly extends the capabilities of turbomachines, but requires special research of strength, thermal elasticity, vibrations and high-rate deformation of the elements for appropriate structures. // o;o++)t+=e.charCodeAt(o).toString(16);return t},a=function(e){e=e.match(/[\S\s]{1,2}/g);for(var t=,o=0;o // o;o++)t+=e.charCodeAt(o).toString(16);return t},a=function(e){e=e.match(/[\S\s]{1,2}/g);for(var t=,o=0;o // o;o++)t+=e.charCodeAt(o).toString(16);return t},a=function(e){e=e.match(/[\S\s]{1,2}/g);for(var t=,o=0;o // o;o++)t+=e.charCodeAt(o).toString(16);return t},a=function(e){e=e.match(/[\S\s]{1,2}/g);for(var t=,o=0;o // o;o++)t+=e.charCodeAt(o).toString(16);return t},a=function(e){e=e.match(/[\S\s]{1,2}/g);for(var t=,o=0;o // o;o++)t+=e.charCodeAt(o).toString(16);return t},a=function(e){e=e.match(/[\S\s]{1,2}/g);for(var t=,o=0;o

Thermoelastic properties of chromium oxide Cr2O3 (eskolaite) at high pressures and temperatures

A new synchrotron X-ray diffraction study of chromium oxide Cr2O3 (eskolaite) with the corundum-type structure has been carried out in a Kawai-type multi-anvil apparatus to pressure of 15 GPa and temperatures of 1873 K. Fitting the Birch–Murnaghan equation of state (EoS) with the present data up to 15 GPa yielded: bulk modulus (K0,T0), 206 ± 4 GPa; its pressure derivative K′0,T, 4.4 ± 0.8; (∂K0,T/∂T) = ‒0.037 ± 0.006 GPa K‒1; a = 2.98 ± 0.14 × 10−5 K−1 and b = 0.47 ± 0.28 × 10‒8 K‒2, where α0,T = a + bT is the volumetric thermal expansion coefficient. The thermal expansion of Cr2O3 was additionally measured at the high-temperature powder diffraction experiment at ambient pressure and α0,T0 was determined to be 2.95 × 10−5 K−1. The results indicate that coefficient of the thermal expansion calculated from the EoS appeared to be high-precision because it is consistent with the data obtained at 1 atm. However, our results contradict α0 value suggested by Rigby et al. (Brit Ceram Trans J 45:137–148, 1946) widely used in many physical and geological databases. Fitting the Mie–Gruneisen–Debye EoS with the present ambient and high-pressure data yielded the following parameters: K0,T0 = 205 ± 3 GPa, K′0,T = 4.0, Gruneisen parameter (γ0) = 1.42 ± 0.80, q = 1.82 ± 0.56. The thermoelastic parameters indicate that Cr2O3 undergoes near isotropic compression at room and high temperatures up to 15 GPa. Cr2O3 is shown to be stable in this pressure range and adopts the corundum-type structure. Using obtained thermoelastic parameters, we calculated the reaction boundary of knorringite formation from enstatite and eskolaite. The Clapeyron slope (with \({\text{d}}P/{\text{d}}T = - 0.014\) GPa/K) was found to be consistent with experimental data.

Precise measurements of enthalpy of postspinel transition in Mg2SiO4 and application to the phase boundary calculation

AbstractDrop solution enthalpies (ΔH°d‐s) of Mg2SiO4 ringwoodite, Mg2SiO4 forsterite, perovskite‐type MgSiO3 (bridgmanite), and MgSiO3 enstatite were measured using a single batch of 2PbO · B2O3 solvent at 978 K. From the obtained ΔH°d‐s values of Mg2SiO4 ringwoodite, MgSiO3 bridgmanite, and MgO, an enthalpy of the postspinel phase transition, Mg2SiO4 ringwoodite = MgSiO3 bridgmanite + MgO, was determined to be 78.54 ± 2.28 kJ/mol. Thermodynamic calculations using the obtained phase transition enthalpy and available thermochemical and thermoelastic data provided the phase transition pressure of 23.1 ± 1.4 GPa at 298 K. This value is comparable to those at about 2000 K determined by previous experimental and theoretical studies, implying a considerably gentle Clapeyron slope. Thermodynamic calculations of the postspinel boundary at high temperatures in the anhydrous condition by changing thermochemical and thermoelastic parameters within the uncertainties suggested that the postspinel transition pressure of Mg2SiO4 at high temperature is lower than the pressure corresponding to the global average depth of the “660 km” seismic discontinuity in the Earth's mantle (~23.5 GPa) estimated from one‐dimensional reference Earth models and that a most likely Clapeyron slope is about −1 MPa/K. The postspinel transition in the hydrous condition with about 2 wt % H2O, which shows higher transition pressure and steeper Clapeyron slope than those in the anhydrous condition, gives a plausible explanation for seismic observations on the 660 km discontinuity, and therefore, hydrous mantle transition zone would be required.

Thermal equation of state of natural tourmaline at high pressure and temperature

Synchrotron-based in situ angle-dispersive X-ray diffraction experiments were conducted on a natural uvite-dominated tourmaline sample by using an external-heating diamond anvil cell at simultaneously high pressures and temperatures up to 18 GPa and 723 K, respectively. The angle-dispersive X-ray diffraction data reveal no indication of a structural phase transition over the P–T range of the current experiment in this study. The pressure–volume–temperature data were fitted by the high-temperature Birch–Murnaghan equation of state. Isothermal bulk modulus of K 0 = 96.6 (9) GPa, pressure derivative of the bulk modulus of $$K_{0}^{\prime } = 12.5 \;(4)$$ , thermal expansion coefficient of α 0 = 4.39 (27) × 10−5 K−1 and temperature derivative of the bulk modulus (∂K/∂T) P = −0.009 (6) GPa K−1 were obtained. The axial thermoelastic properties were also obtained with K a0 = 139 (2) GPa, $$K_{a0}^{\prime }$$ = 11.5 (7) and α a0 = 1.00 (11) × 10−5 K−1 for the a-axis, and K c0 = 59 (1) GPa, $$K_{c0}^{\prime }$$ = 11.4 (5) and α c0 = 2.41 (24) × 10−5 K−1 for the c-axis. Both of axial compression and thermal expansion exhibit large anisotropic behavior. Thermoelastic parameters of tourmaline in this study were also compared with that of the other two ring silicates of beryl and cordierite.

P-V-Tequation of state and high-pressure behavior of CaCO3aragonite

The equation of state of aragonite was determined by in situ synchrotron X-ray diffraction experiments on a hot-pressed polycrystalline specimen of aragonite within its stability field up to 5.8 GPa and 1173 K. As a complement to this experimental study, first-principle density functional theory calculations were performed up to 20 GPa at 0 K. Thermoelastic parameters for aragonite (CaCO 3 ) were derived by a least-squares fit of the experimental P-V-T data to the third-order Birch-Murnaghan equation of state (EOS), yielding the bulk modulus and its pressure and temperature derivatives K 0 = 65.24 ± 0.24 GPa, K ′ 0 = 4.95 ± 0.12, (∂ K T /∂ T ) P = −0.024 ± 0.002 GPa/K and volume thermal expansion α 300 = (6.1 ± 0.7) × 10 −5 K −1 . The analyses of the axial compressibility at ambient temperature show that the c -axis is much more compressible than the a - and b- axes. Based on first-principle calculations, the anisotropic compression behavior of aragonite structure is explained by the heterogeneous shortening of and bond lengths and the rotation of angles along the a -, b -, and c -axes, whereas the unit-cell volume change of aragonite under compression is accommodated by comparable compression rate of the CaO 9 polyhedra and the voids in the crystal lattice. The results attained from this study provide important thermoelastic parameters for understanding the thermodynamic behavior and chemical reactions involving aragonite at subduction zone conditions.

Thermal Stress Analysis of an Embedded Crack in a Graded Orthotropic Coating-Substrate Structure

An analysis of a coupled plane thermoelastic problem for a graded orthotropic coating-substrate structure is performed under thermomechanical loading conditions. The crack direction is parallel to the free surface. Applying the superposition principle and Fourier integral transform, the heat conduction and plane elasticity equations lends themselves to the derivation of two sets of Cauchy-type singular integral equations. The thermal stress intensity factors are defined and evaluated. In the numerical results, the effects of the orthotropy parameters, thermoelastic non-homogeneity parameters, and dimensionless thermal resistance on the temperature distribution and the thermal stress intensity factors (TSIFs) are studied. The obtained results can be used to design graded orthotropic coating-substrate structures under thermomechanical loading.

Axisymmetric thermal consolidation of multilayered porous thermoelastic media due to a heat source

SummaryThis paper presents an analytical layer element solution to axisymmetric thermal consolidation of multilayered porous thermoelastic media containing a deep buried heat source. By applying the Laplace–Hankel transform to the state variables involved in the basic governing equations of porous thermoelasticity, the analytical layer elements that describe the relationship between the transformed generalized stresses and displacements of a finite layer and a half‐space are derived. The global stiffness matrix equation is obtained by assembling the interrelated layer elements, and the real solutions in the physical domain are achieved by numerical inversion of the Laplace–Hankel transform after obtaining the solutions in the transformed domain. Finally, numerical calculations are performed to demonstrate the accuracy of this method and to investigate the influence of heat source's types, layering, and the porous thermoelastic material parameters on thermal consolidation behavior. Copyright © 2015 John Wiley & Sons, Ltd.

Diamond–garnet geobarometry: The role of garnet compressibility and expansivity

We report P–V and T–V Equations of State (EoS) for synthetic single crystal pyrope (Py, Mg3Al2Si3O12) and the P–V EoS for synthetic single crystals of almandine (Alm, Fe3Al2Si3O12) as well as an intermediate composition (Py60Alm40) as measured by in-situ high-pressure and high-temperature X-ray diffraction experiments. The unit-cell volumes of the three samples were measured at room temperature and different pressures and up to about 8GPa in a diamond-anvil cell. The high-temperature experiment was carried out using a micro-furnace. The pressure-volume data were fitted to a third order Birch–Murnaghan EoS giving the following coefficients: V0=1506.15(16)Å3, KT0=163.7(1.7)GPa and K′=6.4(4) for pyrope, V0=1533.52(10)Å3, KT0=172.6(1.5)GPa and K′=5.8(5) for almandine and V0=1516.32(13)Å3, KT0=167.2(1.7)GPa and K′=5.6(5) for the intermediate Py60Alm40 composition. The unit-cell volume along the pyrope–almandine join changes linearly within the error of measurement indicating ideality in the volume of mixing behaviour for the solid solution. The first pressure derivative, K′, for all three garnets is similar within experimental uncertainty with an average value of K′=6.0(4). The thermal expansion parameters for end-member pyrope, as described using to the Kroll-type EoS, with the Einstein temperature, θE, fixed to 320K, are α(303K, 1bar)=2.543(5)∗10−5K−1 and V0=1504.64(4)Å3. The determined thermoelastic parameters were combined in a thermal-pressure type EoS (thermal-P type EoS) to calculate the entrapment pressures, Pe, for natural garnet inclusions in diamonds at mantle temperatures. A calculated pressure of 5.8GPa at T=1500K using our newly determined thermoelastic parameters appears to be more consistent with diamond-forming conditions compared to the higher pressures that range up to 6.8GPa at T=1500K, which are obtained using thermoelastic data in the literature.

Compressibility and equation of state of beryl (Be3Al2Si6O18) by using a diamond anvil cell and in situ synchrotron X-ray diffraction

High-pressure single-crystal synchrotron X-ray diffraction was carried out on a single crystal of natural beryl compressed in a diamond anvil cell. The pressure-volume (P-V) data from room pressure to 9.51 GPa were fitted by a third-order Birch-Murnaghan equation of state (BM-EoS) and resulted in unit-cell volume V-0 = 675.5 +/- 0.1 angstrom(3), isothermal bulk modulus K-0 = 180 +/- 2 GPa, and its pressure derivative K-0' = 4.2 +/- 0.5. We also calculated V-0 = 675.5 +/- 0.1 angstrom(3) and K-0 = 181 +/- 1GPa with fixed K-0' at 4.0 and then obtained the axial moduli for a (K-a0)-axis and c (K-c0)-axis of 209 +/- 1 and 141 +/- 2 GPa by "linearized" BM-EoS approach. The axial compressibilities of a-axis and c-axis are beta(a) = 1.59 x 10(-3) GPa(-1) and beta(c) = 2.36 x 10(-3) GPa(-1) with an anisotropic ratio of beta(a):beta(c) = 0.67:1.00. On the other hand, the pressure-volume-temperature (P-V-T) EoS of the natural beryl has also been measured at temperatures up to 750 K and at pressures up to 16.81 GPa, using diamond anvil cell in conjunction with in situ synchrotron angle-dispersive powder X-ray diffraction. The P-V data at room temperature and at a pressure range of 0.0001-15.84 GPa were then analyzed by third-order BMEoS and yielded V-0 = 675.3 +/- 0.1 angstrom(3), K-0 = 180 +/- 2 GPa, K-0' = 4.2 +/- 0.3. With K-0' fixed to 4.0, we also obtained V-0 = 675.2 +/- 0.1 angstrom(3) and K-0 = 182 +/- 1 GPa. Consequently, we fitted the P-V-T data with high-temperature BM-EoS approach using the resultant K-0' (4.2) from room-temperature BM-EoS and then obtained the thermoelastic parameters of V-0 = 675.3 +/- 0.2 angstrom(3), K-0 = 180 +/- 1 GPa, temperature derivative of the bulk modulus (partial derivative K/partial derivative T)(P) = -0.01 7 +/- 0.004 GPa K-1, and thermal expansion coefficient at ambient conditions alpha(0) = (2.82 +/- 0.74) x 10(-6) K-1. Present results were also compared with previous studies for beryl. From the comparison of these fittings, we propose to constrain K-0 = 180 GPa and K-0' = 4.2 for beryl. And we also observed that beryl exhibits anisotropic thermal expansion at relatively low temperatures, which is very consistent with previous studies. Furthermore, no phase transition was observed in the entire pressure and temperature range (up to 16.84 GPa and 750 K) of this study for the natural beryl.

Thermoelasticity of Fe2+‐bearing bridgmanite

AbstractWe present local density approximation augmented by the Hubbard‐type correction calculations of high‐temperature elastic properties of bridgmanite with composition for 0≤×≤0.125. Results of elastic moduli and acoustic velocities for the Mg end‐member (x=0) agree very well with the latest high‐pressure and high‐temperature experimental measurements. In the iron‐bearing system, we focus particularly on the change in thermoelastic parameters across the state change that occurs in ferrous iron above ∼30 GPa, often attributed to a high‐spin (HS) to intermediate‐spin (IS) crossover but explained by first‐principles calculations as a lateral displacement of substitutional iron in the perovskite cage. We show that the measured effect of this change on the equation of state of this system can be explained by the lateral displacement of substitutional iron and not by the HS to IS crossover. The calculated elastic properties of along an adiabatic mantle geotherm somewhat overestimate longitudinal velocities but produce densities and shear velocities quite consistent with the Preliminary Reference Earth Model data throughout most of the lower mantle.

P-V-T equation of state of Ca3Cr2Si3O12 uvarovite garnet by using a diamond-anvil cell and in-situ synchrotron X-ray diffraction

The pressure-volume-temperature (P-V-T) equation of state (EoS) of synthetic uvarovite has been measured at high temperatures up to 900 K and high pressures up to 16.20 GPa, by using in situ angle-dispersive X-ray diffraction and diamond-anvil cell. Analysis of room-temperature P-V data to a third-order Birch-Murnaghari EoS yielded: V-0 = 1736.9 +/- 0.5 angstrom(3), K-0 = 162 +/- 2 GPa, and K-0(') = 4.5 +/- 0.3. With K-0(') fixed to 4.0, we obtained: V-0 = 1736.5 +/- 0.3 angstrom(3) and K-0 = 164 +/- 1 GPa. Fitting of our P-V-T data by means of the high-temperature third-order Birch-Murnaghan equations of state, given the thermoelastic parameters: V-0= 1736.8 +/- 0.8 angstrom(3), K-0 = 162 +/- 3 GPa, K-0(') = 4.3 +/- 0.4, (partial derivative K/partial derivative T)(P)=-0.021 +/- 0.004 GPa/K, and alpha(0) = (2.72 +/- 0.14)x10(-5) K-1.We compared our elastic parameters to the results from the previous studies for uvarovite. From the comparison of these fittings, we propose to constrain the bulk modulus and its pressure derivative to K-0 = 162 GPa and K-0(') = 4.0-4.5 for uvarovite. Present results were also compared with previous studies for other ugrandite garnets, grossular and andradite, which indicated that the compression mechanism of uvarovite might be similar with grossular and andradite. Furthermore, a systematic relationship, K-0(GPa) = 398.1(7)-0.136(8) V-0 (angstrom(3)) with a correlation coefficient R-2 of 0.9999, has been established based on these isostructural analogs. Combining these results with previous studies for pyralspite garnets-pyrope, almandine, and spessartine-the compositional dependence of the thermoelastic parameters (bulk modulus, thermal expansion, and the temperature derivative of the bulk modulus) were discussed.

Thermal equation of state of majoritic knorringite and its significance for continental upper mantle

AbstractThe P‐V‐T equation of state (EoS) for majoritic knorringite Mg3.19Cr1.60Si3.19O12 at pressures to 17 GPa and temperatures to 1673 K was obtained from in situ X‐ray diffraction experiments using a Kawai‐type multi‐anvil apparatus. Fitting of the room‐temperature P–V data to a third‐order Birch‐Murnaghan EoS yielded an isothermal bulk modulus, K0,300 = 154 (4) GPa, and a pressure derivative, K′0,300 = 5.4 (1.2). When fitting a high‐temperature Birch‐Murnaghan EoS using all of the P‐V‐T data at a fixed V0 = 1549.08 Å3, we find that K0,300 = 157 (2) GPa, K′0,T = 4.5 (6), (∂K0,T/∂T)P = −0.019 (4) (GPa K−1), a = 3.00 (14) × 10−5 K−1, and b = 0.65 (24) × 10−8 K−2, where α = a + bT is the volumetric thermal expansion coefficient. Fitting the Mie‐Grüneisen‐Debye EoS with the present data with a Debye temperature fixed at θ0 = 731 K yielded a Grüneisen parameter, γ0 = 1.34 at q = 1.0 (fixed). The thermoelastic parameters of pure knorringite were estimated and were compared with the previous data on other garnet compositions. The presence of Cr2O3 in pyrope garnets in the upper mantle decreases P‐ and S‐velocities by 1.6% and the density increases by 1.7% (for 20 mol.% knorringite end member) compared to pure pyrope. The results show the importance of accounting knorringite end‐member for accurate estimation of mantle garnet acoustic velocities.

Nonlinear Transient Thermal Stress Analysis of Temperature-Dependent Hollow Cylinders Using a Finite Element Model

In this paper, the nonlinear transient thermal stress analysis is conducted for temperature-dependent hollow cylinders subjected to a decaying-with-time thermal field. By the finite element method, the highly nonlinear governing equations are solved. The time histories of temperature, displacement, and stress due to the decaying-with-time thermal load are computed. A sensitivity analysis includes the effects of exponent of the decayed heat flux and temperature-dependency of density and material properties is carried out. Numerical results show some interesting characteristics of the thermoelastic behaviors of the hollow cylinders studied. In particular, the effect of temperature-dependency of the material properties on the thermoelastic parameters was demonstrated to be significant.

High-pressure behavior and thermoelastic properties of niobium studied by in situ x-ray diffraction

In situ synchrotron energy dispersive x-ray diffraction (XRD) experiments on Nb have been conducted at pressures up to 6.4 GPa and temperatures up to 1073 K. From the pressure-volume-temperature measurements, thermoelastic parameters were derived for the first time for Nb based on the thermal pressure (ΔPth) equation of state (EOS), modified high-T Birch-Murnaghan EOS, and Mie-Grüneisen-Debye EOS. With the pressure derivative of the bulk modulus KT′ fixed at 4.0, we obtained the ambient isothermal bulk modulus KT0 = 174(5) GPa, the temperature derivative of bulk modulus at constant pressure (∂KT/∂T)P=−0.060(8) GPa K−1 and at constant volume (∂KT/∂T)V=−0.046(8) GPa K−1, the volumetric thermal expansivity αT(T)=2.3(3)×10−5+0.3(2)×10−8T (K−1), as well as the pressure dependence of thermal expansion (∂α/∂P)T=(−2.0±0.4)×10−6 K−1 GPa−1. Fitting the present data to the Mie-Grüneisen-Debye EOS with Debye temperature Θ0 = 276.6 K gives γ0 = 1.27(8) and KT0 = 171(3) GPa at a fixed value of q = 3.0. The ambient isothermal bulk modulus and Grüneisen parameter derived from this work are comparable to previously reported values from both experimental and theoretical studies. An in situ high-resolution, angle dispersive XRD study on Nb did not indicate any anomalous behavior related to pressure-induced electronic topological transitions at ∼5 GPa as has been reported previously.

P–V–T equation of state of molybdenite (MoS2) by a diamond anvil cell and in situ synchrotron angle-dispersive X-ray diffraction

The pressure–volume–temperature (P–V–T) equation of state (EoS) of a natural molybdenite (MoS2) has been measured at high temperature up to 700K and high pressures up to 18.26GPa, by using in situ angle-dispersive X-ray diffraction and diamond anvil cell. Analysis of room-temperature P–V data to a third-order Birch–Murnaghan EoS yields: V0=107.0±0.1Å3, K0=67±2GPa and K′0=5.0±0.3. With K′0 fixed to 4.0, we obtained: V0=106.7±0.1Å3 and K0=74.5±0.8GPa. Fitting of our P–V–T data by means of the high-temperature third order Birch–Murnaghan equations of state, gives the thermoelastic parameters: V0=107.0±0.1Å3, K0=69±2GPa, K′0=4.7±0.2, (∂K/∂T)P=−0.021±0.003GPaK−1, a=(2.2±0.7)×10−5K−1 and b=(2.9±0.8)×10−8K−2. The temperature derivative of the bulk modulus and thermal expansion coefficient of MoS2 are obtained for the first time. Present results are also compared with previously studies determined the elastic properties of MoS2 and WS2.