Murnaghan Equation Of State Research Articles

Numerical analysis of density flows in adiabatic two-phase fluids through characteristic finite element method

ABSTRACTThe purpose of this study is to analyze the density flow in adiabatic two-phase fluids through the characteristic finite element method. The fluids are assumed to be liquids. The equations of conservations of mass and momentum for the adiabatic flows and the Birch–Murnaghan equation of state are employed as the governing equations. The employed finite element method is a combination of the characteristic method and the implicit method. The governing equations are divided into two parts: the advection part and the non-advection part. The characteristic method is applied to the advection part. The Hermite interpolation function, which is based on the complete third-order polynomial interpolation using triangular finite element is employed for the interpolation of both velocity and density. Using the discontinuity conditions, an interface translocation method can be derived. The interface of the two flow densities are interpolated through the third-order spline function, using which the curvature of the interface can be directly computed. For the numerical study, the development of density flow over the Tokyo bay is presented. It is detected out that high density area is abruptly diffused over the whole area. According to the differences in the two densities, various flow patterns are computed.

High-pressure in-situ X-ray diffraction and Raman spectroscopy of Ca2AlFeO5 brownmillerite

ABSTRACTThe behavior of Ca2AlFeO5 brownmillerite was studied by in situ synchrotron X-ray diffraction and Raman spectroscopy at 300 K with pressures up to 26.5 and 32.1 GPa, respectively. A reversible structural phase transition was observed. The P–V data were fitted by a third-order Birch–Murnaghan equation of state, and the isothermal bulk modulus was obtained as K0 = 181.9(76) GPa with K0′ = 4.4(17). If K0′ was fixed to 4, K0 was obtained as 183.8(20) GPa. Ca2AlFeO5 brownmillerite shows an axial elastic anisotropy since the b-axis is more compressible than a- and c-axis. Combined with previous results, the isothermal bulk modulus and axial compressibility of Ca2AlFeO5 brownmillerite increase with more Al incorporated in the structure. The Raman spectra of Ca2AlFeO5 brownmillerite were analyzed and the pressure coefficients vary from 2.23 to 4.90 cm−1/GPa. The isothermal mode Grüneisen parameters range from 0.83 to 1.77 and the thermal Grüneisen parameter is determined as 1.08(11).

The syndrome of irreversible lithium-effectuated neurotoxicity (silent): A case report

This paper focuses on predicting and analyzing the tire-moist terrain interaction. The moist terrain (sand) is modelled using Smoothed-Particle Hydrodynamics (SPH) technique. The SPH basic interpolation technique is described, and the necessary interpolation equations are implemented. The soil is modelled using the hydrodynamic elastic-plastic material, while the water is modelled using Murnaghan equation of state. The numerical interaction between both materials is defined using Darcy’s law. The soil moisturizing technique consists of layering water particles on top of sand particles and pressurizing the water into the sand. The moisturizing technique is examined using the direct shear-strength test, and validated against physical measurement carried out in a laboratory under similar soil conditions and bulk density. Finally, the results and the effect of moisture content on tire-moist terrain interaction are discussed and investigated using a previously modelled and validated off-road truck tire size 315/80R22.5.

Thermodynamic properties, electronic and crystallographic structure, and magnetic response of the Sr2HoNbO6 material

En el presente trabajo se utilizó el código Wien2k, en el marco de la teoría del funcional de la densidad de Kohn-Sham, aplicando el método de ondas planas aumentadas y linealizadas (full-potential linearized augmented plane wave, FP- LAPW) y adoptando la aproximación de gradiente generalizado (GGA) de Perdew, Burke y Ernzerhof para la energía de intercambio y correlación, así como la aproximación de densidad local (local density approximation, LDA) para el cálculo de la densidad de estados y la estructura de bandas de la perovskita doble Sr2HoNbO6. Para los cálculos se consideró el grupo Fmm (#225), experimentalmente obtenido a partir de mediciones de difracción de rayos X y del método de refinamiento de Rietveld. El parámetro de red experimental fue de 8.018 Å, el cual concuerda en un 99,2 % con las predicciones teóricas efectuadas a partir de la minimización de la energía mediante la ecuación de estado de Murnaghan. A partir de mediciones de susceptibilidad magnética en función de la temperatura y del ajuste con la ley de Curie, se obtuvo el valor del momento magnético efectivo 10,01 μB. Este valor es muy cercano del esperado teóricamente a partir de las reglas de Hund (10,60 μB). La brecha de energía determinada entre las bandas de valencia y de conducción fue de 3,3 eV, lo que revela el carácter aislante de la perovskita compleja Sr2HoNbO6 para la configuración de espín hacia arriba, en tanto que se observó el carácter semiconductor para la polarización de espín hacia abajo, con una brecha de energía de 0,77 eV. Las propiedades termodinámicas se calcularon a partir de la ecuación de estado usando el modelo cuasi-armónico de Debye. Un comportamiento del calor específico, con CV≈CP, se encontró a temperaturas inferiores a T = 500 K, con valores del límite de Dulong-Petit que doblaban los que se han reportado para materiales del tipo de la perovskita. © 2018. Acad. Colomb. Cienc. Ex. Fis. Nat.

Equation of state and second-order elastic constants of portlandite Ca(OH)2 and brucite Mg(OH)2

Hydroxide minerals brucite Mg(OH)2 and portlandite Ca(OH)2 (space group $$P\bar {3}m1$$ ) are very important phases for several geological and industrial applications which often require the knowledge of the mechanical properties. In the present work, the equation of state (EoS) and the second-order elastic constants of the two minerals were calculated by ab initio quantum mechanical methods. The aims are extending the knowledge of their important applicative mechanical properties and providing a consistent relative dataset. In addition, the simple crystal-chemical composition and structure of Ca(OH)2 and Mg(OH)2 is ideal to simulate and characterize the effect of the proton disorder on the elastic properties, which could be useful for the comprehension of more complex hydrous minerals and synthetic phases. The third-order Birch–Murnaghan EoS parameters obtained in the present study were V0 = 39.59(1) A3, K0 = 48.0(9) GPa and K′ = 9.1(3), and V0 = 54.0(7) A3, K0 = 30.1(9) GPa and K′ = 8.5(4) for Mg(OH)2 and Ca(OH)2, respectively. Axial compressibilities were found to be in ratio β(a):β(c) = 1.000:3.600 for brucite, and 1.000:3.777 for portlandite. The theoretical results agree with the general trend experimentally observed in the available literature, and further extend the knowledge of the mechanical properties of the two phases. The results could be very helpful for petro-geological investigations and for the synthesis and use of concrete nanocomposites and layered double hydroxides with tailored mechanical properties.

Phase transition and dynamics of iron under ramp wave compression

The ramp wave compression experiments of iron with different thicknesses were performed on the magnetically driven ramp loading device CQ-4. Numerical simulations of this process were done with Hayes multi-phase equation of state (H-MEOS) and dynamic equations of phase transition. The calculated results of H-MEOS are in good agreement with those of shock phase transition, but are different from those under ramp wave compression. The reason for this is that the bulk modulus of the material in the Hayes model and the wave velocity are considered constant. Shock compression is a jump from the initial state to the final state, and the sound speed is related to the slope of the Rayleigh line. However, ramp compression is a continuous process, and the bulk modulus is no longer a constant but a function of pressure and temperature. Based on Murnaghan equation of state, the first-order correction of the bulk modulus on pressure in the Hayes model was carried out. The numerical results of the corrected H-MEOS agree well with those of pure iron in both ramp and shock compression phase transition experiments. The calculated results show that the relaxation time of iron is about 30 ns and the phase transition pressure is about 13 GPa. There are obvious differences between the isentropic and adiabatic process in terms of pressure–specific volume and temperature–pressure. The fluctuation of the sound speed after 13 GPa is caused by the phase transition.

A simplified approximate model of compressible hypervelocity penetration

A simplified approximate model considering rod/target material’s compressibility is proposed for hypervelocity penetration. We study the effect of shockwaves on hypervelocity penetration whenever the compressibility of the rod is much larger, analogously, and much less than that of the target, respectively. The results show that the effect of shockwaves is insignificant up to 12 km/s, so the shockwave is neglected in the present approximate model. The Murnaghan equation of state is adopted to simulate the material behaviors in penetration and its validity is proved. The approximate model is finally reduced to an equation depending only on the penetration velocity and a simple approximate solution is achieved. The solution of the approximate model is in agreement with the result of the complete compressible model. In addition, the effect of shockwaves on hypervelocity penetration is shown to weaken material’s compressibility and reduce the interface pressure of the rod/target, and thus the striking/protective performance of the rod/target is weakened, respectively. We also conduct an error analysis of the interface pressure and penetration efficiency. With a velocity change of 1.6 times the initial sound speed for the rod or target, the error of the approximate model is very small. For metallic rod–target combinations, the approximate model is applicable even at an impact velocity of 12 km/s.

Ab-initio study of thermodynamic stability, thermoelectric and optical properties of perovskites ATiO3 (A=Pb, Sn)

The physical behavior of perovskites ATiO3 (A=Pb, Sn) has been explored by using density functional theory based full-potential linearized-augmented-plane-wave plus local-orbital (FP-LAPW+lo) method. The lattice parameters calculated from the optimized structures by using Murnaghan equation of state and Chapin's method have been found in good agreement with the available literature that ensures the reliability of the adopted methodology. Moreover, the optoelectronic and thermoelectric properties have been elaborated by using modified Becke-Johnson exchange potential. The optical behavior has been explored in terms the dielectric constants, refractive indices, absorption spectra and optical loss factors. The absorption spectra of these materials reveal a large absorption in the visible and low ultraviolet part of incident light. The thermoelectric properties of ATiO3 are explained in terms of electrical conductivities, thermal conductivities, power factors, and the specific heat capacities. The ATiO3family of pervoskites has been found to exhibit the bandgaps falling in the visible region of solar spectrum and show high values of thermal efficiency that make them potential multifunctional candidates for optoelectronic and energy harvesting applications.

Structural, electronic, optical, thermodynamic and elastic properties of the zinc-blende AlxIn1-xN ternary alloys: A first principles calculations

The structural, electronic, optical and thermodynamic properties of the AlxIn1-xN (x = 0, 0.25, 0.50, 0.75 and 1) ternary alloys were investigated using the full potential linearized augmented plane wave (FP-LAPW) method in the framework of density functional theory (DFT). Optimized lattice parameter, bulk modulus and its pressure derivative were determined from suitable fit of the total energy versus volume with Murnaghan equation of state (EOS) for all considered alloys. Variations of the lattice parameter and bulk modulus with the Al concentration (x) deviate from Vegard’s law. Electronic band structure, dielectric function and refractive indices were investigated and computed for the considered alloys. It is found that the variations of the band gap, the static dielectric constant and static refractive index versus the Aluminum Al concentration obey to a quadratic polynomial. Temperature and pressure dependencies of the Gibbs free energy G, isochoric heat capacity CV, entropy S and Debye temperature θD were investigated via the Debye quasi-harmonic model for the Al0.5In0.5N ternary alloy. Furthermore, the elastic constants Cij, the bulk modulus B, Shear modulus G with Young modulus E and the Poison’s ratio v with the compressibility B/G were carried out in the cubic phase. Deduced results agree well with the available theoretical and experimental results.

P–V–T equation of state of rhodium oxyhydroxide

ABSTRACTA high pressure X-ray diffraction study of RhOOH was carried out up to 17.44 GPa to investigate the compression behavior of an oxyhydroxide with an InOOH-related structure. A fit to the third-order Birch–Murnaghan equation of state gave K0 = 208 ± 6 GPa, and K′ = 9.4 ± 1.3. The temperature derivative of the bulk modulus was found to be ∂K/∂T = −0.06 ± 0.02 GPa K−1. The refined parameters for volume thermal expansion were α0 = 2.7 ± 0.3 × 10−5 K−1; α1 = 1.7 ± 1.1 × 10−8 K−2 in the polynomial form (α(T) = α0 + α1(T−300)). Our results show that RhOOH is very incompressible, and has a higher bulk modulus than other InOOH-structured oxyhydroxides (e.g. δ-AlOOH, ε-FeOOH, and γ-MnOOH).

Theoretical and experimental study of the electronic, crystalline, morphologic, compositional, magnetic and dielectric properties of the Sr2DyNbO6 material

Se reportan resultados experimentales y teóricos de estructura cristalina, morfología, carácter magnético y eléctrico, y estructura electrónica para el material cerámico Sr2DyNbO6. Las muestras fueron producidas mediante reacción sólida. Resultados de difracción de rayos X muestran que el material cristaliza en una estructura monoclínica, grupo espacial P21/n. Imágenes de MEB muestran superficies granulares submicrométricas. La susceptibilidad en función de la temperatura revela una respuesta paramagnética con momento magnético 10.28μB. La histéresis de polarización en función del campo eléctrico a 300K permitió obtener una constante dieléctrica de 264.28. Cálculos de estructura electrónica por DFT sugieren que el material es semiconductor con brecha de energía 3.21 eV para la orientación espín arriba y 0.26 eV para espín abajo. El momento magnético calculado es 10.0μB, muy próximo del valor medido. Los parámetros de red obtenidos mediante la ecuación de Murnaghan están de acuerdo con los resultados experimentales en un 98.5%.

Thermal equation of state of goethite (α-FeOOH)

ABSTRACT The pressure–volume–temperature (P–V–T) equation of state (EoS) of natural goethite (α-FeOOH) has been determined by an X-ray diffraction study using synchrotron radiation. Fitting the volume data to the third-order Birch–Murnaghan EoS yielded an isothermal bulk modulus, B 0 of 85.9(15) GPa, and a pressure derivative of the bulk modulus, B′, of 12.6(8). The temperature derivative of the bulk modulus, (∂B/∂T)P, was –0.022(9) GPa K−1. The thermal expansion coefficient α 0 was determined to be 4.0(5) × 10−5 K−1.

Equation of state and lattice parameter of SnO2 nanomaterial

We developed a simple theoretical model to study the effect of pressure, temperature, shape and size on nanomaterials. We used the model to study the Equation of state (EOS) and pressure dependence of lattice parameter of SnO2­ nanomaterial. We selected SnO2 as an example because of the fact that the required experimental data are available so that a comparison of the results may be presented. We used the model to study the compression behaviour at room temperature and compared our results with the experimental data as well as with those based on Birch- Murnaghan Equation of state (BMEOS). Our results are found to present a good agreement with the experimental data as well as with those based on BMEOS. Due to the simplicity and applicability of the model, we extended our studies at different temperatures i.e. 300 K, 500 K and 700 K. A shift in the isotherms has been obtained. We also included the effect of shape and size in the EOS model to make it widely applicable for nanosystems. The results of pressure dependence of lattice parameter for SnO2 are compared with available experimental data. A good agreement between theory and experiment supports the validity of the model developed.

Sensitivity analysis of truck tyre hydroplaning speed using FEA-SPH model

The hydroplaning phenomenon is a complex multi-physics problem that may affect any vehicle under wet road conditions. It is crucial to understand hydroplaning phenomenon to improve passenger safety on highways. This paper focuses on studying the hydroplaning of different truck tyres. The study includes the effect of inflation pressure, load, tread depth and water film thickness on hydroplaning speed. The tyres used in this study are the Goodyear's off-road RHD 315/80R22.5 tyre and the UOIT FEA Michelin XOne line energy T 445/50R22.5 tyre. The analysis is performed using an FEA code named Pam-Crash from ESI Group. Water is modelled using Murnaghan equation of state and smooth particle hydrodynamics (SPH) method. The simulation results are validated against Horne's equation for truck tyres. An empirical equation is developed to include various tyre parameters.

The compression behavior of blödite at low and high temperature up to ∼10 GPa: Implications for the stability of hydrous sulfates on icy planetary bodies

Recent satellite inferences of hydrous sulfates as recurrent minerals on the surface of icy planetary bodies link with the potential mineral composition of their interior. Blödite, a mixed Mg-Na sulfate, is here taken as representative mineral of icy satellites surface to investigate its crystal structure and stability at conditions of the interior of icy bodies. To this aim we performed in situ synchrotron angle-dispersive X-ray powder diffraction experiments on natural blödite at pressures up to ∼10.4GPa and temperatures from ∼118.8K to ∼490.0K using diamond anvil cell technique to investigate the compression behavior and establish a low-to-high temperature equation of state that can be used as reference when modeling the interior of sulfate-rich icy satellites such as Ganymede.The experimentally determined volume expansivity, α, varies from 7.6 (7) 10−5K−1 at 0.0001GPa (from 118.8 to 413.15K) to 2.6 (3) 10−5K−1 at 10GPa (from 313.0 to 453.0K) with a δα/δP coefficient = −5.6(9)10−6GPa−1K−1.The bulk modulus calculated from the least squares fitting of P-V data on the isotherm at 413K using a second-order Birch - Murnaghan equation of state is 38(5)GPa, which gives the value of δK/δT equal to 0.01(5)GPa K−1. The thermo-baric behavior of blödite appears strongly anisotropic with c lattice parameter being more deformed with respect to a and b.Thermogravimetric analyses performed at ambient pressure showed three endotherms at 413K, 533K and 973K with weight losses of approximately 11%, 11% and 43% caused by partial dehydration, full dehydration and sulfate decomposition respectively. Interestingly, no clear evidence of dehydration was observed up to ∼453K and ∼10.4GPa, suggesting that pressure acts to stabilize the crystalline structure of blödite.The data collected allow to write the following equation of state,V(P, T)=V0[1+7.6(7)10−5ΔT−0.026(3)P−5.6(9)10−6PΔT−6.6(9)10−6PΔT)]from which the density of blödite can be determined at conditions of the mantle of the large icy satellites of Jupiter.Blödite has higher density, bulk modulus and thermal stability than similar hydrous sulfates (e.g. mirabilite and epsomite) implying, therefore, a different contribution of these minerals to the extent of deep oceans in icy planets and their distribution over the local geotherms.

Pressure-induced zircon to monazite phase transition in Y1–х La х PO4: First-principles calculations

Density functional theory was used to study pressure-induced phase transitions of zircon to monazite in doped yttrium orthophosphate, Y1–хLaхPO4, for х = 0, 0.0625, 0.125. The pressures of the phase transition, the elastic moduli and the universal elastic anisotropy index were calculated. It was shown that with increasing lanthanum concentration in Y1–xLaxPO4, the transition pressure increases. According to the Birch–Murnaghan equation of state, this effect is associated with a decrease in the critical volume. The increased stability of the doped zircon phase compared to YPO4 is attributed to the more significant increase in the anisotropy and distortions of REO8 polyhedra and RE–O–P chains found for the optimized structures at critical volumes.

Rigid and eroding projectile penetration into concrete targets based on an extended dynamic cavity expansion model

A hyperbolic yield criterion and Murnaghan equation of state were introduced to describe the plastic behavior of concrete material under projectile penetration, and an extended dynamic cavity expansion model was proposed. Then, a unified one-dimensional resistance of concrete target to projectile penetration was formulated, in which the projectile nose shape influences were taken into account by three non-dimensional coefficients. Furthermore, combined with the Newton's second law and Alekseevskii-Tate equations, both rigid and eroding projectile penetration models into concrete targets were established. By comparing with the existing tests data as well as prediction results of previous model based on the linear yield criterion and equation of state, the proposed models were verified. Besides, a series of practical parameters of hyperbolic yield criterion and Murnaghan EOS for the extended dynamic cavity expansion model were given and verified.

Ab-initio study of structural, electronic and thermodynamic properties of Ba2YTaO6

The structural, electronic and thermodynamic properties of cubic double perovskite Ba2YTaO6 are calculated by using the plane wave within density functional theory (DFT) framework employing the generalized gradient approximation (GGA). The ground state quantities including the lattice parameter, bulk moduli and its pressure derivative are fitted by the Birch–Murnaghan equation of state. The calculated energy band indicates that Ba2YTaO6 has a direct band gap of 3.42 eV at [Formula: see text] point in the Brillouin zone and the energy band near Fermi level is determined by the density of states of O 2[Formula: see text], Ta 5[Formula: see text] and Y 4[Formula: see text] electrons. The thermodynamic properties including Debye temperature, bulk moduli and heat capacity of various pressures and temperatures are calculated and analyzed. Results indicate that the temperature and induced pressure have significant effect on the thermodynamic properties of Ba2YTaO6.

Atomistic modeling of structure II gas hydrate mechanics: Compressibility and equations of state

This work uses density functional theory (DFT) to investigate the poorly characterized structure II gas hydrates, for various guests (empty, propane, butane, ethane-methane, propane-methane), at the atomistic scale to determine key structure and mechanical properties such as equilibrium lattice volume and bulk modulus. Several equations of state (EOS) for solids (Murnaghan, Birch-Murnaghan, Vinet, Liu) were fitted to energy-volume curves resulting from structure optimization simulations. These EOS, which can be used to characterize the compressional behaviour of gas hydrates, were evaluated in terms of their robustness. The three-parameter Vinet EOS was found to perform just as well if not better than the four-parameter Liu EOS, over the pressure range in this study. As expected, the Murnaghan EOS proved to be the least robust. Furthermore, the equilibrium lattice volumes were found to increase with guest size, with double-guest hydrates showing a larger increase than single-guest hydrates, which has significant implications for the widely used van der Waals and Platteeuw thermodynamic model for gas hydrates. Also, hydrogen bonds prove to be the most likely factor contributing to the resistance of gas hydrates to compression; bulk modulus was found to increase linearly with hydrogen bond density, resulting in a relationship that could be used predictively to determine the bulk modulus of various structure II gas hydrates. Taken together, these results fill a long existing gap in the material chemical physics of these important clathrates.

Model for gas hydrates applied to CCS systems part I. Parameter study of the van der Waals and Platteeuw model

In this study, divided in a series of three articles, the model for pure CO2 hydrate by Jäger et al. [Fluid Phase Equilib. 338 (2013) 100–113] has been improved and extended to other gases relevant in Carbon Capture and Storage (CCS) applications. The new gas hydrate model is inspired by the currently most accurate model available for natural gas hydrates by Ballard and Sloan [Fluid Phase Equilib. 194 (2002) 371–383], which belongs to the family of van der Waals and Platteeuw (vdWP) models [Adv. Chem. Phys. 2 (1959) 1]. The new model is combined with highly accurate equations of state (EoS) in form of the Helmholtz energy for fluid phases and with Gibbs energy models for pure solid phases. Part I describes a critical analysis of the main parameters of the vdWP-based hydrate model. The influences of the specific hydrate volume, of the Langmuir constant, and of the EoSs used for other phases than hydrate on the predicted hydrate composition and on phase equilibria with gas hydrates were investigated. A new correlation for the pressure dependency of the volume of gas hydrates forming structures sI and sII has been developed. The correlation based on the Murnaghan EoS [Proc. Natl. Acad. Sci. U. S. A. 30 (1944) 244] has good extrapolating behavior and behaves in a physically reasonable manner. It is shown that all experimental data for hydrate formers including mixed hydrates can be represented reasonably well by a universal bulk modulus around 10 GPa. Furthermore, it was found that the bulk modulus affects phase equilibria at high pressures while its impact on phase equilibria at moderate and low pressures below about 30 MPa is negligible. A strong influence of the Langmuir constant on the hydrate composition was observed, especially in case of small cavities of both sI and sII hydrate structures. Additionally, the influence of EoSs used for other phases than hydrate on the accuracy of quadruple point predictions is discussed. A multi-property fitting algorithm developed for optimization of parameters of the new hydrate model is introduced in part II. Results of the model including phase equilibria with hydrates, composition of hydrates, and enthalpy of formation of hydrates are provided in part III. The model has been implemented in the software package TREND 2.0 by Span et al. [Thermodynamic Reference and Engineering Data 2.0. (2015) Lehrstuhl fuer Thermodynamik, Ruhr-Universitaet Bochum].