scholarly journals Anharmonic Effects on the Thermodynamic Properties of Quartz from First Principles Calculations

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1366
Author(s):  
Mara Murri ◽  
Mauro Prencipe
Keyword(s):  
Phase Transition ◽  
Thermodynamic Properties ◽  
Equations Of State ◽  
Ambient Pressure ◽  
Beta Phase ◽  
Thermodynamic Quantities ◽  
Anharmonic Effects ◽  
Displacive Phase Transition ◽  
Intrinsic Anharmonicity ◽  
Good Agreement

The simple chemistry and structure of quartz together with its abundance in nature and its piezoelectric properties make convenient its employment for several applications, from engineering to Earth sciences. For these purposes, the quartz equations of state, thermoelastic and thermodynamic properties have been studied since decades. Alpha quartz is stable up to 2.5 GPa at room temperature where it converts to coesite, and at ambient pressure up to 847 K where it transforms to the beta phase. In particular, the displacive phase transition at 847 K at ambient pressure is driven by intrinsic anharmonicity effects (soft-mode phase transition) and its precise mechanism is difficult to be investigated experimentally. Therefore, we studied these anharmonic effects by means of ab initio calculations in the framework of the statistical thermodynamics approach. We determined the principal thermodynamic quantities accounting for the intrinsic anharmonicity and compared them against experimental data. Our results up to 700 K show a very good agreement with experiments. The same procedures and algorithms illustrated here can also be applied to determine the thermodynamic properties of other crystalline phases possibly affected by intrinsic anharmonic effects, that could partially invalidate the standard quasi-harmonic approach.

scholarly journals Thermodynamic properties of black holes in de Sitter space

2016 ◽  
Vol 32 (02) ◽  
pp. 1750017 ◽  
Author(s):  
Huai-Fan Li ◽  
Meng-Sen Ma ◽  
Ya-Qin Ma
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Heat Capacity ◽  
Black Hole ◽  
Thermodynamic Properties ◽  
Thermodynamic Quantities ◽  
De Sitter ◽  
First Law Of Thermodynamics ◽  
Effective Temperatures ◽  
Sds Black Hole

We study the thermodynamic properties of Schwarzschild–de Sitter (SdS) black hole and Reissner–Nordström–de Sitter (RNdS) black hole in view of global and effective thermodynamic quantities. Making use of the effective first law of thermodynamics, we can derive the effective thermodynamic quantities of de Sitter black holes. It is found that these effective thermodynamic quantities also satisfy Smarr-like formula. Especially, the effective temperatures are nonzero in the Nariai limit. By calculating heat capacity and Gibbs free energy, we find SdS black hole is always thermodynamically stable and RNdS black hole may undergoes phase transition at some points.

Deviation of the Calculated of Density of Refrigerant Fluids in Both Super and Sub Critical Regions

2011 ◽  
Author(s):  
Neda Mobinipouya
Keyword(s):  
Thermodynamic Properties ◽  
Speed Of Sound ◽  
Equations Of State ◽  
Numerical Procedure ◽  
Corresponding States ◽  
Temperature Range ◽  
Critical Regions ◽  
Two Parameter ◽  
Good Agreement

A numerical procedure has successfully predicted accurate values of thermodynamic properties in seven cubic equations of state (EOS) in predicting thermodynamic properties of nine ozone-safe refrigerants both in super and sub-critical regions. Refrigerants include R22, R32, R123, R124, R125, R134a, R141b, R143, and R152a and equations of state, considered here, are Ihm-Song-Mason (ISM), Peng-Robinson (PR) [2], Redlich-Kwong (RK), Soave-Redlikh-Kwong (SRK), Modified Redlickh-Kwong (MRK), Nasrifar-Moshfeghian (NM), and TCC were shown in this paper. In general, the results are in favor of the preference of TCC and PR EOS over other remaining EOS’s in predicting gas densities of all aforementioned refrigerants in both super and sub critical regions. Typically, PR and SRK are in good agreement with those obtained from recent correlations and speed of sound measurements. Therefore, these two EOS stand over other EOS both in sub and super critical regions. All EOS follow two-parameter principle of corresponding states at T/Tc higher than 8 and lower than 1 except NM EOS. In the temperature range 1<T/Tc<8, PR and SRK still follow above mentioned principle. The same trend has been observed for other refrigerants.

Phase transition and thermodynamic properties of ThO 2 : Quasi-harmonic approximation calculations and anharmonic effects

2014 ◽  
Vol 23 (1) ◽  
pp. 017101 ◽  
Author(s):  
Qiang Li ◽  
Jun-Sheng Yang ◽  
Duo-Hui Huang ◽  
Qi-Long Cao ◽  
Fan-Hou Wang
Keyword(s):  
Phase Transition ◽  
Thermodynamic Properties ◽  
Harmonic Approximation ◽  
Anharmonic Effects

scholarly journals Thermodynamics and phase transition in rotational Kiselev black hole

2019 ◽  
Vol 34 (30) ◽  
pp. 1950185 ◽  
Author(s):  
Zhaoyi Xu ◽  
Yi Liao ◽  
Jiancheng Wang
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Thermodynamic Properties ◽  
Mass Formula ◽  
Order Approximation ◽  
Kerr Black Hole ◽  
Strength Parameter ◽  
Thermodynamic Quantities ◽  
State Formula ◽  
Thermodynamic Geometry

In this paper, we investigate the thermodynamic properties of rotational Kiselev black holes (KBH). Specifically, we use the first-order approximation of the event horizon (EH) to calculate thermodynamic properties for general equations of state [Formula: see text]. These thermodynamic properties include areas, entropies, horizon radii, surface gravities, surface temperatures, Komar energies and irreducible masses at the Cauchy horizon (CH) and EH. We study the products of these thermodynamic quantities, we find that these products are determined by the equation of state [Formula: see text] and strength parameter [Formula: see text]. In the case of the quintessence matter [Formula: see text], radiation [Formula: see text] and dust [Formula: see text], we discuss their properties in detail. We also generalize the Smarr mass formula and Christodoulou–Ruffini mass formula to rotational KBH. Finally, we study the phase transition and thermodynamic geometry for rotational KBH with radiation [Formula: see text]. Through analysis, we find that this phase transition is a second-order phase transition. Furthermore, we also obtain the scalar curvature in the thermodynamic geometry framework, indicating that the radiation matter may change the phase transition condition and properties for Kerr black hole.

Mechanical, Dynamical and Thermodynamic Properties of Al-3wt%Mg from First Principles

2017 ◽  
Vol 72 (6) ◽  
pp. 527-534 ◽  
Author(s):  
Rong Yang ◽  
Bin Tang ◽  
Tao Gao
Keyword(s):  
Thermodynamic Properties ◽  
Density Of States ◽  
First Principles ◽  
Phonon Dispersion ◽  
Ambient Pressure ◽  
Structural Parameter ◽  
Partial Density ◽  
Phonon Dispersion Curves ◽  
Hardening Mechanisms ◽  
Good Agreement

AbstractThe mechanical, dynamical and thermodynamic properties of Al-3wt%Mg have been investigated using the first-principles method. The calculated structural parameter is in good agreement with previous works. Results for the elastic modulus, stress-strain relationships, ideal tensile and shear strengths are presented. Al-3wt%Mg is found to have larger moduli and higher strengths than Al, which is consistent with its exploitation in Al precipitate-hardening mechanisms. The partial density of states (PDOS) show that the partly covalent-like bonding through Al p-Mg s hybridization is the origin of excellent mechanical properties of Al-3wt%Mg. The phonon dispersion curves indicate that Al-3wt%Mg is dynamically stable at ambient pressure and 0 K. Furthermore, the Helmholtz free energy ΔF, the entropy S, the constant-volume specific heat CV and the phonon contribution to the internal energy ΔE are predicted using the phonon density of states. We expect that our work can provide useful guidance to help with the performance of Al-3wt%Mg.

scholarly journals In situ Infrared Spectra for Hydrous Forsterite up to 1243 K: Hydration Effect on Thermodynamic Properties

Minerals ◽  
2019 ◽  
Vol 9 (9) ◽  
pp. 512 ◽  
Author(s):  
Liu ◽  
Wang ◽  
Smyth ◽  
Zhang ◽  
Wang ◽  
...  
Keyword(s):  
Thermodynamic Properties ◽  
Temperature Dependence ◽  
Room Temperature ◽  
Equations Of State ◽  
Negative Temperature ◽  
Positive Temperature ◽  
Hydration Effect ◽  
Hydrogen Substitution ◽  
Intrinsic Anharmonicity

Hydrogen substitution has significant effect on the physical properties of olivine, the most abundant mineral in the upper mantle. We collected high-temperature polarized Fourier Transform infrared (FTIR) spectra on hydrous forsterite (Mg-pure olivine) crystals, which were synthesized at 12 GPa, 1473–1673 K. The modes at 3612, 3578, 3566, 3551 cm−1 show comparable negative temperature dependence, and the magnitude of (∂vi/∂T)P decreases dramatically with frequency increasing. Whereas, the peak at 3477 cm−1, which is attributed to protonation along the O1...O2 edge on the Si tetrahedron, has a positive temperature dependence. The absorbance intensities of all these OH bands remained almost the same when quenched to room temperature. On the other hand, we also evaluate the hydration effect on the thermodynamic properties (heat capacities). For the anhydrous forsterite sample, the intrinsic anharmonicity could significantly increase the heat capacity by 5~6% when extrapolated to 2000 K. Hydration further increase such difference to ~9%, in both the cases of M-substitution or Si-substitution. Hence, hydration in olivine has significant impact on the anharmonic contribution to the thermodynamic properties, as well as Equations of State and equilibrium isotope fractionation β-factor at high-P,T conditions in the deep mantle.

RELATIVISTIC SOMMERFELD LOW TEMPERATURE EXPANSION

2007 ◽  
Vol 16 (02n03) ◽  
pp. 285-289
Author(s):  
O. LOURENÇO ◽  
M. DUTRA ◽  
A. DELFINO ◽  
J. S. SÁ MARTINS
Keyword(s):  
Phase Transition ◽  
Equation Of State ◽  
Low Temperature ◽  
Gas Phase ◽  
Thermodynamic Quantities ◽  
Many Body ◽  
Temperature Expansion ◽  
Fermionic Systems ◽  
Walecka Model ◽  
Good Agreement

We derive a relativistic Sommerfeld expansion for thermodynamic quantities in many-body fermionic systems. The expansion is used to generate the equation of state of the Walecka model and its isotherms. We find that these results are in good agreement with numerical calculations, even when the expansion is truncated at its lowest order, in the low temperature regime, defined by T/xf ≪ 1. Although the interesting region near the liquid-gas phase transition is excluded by this criterion, the expansion may still find usefulness in the study of very cold nuclear matter systems, such as neutron stars.

Anharmonic perturbation theory to 0(λ4): Equation of state for Kr from the Aziz potential

1992 ◽  
Vol 70 (1) ◽  
pp. 31-39 ◽  
Author(s):  
Ramesh C. Shukla ◽  
Hermann Hübschle
Keyword(s):  
Perturbation Theory ◽  
Thermodynamic Properties ◽  
Potential Function ◽  
Phonon Dispersion ◽  
Perturbation Expansion ◽  
Lattice Parameter ◽  
Thermodynamic Quantities ◽  
Specific Heats ◽  
Experimental Values ◽  
Good Agreement

We carry out a complete calculation of the thermodynamic properties of Kr from a potential function, the Aziz potential, including the three-body Axilrod–Teller contribution, and the (λ4) anharmonic perturbation theory proposed by Shukla and Cowley (Phys. Rev. B: Solid State, 3, 4055 (1971)), where λ is the Van Hove ordering parameter. Along with the λ4 results, in the high-temperature (HT) limit (T > θD, where θD is the Debye temperature), we also present the results for the quasi-harmonic (QH) theory (calculated for all temperatures), the lowest order (λ2) perturbation theory (PT), as well as results from those theories that involve a subset of diagrams (contributions) of 0(λ4), both in the HT limit. This work represents the first calculation of the thermodynamic properties of Kr with the λ2 and λ4 anharmonic PT from a potential function not fitted to the crystal data. The Aziz potential gives an excellent description of phonon-dispersion curves in the three principal symmetry directions. The QH results are in good agreement with the experimental values for most of the thermodynamic quantities for temperatures up to <Tm/3 (Tm is the melting temperature) except for the isothermal bulk modulus (BT) where the agreement is poor in 0 K < T < 25 K and good up to 2Tm/3. The λ2 PT results are only slightly better than the corresponding QH results in the temperature range of < Tm/2. The inclusion of the λ4 PT enhances the results for the Aziz potential significantly. The calculated lattice parameter (a0) is in excellent agreement with experimental values up to 3Tm/4. For T > 3Tm/4, a0 rises rapidly and there is an indication of the breakdown of the perturbation expansion. The values for specific heats at constant volume (Cv) and constant pressure (Cp) and volume expansion (β) are in very good agreement with experiment up to 60% of Tm. The other schemes (with the exception of Ladder) that utilize a subset of diagrams of 0(λ4), which were so successful for the model of a Lennard–Jones solid (viz., ISC (improved self-consistent), λ4-Ladder etc.), are not so useful for this potential. This is due to the heavy cancellation of diagrams in these sets. The ring diagram scheme proposed here for the Aziz potential gives better results than the ISC scheme.

Some Properties of Molten KCl at High Density Studied by MD Simulation

1981 ◽  
Vol 36 (10) ◽  
pp. 1106-1111 ◽  
Author(s):  
Ryuzo Takagi ◽  
Isao Okada ◽  
Kazutaka Kawamura
Keyword(s):  
Molecular Dynamics ◽  
Monte Carlo ◽  
Thermodynamic Properties ◽  
Diffusion Coefficients ◽  
Md Simulation ◽  
Ambient Pressure ◽  
The Self ◽  
Self Diffusion ◽  
Dynamics Simulations ◽  
Good Agreement

Molecular dynamics simulations of molten KCl have been performed at 1173 K with the molar volumes of 52.0 (the value under ambient pressure), 50.0, 48.0 and 45.0 cm3 mol-1 . Some thermodynamic properties at higher densities have been evaluated, which are generally in good agreement with the experimentally obtained ones and Monte Carlo results. Both at normal and higher densities, the self-exchange velocities of neighbouring unlike ions (SEV) are found to be proportional to the internal mobilities with nearly the same constant as derived previously for molten LiCl, RbCl and their 1 : 1 mixture. Calculated transport properties such as the SEV and the self-diffusion coefficients considerably decrease with increasing density, while the configuration does not change much.

Calibration of excess thermodynamic properties and elastic constant variations associated with the alpha beta phase transition in quartz

1998 ◽  
Vol 83 (1-2) ◽  
pp. 2-22 ◽  
Author(s):  
Michael A. Carpenter ◽  
Ekhard K. H. Salje ◽  
Ann Graeme-Barber ◽  
Bernd Wruck ◽  
Martin T. Dove ◽  
...  
Keyword(s):  
Phase Transition ◽  
Thermodynamic Properties ◽  
Elastic Constant ◽  
Beta Phase ◽  
Excess Thermodynamic Properties ◽  
Alpha Beta
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