Equations of State and the ellipsometry diagnostics

AbstractAn overview of the equations of state (EOS) with a short summary of shock wave experiments with laser induced impact flyer, relevant to EOS study, is presented. The “old-new” ellipsometry is suggested and described for the EOS research. The detection of phase transitions of the first kind (solid-solid) as well as phase transition of the second kind (Curie point as an example) is demonstrated. Furthermore, the temperature measurements are not possible without the knowledge of the emissivity, a parameter that can be measured by using ellipsometry techniques.

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Prediction of 10-fold coordinated TiO2 and SiO2 structures at multimegabar pressures

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1500604112 ◽

2015 ◽

Vol 112 (22) ◽

pp. 6898-6901 ◽

Cited By ~ 32

Author(s):

Matthew J. Lyle ◽

Chris J. Pickard ◽

Richard J. Needs

Keyword(s):

Phase Transition ◽

Phase Transitions ◽

Electronic Properties ◽

First Principles ◽

Pressure Range ◽

Extrasolar Planets ◽

Equations Of State ◽

Space Group ◽

P Type ◽

Pressure Phase

We predict by first-principles methods a phase transition in TiO2 at 6.5 Mbar from the Fe2P-type polymorph to a ten-coordinated structure with space group I4/mmm. This is the first report, to our knowledge, of the pressure-induced phase transition to the I4/mmm structure among all dioxide compounds. The I4/mmm structure was found to be up to 3.3% denser across all pressures investigated. Significant differences were found in the electronic properties of the two structures, and the metallization of TiO2 was calculated to occur concomitantly with the phase transition to I4/mmm. The implications of our findings were extended to SiO2, and an analogous Fe2P-type to I4/mmm transition was found to occur at 10 TPa. This is consistent with the lower-pressure phase transitions of TiO2, which are well-established models for the phase transitions in other AX2 compounds, including SiO2. As in TiO2, the transition to I4/mmm corresponds to the metallization of SiO2. This transformation is in the pressure range reached in the interiors of recently discovered extrasolar planets and calls for a reformulation of the equations of state used to model them.

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Phase Transitions

An Introduction to Statistical Mechanics and Thermodynamics ◽

10.1093/oso/9780198853237.003.0017 ◽

2019 ◽

pp. 205-222

Author(s):

Robert H. Swendsen

Keyword(s):

Phase Transition ◽

Free Energy ◽

Phase Transitions ◽

Helmholtz Free Energy ◽

Equations Of State ◽

Van Der Waals ◽

Ideal Gas ◽

Phase Rule ◽

Clapeyron Equation ◽

Maxwell Construction

Phase transitions are introduced using the van der Waals gas as an example. The equations of state are derived from the Helmholtz free energy of the ideal gas. The behavior of this model is analyzed, and an instability leads to a liquid-gas phase transition. The Maxwell construction for the pressure at which a phase transition occurs is derived. The effect of phase transition on the Gibbs free energy and Helmholtz free energy is shown. Latent heat is defined, and the Clausius–Clapeyron equation is derived. Gibbs' phase rule is derived and illustrated.

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Phase Transition Behavior of Solids under Shock Compression

Materials Science Forum ◽

10.4028/www.scientific.net/msf.638-642.1053 ◽

2010 ◽

Vol 638-642 ◽

pp. 1053-1058 ◽

Cited By ~ 1

Author(s):

Tsutomu Mashimo

Keyword(s):

Phase Transition ◽

High Pressure ◽

Phase Transitions ◽

Equations Of State ◽

Relaxation Times ◽

Inorganic Materials ◽

High Pressure Phase ◽

High Time Resolution ◽

Compression Process ◽

Pressure Phase

Through the measurement of Hugoniot parameters, we can get useful information about high-pressure phase transitions, equations of state (EOS), etc. of solids, without pressure calibration. And, we can discuss the transition dynamics, because the relaxation times of phase transition and compression process are of the same order. We have performed the Hugoniot-measurement experiments on various kinds of compound materials including oxides, nitrides, borides and chalcogenides by using a high time-resolution streak photographic system combined with the propellant guns. The structure-phase transitions have been observed for several kinds of inorganic materials, TiO2, ZrO2, Gd3Ga5O12, AlN, ZnS, ZnSe, etc. The phase transition pressures under shock and static compressions of metals, ionic materials, semiconductors and some ceramics are consistent with each other. Those are not consistent for strong covalent bonding materials such as C, BN and SiO2. Here, the Hugoniot compression data are reviewed, and the shock-induced phase transitions and the dynamics are discussed, as well as the EOS of the high-pressure phase up to evem 1 TPa.

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Shock Wave Induced Phase Transition from Crystalline to Amorphous State of Lead Nitrate Crystal

CrystEngComm ◽

10.1039/d1ce01366a ◽

2021 ◽

Author(s):

A. Sivakumar ◽

Eniya Palaniyasan ◽

S. Sahaya Jude Dhas ◽

Raju Kumar ◽

Abdulrahman Ibrahim Almansour ◽

...

Keyword(s):

Phase Transition ◽

Shock Wave ◽

Phase Transitions ◽

Lead Nitrate ◽

Amorphous State ◽

Wave Induced

The promising prospects arising out of the phase transitions of materials at shocked conditions is an emerging field at the frontier of structural science. In this communication, dynamic shock wave...

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High-pressure phase transitions in the rare-earth orthoferrite LaFeO3

Acta Crystallographica Section B Structural Science Crystal Engineering and Materials ◽

10.1107/s2052520614007379 ◽

2014 ◽

Vol 70 (3) ◽

pp. 452-458 ◽

Cited By ~ 15

Author(s):

Martin Etter ◽

Melanie Müller ◽

Michael Hanfland ◽

Robert E. Dinnebier

Keyword(s):

Phase Transition ◽

High Pressure ◽

Phase Transitions ◽

Equations Of State ◽

Spin Transition ◽

Structural Phase ◽

Two Phase ◽

Pressure Derivative ◽

Temperature Isotherm ◽

Hydrostatic Limit

Sequential Rietveld refinements were applied on high-pressure synchrotron powder X-ray diffraction measurements of lanthanum ferrite (LaFeO3) revealing two phase transitions on the room-temperature isotherm up to a pressure of 48 GPa. The first structural phase transition of second order occurs at a pressure of 21.1 GPa, changing the space group fromPbnmtoIbmm. The second transition, involving a isostructural first-order phase transition, occurs at approximately 38 GPa, indicating a high-spin to low-spin transition of the Fe3+ion. Following the behavior of the volume up to the hydrostatic limit of methanol–ethanol it was possible to use inverted equations of state (EoS) to determine a bulk modulus ofB0= 172 GPa and a corresponding pressure derivative ofB′0= 4.3. In addition, the linearized version of the inverted EoS were used to determine the corresponding moduli and pressure derivatives for each lattice direction.

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Tidal deformability and other global parameters of compact stars with strong phase transitions

Astronomy and Astrophysics ◽

10.1051/0004-6361/201833969 ◽

2019 ◽

Vol 622 ◽

pp. A174 ◽

Cited By ~ 24

Author(s):

M. Sieniawska ◽

W. Turczański ◽

M. Bejger ◽

J. L. Zdunik

Keyword(s):

Phase Transition ◽

Phase Transitions ◽

Neutron Star ◽

Neutron Stars ◽

Equations Of State ◽

Dense Matter ◽

Compact Stars ◽

High Mass ◽

Density Jump ◽

Strong Phase

Context. Using parametric equations of state (relativistic polytropes and a simple quark bag model) to model dense-matter phase transitions, we study global, measurable astrophysical parameters of compact stars such as their allowed radii and tidal deformabilities. We also investigate the influence of stiffness of matter before the onset of the phase transitions on the parameters of the possible exotic dense phase. Aims. The aim of our study is to compare the parameter space of the dense matter equation of state permitting phase transitions to a sub-space compatible with current observational constraints such as the maximum observable mass, tidal deformabilities of neutron star mergers, radii of configurations before the onset of the phase transition, and to give predictions for future observations. Methods. We studied solutions of the Tolman-Oppenheimer-Volkoff equations for a flexible set of parametric equations of state, constructed using a realistic description of neutron-star crust (up to the nuclear saturation density), and relativistic polytropes connected by a density-jump phase transition to a simple bag model description of deconfined quark matter. Results. In order to be consistent with recent observations of massive neutron stars, a compact star with a strong high-mass phase transition cannot have a radius smaller than 12 km in the range of masses 1.2 − 1.6 M⊙. We also compare tidal deformabilities of stars with weak and strong phase transitions with the results of the GW170817 neutron star merger. Specifically, we study characteristic phase transition features in the Λ1 − Λ2 relation, and estimate the deviations of our results from the approximate formulæ for Λ∼ − R (M1) and Λ-compactness proposed in the literature. We find constraints on the hybrid equations of state to produce stable neutron stars on the twin branch. For the exemplary equations of state most of the high-mass twins occur for the minimum values of the density jump λ = 1.33 − 1.54; corresponding values of the square of the speed of sound are α = 0.7 − 0.37. We compare results with observations of gravitational waves and with the theoretical causal limit and find that the minimum radius of a twin branch is between 9.5 and 10.5 km, and depends on the phase transition baryon density. For these solutions the phase transition occurs below 0.56 fm−3.

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Electric properties of olive oil under pressure

European Food Research and Technology ◽

10.1007/s00217-021-03761-7 ◽

2021 ◽

Author(s):

L. T. Pawlicki ◽

R. M. Siegoczyński ◽

S. Ptasznik ◽

K. Marszałek

Keyword(s):

Molecular Structure ◽

Phase Transition ◽

Phase Diagram ◽

Phase Transitions ◽

Olive Oil ◽

Material Parameters ◽

First Order ◽

Long Time ◽

Capacitive Reactance ◽

First Order Phase

AbstractThe main purpose of the experiment was a thermodynamic research with use of the electric methods chosen. The substance examined was olive oil. The paper presents the resistance, capacitive reactance, relative permittivity and resistivity of olive. Compression was applied with two mean velocities up to 450 MPa. The results were shown as functions of pressure and time and depicted on the impedance phase diagram. The three first order phase transitions have been detected. All the changes in material parameters were observed during phase transitions. The material parameters measured turned out to be the much more sensitive long-time phase transition factors than temperature. The values of material parameters and their dependence on pressure and time were compared with the molecular structure, arrangement of molecules and interactions between them. Knowledge about olive oil parameters change with pressure and its phase transitions is very important for olive oil production and conservation.

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Room-temperature NaI/H2O compression icing: solute–solute interactions

Physical Chemistry Chemical Physics ◽

10.1039/c7cp03919k ◽

2017 ◽

Vol 19 (39) ◽

pp. 26645-26650 ◽

Cited By ~ 20

Author(s):

Qingxin Zeng ◽

Chuang Yao ◽

Kai Wang ◽

Chang Q. Sun ◽

Bo Zou

Keyword(s):

Phase Transition ◽

Phase Transitions ◽

Bond Energy ◽

Room Temperature ◽

Solute Concentration ◽

Solute Interaction ◽

Solute Interactions

H–O bond energy governs the PCx for Na/H2O liquid–VI–VII phase transition. Solute concentration affects the path of phase transitions differently with the solute type. Solute–solute interaction lessens the PC2 sensitivity to compression. The PC1 goes along the liquid–VI boundary till the triple phase joint.

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The origin of the lattice thermal conductivity enhancement at the ferroelectric phase transition in GeTe

npj Computational Materials ◽

10.1038/s41524-021-00523-7 ◽

2021 ◽

Vol 7 (1) ◽

Author(s):

Đorđe Dangić ◽

Olle Hellman ◽

Stephen Fahy ◽

Ivana Savić

Keyword(s):

Phase Transition ◽

Thermal Conductivity ◽

Phase Transitions ◽

Thermoelectric Materials ◽

Ferroelectric Phase Transition ◽

Lattice Thermal Conductivity ◽

Ferroelectric Phase ◽

Structural Phase ◽

High Symmetry ◽

Structural Phase Transitions

AbstractThe proximity to structural phase transitions in IV-VI thermoelectric materials is one of the main reasons for their large phonon anharmonicity and intrinsically low lattice thermal conductivity κ. However, the κ of GeTe increases at the ferroelectric phase transition near 700 K. Using first-principles calculations with the temperature dependent effective potential method, we show that this rise in κ is the consequence of negative thermal expansion in the rhombohedral phase and increase in the phonon lifetimes in the high-symmetry phase. Strong anharmonicity near the phase transition induces non-Lorentzian shapes of the phonon power spectra. To account for these effects, we implement a method of calculating κ based on the Green-Kubo approach and find that the Boltzmann transport equation underestimates κ near the phase transition. Our findings elucidate the influence of structural phase transitions on κ and provide guidance for design of better thermoelectric materials.

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