Phase Transitions

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.

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

2015 ◽  
Vol 112 (22) ◽  
pp. 6898-6901 ◽  
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.

CHARACTERISTIC TEMPERATURES OF FIRST-ORDER FERROELECTRIC PHASE TRANSITION: EFFECTIVE FIELD APPROACH

2012 ◽  
Vol 02 (02) ◽  
pp. 1241007 ◽  
Author(s):  
C. L. WANG ◽  
C. ARAGÓ ◽  
M. I. MARQUÉS
Keyword(s):  
Free Energy ◽  
Phase Transitions ◽  
Helmholtz Free Energy ◽  
Ferroelectric Phase ◽  
Effective Field ◽  
Static Properties ◽  
Field Approach ◽  
First Order ◽  
Characteristic Temperatures ◽  
Ferroelectric Phase Transitions

The explicit expression of Helmholtz free energy has been obtained from the equation of state from effective field approach. From the Helmholtz free energy, four characteristic temperatures describing a first-order ferroelectric phase transitions have been determined. The physical meaning of coefficients in Landau-type free energy has been revealed by comparison with the expanding Helmholtz function. Temperature dependence of polarization under different bias, and hysteresis loops at different temperatures are presented and discussed. These results provide the basic understandings of the static properties of first-order ferroelectric phase transitions.

Dyonic and Magnetic Black Holes with Rational Nonlinear Electrodynamics

2020 ◽  
Author(s):  
Sergey Kruglov
Keyword(s):  
Black Holes ◽  
Heat Capacity ◽  
Black Hole ◽  
Free Energy ◽  
Phase Transitions ◽  
Helmholtz Free Energy ◽  
Magnetic Charge ◽  
The Self ◽  
Nonlinear Electrodynamics ◽  
Dual Case

The principles of causality and unitarity are studied within rational nonlinear electrodynamics proposed earlier. We investigate dyonic and magnetized black holes and show that in the self-dual case, when the electric charge equals the magnetic charge, corrections to Coulomb's law and Reissner-Nordstrom solutions are absent. In the case of the magnetic black hole, the Hawking temperature, the heat capacity and the Helmholtz free energy are calculated. It is shown that there are second-order phase transitions and it was demonstrated that at some range of parameters the black holes are stable.

VAPOR–LIQUID EQUILIBRIUM MODELING FOR MIXTURES OF HFC-32 + ISOBUTANE AND HFC-32 + HFO-1234ze(E)

2011 ◽  
Vol 19 (02) ◽  
pp. 93-97 ◽  
Author(s):  
RYO AKASAKA
Keyword(s):  
Free Energy ◽  
Helmholtz Free Energy ◽  
Equations Of State ◽  
Dew Point ◽  
Working Fluid ◽  
Liquid Equilibrium ◽  
Vapor Liquid Equilibrium ◽  
Equilibrium Modeling ◽  
Independent Variables ◽  
Vapor Liquid

Vapor–liquid equilibrium (VLE) have been successfully modeled for the binary mixtures of difluoromethane (HFC-32) + isobutane and difluoromethane + trans-1,3,3,3-tetrafluoropropene (HFO-1234ze(E)). These mixtures are considered as possible replacements for conventional refrigerants far from negligible global warming potential (GWP). A multifluid approach explicit in the Helmholtz free energy forms the basis of the model. The independent variables are the temperature, density, and composition. Accurate published equations of state for pure HFC-32, isobutane, and HFO-1234ze(E) are incorporated to calculate the Helmholtz free energy of each component. Typical uncertainties of bubble- and dew-point pressures calculated using the model are within 2%. Although adjustable parameters of the model are determined only from experimental VLE data, it is highly probable that the model reasonably predicts other thermodynamic properties such as enthalpy and heat capacities. Therefore, the model allows practical design and simulation of refrigeration systems using the mixtures as a working fluid.

TOWARDS A MOLECULAR THEORY FOR THE VAN DER WAALS–MAXWELL DESCRIPTION OF FLUID PHASE TRANSITIONS

2002 ◽  
Vol 01 (02) ◽  
pp. 381-406 ◽  
Author(s):  
ANDRIY KOVALENKO ◽  
FUMIO HIRATA
Keyword(s):  
Hydrogen Bonding ◽  
Phase Transitions ◽  
Phase Diagrams ◽  
Equations Of State ◽  
Van Der Waals ◽  
Fluid Phase ◽  
Carbon Aerogel ◽  
Molecular Fluids ◽  
Wide Range ◽  
Realistic Interaction

We briefly review developments of theories for phase transitions of molecular fluids and mixtures, from semi-phenomenological approaches providing equations of state with adjustable parameters to first-principles microscopic methods qualitatively correct for a variety of molecular models with realistic interaction potentials. We further present the generalization of the van der Waals–Maxwell description of fluid phase diagrams to account for chemical specificities of polar molecular fluids, such as hydrogen bonding. Our theory uses the reference interaction site model (RISM) integral equation approach complemented with the new closure we have proposed (KH approximation), successful over a wide range of density from gas to liquid. The RISM/KH theory is applied to the known three-site models of water, methanol, and hydrogen fluoride. It qualitatively reproduces their vapor-liquid phase diagrams and the structure in the gas as well as liquid phases, including hydrogen bonding. Furthermore, phase transitions of water and methanol sorbed in nanoporous carbon aerogel are described by means of the replica generalization of the RISM approach we have developed. The changes as compared to the bulk fluids are in agreement with simulations and experiment. The RISM/KH theory is promising for description of phase transitions in various associating fluids, in particular, electrolyte as well as non-electrolyte solutions and ionic liquids.

THE ISOSPIN DEPENDENCE OF THE NUCLEAR PHASE TRANSITION NEAR THE CRITICAL POINT

2010 ◽  
Vol 19 (08n09) ◽  
pp. 1570-1576
Author(s):  
Z. CHEN ◽  
R. WADA ◽  
A. BONASERA ◽  
T. KEUTGEN ◽  
K. HAGEL ◽  
...  
Keyword(s):  
Phase Transition ◽  
Molecular Dynamics ◽  
Free Energy ◽  
Phase Transitions ◽  
Critical Point ◽  
Critical Phenomena ◽  
Critical Points ◽  
Liquid Mixtures ◽  
Nuclear Phase ◽  
Isospin Dependence

The experimental results reveal the isospin dependence of the nuclear phase transition in terms of the Landau Free Energy description of critical phenomena. Near the critical point, different ratios of the neutron to proton concentrations lead to different critical points for the phase transition which is analogous to the phase transitions in He 4- He 3 liquid mixtures. The antisymmetrized molecular dynamics (AMD) and GEMINI models calculations were also performed and the results will be discussed as well.

Phase Transition Behavior of Solids under Shock Compression

2010 ◽  
Vol 638-642 ◽  
pp. 1053-1058 ◽  
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.

scholarly journals ON THE NONSTATIONARY PARAMETER OF STATE FOR DARK MATTER

2018 ◽  
pp. 44-48
Author(s):  
Amangeldyieva A ◽  
Kairatkyzy D. ◽  
Konysbayev T.
Keyword(s):  
Dark Matter ◽  
Van Der Waals ◽  
Ideal Gas ◽  
Negative Power ◽  
Clapeyron Equation ◽  
Planck Time

The purpose of work is a conclusion non-stationary the equations of a condition of WIMP-gas for their various models - ideal gas (Mendeleyev-Clapeyron equation), non-ideal gas (equations type of Van der Waals and Dieterichi). It is shown that their general dependence on time has the negative power. Therefore, the closer to the Planck time, and also to the time of WIMP particles birth, the more state of non-baryonic substance differ from the dust-like one.

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