Calculation of theP–Tphase diagram of nitrogen using a mean field model

2017 ◽  
Vol 31 (31) ◽  
pp. 1750245 ◽  
Author(s):  
Y. Enginer ◽  
G. Algul ◽  
H. Yurtseven
Keyword(s):  
Phase Diagram ◽  
Molecular Nitrogen ◽  
Mean Field ◽  
Quadratic Function ◽  
Order Parameters ◽  
Free Energies ◽  
Mean Field Model ◽  
Phase Line ◽  
T Phase ◽  
Quadratic Coupling

The P–T phase diagram is calculated at low and moderate pressures by obtaining the phase line equations for the transitions considered in nitrogen using the Landau phenomenological model. For some transitions, a quadratic coupling between the order parameters is taken into account in the expansion of free energies in terms of the order parameters. A quadratic function in T and P is fitted to the experimental P–T data from the literature and the fitted parameters are determined.It is shown that the model studied here describes the observed data adequately, which can also be used to predict the thermodynamic properties of the phases of the molecular nitrogen within the temperatures and pressures of the P–T phase diagram of this system.

A Phase Diagram for the Ice VI–VII–VIII Transitions

1998 ◽  
Vol 12 (08) ◽  
pp. 271-279 ◽  
Author(s):  
H. Yurtseven ◽  
S. Salihoğlu
Keyword(s):  
Phase Diagram ◽  
Phase Transitions ◽  
Field Model ◽  
Mean Field ◽  
Calculated Phase Diagram ◽  
Mean Field Model ◽  
Phase Line ◽  
Calculated Phase ◽  
The Mean ◽  
T Phase

In this study we obtain the P–T phase diagram for the ice VI–VII–VIII phase transitions by means of the mean field model developed here. We have fitted the experimentally measured P–T data to our phase line equations. Our calculated phase diagram describes adequately the observed behavior of the ice VI–VII–VIII phase transitions.

scholarly journals Calculation of the T-P phase diagrams for the halogenomethane compounds (CCl-=SUB=-4-n-=/SUB=-Br-=SUB=-n-=/SUB=-, n=0, 1, 2, 4) using the mean field theory -=SUP=-*-=/SUP=-

2019 ◽  
Vol 61 (2) ◽  
pp. 339
Author(s):  
H. Yurtseven ◽  
S.B. Isik ◽  
E. Kilit Dogan
Keyword(s):  
Phase Diagrams ◽  
Mean Field Theory ◽  
Mean Field ◽  
Face Centered Cubic ◽  
Mean Field Model ◽  
Phase Line ◽  
Component Systems ◽  
Two Component Systems ◽  
The Mean ◽  
Face Centered

AbstractThe T – P phase diagrams of the halogenomethane compounds (CCl_4 – _ n Br_ n , n = 0, 1, 2, 4) are calculated using a mean field model. By expanding the free energy in terms of the order parameters for the transitions of the liquid (L), rhombohedral (R), face-centered cubic (FCC) and monoclinic (M) phases in those compounds, the phase line equations are derived and they are fitted to the experimental data from the literature. This method of calculating the T – P phase diagram is satisfactory to explain the T – P measurements for the halogenomethane compounds and it can also be applied to two-component systems.

scholarly journals Phase diagram of the mean field model of simplicial gravity

1999 ◽  
Vol 542 (1-2) ◽  
pp. 413-424 ◽  
Author(s):  
P. Bialas ◽  
Z. Burda ◽  
D. Johnston
Keyword(s):  
Phase Diagram ◽  
Field Model ◽  
Mean Field ◽  
Mean Field Model ◽  
The Mean

scholarly journals Field-induced tricritical phenomenon and magnetic structures in magnetic Weyl semimetal candidate NdAlGe

2021 ◽  
Author(s):  
Jun Zhao ◽  
Wei Liu ◽  
Aziz Ur Rahman ◽  
Fanying Meng ◽  
Langsheng Ling ◽  
...  
Keyword(s):  
Phase Diagram ◽  
Critical Exponents ◽  
Tricritical Point ◽  
Mean Field ◽  
Scaling Analysis ◽  
Topological Properties ◽  
Mean Field Model ◽  
Spin Configuration ◽  
Magnetic Structures ◽  
Weyl Semimetal

Abstract Non-centrosymmetric NdAlGe is considered to be a candidate for magnetic Weyl semimetal in which the Weyl nodes can be moved by magnetization. Clarification of the magnetic structures and couplings in this system is thus crucial to understand its magnetic topological properties. In this work, we conduct a systematical study of magnetic properties and critical behaviors of single-crystal NdAlGe. Angle-dependent magnetization exhibits strong magnetic anisotropy along the c-axis and absolute isotropy in the ab-plane. The study of critical behavior with H//c gives critical exponents β = 0.236(2), γ = 0.920(1), and δ = 4.966(1) at critical temperature TC = 5.2(2) K. Under the framework of the universality principle, M(T, H) curves are scaled into universality curves using these critical exponents, demonstrating reliability and self-consistency of the obtained exponents. The critical exponents of NdAlGe are close to the theoretical prediction of a tricritical mean-field model, indicating a field-induced tricritical behavior. Based on the scaling analysis, a H −T phase diagram for NdAlGe with H//c is constructed, revealing a ground state with an up-up- down spin configuration. The phase diagram unveils multiple phases including up-up-down domains, up-up-down ordering state, polarized ferromagnetic (PFM), and paramagnetic (PM) phases, with a tricritical point (TCP) located at the intersection [TT CP = 5.27(1) K, HT CP = 30.1(3) kOe] of up-up-down, PFM, and PM phases. The multiple phases and magnetic structures imply a delicate competition and balance between variable interactions and couplings, laying a solid foundation for unveiling topological properties and critical phenomena in this system.

Joint Evolution of Two Domany–Kinzel Cellular Automata

1997 ◽  
Vol 11 (10) ◽  
pp. 1245-1255 ◽  
Author(s):  
Emílio P. Gueuvoghlanian ◽  
Tânia Tomé
Keyword(s):  
Phase Diagram ◽  
Cellular Automata ◽  
Mean Field ◽  
Order Parameters ◽  
Pair Approximation ◽  
Two Systems ◽  
Joint Dynamics ◽  
Analytical Approaches ◽  
Joint Evolution ◽  
Mean Field Approximations

We analyze the joint dynamics of two systems each one evolving in time according to the Domany–Kinzel rules. Two prescriptions for the joint evolution are studied. We make analytical approaches, based on dynamical mean-field approximations at the level of three-site correlations, to obtain the phase diagram. Also, the susceptibilities associated with the order parameters are calculated by using a pair approximation.

Application of TDGL Model to B2 Type Ordering with Two Step Phase Separation in Fe-Ni-Al Alloys

2013 ◽  
Vol 1535 ◽  
Author(s):  
Ryuichiro Oguma ◽  
Syo Matsumura ◽  
Minoru Doi ◽  
Satoshi Hata ◽  
Keisuke Ogata
Keyword(s):  
Phase Separation ◽  
Electron Tomography ◽  
Kinetic Equations ◽  
Mean Field ◽  
Three Dimensional ◽  
Al Alloys ◽  
Order Parameters ◽  
Free Energies ◽  
Ginzburg Landau ◽  
Domain Structures

ABSTRACTFormation of domain structures in two-step phase separation in Fe-based Fe-Ni-Al alloys are investigated by applying a time-dependent Ginzburg-Landau (TDGL) model. The present authors recently developed a TDGL formulation for ordering processes of B2 and D03 in binary alloys, taking into account the symmetrical relationships between these ordered phases. In this formulation, multiple types of variants of the structures are represented by three order parameters which can be measured independently through crystal structure factors. Mean-field free energies are defined in a form of Landau type expansion with the order parameters and a composition parameter. Interfacial energies due to local variations of degrees of order and composition are given in a gradient square approximation. Kinetic equations for time-evolution of the order parameters and the composition one are derived from the Ginzburg-Landau type potential consisting of the mean-field free energies and the interfacial energy terms. On the other hand, coauthors have investigated domain structures in two-step phase separation of Fe-based Fe-Ni-Al alloys. The evolution of three-dimensional domain structures and composition profiles has been analyzed by electron tomography imaging and energy-dispersive X-ray spectroscopy. In this work the authors performed three-dimensional numerical simulations assuming the thermal processing. The results of the simulations well reproduced the characteristics of the micro-structures obtained from the observations.

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