scholarly journals Фазовые превращения в однокомпонентных многофазных системах: фазово-полевой подход

2022 ◽  
Vol 92 (2) ◽  
pp. 187
Author(s):  
В.Г. Лебедев
Keyword(s):  
Phase Transitions ◽  
Gibbs Energy ◽  
Phase Field ◽  
Complete System ◽  
Nonequilibrium System ◽  
Phase Model ◽  
Multiphase Model ◽  
Two Phase ◽  
Dissipative Dynamics ◽  
Phase Fields

The problems of constructing a multiphase model of the phase field for the processes of phase transitions of the first kind are considered. Based on the Gibbs energy of the complete system expressed in terms of antisymmetrized combinations of phase fields, it is shown that the equations of dissipative dynamics of a locally nonequilibrium system follow from the condition of its monotonic decrease, preserving the normalization of the sum of variables by one and the following properties of the previously known two-phase model.

Metastable Two-Phase Field(A2+B2) in Co-Al-Fe and Co-Al Alloy Systems

2004 ◽  
Vol 449-452 ◽  
pp. 61-64 ◽  
Author(s):  
Takao Kozakai ◽  
Tadaaki Shikama ◽  
Toshiyuki Koyama ◽  
Minoru Doi
Keyword(s):  
Phase Field ◽  
Composition Gradient ◽  
Al Alloy ◽  
Limit Curve ◽  
Compositional Gradient ◽  
Two Phase ◽  
Transmission Electron ◽  
Phase Fields ◽  
Short Time ◽  
Alloy Systems

Precipitation of disordered bcc Co (A2) particles has been investigated in Co-rich B2 ordered Co-Al-Fe and Co-Al alloys by means of a macroscopic composition gradient method using a transmission electron microscope. When Co-Al-Fe ternary and Co-Al binary alloys were annealed at 823-1023K for a relatively short time, bcc disordered particles precipitated within B2 ordered matrix, followed by the formation of equilibrium fcc α-Co (A1) on the phase boundaries. The precipitation limit of metastable A2 phase was evaluated using the binary and ternary specimens with macroscopic compositional gradient. As a result, it was found that the limits are located within the equilibrium A1+B2 two-phase fields in both ternary and binary alloy systems, and that the limit curve on the isothermal section at 923K for Co-Al-Fe system successfully connects with the phase boundary of A2+B2 two-phase field at the Co-Fe binary side of the ternary system.

scholarly journals Pathways connecting two opposed bilayers with a fusion pore: a molecularly-informed phase field approach

Soft Matter ◽  
2020 ◽  
Vol 16 (2) ◽  
pp. 366-374 ◽  
Author(s):  
Yucen Han ◽  
Zirui Xu ◽  
An-Chang Shi ◽  
Lei Zhang
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Fusion Pore ◽  
Two Phase ◽  
Field Approach ◽  
Amphiphilic Molecules ◽  
Phase Fields

A phase field model with two phase fields, representing the concentration and the head–tail separation of amphiphilic molecules, respectively, has been constructed using an extension of the Ohta–Kawasaki model (Macromolecules, 1986, 19, 2621–2632).

Mathematical Models for Solid-Solid Phase Transitions Driven by Configurational Forces

2013 ◽  
Vol 774-776 ◽  
pp. 488-492
Author(s):  
Pei Cheng Zhu
Keyword(s):  
Phase Transitions ◽  
Mathematical Models ◽  
Shape Memory ◽  
Phase Field ◽  
Mean Curvature ◽  
Solid Phase ◽  
Configurational Forces ◽  
Two Phase ◽  
Phase Field Models ◽  
Martensitic Phase Transformations

Two phase-field models for solid-solid phase transitions driven by configurational forces are reviewed, and the formulation of the models is briefly presented for the non-conserved case, as an example. Applications include martensitic phase transformations in, e.g., shape memory alloys and sintering in ceramic producing. They are compared with two other famous models for phase transitions that are driven by mean curvature.

Investigation on Liquid Segregation during Rheo-Casting Process Based on Eulerian-Granular Multiphase Model

2016 ◽  
Vol 256 ◽  
pp. 113-118
Author(s):  
Jiao Jiao Wang ◽  
Qiang Zhu ◽  
Fan Zhang ◽  
Da Quan Li ◽  
You Feng He
Keyword(s):  
Casting Process ◽  
Phase Model ◽  
Multiphase Model ◽  
Forming Process ◽  
Two Phase ◽  
Finite Element Software ◽  
Liquid Phases ◽  
Three Phase ◽  
Liquid Segregation ◽  
Semi Solid

A crucial problem concerned with the semi-solid forming process is the liquid segregation phenomena during shape formation, especially for rheo-casting process. Liquid segregation occurs due to the separation phenomena of the solid grain and the liquid phase. In this work, using commercial finite element software, the liquid segregation during rheo-casting process was numerically investigated by Eulerian-granular multiphase model based on the comparable results of single phase model, Eulerian-granular two-phase and three-phase model, along with Eulerian-granular DDPM three-phase model. In the study, solid grains and liquid phases were regarded as rigid material and non-Newtonian fluid at microscale, separately. This validation was experimentally proved and also compared to the proposed relationship of power law, Herschel-Bulkley model with yield stress at macroscale.

scholarly journals Hierarchy of consistent n-component Cahn–Hilliard systems

2014 ◽  
Vol 24 (14) ◽  
pp. 2885-2928 ◽  
Author(s):  
Franck Boyer ◽  
Sebastian Minjeaud
Keyword(s):  
Phase Field ◽  
Multiphase Flows ◽  
Field Model ◽  
Phase Field Model ◽  
Numerical Results ◽  
Phase Model ◽  
Navier Stokes ◽  
Two Phase ◽  
Two Phases ◽  
Well Posed

In this paper, we propose a new generalization of the well-known Cahn–Hilliard two-phase model for the modeling of n-phase mixtures. The model is derived using the consistency principle: we require that our n-phase model exactly coincides with the classical two-phase model when only two phases are present in the system. We give conditions for the model to be well-posed. We also present numerical results (including simulations obtained when coupling the Cahn–Hilliard system with the Navier–Stokes so as to obtain a phase-field model for multiphase flows) to illustrate the capability of such modeling.

A compressible single-temperature conservative two-phase model with phase transitions

2014 ◽  
Vol 76 (5) ◽  
pp. 282-311 ◽  
Author(s):  
G. La Spina ◽  
M. de' Michieli Vitturi ◽  
E. Romenski
Keyword(s):  
Phase Transitions ◽  
Phase Model ◽  
Two Phase ◽  
Single Temperature

scholarly journals Thermodynamics of phase transitions in the subsolidus domain of the FeO–MgO–TiO2 system

2021 ◽  
pp. 12-15
Author(s):  
O.M. Borysenko ◽  
S.M. Logvinkov ◽  
G.M. Shabanova ◽  
I.A. Ostapenko
Keyword(s):  
Phase Transitions ◽  
Gibbs Energy ◽  
Phase Equilibria ◽  
Thermodynamic Data ◽  
Exchange Reactions ◽  
Two Phase ◽  
Free Gibbs Energy ◽  
Temperature Range ◽  
System Changes ◽  
Temperature Ranges

This paper gives consideration to the three-component FeO–MgO–TiO2 system that is a part of the four-component MgO–Al2O3–FeO–TiO2 system which serves to produce materials with valuable properties. The structure of binary FeO–TiO2 and MgO–TiO2 systems is described and the available data on the FeO–MgO–TiO2 system are analyzed. We present the thermodynamic data on all system compounds and calculate change of the free Gibbs energy in the temperature range of 800 to 1900 K for three exchange reactions. It was established that the triangulation of the FeO–MgO–TiO2 system changes in three following temperature ranges: at the temperatures of up to 1115 К, at 1115 to 1413 К (the restructuring of conodes here occurs) and above 1413 K (stable pseudobrookite is formed). It was shown that the following two-phase equilibria are stable: MgTi2O5–FeTiO3, FeTiO3–MgTiO3, MgTiO3–Fe2TiO4, Fe2TiO4–Mg2TiO4 and Mg2TiO4–FeO at the temperatures of up to 1115 K; MgTi2O5–FeTiO3, FeTiO3–MgTiO3, FeTiO3–Mg2TiO4, Fe2TiO4–Mg2TiO4 and Mg2TiO4–FeO in the temperature range of 1115 to 1413 K; and MgTi2O5–FeTi2O5, MgTi2O5–FeTiO3, FeTiO3–MgTiO3, FeTiO3–Mg2TiO4, Fe2TiO4–Mg2TiO4 and Mg2TiO4–FeO at the temperatures of above 1413 K.

A TEM study of the influence of microstructure on the superplastic behavior of a U-5.8 wt.% Nb alloy

1986 ◽  
Vol 44 ◽  
pp. 568-569
Author(s):  
G. Mackiewicz Ludtka
Keyword(s):  
Grain Size ◽  
Heating Rate ◽  
Phase Field ◽  
Single Phase ◽  
Superplastic Behavior ◽  
Two Phase ◽  
Single Phase Field

Historically, metals exhibit superplasticity only while forming in a two-phase field because a two-phase microstructure helps ensure a fine, stable grain size. In the U-5.8 Nb alloy, superplastici ty exists for up to 2 h in the single phase field (γ1) at 670°C. This is above the equilibrium monotectoid temperature of 647°C. Utilizing dilatometry, the superplastic (SP) U-5.8 Nb alloy requires superheating to 658°C to initiate the α+γ2 → γ1 transformation at a heating rate of 1.5°C/s. Hence, the U-5.8 Nb alloy exhibits an anomolous superplastic behavior.

Two-phase model for human classical conditioning.

1968 ◽  
Vol 78 (3, Pt.1) ◽  
pp. 359-368 ◽  
Author(s):  
William F. Prokasy ◽  
Martha A. Harsanyi
Keyword(s):  
Classical Conditioning ◽  
Phase Model ◽  
Two Phase
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