Liquid phase stratification induced by large temperature gradient during spinodal decomposition in Fe–Cr alloys: A phase-field study

2021 ◽  
pp. 2150374
Author(s):  
Lifei Du ◽  
Runbo Tian ◽  
Tiantian Shi ◽  
Youqi Cao
Keyword(s):  
Liquid Phase ◽  
Temperature Gradient ◽  
Spinodal Decomposition ◽  
Phase Field ◽  
Anisotropic Diffusion ◽  
Phase Field Model ◽  
Solute Diffusion ◽  
Large Temperature ◽  
Cahn Hilliard Equation ◽  
Kinetics Of

The spinodal decomposition in Fe-40at.%Cr binary alloy is numerically studied by implementing the phase-field model based on Cahn–Hilliard equation. Effects of different temperature gradients on the solute distributing characteristics during the spinodal decomposition are investigated. In the system with a temperature gradient, the phase decomposition happens gradually from low temperature to high temperature, and a metastable stratification is achieved with specified temperature distribution. The critical temperature and corresponding temperature gradient are specified for the obvious solute stratification in the binary Fe–Cr alloy. The kinetics of the solute diffusion during the spinodal decomposition is discussed to reveal the liquid phase stratification induced by the anisotropic diffusion with the nonuniform temperature field. Therefore, tailoring the heat treatment during the spinodal decomposition in Fe–Cr binary alloys might be an efficient way to obtain nanometer coherent microstructures with specified solute distribution.

Effect of boundary heat flux on columnar formation in binary alloys: A phase-field study

2018 ◽  
Vol 32 (06) ◽  
pp. 1850078 ◽  
Author(s):  
Lifei Du ◽  
Peng Zhang ◽  
Shaomei Yang ◽  
Jie Chen ◽  
Huiling Du
Keyword(s):  
Heat Flux ◽  
Temperature Gradient ◽  
Phase Field ◽  
Phase Field Model ◽  
Solute Diffusion ◽  
Liquid Interfaces ◽  
Cu Alloy ◽  
Temperature Distributions ◽  
Alloy Heat ◽  
Solid Liquid

A non-isothermal phase-field model was employed to simulate the columnar formation during rapid solidification in binary Ni–Cu alloy. Heat flux at different boundaries was applied to investigate the temperature gradient effect on the morphology, concentration and temperature distributions during directional solidifications. With the heat flux input/extraction from boundaries, coupling with latent heat release and initial temperature gradient, temperature distributions are significantly changed, leading to solute diffusion changes during the phase-transition. Thus, irregular columnar structures are formed during the directional solidification, and the concentration distribution in solid columnar arms could also be changed due to the different growing speeds and temperature distributions at the solid–liquid interfaces. Therefore, applying specific heat conditions at the solidifying boundaries could be an efficient way to control the microstructure during solidifications.

scholarly journals Optimal control of stochastic phase-field models related to tumor growth

2020 ◽  
Vol 26 ◽  
pp. 104
Author(s):  
Carlo Orrieri ◽  
Elisabetta Rocca ◽  
Luca Scarpa
Keyword(s):  
Optimal Control ◽  
Tumor Growth ◽  
Phase Field ◽  
Phase Field Model ◽  
Growth Dynamics ◽  
Necessary Optimality Conditions ◽  
Reaction Diffusion ◽  
Adjoint System ◽  
Reaction Diffusion Equation ◽  
Cahn Hilliard Equation

We study a stochastic phase-field model for tumor growth dynamics coupling a stochastic Cahn-Hilliard equation for the tumor phase parameter with a stochastic reaction-diffusion equation governing the nutrient proportion. We prove strong well-posedness of the system in a general framework through monotonicity and stochastic compactness arguments. We introduce then suitable controls representing the concentration of cytotoxic drugs administered in medical treatment and we analyze a related optimal control problem. We derive existence of an optimal strategy and deduce first-order necessary optimality conditions by studying the corresponding linearized system and the backward adjoint system.

Microstructure evolution in multilayer c-TiAlN/TiN coatings during spinodal decomposition — A phase-field study

2016 ◽  
Vol 01 (01) ◽  
pp. 1650002 ◽  
Author(s):  
Jingjing Zhou ◽  
Lijun Zhang ◽  
Li Chen ◽  
Hong Wu ◽  
Yong Du
Keyword(s):  
Spinodal Decomposition ◽  
Microstructure Evolution ◽  
Phase Field ◽  
Phase Field Model ◽  
Dislocation Motion ◽  
Combined Model ◽  
Modulation Period ◽  
Tin Coatings ◽  
Good Agreement ◽  
Modulation Ratio

By means of the combined model, i.e., the phase-field model with finite interface dissipation in combination with the modified Cahn–Hilliard model, together with the materials parameters comprehensively verified in monolithic c-TiAlN coatings, the microstructure evolution in multilayer c-Ti[Formula: see text]Al[Formula: see text]N/TiN coatings annealed at [Formula: see text]C was quantitatively simulated by directly comparing with the experimental data. The sharp interface between c-TiN and c-Ti[Formula: see text]Al[Formula: see text]N layers in the as-deposited state was found to change into a diffuse one, which can act as highly effective obstacles against dislocation motion. Moreover, the simulations indicate that the spinodal decomposition occurs in the Ti[Formula: see text]Al[Formula: see text]N layer and the decomposed layer becomes thinner, which is in good agreement with the experimental observation. In addition, the effect of modulation period and modulation ratio on microstructure evolution in c-Ti[Formula: see text]Al[Formula: see text]N/TiN coating was further studied. The relatively smaller modulation period can generate more layers in the real scale of coatings, which can help to strengthen the coatings due to refinement of grains and restriction of dislocations. As for the modulation ratio, when the value decreases from 5:1 to 1:1, Ti atoms in the decomposed layer disappear faster. A further extension into a larger-sized simulation was also performed.

A phase field model for a solid–liquid phase transition

2011 ◽  
Vol 38 (7) ◽  
pp. 477-480 ◽  
Author(s):  
Michele Ciarletta ◽  
Mauro Fabrizio ◽  
Vincenzo Tibullo
Keyword(s):  
Phase Transition ◽  
Liquid Phase ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Liquid Phase Transition ◽  
Solid Liquid

scholarly journals On a phase field model for solid-liquid phase transitions

2012 ◽  
Vol 32 (6) ◽  
pp. 1997-2025 ◽  
Author(s):  
Sylvie Benzoni-Gavage ◽  
◽  
Laurent Chupin ◽  
Didier Jamet ◽  
Julien Vovelle ◽  
...  
Keyword(s):  
Phase Transitions ◽  
Liquid Phase ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Solid Liquid

Evolution kinetics of interstitial loops in irradiated materials: a phase-field model

2011 ◽  
Vol 20 (1) ◽  
pp. 015011 ◽  
Author(s):  
Shenyang Hu ◽  
Charles H Henager ◽  
Yulan Li ◽  
Fei Gao ◽  
Xin Sun ◽  
...  
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Kinetics Of

scholarly journals Effect of the Particle Size Distribution on the Cahn-Hilliard Dynamics in a Cathode of Lithium-Ion Batteries

Batteries ◽  
2020 ◽  
Vol 6 (2) ◽  
pp. 29
Author(s):  
Pavel L’vov ◽  
Renat Sibatov
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Phase Field ◽  
Single Phase ◽  
Field Model ◽  
Phase Field Model ◽  
Hilliard Equation ◽  
Wide Range ◽  
Cahn Hilliard Equation

The phase-field model based on the Cahn-Hilliard equation is employed to simulate lithium intercalation dynamics in a cathode with particles of distributed size. We start with a simplified phase-field model for a single submicron particle under galvanostatic condition. We observe two stages associated with single-phase and double-phase patterns typical for both charging and discharging processes. The single-phase stage takes approximately 10–15% of the process and plays an important role in the intercalation dynamics. We establish the laws for speed of front propagation and evolution of single-phase concentration valid for different sizes of electrode particles and a wide range of temperatures and C-rates. The universality of these laws allows us to formulate the boundary condition with time-dependent flux density for the Cahn-Hilliard equation and analyze the phase-field intercalation in a heterogeneous cathode characterized by the particle size distribution.

Microscopic Phase Field Study on the Kinetics of Order-Disorder Transition of APDBs Formed between DO22 Phases during Stress Aging

2014 ◽  
Vol 789 ◽  
pp. 530-535 ◽  
Author(s):  
Ming Yi Zhang ◽  
Guang Quan Yue ◽  
Jia Zhen Zhang ◽  
Kun Yang ◽  
Zheng Chen
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Domain Boundary ◽  
Phase Field Model ◽  
Antiphase Domain ◽  
Phase Layer ◽  
Disorder Transition ◽  
Disordered Phase ◽  
Kinetics Of ◽  
Microscopic Phase Field Model

Kinetics of order-disorder transition at antiphase domain boundary (APDB) formed between DO22 (Ni3V) phases during stress aging was investigated using microscopic phase field model. The results demonstrated that whether order-disorder transition happens or not depends on the atomic structure of the APDB. Accompanied with the depletion of V and enrichment of Ni and Al, order-disorder transition happened at the APDB (001)//(002). Whereas at the APDB {100}·1⁄2[100], which remains ordered with temporal evolution, Ni and Al enrich and V depletes. Composition evolution of APDB with order-disorder transition favors the nucleation of the L12 and disordered phase. Some of the grains grew bigger while the others disappeared, accompanying the formation of disordered phase layer during order-disorder transition of APDBs, and the order-disorder transition of APDBs can be considered as accompanying process of coarsening of ordered domain phases and growth of disordered phases.

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