A computational thermodynamics approach to the Gibbs–Thomson effect

Shahandeh, Sina; Nategh, S.

doi:10.1016/j.msea.2006.08.062

Cited by 21 publications

(10 citation statements)

References 17 publications

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“…Therefore, the area increment can be expressed as,

d A = (\frac{1}{R_{1}} + \frac{1}{R_{2}}) d V = κ d V

During the virtual interfacial movement, the total change in free energy is

- Δ G d V - σ κ d V

, which includes the change in driving force and the change in interfacial free energy. [ 27–29 ] According to the dynamics of the sharp‐interface model, such as Stefan model, the normal velocity of interface is proportional to the total free energy change per unit volume,

v_{⊥} = β (- Δ G - σ κ)

where β is the dynamic coefficient, and σ is the interfacial tension.…”

Section: Resultsmentioning

confidence: 99%

“…as the specific expression of doublewell function, thus the specific expression of interpolation function can be derived as p( ) ). Based on the constraint of the interpolation function p(0) = 0 and p(1) = 1, we can obtain the following results,(28) and(30), the dynamic coefficient of sharp interface can be expressed as, ,(30), and (32) present a set of equations to express the interfacial width W , the interfacial tension and dynamic coefficient of sharp interface in terms of dynamic coefficient of diffuse interface M, gradient energy coefficient and barrier energy H. Conversely, we can also express M, , and H in terms of W , , and , ), (34), and (35) give the way to calculate the coefficients of Equation(2). As the dynamical equation of diffuse interface, Equation…”

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confidence: 99%

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Explicit Dynamics of Diffuse Interface in Phase‐Field Model

Yang

Huang

Liu

et al. 2020

Advcd Theory and Sims

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Interfaces play an important role during phase transition and interfacial chemical reactions. In this paper, three different methods are introduced to analyze the explicit dynamics of the diffuse interface by means of phase-field model, and these methods are based on three independent perspectives: non-dispersive propagation of the interfacial waveform, the flux density and sources/sinks analysis of continuity equation, and the moving interfacial coordinate transformation. These theoretical derivations not only present the relationship between the diffuse interfacial velocity and the effect of driving force and interfacial curvature, but also clarify the equivalent method between the phase-field dynamics and the sharp-interfacial dynamics, which reveals the physical meaning of the diffuse interfacial dynamical equation from different perspectives. The present study advances the understanding of the interfacial phase transition and provides theoretical insights for the phase-field model and numerical simulation.

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“…Therefore, the area increment can be expressed as,

d A = (\frac{1}{R_{1}} + \frac{1}{R_{2}}) d V = κ d V

During the virtual interfacial movement, the total change in free energy is

- Δ G d V - σ κ d V

v_{⊥} = β (- Δ G - σ κ)

where β is the dynamic coefficient, and σ is the interfacial tension.…”

Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

Explicit Dynamics of Diffuse Interface in Phase‐Field Model

Yang

Huang

Liu

et al. 2020

Advcd Theory and Sims

View full text Add to dashboard Cite

show abstract

“…The free energy in a certain state system is lower, which state is more stable [15] . To the M2 high speed steel, the extra energy comes from internal pressure of carbide, it can be written as…”

Section: Spheroidizing and Coarsening Mechanism Of Carbidementioning

confidence: 99%

“…As-cast specimens were arranged in two teams. One was isothermally reheated at 1 423 K for four different times (15,30, 60 and 120 min), finally water quenched rapidly except for the one at 120 min, to decompose the M 2 C carbide and spheroidize the products. The other was reheated at 1 473 K for four different holding times (15,30, 60 and 120 min), also quenched, to aggregate the particles.…”

Section: Materials and Processingmentioning

confidence: 99%

Evolving mechanism of eutectic carbide in as-cast AISI M2 high-speed steel at elevated temperature

Zhou

Shen

Chen

et al. 2010

J. Shanghai Jiaotong Univ. (Sci.)

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The evolution in type, size and shape of carbides in as-cast American Iron and Steel Institute (AISI) M2 high-speed steel before and after annealing were investigated. The micromechanism which was responsible for those changes was also analyzed and discussed. At the initial stage of reheating, metastable M2C-type carbide decomposed continuously. M6C-type carbide nucleated at the interface of M2C/γ firstly and grow from surface to center. Then MC-type carbide nucleated at both surface of M6C/M6C and inner of M6C. With the increasing decomposition of the metastable M2C-type carbide, the rod-shaped construction of eutectic carbide began necking, fracturing and spheroidizing gradually. Held enough time or reheated at higher temperature, particle-shaped product aggregated and grew up apparently, while secondary carbide precipitated in cell and grew up less significantly than the former. Based on the above microstructural observation, the thermodynamic mechanism for decomposition of M2C carbide, for spheroidization of products, and for the growth of particles were analyzed. The rate equations of carbides evolution were derived, too. It shows that the evolving rate is controlled by diffusion coefficients of alloy atoms, morphology of eutectic carbides and heating temperature.

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“…The concentrations at the interface, x M j (R), are given by the equilibrium phase diagram for a planar precipitate/matrix interface. However, the equilibrium concentrations of two phases at the interface depend on the interface curvature associated with the size of the precipitates, which is called the Gibbs-Thomson effect [36,37]. The Gibbs-Thomson equation for calculating the interface composition at the matrix side is given as:…”

Section: Growth Modelmentioning

confidence: 99%

Modeling Precipitation Hardening and Yield Strength in Cast Al-Si-Mg-Mn Alloys

Cinkilic

Yan

Luo

2020

Metals

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An integrated precipitation and strengthening model, incorporating the effect of precipitate morphology on precipitation kinetics and yield strength, is developed based on a modified Kampmann–Wagner numerical (KWN) framework with a precipitate shape factor. The optimized model was used to predict the yield strength of Al-Si-Mg-Mn casting alloys produced by vacuum high pressure die casting at various aged (T6) conditions. The solid solution strengthening contribution of Mn, which is a common alloying element to avoid die soldering, was included in the model to increase the prediction accuracy. The experimental results and simulations show good agreement and the model is capable of reliably predicting yield strength of aluminum die castings after T6 heat treatment, providing a useful tool to tailor heat treatment for a variety of applications.

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A computational thermodynamics approach to the Gibbs–Thomson effect

Cited by 21 publications

References 17 publications

Explicit Dynamics of Diffuse Interface in Phase‐Field Model

Explicit Dynamics of Diffuse Interface in Phase‐Field Model

Evolving mechanism of eutectic carbide in as-cast AISI M2 high-speed steel at elevated temperature

Modeling Precipitation Hardening and Yield Strength in Cast Al-Si-Mg-Mn Alloys

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