Microstructural development involving nucleation and growth phenomena simulated with the Phase Field method

Simmons, Jeff; Wen, Youhai; Chen, Shen; Wang, Y.Z.

doi:10.1016/j.msea.2003.09.019

Cited by 98 publications

(58 citation statements)

References 27 publications

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“…32 An alternative method for incorporating nucleation into phase-field simulations relies on explicitly incorporating nuclei throughout the simulation time by relying on classical nucleation theory. [29][30][31]33,34 The probability for nucleation of a new phase at a random location in space and time is determined, and nuclei are ''seeded'' accordingly. Once a nucleus forms, it occupies a definite volume of space, which in turn yields a zero event probability for formation of additional nuclei within the same volume.…”

Section: Nucleation Modelingmentioning

confidence: 99%

“…Once a nucleus forms, it occupies a definite volume of space, which in turn yields a zero event probability for formation of additional nuclei within the same volume. 29,30,32 The stochastic nucleation process can thus be approximated by a Poisson distribution:…”

Section: Nucleation Modelingmentioning

confidence: 99%

“…A strategy to avoid this limitation has been proposed by Simmon and coworkers. [29][30][31] This approach is based on assuming that nucleation events are essentially stochastic processes which can be modeled through a Poisson distribution. The parameters for the classical nucleation theory formulation are defined in terms of kinetic and thermodynamic properties of the system in question.…”

Section: Introductionmentioning

confidence: 99%

“…[29][30][31] The proposed nucleation model will be incorporated into a multiphase field model derived from previous works [26][27][28] for the evolution of grains of Cu 6 Sn 5 under different conditions. We will show different morphologies of IMC grains and layers during lead-free soldering as a function of material parameters.…”

Section: Introductionmentioning

confidence: 99%

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Formation and Growth of Intermetallic Compound Cu6Sn5 at Early Stages in Lead-Free Soldering

Park

Arróyave

2010

Journal of Elec Materi

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In this work, the early stages of the formation and growth of the intermetallic compound Cu 6 Sn 5 during soldering reactions between a Cu substrate and liquid Sn are examined through phase-field simulations. The liquid Sn-based solder (L phase) and the copper substrate (a phase) are considered to be under metastable equilibrium conditions that eventually lead to nucleation of the Cu 6 Sn 5 intermetallic compound (IMC) (g phase) at the solid/liquid interface. Nucleation is incorporated into the model through a classical treatment considering that individual nucleation events follow a Poisson distribution function. The driving forces for the nucleation and phase transformations are obtained by coupling the phase-field simulations to CALPHAD models. In the phase-field simulations, physical properties such as liquid surface as well as IMC interfacial energies are treated parametrically to probe the behavior of the system under various growth conditions. The simulations are compared with previous works and are shown to have good (qualitative) agreement with recent detailed studies on the early stages of the interaction between Cu and liquid Sn.

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Section: Nucleation Modelingmentioning

confidence: 99%

Section: Nucleation Modelingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Formation and Growth of Intermetallic Compound Cu6Sn5 at Early Stages in Lead-Free Soldering

Park

Arróyave

2010

Journal of Elec Materi

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“…Such microstructures are usually achieved by special multi-stage heat treatments, which are generally complex and costly. Some authors have already shown that such bimodal, or even multimodal, size distributions of γ' particles can also be achieved by a series of γ' nucleation bursts during continuous cooling from the solution annealed state [15][16][17][18][19][20][21][22]. Thereby, the individual particle populations precipitate at different temperatures and from different chemical compositions of the γ matrix.…”

Section: Introductionmentioning

confidence: 99%

Evolution of Size and Morphology of γ' Precipitates in UDIMET 720 Li during Continuous Cooling

Radis¹,

Schaffer²,

Albu³

et al. 2008

Superalloys 2008 (Eleventh International Symposium)

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In this work, an analysis of the evolution of precipitates in the nickel-base superalloy UDIMET 720 Li during continuous cooling is carried out. Starting from the solution-annealed condition, the precipitation kinetics, the distribution and the morphology of particles during continuous cooling is studied experimentally by SEM, EFTEM and FIB. The results are compared to simulations using the software MatCalc. Depending on the cooling rate, discontinuous precipitation as well as monomodal and multi-modal distributions are observed. The precipitate microstructure of various samples is investigated and evaluated quantitatively to determine the precipitate distribution parameters. The experimental results are discussed and compared with the results of the simulation. Finally, two parameter studies are carried out which indicate the sensitivity of the simulation results on the input data, i.e. the thermodynamic and diffusion databases.

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Phase‐Field Simulations of the Morphology Formation in Evaporating Crystalline Multicomponent Films

Ronsin

Harting

2022

Advcd Theory and Sims

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In numerous solution-processed thin films, a complex morphology resulting from liquid-liquid phase separation (LLPS) or from polycrystallization arises during the drying or subsequent processing steps. The morphology has a strong influence on the performance of the final device but unfortunately, the process-structure relationship is often poorly and only qualitatively understood. This is because many different physical mechanisms (miscibility, evaporation, crystallization, diffusion, and advection) are active at potentially different time scales and because the kinetics plays a crucial role: the morphology develops until it is kinetically quenched far from equilibrium. In order to unravel the various possible structure formation pathways, a unified theoretical framework that takes into account all these physical phenomena is proposed. This phase-field simulation tool is based on the Cahn-Hilliard equations for diffusion and the Allen-Cahn equation for crystallization and evaporation, which are coupled to the equations for the dynamics of the fluid. The behavior of the coupled model based on simple test cases is discussed and verified. Furthermore, how this framework allows to investigate the morphology formation in a drying film undergoing evaporation-induced LLPS and crystallization, which is typically a situation encountered, is illustrated, for example, in organic photovoltaics applications.

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Microstructural development involving nucleation and growth phenomena simulated with the Phase Field method

Cited by 98 publications

References 27 publications

Formation and Growth of Intermetallic Compound Cu6Sn5 at Early Stages in Lead-Free Soldering

Formation and Growth of Intermetallic Compound Cu6Sn5 at Early Stages in Lead-Free Soldering

Evolution of Size and Morphology of γ' Precipitates in UDIMET 720 Li during Continuous Cooling

Phase‐Field Simulations of the Morphology Formation in Evaporating Crystalline Multicomponent Films

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Microstructural development involving nucleation and growth phenomena simulated with the Phase Field method

Cited by 98 publications

References 27 publications

Formation and Growth of Intermetallic Compound Cu6Sn5 at Early Stages in Lead-Free Soldering

Formation and Growth of Intermetallic Compound Cu6Sn5 at Early Stages in Lead-Free Soldering

Evolution of Size and Morphology of &#947;' Precipitates in UDIMET 720 Li during Continuous Cooling

Phase‐Field Simulations of the Morphology Formation in Evaporating Crystalline Multicomponent Films

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Evolution of Size and Morphology of γ' Precipitates in UDIMET 720 Li during Continuous Cooling