Analytical treatment of diffusion during precipitate growth in multicomponent systems

Chen, Qing; Jeppsson, Johan; Ågren, John

doi:10.1016/j.actamat.2007.12.037

Cited by 83 publications

(73 citation statements)

References 8 publications

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“…Specific examples of the PSD approach are found in Refs. [5][6][7][8]. Several models address the problem of precipitation in multicomponent alloys by using the extremum principle and the mean-field approach [9,10].…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of precipitation in multicomponent Ni-base alloys

Rougier¹,

Jacot²,

Gandin³

et al. 2013

Acta Materialia

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A comprehensive particle size distribution model has been developed for the simulation of c 0 precipitation in multicomponent Ni alloys. Nucleation, growth and coarsening of the precipitates are described by a particle size distribution. The growth rate of each precipitate class is calculated with a multi-component diffusion model formulated for non-diagonal matrices of diffusion coefficients. The model is fully coupled with CALPHAD calculations of the thermodynamic equilibrium at the interface, including a direct treatment of the effect of curvature through modification of the Gibbs free energy. An optimization strategy was developed to minimize the computational cost. The model was used to simulate ageing heat treatment at 600°C of Ni-7.56 at.% Al-8.56 at.% Cr, which was studied experimentally by Booth-Morrison and others (Booth-Morrison C, Weninger J, Sudbrack CK, Mao Z, Noebe RD, Seidman DN. Acta Mater 2008;56:3422; Mao Z, Booth-Morrison C, Sudbrack CK, Martin G, Seidman DN. Acta Mater 2012;60:1871). The comparisons showed that the precipitation stages of c 0 precipitates are correctly captured by the numerical model. It was shown that non-diagonal diffusion coefficients substantially influence the selection of the operating tie-line and the overall transformation kinetics. With non-diagonal diffusion matrices, complex phenomena such as uphill diffusion of Cr due to the Al gradients were evidenced and explained.

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Section: Introductionmentioning

confidence: 99%

Numerical simulation of precipitation in multicomponent Ni-base alloys

Rougier¹,

Jacot²,

Gandin³

et al. 2013

Acta Materialia

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“…A general growth rate model [32] for precipitate particles in multicomponent systems has been developed and implemented. Evolution of mean radius, number density, volume fraction, and size distribution of precipitate particles can be simulated using TC-PRISMA, see Figure 17.…”

Section: Kmentioning

confidence: 99%

The Development and Validation of a New Thermodynamic Database for Ni-based Alloys ................................... 803

Bratberg¹,

Mao²,

Kjellqvist³

et al. 2012

Superalloys 2012 (Twelfth International Symposium)

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Thermodynamic databases developed using the CALPHAD method has been successfully applied to the modeling and simulation of Ni based superalloys for more than fifteen years. Such databases when combined with suitable software, such as Thermo-Calc, can be used for accelerating alloy design as well as improving understanding of existing alloys in terms of their processing and in-service behavior. Additionally, such databases are also essential to the modeling of microstructural evolution using methods such as phase field or mean field approaches.A new thermodynamic database, TCNI6, has been developed for Ni-based superalloys based on the critical evaluation, using the CALPHAD method, of all the constituent binary systems across their full range of composition and many of the ternary systems containing Ni, as well as a number of other key ternary systems. The database has also been validated where possible against higher order systems as well.Together with the new mobility database, MOBNI3, which contains descriptions for the atomic mobility for respectively the γ (A1), γ' (L1 2 ), α (A2), β (B2) and liquid phases, TCNI6 can be used with software such as DICTRA to predict different kinetic aspects taking all relevant phases into account, e.g. the simulation of interdiffusion across Ni-based coatings.A new user friendly computational tool, TC-PRISMA, which simulates the kinetics of precipitation processes, is demonstrated utilizing these new databases and combined with interface property data. Engineering applications of precipitation modelling are validated against experimental data.

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“…In contrast with the accurate but computationally expensive phase field approach [13], the KWN approach has been gaining popularity [14][15][16][17][18][19][20][21][22][23][24][25][26] recently. This is due to its mathematical simplicity and convenient coupling with the CALPHAD database, enabling an efficient treatment of multi-scale, multi-component industrially significant problems [14][15][16][17][18][19][20][21][22][23][24][25]. It should be noted that the coupling of the KWN model with the thermodynamic databases developed in the CALPHAD research community is a scale-bridging feature as the databases could be established on the base of first principle calculations [27,28].…”

Section: Introductionmentioning

confidence: 99%

“…The temporal evolution of the size distribution is then tracked by following the size evolution of each discrete size class. This modeling framework and its CALPHAD-coupled multi-component extensions have been seen as a key microstructure chain model in an Integrated Computational Materials Engineering (ICME) modeling framework to optimize alloy chemistry and heat treatment parameters for many industrial metallic materials [14][15][16][17][18][19][20][21][22][23][24][25][26]. In the most recent extension of the KWN approach, the assumption of the precipitate particles being spherical has been released enabling a better treatment of needle-shaped particles' precipitation kinetics in aluminum alloys [30,31].…”

Section: Introductionmentioning

confidence: 99%

Modeling over-ageing in Al-Mg-Si alloys by a multi-phase CALPHAD-coupled Kampmann-Wagner Numerical model

Tang

Marioara

et al. 2017

Acta Materialia

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The formation of the equilibrium precipitation phase during ageing treatment of Al-Mg-Si alloys is preceded by a series of metastable phases. Given inappropriate ageing time, higher ageing temperature or elevated temperature service condition, β'', the main hardening phase, would be replaced by the more stable metastable phases such as β', B', U1 and U2. The post-β'' microstructure evolution, called "over-ageing", leads to a steep drop in the hardness evolution curve. This paper aims to predict directly over-ageing in Al-Mg-Si alloys by extending a CALPHAD-coupled Kampmann-Wagner Numerical framework towards handling the coexistence of several types of stoichiometric particles of different phases. We demonstrate how the proposed modeling framework, calibrated with a limited amount of experimental measurement data, can aid in understanding the precipitation kinetics of a mix of different types particles.Simulation results will be presented for some earlier reported transmission electron microscopy measurements [1] to shed light on how the alloy composition and ageing treatment influence the post-β'' phase selection.

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Analytical treatment of diffusion during precipitate growth in multicomponent systems

Cited by 83 publications

References 8 publications

Numerical simulation of precipitation in multicomponent Ni-base alloys

Numerical simulation of precipitation in multicomponent Ni-base alloys

The Development and Validation of a New Thermodynamic Database for Ni-based Alloys ................................... 803

Modeling over-ageing in Al-Mg-Si alloys by a multi-phase CALPHAD-coupled Kampmann-Wagner Numerical model

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