Kinetic pathways for phase separation: An atomic-scale study in Ni–Al–Cr alloys

Mao, Zugang; Booth-Morrison, Christopher; Sudbrack, Chantal K.; Martin, G.; Seidman, David N.

doi:10.1016/j.actamat.2011.10.046

Cited by 56 publications

(35 citation statements)

References 45 publications

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“…To our knowledge such clear evidence of a compositional change in particles during phase separation has not yet been observed in Co-Al-W alloys, and is commonly very hard to exhibit [58]. Comparing the experimental and theoretical rate constants for the temporal evolution of the mean size of the precipitates have allowed for the determination of the interfacial γ/γ' energy σ, in fully coupling thermodynamics (from the CALPHAD method [46]) and kinetics.…”

Section: Coarsening Regimementioning

confidence: 99%

Kinetics pathway of precipitation in model Co-Al-W superalloy

et al. 2018

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Abstract:The early stages of precipitation of the γ ' phase in a model Co based superalloy (Co-9.1Al-7W (at.%)) have been investigated at 900 °C using electron microscopy and atom probe tomography. Nucleation, growth and coarsening stages have been studied with a focus on the temporal evolution of the precipitate composition in the light of recent theoretical developments on phase separation in multicomponent alloys. The experimental data have been confronted to the theories of nucleation and coarsening recently developed for such alloys, which are valid for non-ideal and non-dilute systems, and predict the temporal evolution of both the matrix and precipitate compositions. The rate constant for the mean size evolution of the particles, as derived from experiments, has been compared to the one predicted by the mentioned coarsening theory that accounts for a more accurate description of the thermodynamics of the phases, as compared with more classical approaches. From this comparison the γ/γ' interfacial energy was derived and found equal to ~48 mJ/m 2 . the exponents for the temporal evolution of average particles size, number of particles per unit volume were found identical to those for binary alloys during the coarsening regime, as expected, and the temporal evolutions of compositions in both γ and γ' phases were found to evolve as predicted by theory. Indeed, the W content in the particles, measured from atom probe tomography (APT) experiments, was found to significantly decrease with time and the observed evolution is remarkably well described by the theory and therefore is shown to originate from the competition between diffusion and capillarity.

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Section: Coarsening Regimementioning

confidence: 99%

Kinetics pathway of precipitation in model Co-Al-W superalloy

et al. 2018

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“…These conditions correspond to those employed by BoothMorrison et al for the Atom Probe Tomography (APT) observations of γ' precipitates in Ni-Al-Cr alloys [19][20][21]. Initially, the alloy is assumed to be free of γ' precipitates.…”

Section: Resultsmentioning

confidence: 92%

“…The diffusion matrix is an input of the model and is given in Table 1. It was taken from the data published by Mao et al [20], which is based on Monte-Carlo simulations for the diffusion-driven growth of γ' precipitates. The other input parameters are summarised in Table 2.…”

Section: Resultsmentioning

confidence: 99%

Numerical Simulation of Microstructure Formation during Solidification and Heat Treatments of Ni Base Superalloys

Rougier¹,

Jacot²,

Gandin³

et al. 2012

Superalloys 2012 (Twelfth International Symposium)

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A comprehensive modelling approach has been developed for the simulation of microstructure formation during solidification and heat treatment in Ni-base superalloys. The microsegregation taking place during solidification is simulated using the pseudofront tracking (PFT) technique. This finite volume method calculates the concentration profiles in primary γ and the proportion of liquid and γ' in the interdendritic regions. The same model is then used to describe the dissolution of the interdendritic γ' particles during the subsequent solution heat treatment. The concentrations in primary γ predicted with the PFT model are then used to calculate the evolution of the γ' precipitates and their size distributions at different locations in a dendrite arm during heat treatment. This is achieved with a precipitate size distribution (PSD) model. The classes of the distribution are created and tracked based on classical nucleation theory and a semi-analytical model for the growth of the precipitates as a function of their radius and the matrix supersaturation. The PFT and PSD models are both coupled with Thermo-Calc, which is used for the computation of the concentrations at the γ/liquid and γ/γ' interfaces, for the Gibbs-Thomson effect in precipitates, and to calculate non-diagonal diffusion matrices based on a mobility database. The precipitation model was applied to a Ni-Al-Cr alloy and the results were compared with experimental data from the literature. Experimental and simulation results are in good qualitative agreement. The main phenomena taking place during precipitation, i.e. nucleation, growth and coarsening, are well reproduced by the precipitation model. Some discrepancies were observed on the precipitate number density, which were attributed to the homogeneous nucleation model. The full modelling sequence was then applied to Ni-Al in order to assess the influence of an incomplete homogenization heat treatment on the formation of γ' precipitates.

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“…The choice of the system is given in Table 1. It is inspired from one of the configuration studied by Booth-Morrison et al [32] and Mao et al [16] by APT, later also considered by Rougier et al [13,15]. The alloy composition is Ni -7.56 at.% Al -8.56 at.% Cr and the aging temperature is 600 °C.…”

Section: Applicationmentioning

confidence: 99%

“…But recent simulations were also carried out with the goal to reach a direct representation of the precipitates in an elementary volume, for instance using the Monte-Carlo method [16]. Comparison of simulations with Atom Probe Tomography (APT) for chosen ternary alloys subject to interrupted isothermal holding clearly revealed the role of interaction between chemical species on the diffusion kinetics and the effect of curvature on thermodynamic equilibrium.…”

Section: Introductionmentioning

confidence: 99%

An analytical model with interaction between species for growth and dissolution of precipitates

Guillemot

Gandin

2017

Acta Materialia

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An analytical model for growth in a semi-infinite matrix with cross-diffusion between species is presented. Application is given for precipitation of the -phase in the -matrix during isothermal holding at 600 °C in the Ni -7.56 at.% Al -8.56 at.% Cr alloy. The exact time-dependent solutions for the solute profiles and the growth kinetics are validated with a numerical front-tracking simulation. The simulation of cross diffusion terms in a multicomponent alloy is thus demonstrated. Extension of the analytical solution is given for growth in a matrix of finite size. The driving force is then based on a mathematical estimation of the far-field composition. The Gibbs-Thomson effect is also accounted for to consider the effect of curvature on the equilibrium tie-lines. Comparison of analytical solution with the numerical front-tracking simulation shows excellent agreement. Results also point out the detrimental approximation of using the average composition of the matrix for computing the driving force as well as the limitation of the solution proposed by Chen et al. [Acta Mater. 56 (2008) 1890. A detailed discussion is finally given on the origin of oscillations observed for the time evolution of the precipitate radius which alternates between growth and dissolution regimes, pointing out the combined role of solute fluxes and tie-lines compositions at the precipitate/matrix interface.

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Kinetic pathways for phase separation: An atomic-scale study in Ni–Al–Cr alloys

Cited by 56 publications

References 45 publications

Kinetics pathway of precipitation in model Co-Al-W superalloy

Kinetics pathway of precipitation in model Co-Al-W superalloy

Numerical Simulation of Microstructure Formation during Solidification and Heat Treatments of Ni Base Superalloys

An analytical model with interaction between species for growth and dissolution of precipitates

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