Nucleation and growth of γ′-Precipitates in Ni-14 at.% Al

Wendt, H.; Haasen, P.

doi:10.1016/0001-6160(83)90163-3

Cited by 164 publications

(47 citation statements)

References 17 publications

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“…shown that the present model fits the data on size evolution of L1 2 ordered Ni 3 Al precipitates in the in Ni-14 at% Al applying diffusion-controlled growth at a constant density of precipitates (which is consistent with data in [44]), with a limited amount of growth of precipitates prior to reaching the isothermal ageing temperature. Also the data on evolution of size of L1 2 ordered Ni 3 Al precipitates in the in Ni-6.5 at%Al-9.5 at%Cr alloy fits the present new model.…”

Section: Precipitation Of the L12 Ordered Ni3al Precipitates In Ni-alsupporting

confidence: 88%

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A new model for diffusion-controlled precipitation reactions using the extended volume concept

Starink

2014

Thermochimica Acta

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In this work a new model for diffusion-controlled precipitation reactions is derived, IntroductionDiffusion-controlled precipitation reactions are important in a wide variety of commercially important materials. It is important to have available an accurate model for the kinetics of the reaction as heat treatment can determine a range of properties.Preferably such a kinetic model should be accurate, transparent, avoid computationally expensive implementations, and lead to analysis methods that are widely applicable.The objective of this work is to derive and test a new model for diffusion-controlled precipitation reactions that meets these criteria.Diffusion-controlled precipitation reactions can be thought of as being the combination of 4 overlapping processes: nucleation, growth, soft impingement and coarsening.Several attempts at providing a computationally friendly suitable framework for predicting the progress of diffusion-controlled reactions incorporating a treatment of impingement have been published (see e.g. [1,2,3]), and some less computationally friendly attempts at models have been published more recently [4]. The present paper focuses primarily on the treatment of soft impingement.One group of existing modelling approaches is based on direct consideration of the diffusion flux at the interface. For instance, the numerical method formulated by Kampmann and Wagner [5], as applied by several authors (e.g. [6,7,8,9]), treats the growth of individual spherical particles following the equation:where R is the radius of a growing particle, D is the diffusion constant, c p is the solute concentration in the precipitate, c m is the solute concentration at the precipitate/matrix interface that is evaluated by the Gibbs-Thompson relationship [10,11], ) (t c is the mean concentration of the matrix. A characteristic of this approach is that the interaction of the diffusional growth of the various particles is drastically simplified: a spherical geometry of diffusion field is assumed and interaction is described through a single parameter, the mean concentration ) (t c . We can term this a mean field approach.Published as: Starink, M.J. (2014) Thermochimica Acta, 596, pp. 109-119 3 Some of the users of KW model have described this treatment of impingement as 'a simple response equation ' [12], i.e. it is an approximation for which the accuracy is as yet unproven and it has been suggested that the mean field approach underestimates impingement because it ignores a geometrical component to the impingement process [13]. The contribution of a geometrical component has been investigated in [13,14].Benefits of the KW approach are that basic capillarity effects can be included and that, in principle and at some computational costs, the numerical scheme can be implemented to model different groups of precipitates and (in principle 1 ) incorporate coarsening [7,8]. The models described by Svoboda, Fisher and co-workers [15,16] applying the thermodynamic extremal principle (first described by Onsager [17]) empl...

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Section: Precipitation Of the L12 Ordered Ni3al Precipitates In Ni-alsupporting

confidence: 88%

“…Data on the evolution of size and volume fraction of L1 2 ordered Ni 3 Al precipitates in Ni-14 at% Al and Ni-6.5 at%Al-9.5 at%Cr alloys was presented in [44] and [45], respectively, and several interpretations of the data have been published in the literature (see eg.…”

Section: Precipitation Of the L12 Ordered Ni3al Precipitates In Ni-almentioning

confidence: 99%

A new model for diffusion-controlled precipitation reactions using the extended volume concept

Starink

2014

Thermochimica Acta

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“…The classical solid state homogenous nucleation theory (8)(9)(10)(11)(12) defines the free energy AG* required for a spherical nucleus as:…”

Section: Conventionalmentioning

confidence: 99%

γ' Formation in a Nickel-Base Disk Superalloy

Gabb¹,

Backman²,

Wei³

et al. 2000

Superalloys 2000 (Ninth International Symposium)

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A streamlined,physics-based kinetic model was formulated, calibrated, and validated on a nickel-base superalloy. It was designed to be simplified and streamlined, to speed up calculations and facilitate linkage to finite element modeling thermal codes. The model describes and predicts the formation of y' precipitates during the heat treatment process. Standardized experimental methods were employed to calibrate and initially validate the microstructure model. The model was then validated on an oil-quenched generic disk. Predictions of primary cooling y' size and area fraction agreed well with experimental measurements over a large range of values and cooling rates.

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“…Due to the technological importance of commercial alloys, model Ni-based alloys have warranted extensive investigation in the earliest stages of phase separation. This is particularly true for Ni-Al alloys, where the governing thermodynamics can be assessed in a fairly straightforward manner, and studied by small-angle and wide-angle neutron scattering [2,3], atom-probe field-ion microscopy [4], conventional transmission electron microscopy (CTEM) [5,6], and highresolution electron microscopy (HREM) [7]. Due to the inadequate spatial and analytical resolution and other experimental limitations of these techniques, understanding of the earliest stages of decomposition is still incomplete.…”

Section: Introductionmentioning

confidence: 99%

Temporal evolution of the nanostructure and phase compositions in a model Ni–Al–Cr alloy

et al. 2006

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In a Ni-5.2 Al-14.2 Cr at.% alloy with moderate solute supersaturations and a very small c/c 0 lattice parameter misfit, the nanostructural and compositional pathways during c 0 (L1 2 ) precipitation at 873 K are investigated using atom-probe tomography, conventional transmission electron microscopy, and hardness measurements. Nucleation of high number densities (N v > 10 23 m À3 ) of solute-rich precipitates (mean radius = AERae = 0.75 nm), with a critical nucleus composition of Ni-18.3 ± 0.9 Al-9.3 ± 0.7 Cr at.%, initiates between 0.0833 and 0.167 h. With increasing aging time (a) the solute concentrations decay in spheroidal precipitates (AERae < 10 nm); (b) the observed early-stage coalescence peaks at maximum N v in coincidence with the smallest interprecipitate spacing; and (c) the reaction enters a quasi-stationary regime where growth and coarsening operate concomitantly. During this quasi-stationary regime, the c (face-centered cubic)-matrix solute supersaturations decay with a power-law dependence of about À1/3, while the dependencies of AERae and N v are 0.29 ± 0.05 and À0.64 ± 0.06 at a coarsening rate slower than model predications. Coarsening models allow both equilibrium phase compositions to be determined from the compositional measurements. The observed early-stage coalescence is discussed in further detail.

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Nucleation and growth of γ′-Precipitates in Ni-14 at.% Al

Cited by 164 publications

References 17 publications

A new model for diffusion-controlled precipitation reactions using the extended volume concept

A new model for diffusion-controlled precipitation reactions using the extended volume concept

γ' Formation in a Nickel-Base Disk Superalloy

Temporal evolution of the nanostructure and phase compositions in a model Ni–Al–Cr alloy

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Nucleation and growth of γ′-Precipitates in Ni-14 at.% Al

Cited by 164 publications

References 17 publications

A new model for diffusion-controlled precipitation reactions using the extended volume concept

A new model for diffusion-controlled precipitation reactions using the extended volume concept

&#947;' Formation in a Nickel-Base Disk Superalloy

Temporal evolution of the nanostructure and phase compositions in a model Ni–Al–Cr alloy

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γ' Formation in a Nickel-Base Disk Superalloy