Deduction of activation energy for diffusion by analyzing soft impingement in non-isothermal solid-state precipitation

Fan, Kai; Liu, F.; Zhang, K.; Gao, Yang; Zhou, Yaohe

doi:10.1016/j.jcrysgro.2009.09.003

Cited by 8 publications

(4 citation statements)

References 28 publications

(39 reference statements)

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“…This value is lower than the value for the Al 3 Sc phase precipitation determined by Jo and Fujikawa [29] in Al0.15 at.%Sc alloy (Q = 124 kJ mol −1 ). However, it agrees within accuracy with the apparent activation energy Q for precipitation of the Al 3 Sc phase in the cold-rolled Al0.2Sc0.1Zr alloys (Q = (120 ± 6) kJ mol −1 ) [9], in Al0.2 wt%Sc alloy (Q = 113 kJ mol −1 ) [30] and in the cold-rolled AlMnScZr alloy (Q = (106 ± 13) kJ mol −1 ) [16]. The apparent activation energy of the eect B was calculated as Q = (152 ± 33) kJ mol −1 .…”

Section: Resultssupporting

confidence: 72%

Microstructure, Thermal and Mechanical Properties of Non-Isothermally Annealed Al-Sc-Zr and Al-Mn-Sc-Zr Alloys Prepared by Powder Metallurgy

et al. 2012

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This paper reports results of a study aimed at understanding the precipitation processes occurring during the annealing of two AlScZr-based alloys with and without Mn prepared by powder metallurgy with subsequent hot extrusion at 350• C. Samples were isochronally annealed up to ≈ 570 • C. Precipitation behaviour was studied by electrical resistometry and dierential scanning calorimetry. Mechanical properties were monitored by microhardness HV1 measurements. Transmission electron microscopy examinations and X-ray diraction of specimens quenched from temperatures of signicant resistivity changes helped to identify the microstructural processes responsible for these changes. Fine (sub)grain structure develops and ne coherent Al3Sc and/or Al3(Sc,Zr) particles precipitate during extrusion in both alloys. The distinct changes in resistivity (at temperatures above ≈ 330• C) of the AlMnScZr alloy are mainly caused by precipitation of Mn-containing particles. The easier diusion of Mn atoms along the (sub)grain boundaries is responsible for the precipitation of the Al6Mn and/or Al6(Mn,Fe) particles at relatively lower temperatures compared to the temperature range of precipitation of these particles in the classical mould-cast AlMnScZr alloys The apparent activation energy for precipitation of the Al3Sc and Al6Mn particles in the AlMnScZr alloy was determined as (106 ± 10) kJ mol −1 and (152 ± 33) kJ mol −1 , respectively.

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Section: Resultssupporting

confidence: 72%

Microstructure, Thermal and Mechanical Properties of Non-Isothermally Annealed Al-Sc-Zr and Al-Mn-Sc-Zr Alloys Prepared by Powder Metallurgy

et al. 2012

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“…-A comparison of data on precipitation in an Al-Si alloy [66] with a non-isothermal version of the Fan et al model [32] in [67] shows that the fit of the Fan et al…”

Section: Comparisons With Experimental Data and Existing Modelsmentioning

confidence: 98%

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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“…As a typical nucleation/growth controlled process, the precipitation is well known as the formation of new-phase particles from supersaturated solid solution [8][9][10]. So far, our recent theoretical works about the precipitation kinetics were mainly focused on the soft impingement model [11][12][13][14][15]. In view of the previous works, it must be noted that, any precipitation from the supersaturated solid solution is connected with the solute distribution, which inevitably refers to the initial condition of the matrix phase [16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Microstructure Evolution in Undercooled Ni-Si Melt

Fan

Liu

et al. 2013

MSF

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Upon non-equilibrium solidification, the intrinsic parameters, such as moving velocity, temperature, solute partition coefficient, and liquid and solid concentrations at the interface, deviate from their equilibrium characteristics, and the morphology of the as-solidified structure and the grain size are influenced by the non-equilibrium liqulid/solid transformation, which further influences the subquent solidstate transformation. Adopting molten glass purification technology combined with cycle superheating method, the microstructure evolution of Ni-11at.%Si alloy in different undercooling was investigated. It was found that, with the increase of the initial undercooling, grain refinement occurred in microstructures of undercooled Ni-11at.%Si alloy. Meanwhile, the NL model was used to discuss the two different dendrite morphologies. According to Karmas model for dendrite fragmentation, the grain refinement of undercooled Ni-11at.%Si alloy was in good agreement with the experimental data, and the grain size was reduced with the increasing ΔT. The energy-dispersive spectroscopy (EDS) measurement was applied to analyze the solid solubility of Si atom in α-Ni matrix. It was found that the solid solubility of Si atom in α-Ni matrix increased with undercooling. At the undercooling of T>220K , a complete solute trapping occurred.

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Deduction of activation energy for diffusion by analyzing soft impingement in non-isothermal solid-state precipitation

Cited by 8 publications

References 28 publications

Microstructure, Thermal and Mechanical Properties of Non-Isothermally Annealed Al-Sc-Zr and Al-Mn-Sc-Zr Alloys Prepared by Powder Metallurgy

Microstructure, Thermal and Mechanical Properties of Non-Isothermally Annealed Al-Sc-Zr and Al-Mn-Sc-Zr Alloys Prepared by Powder Metallurgy

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

Microstructure Evolution in Undercooled Ni-Si Melt

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