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Open AccessArticle

Analytical Modeling of the Mixed-Mode Growth and Dissolution of Precipitates in a Finite System

Department of Mining, Metallurgy and Materials Engineering, Aluminum Research Center–REGAL, Laval University, 1065, ave de la Médecine, Québec, QC G1V 0A6, Canada
Linamar Corporation—The Center, 700 Woodlawn Road West, Guelph, ON N1K 1G4, Canada
Rio Tinto, Arvida Research and Development Centre, 1955, Mellon Blvd, Saguenay, QC G7S 4K8, Canada
Linamar Montupet Light Metal Division, 3, rue de Nogent, 60290 Laigneville, France
Author to whom correspondence should be addressed.
Metals 2019, 9(8), 889;
Received: 25 July 2019 / Revised: 8 August 2019 / Accepted: 12 August 2019 / Published: 14 August 2019
(This article belongs to the Special Issue Phase Transformations in Aluminium Alloys)
PDF [4959 KB, uploaded 20 August 2019]


In this paper, a novel analytical modeling of the growth and dissolution of precipitates in substitutional alloys is presented. This model uses an existing solution for the shape-preserved growth of ellipsoidal precipitates in the mixed-mode regime, which takes into account the interfacial mobility of the precipitate. The dissolution model is developed by neglecting the transient term in the mass conservation equation, keeping the convective term. It is shown that such an approach yields the so-called reversed-growth approximation. A time discretization procedure is proposed to take into account the evolution of the solute concentration in the matrix as the phase transformation progresses. The model is applied to calculate the evolution of the radius of spherical θ-Al2Cu precipitates in an Al rich matrix at two different temperatures, for which growth or dissolution occurs. A comparison of the model is made, with the results obtained using the numerical solver DICTRA. The very good agreement obtained for cases where the interfacial mobility is very high indicates that the time discretization procedure is accurate. View Full-Text
Keywords: growth; dissolution; interfacial mobility; mixed-mode; reversed-growth; Al–Cu; DICTRA growth; dissolution; interfacial mobility; mixed-mode; reversed-growth; Al–Cu; DICTRA

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Naseri, T.; Larouche, D.; Martinez, R.; Breton, F.; Massinon, D. Analytical Modeling of the Mixed-Mode Growth and Dissolution of Precipitates in a Finite System. Metals 2019, 9, 889.

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