Surface nucleation and anisotropic growth model for solid state reactions

Mario A. Bianchet; Graciela Rigotti; Miguel A. Blesa

doi:10.1016/0167-2738(90)90254-O

Surface nucleation and anisotropic growth model for solid state reactions

Mario A. Bianchet, Graciela Rigotti, Miguel A. Blesa

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Mathematical equations are derived that relate the extent of reaction α to time for the case of a reaction starting through surface nucleation and proceeding inwards and laterally through two growth-rate constants. The model is based in Avrami's theorem, and may therefore be considered as a modified Avrami model. The relation between -In(1-α) and time involves first-order Bessel functions Y₁[2ωμ(t)] and J₁[2ωμ(t)], where μ(t)=exp(-k_n t 2) and ω2,=σδ₀k₁k_n^-1, ω is one of the model basic parameters. The final equations may be solved analytically under certain conditions, and numerically in the more general cases.

Original language	English (US)
Pages (from-to)	21-27
Number of pages	7
Journal	Solid State Ionics
Volume	42
Issue number	1-2
DOIs	https://doi.org/10.1016/0167-2738(90)90254-O
State	Published - Sep 1990
Externally published	Yes

ASJC Scopus subject areas

General Chemistry
General Materials Science
Condensed Matter Physics

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10.1016/0167-2738(90)90254-O

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title = "Surface nucleation and anisotropic growth model for solid state reactions",

abstract = "Mathematical equations are derived that relate the extent of reaction α to time for the case of a reaction starting through surface nucleation and proceeding inwards and laterally through two growth-rate constants. The model is based in Avrami's theorem, and may therefore be considered as a modified Avrami model. The relation between -In(1-α) and time involves first-order Bessel functions Y1[2ωμ(t)] and J1[2ωμ(t)], where μ(t)=exp(-kn t 2) and ω2,=σδ0k1kn-1, ω is one of the model basic parameters. The final equations may be solved analytically under certain conditions, and numerically in the more general cases.",

author = "Bianchet, {Mario A.} and Graciela Rigotti and Blesa, {Miguel A.}",

note = "Funding Information: To CICPBA for Doctoral Fellowship to M. Bian-chet and partial support. G. Rigotti is a member of CICPBA and M.A. Blesa is a membero f CONICET. Copyright: Copyright 2014 Elsevier B.V., All rights reserved.",

year = "1990",

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doi = "10.1016/0167-2738(90)90254-O",

language = "English (US)",

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journal = "Solid State Ionics",

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T1 - Surface nucleation and anisotropic growth model for solid state reactions

AU - Bianchet, Mario A.

AU - Rigotti, Graciela

AU - Blesa, Miguel A.

N1 - Funding Information: To CICPBA for Doctoral Fellowship to M. Bian-chet and partial support. G. Rigotti is a member of CICPBA and M.A. Blesa is a membero f CONICET. Copyright: Copyright 2014 Elsevier B.V., All rights reserved.

PY - 1990/9

Y1 - 1990/9

N2 - Mathematical equations are derived that relate the extent of reaction α to time for the case of a reaction starting through surface nucleation and proceeding inwards and laterally through two growth-rate constants. The model is based in Avrami's theorem, and may therefore be considered as a modified Avrami model. The relation between -In(1-α) and time involves first-order Bessel functions Y1[2ωμ(t)] and J1[2ωμ(t)], where μ(t)=exp(-kn t 2) and ω2,=σδ0k1kn-1, ω is one of the model basic parameters. The final equations may be solved analytically under certain conditions, and numerically in the more general cases.

AB - Mathematical equations are derived that relate the extent of reaction α to time for the case of a reaction starting through surface nucleation and proceeding inwards and laterally through two growth-rate constants. The model is based in Avrami's theorem, and may therefore be considered as a modified Avrami model. The relation between -In(1-α) and time involves first-order Bessel functions Y1[2ωμ(t)] and J1[2ωμ(t)], where μ(t)=exp(-kn t 2) and ω2,=σδ0k1kn-1, ω is one of the model basic parameters. The final equations may be solved analytically under certain conditions, and numerically in the more general cases.

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JF - Solid State Ionics

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ER -

Surface nucleation and anisotropic growth model for solid state reactions

Abstract

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