Measurement and analysis of grain boundary grooving by volume diffusion

S. C. Hardy; G. B. McFadden; S. R. Coriell; P. W. Voorhees; R. F. Sekerka

doi:10.1016/0022-0248(91)90061-9

Measurement and analysis of grain boundary grooving by volume diffusion

S. C. Hardy^*, G. B. McFadden, S. R. Coriell, P. W. Voorhees, R. F. Sekerka

^*Corresponding author for this work

Materials Science and Engineering

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

36 Scopus citations

Abstract

Experimental measurements of isothermal grain boundary grooving by volume diffusion are carried out for Sn bicrystals in the Sn-Pb system near the eutectic temperature. The dimensions of the groove increase with a temporal exponent of 1 3, and measurement of the associated rate constant allows the determination of the product of the liquid diffusion coefficient D and the capillarity length Γ associated with the interfacial free energy of the crystal-melt interface. We generalize the small-slope theory of Mullins to the entire range of dihedral angles by using a boundary integral formulation of the associated free boundary problem, and obtain excellent agreement with experimental groove shapes. By using the diffusivity measured by Jordon and Hunt, we deduce that our measured values of Γ agree to within 5% with the values obtained from experiments by Gunduz and Hunt on grain boundary grooving in a temperature gradient.

Original language	English (US)
Pages (from-to)	467-480
Number of pages	14
Journal	Journal of Crystal Growth
Volume	114
Issue number	3
DOIs	https://doi.org/10.1016/0022-0248(91)90061-9
State	Published - Nov 1991

ASJC Scopus subject areas

Condensed Matter Physics
Inorganic Chemistry
Materials Chemistry

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10.1016/0022-0248(91)90061-9

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@article{8e2edea9783841cdaaf88ef50118d2cb,

title = "Measurement and analysis of grain boundary grooving by volume diffusion",

abstract = "Experimental measurements of isothermal grain boundary grooving by volume diffusion are carried out for Sn bicrystals in the Sn-Pb system near the eutectic temperature. The dimensions of the groove increase with a temporal exponent of 1 3, and measurement of the associated rate constant allows the determination of the product of the liquid diffusion coefficient D and the capillarity length Γ associated with the interfacial free energy of the crystal-melt interface. We generalize the small-slope theory of Mullins to the entire range of dihedral angles by using a boundary integral formulation of the associated free boundary problem, and obtain excellent agreement with experimental groove shapes. By using the diffusivity measured by Jordon and Hunt, we deduce that our measured values of Γ agree to within 5% with the values obtained from experiments by Gunduz and Hunt on grain boundary grooving in a temperature gradient.",

author = "Hardy, {S. C.} and McFadden, {G. B.} and Coriell, {S. R.} and Voorhees, {P. W.} and Sekerka, {R. F.}",

note = "Funding Information: The authors are grateful for helpful conversations with W.W. Mullins and R.J. Schaefer. This work was conducted with the support of the Microgravity Science and Applications Division of the National Aeronautics and Space Administration, and the Applied and Computational Mathematics Program of the Defense Advanced Research Projects Agency. One of us (R.F.S.) was partially supported by the National Science Foundation under Grant DMR 8912752. Some of the work was performed while one of the authors (G.B.M.) was visiting the Institute for Mathematics and its Applications (IMA) at the University of Minnesota, whose hospitality is gratefully acknowledged. Numerical calculations were performed at the Minnesota Supercomputer Center through an NSF grant to the IMA.",

year = "1991",

month = nov,

doi = "10.1016/0022-0248(91)90061-9",

language = "English (US)",

volume = "114",

pages = "467--480",

journal = "Journal of Crystal Growth",

issn = "0022-0248",

publisher = "Elsevier",

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T1 - Measurement and analysis of grain boundary grooving by volume diffusion

AU - Hardy, S. C.

AU - McFadden, G. B.

AU - Coriell, S. R.

AU - Voorhees, P. W.

AU - Sekerka, R. F.

N1 - Funding Information: The authors are grateful for helpful conversations with W.W. Mullins and R.J. Schaefer. This work was conducted with the support of the Microgravity Science and Applications Division of the National Aeronautics and Space Administration, and the Applied and Computational Mathematics Program of the Defense Advanced Research Projects Agency. One of us (R.F.S.) was partially supported by the National Science Foundation under Grant DMR 8912752. Some of the work was performed while one of the authors (G.B.M.) was visiting the Institute for Mathematics and its Applications (IMA) at the University of Minnesota, whose hospitality is gratefully acknowledged. Numerical calculations were performed at the Minnesota Supercomputer Center through an NSF grant to the IMA.

PY - 1991/11

Y1 - 1991/11

N2 - Experimental measurements of isothermal grain boundary grooving by volume diffusion are carried out for Sn bicrystals in the Sn-Pb system near the eutectic temperature. The dimensions of the groove increase with a temporal exponent of 1 3, and measurement of the associated rate constant allows the determination of the product of the liquid diffusion coefficient D and the capillarity length Γ associated with the interfacial free energy of the crystal-melt interface. We generalize the small-slope theory of Mullins to the entire range of dihedral angles by using a boundary integral formulation of the associated free boundary problem, and obtain excellent agreement with experimental groove shapes. By using the diffusivity measured by Jordon and Hunt, we deduce that our measured values of Γ agree to within 5% with the values obtained from experiments by Gunduz and Hunt on grain boundary grooving in a temperature gradient.

AB - Experimental measurements of isothermal grain boundary grooving by volume diffusion are carried out for Sn bicrystals in the Sn-Pb system near the eutectic temperature. The dimensions of the groove increase with a temporal exponent of 1 3, and measurement of the associated rate constant allows the determination of the product of the liquid diffusion coefficient D and the capillarity length Γ associated with the interfacial free energy of the crystal-melt interface. We generalize the small-slope theory of Mullins to the entire range of dihedral angles by using a boundary integral formulation of the associated free boundary problem, and obtain excellent agreement with experimental groove shapes. By using the diffusivity measured by Jordon and Hunt, we deduce that our measured values of Γ agree to within 5% with the values obtained from experiments by Gunduz and Hunt on grain boundary grooving in a temperature gradient.

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Measurement and analysis of grain boundary grooving by volume diffusion

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