Diffusion fields associated with size and shape coarsening of oblate spheroids |
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Authors: | Yiwen Mou J M Howe |
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Affiliation: | (1) Present address: the Department of Materials Science and Engineering, University of Virginia, USA;(2) AFE Technologies, 22901 Charlottesville, VA;(3) the Department of Materials Science and Engineering, University of Virginia, 22903 Charlottesville, VA |
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Abstract: | The diffusion field or solute concentration distributed around an oblate spheroidal particle simulating a disc-shaped precipitate
has been solved for varying particle aspect ratios and varying concentrations along the precipitate surface because of the
curvature effect. With oblate spheroidal coordinates, the principal curvatures of the oblate spheroidal surface are derived
as functions of the angular variable, and the Laplace field equation is separated into two Legendre equations on the angular
variable and on the radial variable. The analytical solution to the Laplace equation, fitting the present boundary conditions,
is secured as the sum of a Legendre function and a Legendre series composed of Legendre functions of the second kind with
imaginary arguments. The Legendre function gives the concentration distribution with an ignored curvature effect, whereas
the series shows the contribution from the curvature effect. Numerical results of normalized concentrations are presented
as functions of the radial and angular variables for selected aspect ratios. The concentration distributions around both oblate
and prolate spheroidal particles are shown to reduce to the concentration distributed around a spherical particle when the
aspect ratio of the spheroids approaches unity. |
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Keywords: | |
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