Diffusion fields associated with size and shape coarsening of oblate spheroids

Journal Article · Wed Jan 01 04:00:00 EST 1997 · Metallurgical and Materials Transactions. A, Physical Metallurgy and Materials Science

DOI:https://doi.org/10.1007/s11661-997-0081-y· OSTI ID:438582

Mou, Y; Howe, J M ^[1]

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1. Univ. of Virginia, Charlottesville, VA (United States). Dept. of Materials Science and Engineering

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.

• Sponsoring Organization: USDOE
• OSTI ID: 438582
• Journal Information: Metallurgical and Materials Transactions. A, Physical Metallurgy and Materials Science, Journal Name: Metallurgical and Materials Transactions. A, Physical Metallurgy and Materials Science Journal Issue: 1 Vol. 28; ISSN 1073-5623; ISSN MMTAEB
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
ALLOYS
BOUNDARY CONDITIONS
CHEMICAL COMPOSITION
CONCENTRATION RATIO
DIFFUSION
KINETICS
LAPLACE EQUATION
LEGENDRE POLYNOMIALS
MATHEMATICAL MODELS
PRECIPITATION
SOLUTES