Self-similarity and coarsening of three dimensional particles on a one or two dimensional matrix

Jorge Vinals, W. W. Mullins

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

We examine the validity of the hypothesis of self-similarity in systems coarsening under the driving force of interface energy reduction in which three dimensional particles are intersected by a one or two dimensional diffusion matrix, In both cases, solute fluxes onto the surface of the particles, assumed spherical, depend on both particle radius and interparticle distance. We argue that overall mass conservation requires independent scalings for particle sizes and interparticle distances under magnification of the structure, and predict power law growth for the average particle size in the case of a one dimensional matrix (3D/1D), and a weak breakdown of self-similarity in the two dimensional case (3D/2D). Numerical calculations confirm our predictions regarding self-similarity and power law growth of average particle size with an exponent 1/7 for the 3D/1D case, and provide evidence for the existence of logarithmic factors in the laws of boundary motion for the 3D/2D case. The latter indicate a weak breakdown of self-similarity.

Original languageEnglish (US)
Pages (from-to)621-628
Number of pages8
JournalJournal of Applied Physics
Volume83
Issue number2
DOIs
StatePublished - Jan 15 1998

Fingerprint

breakdown
magnification
conservation
solutes
exponents
scaling
radii
matrices
predictions
energy

Cite this

Self-similarity and coarsening of three dimensional particles on a one or two dimensional matrix. / Vinals, Jorge; Mullins, W. W.

In: Journal of Applied Physics, Vol. 83, No. 2, 15.01.1998, p. 621-628.

Research output: Contribution to journalArticle

@article{88e3736ffa6b404db2801094b1eac69f,
title = "Self-similarity and coarsening of three dimensional particles on a one or two dimensional matrix",
abstract = "We examine the validity of the hypothesis of self-similarity in systems coarsening under the driving force of interface energy reduction in which three dimensional particles are intersected by a one or two dimensional diffusion matrix, In both cases, solute fluxes onto the surface of the particles, assumed spherical, depend on both particle radius and interparticle distance. We argue that overall mass conservation requires independent scalings for particle sizes and interparticle distances under magnification of the structure, and predict power law growth for the average particle size in the case of a one dimensional matrix (3D/1D), and a weak breakdown of self-similarity in the two dimensional case (3D/2D). Numerical calculations confirm our predictions regarding self-similarity and power law growth of average particle size with an exponent 1/7 for the 3D/1D case, and provide evidence for the existence of logarithmic factors in the laws of boundary motion for the 3D/2D case. The latter indicate a weak breakdown of self-similarity.",
author = "Jorge Vinals and Mullins, {W. W.}",
year = "1998",
month = "1",
day = "15",
doi = "10.1063/1.366751",
language = "English (US)",
volume = "83",
pages = "621--628",
journal = "Journal of Applied Physics",
issn = "0021-8979",
publisher = "American Institute of Physics Publising LLC",
number = "2",

}

TY - JOUR

T1 - Self-similarity and coarsening of three dimensional particles on a one or two dimensional matrix

AU - Vinals, Jorge

AU - Mullins, W. W.

PY - 1998/1/15

Y1 - 1998/1/15

N2 - We examine the validity of the hypothesis of self-similarity in systems coarsening under the driving force of interface energy reduction in which three dimensional particles are intersected by a one or two dimensional diffusion matrix, In both cases, solute fluxes onto the surface of the particles, assumed spherical, depend on both particle radius and interparticle distance. We argue that overall mass conservation requires independent scalings for particle sizes and interparticle distances under magnification of the structure, and predict power law growth for the average particle size in the case of a one dimensional matrix (3D/1D), and a weak breakdown of self-similarity in the two dimensional case (3D/2D). Numerical calculations confirm our predictions regarding self-similarity and power law growth of average particle size with an exponent 1/7 for the 3D/1D case, and provide evidence for the existence of logarithmic factors in the laws of boundary motion for the 3D/2D case. The latter indicate a weak breakdown of self-similarity.

AB - We examine the validity of the hypothesis of self-similarity in systems coarsening under the driving force of interface energy reduction in which three dimensional particles are intersected by a one or two dimensional diffusion matrix, In both cases, solute fluxes onto the surface of the particles, assumed spherical, depend on both particle radius and interparticle distance. We argue that overall mass conservation requires independent scalings for particle sizes and interparticle distances under magnification of the structure, and predict power law growth for the average particle size in the case of a one dimensional matrix (3D/1D), and a weak breakdown of self-similarity in the two dimensional case (3D/2D). Numerical calculations confirm our predictions regarding self-similarity and power law growth of average particle size with an exponent 1/7 for the 3D/1D case, and provide evidence for the existence of logarithmic factors in the laws of boundary motion for the 3D/2D case. The latter indicate a weak breakdown of self-similarity.

UR - http://www.scopus.com/inward/record.url?scp=4344609810&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4344609810&partnerID=8YFLogxK

U2 - 10.1063/1.366751

DO - 10.1063/1.366751

M3 - Article

AN - SCOPUS:4344609810

VL - 83

SP - 621

EP - 628

JO - Journal of Applied Physics

JF - Journal of Applied Physics

SN - 0021-8979

IS - 2

ER -