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Factors affecting particle-coarsening kinetics and size distribution

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Abstract

The Lifshitz-Slyozov-Wagner (LSW) theory was developed to model kinetics of precipitate growth from supersaturated solid solutions. The theory corresponds to a zero volume fraction approximation but has been modified for finite volume fractions in order to correspond to real situations. The LSW theory has been applied to study coarsening of grains in liquid-phase sintering and to the coarsening of pores in solid-state sintering systems. There are some additional factors not considered in the LSW theory which can influence the coarsening kinetics depending on the system. It is important, therefore, to incorporate these factors into a coarsening model for better analysis of experimental data. The experimental evidence for the effects of these additional factors is reviewed together with the theoretical modifications made to the basic LSW theory in order to incorporate these factors.

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Abbreviations

r :

Radius of the particle

r c :

Critical particle radius

Cy :

Solute concentration in equilibrium with a particle of radiusr

C e :

Solute concentration in equilibrium with a particle of infinite radius

σ:

Particle/matrix interfacial energy

α, γ:

Constant

V m :

Molar volume of the precipitate

\(\bar r\) :

Mean radius of the particle at timet

\(\bar r\) 0 :

Mean radius of the particle at the onset of coarsening

Q :

Volume fraction of the precipitate

k T2 :

Sink factor

D eff :

Effective diffusion coefficient

D gb :

Diffusion coefficient along the grain boundary

D d :

Diffusion coefficient along the dislocation

Z :

Number of dislocation lines crossing the surface

q :

Dislocation pipe cross-section

l :

Average length of the dislocation

E 1 :

Elastic strain energy due to lattice mismatch between precipitate and matrix

E 3 :

Elastic interaction energy due to overlapping of strain fields

μ:

Shear modulus of the matrix

μ′:

Shear modulus of the precipitate

τg :

Time between contacts due to gravity

τbr :

Time between contacts due to Brownian motion

τf :

Time required to fuse two particles

τor :

Time required to remove a particle by Ostwald ripening

U A :

Driving force correction factor

X Bos :

Solubility of componentB in the solid phase

k LSW :

LSW rate constant

J rε :

Flux of the ith component for the sth phase

D 1 :

Diffusion coefficient of the ith component

\(\bar c\) :

Average concentration of ith component in the matrix

c rε :

Equilibrium concentration of theith component at the sth phase particle/matrix interface

σ:

Equal tor/\(\bar r\)

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  1. Department of Metallurgical and Materials Engineering, Illinois Institute of Technology, 60616, Chicago, Illinois, USA

    C. S. Jayanth & Philip Nash

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Jayanth, C.S., Nash, P. Factors affecting particle-coarsening kinetics and size distribution. J Mater Sci 24, 3041–3052 (1989). https://doi.org/10.1007/BF01139016

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