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Philosophical Magazine A Volume 81, 2001 - Issue 3
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Original Articles

Grouping method for the approximate solution of a kinetic equation describing the evolution of point-defect clusters

S. I. Golubov State Scientific Centre of Russian Federation, Institute of Physics and Power Engineering, Bondarenko Square I, Obninsk, 249020, Russian Federation
,
A. M. Ovcharenko State Scientific Centre of Russian Federation, Institute of Physics and Power Engineering, Bondarenko Square I, Obninsk, 249020, Russian Federation
,
A. V. Barashev Materials Science and Engineering, Department of Engineering, The University of Liverpool, Brownlow Hill, Liverpool, L69 3GH, UK
&
B. N. Singh Materials Research Department, Ris⊘ National Laboratory, DK-4000, Roskilde, Denmark
Pages 643-658 | Received 14 Feb 2000, Accepted 06 Jun 2000, Published online: 05 Aug 2009
 
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Abstract

An approximate method for the numerical solution of a kinetic equation describing the nucleation, growth and coarsening of point-defect clusters or second-phase precipitates is of interest for many applications in solid-state physics. In the present paper the validity of a grouping method developed by Kiritani (1973, J. phys. Soc. Japan 35, 95) is examined. In this method, which is the only one proposed up to now, a group of equations is replaced by an ‘averaged’ equation. Significant disagreement between the group kinetic equation and the original kinetic equation is revealed and the reasons for this are specified. A new grouping method based on the original equation is proposed and application of the method for the solution of two problems is demonstrated by comparing the results of numerical and analytical calculations.

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