A stochastic theory for clustering of quenched-in vacancies—2. A solvable model |
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Authors: | G Ananthakrishna |
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Institution: | (1) Reactor Research Centre, 603 102 Kalpakkam |
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Abstract: | The model introduced for clustering of quenched-in vacancies in the first part of this series of papers is considered. Using
a generating function, the rate equations are converted into a first order partial differential equation for the generating
function coupled to a differential equation for the rate of change of the concentration of single vacancy units. A decoupling
scheme is effected which gives an exponentially decaying solution with a very short time constant for the concentration of
single vacancy units. The differential equation for the generating function is solved for times larger than the time required
for the concentration of single vacancy units to reach its asymptotic value. The distribution for the size of the clusters
is obtained by inverting the solution thus obtained. Several results that follow are shown to be in reasonably good agreement
with the experimental results. |
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Keywords: | Vacancy units vacancy loops stacking fault tetrahedra generating function Fokker-Planck equation |
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