Abstract
The problem of clustering of quenched-in vacancies into various types of extended defects is considered. A master equation for the evolution of the concentration of clusters of various sizes is written down with general transition rates. It is shown that this model represents a continuous time non-stationary Markoff process. A particular choice of transition rates corresponding to the formation of vacancy loops and stacking fault tetrahedra is considered in some detail. It is shown that this choice of transition rates allows us to obtain the solution for the concentration of the single vacancy units, and hence yields some information on the nucleation time. Further, the transition matrix becomes stationary and doubly stochastic due to the short time constant of the concentration of single vacancy units. This in turn leads to an unphysical stationary state. Finally we show how the rate equations for the irradiated situation can be written down and derive the phenomenological rate equations that are conventionally used.
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Ananthakrishna G, Sudarshan E C G and Vittorio Gorini 1975Rep. Math. Phys. 8 25
Ananthakrishna G 1977 RRC Report No. 19
Ananthakrishna G 1979aPramana 13 (referred to as paper II)
Ananthakrishna G 1979bPramana (in press) referred to as paper III
Ananthakrishna G 1979cPramana (in press) referred to as paper IV
Bullough R, Eyre B L and Krishan K 1975Proc. R. Soc. London A346 81 and appropriate references cited therein
Cotterill R M J 1965 inLattice defects in quenched metals eds R M J Cotterill, M Doyema, J J Jackson and M Meshie, (New York: Academic), p. 97
Fano U 1957Rev. Mod. Phys. 29 74
Harkness S D and Li C Y 1969 inRadiation damage in reactor materials Proceedings of Symposium, Vienna, Vol. 2
Hayns M R 1976J. Nucl. Mater. 59 175
Jain K C and Siegel R W 1972aPhilos. Mag. 25 105
Jain K C and Siegel R W 1972bPhilos. Mag. 26 1637
Katz J L and Wiedersich H 1971J. Chem. Phys. 55 1414
Kiritani M 1964J. Phys. Soc. Jpn. 19 618
Kiritani M, Nishikawa T and Yoshida S 1969J. Phys. Soc. Jpn. 27 67
Kiritani M 1973J. Phys. Soc. Jpn. 35 95
Kiritani M 1976 Private Communication
Kiritani M, Shimomura Y and Yoshida S 1964J. Phys. Soc. Jpn. 19 1624
Noris D I R 1972Rad. Effects 14 1971
Okubo S and Ishihara 1971J. Math. Phys. 12 2498
Wang M C and Uhlenbeck G E 1945Rev. Mod. Phys. 17 323
Westmacott H 1966Philos. Mag. 19 618
Weidersich H 1974The physics of irradiation produced voids Consultant Symposium ed R S Nelson, AERE R 7134, Harewell
Wieberg J and Vingsbo O 1977Phys. Rev. B 15 5129
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Ananthakrishna, G. Stochastic theory for clustering of quenched-in vacancies—1. General mathematical properties. Pramana - J. Phys. 12, 527–541 (1979). https://doi.org/10.1007/BF02872124
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DOI: https://doi.org/10.1007/BF02872124