A rigorous mathematical approach based on an inhomogeneous (marked) Poisson point process is presented to extend previously proposed treatment of transformation kinetics to situations in which nuclei are not homogeneously located in space. The potential of the proposed methodology is illustrated by applying it to the case of nucleus intensity varying along a single preferential direction. The exact analytical solutions presented here significantly broaden the range of analytical solutions available to formal kinetics regarding nuclei location deviating from the classical "randomly" located nuclei assumption.
Transformation kinetics for inhomogeneous nucleation / P.R. Rios, E. Villa. - In: ACTA MATERIALIA. - ISSN 1359-6454. - 57:4(2009), pp. 1199-1208.
Transformation kinetics for inhomogeneous nucleation
E. VillaUltimo
2009
Abstract
A rigorous mathematical approach based on an inhomogeneous (marked) Poisson point process is presented to extend previously proposed treatment of transformation kinetics to situations in which nuclei are not homogeneously located in space. The potential of the proposed methodology is illustrated by applying it to the case of nucleus intensity varying along a single preferential direction. The exact analytical solutions presented here significantly broaden the range of analytical solutions available to formal kinetics regarding nuclei location deviating from the classical "randomly" located nuclei assumption.
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