  The influence of non-uniform distribution of nuclei on crystallization
kinetics of amorphous materials is investigated. This case cannot be described
by the well-known Johnson-Mehl-Avrami (JMA) equation, which is only valid under
the assumption of a spatially homogeneous nucleation probability. The results
of computer simulations of crystallization kinetics with nuclei distributed
according to a cluster and a hardcore distribution are compared with JMA
kinetics. The effects of the different distributions on the so-called Avrami
exponent $n$ are shown. Furthermore, we calculate the small-angle scattering
curves of the simulated structures which can be used to distinguish
experimentally between the three nucleation models under consideration.
