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Zusammenfassung

Abstract: The micro structural development during nucleation and growth processes is studied numerically. Most of the studies are for the simple case of constant nucleation and growth rates, but a brief discussion is made of the effect of time-dependent nucleation and growth. A three dimensional code is used which accounts for not only the nucleation and growth of individual new grains, but also the effects of grain impingement, and which allows for the study of both homogeneous and heterogeneous nucleation. The microstructures are characterized by the grain size distribution (GSD) and the cluster size distribution (CSD), respectively. In the case of homogeneous nucleation, the development of GSD and CSD can be scaled using the Abram time taiga and Abram length delta_Av, which are related to the nucleation and growth rates. Both scaling constants have a simple physical meaning: the average grain size after the completion of the phase transformation is given by delta_Av, and the transformation half-time is approximately equal to taiga. The formation of a continuous chain of new phase grains (percolation transition) is observed at ~ 30 per cent transformation degree, and the geometry of the largest cluster near the percolation threshold has fractal characteristics with a fractal dimension of ~ 2.5. The presence of preferred sites of nucleation (heterogeneous nucleation), such as grain boundaries, significantly modifies the microstructures when the spacing of nucleation sites is much larger than the Abram length, the main effects being a reduced percolation threshold and an elongate grain shape. Some applications to the olivine-spinal transformation in subducting slabs and to the crystallization in a hypothetical magma ocean are discussed.