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Extensions to the Ivantsov dendrite growth model are presented, which allow for increased solute levels in the field ahead of the dendrite tip. This model is intended for use with video-microscopy experimental results taken from synchrotron radiography sources. Ideally, the composition and composition gradient at the solid-liquid interface would be measured. However, due to the spatial resolution limitations, it is difficult to accurately measure the composition at the interface. This paper sets out an extended description of the theory where measurements ahead of the tip determine the operating conditions at the tip. This extended model of dendritic growth may be incorporated into solidification process models, thus improving predictions where the solute field ahead of the tip may change due to solutal build up from neighbouring dendrites. It is shown that growth arrest is predicted in cases where local solutal enrichment reaches a critical level. A distinction between global and local tip undercooling is made. The usefulness of this model is demonstrated with an application to experimental results for a binary (Al-Ge) alloy.
S. McFadden, D.J. Browne, A generalized version of an Ivantsov-based dendrite growth model incorporating a facility for solute measurement ahead of the tip, Computational Materials Science, vol.55, pages 245-254, 2012