  In this study, an alloy phase-field model is used to simulate solidification
microstructures at different locations within a solidified molten pool. The
temperature gradient $G$ and the solidification velocity $V$ are obtained from
a macroscopic heat transfer finite element simulation and provided as input to
the phase-field model. The effects of laser beam speed and the location within
the melt pool on the primary arm spacing and on the extent of Nb partitioning
at the cell tips are investigated. Simulated steady-state primary spacings are
compared with power law and geometrical models. Cell tip compositions are
compared to a dendrite growth model. The extent of non-equilibrium interface
partitioning of the phase-field model is investigated. Although the phase-field
model has an anti-trapping solute flux term meant to maintain local interface
equilibrium, we have found that during simulations it was insufficient at
maintaining equilibrium. This is due to the fact that the additive
manufacturing solidification conditions fall well outside the allowed limits of
this flux term.
