  In this work, the effect of building direction on the microstructure
evolution of laser-powder bed fusion (LPBF) processed AlSi10Mg alloy was
investigated. The building direction, as shown in experimentally fabricated
parts, can influence the solidification behavior and promote morphological
transitions in cellular dendritic microstructures. We develop a thermal model
to systemically address the impact of laser processing conditions, and building
direction on the thermal characteristics of the molten pool during laser
processing of AlSi10Mg alloy. We then employ a multi-order parameter phase
field model to study the microstructure evolution of LPBF-AlSi10Mg in the
dilute limit, using the underlying thermal conditions for horizontal and
vertical building directions as input. The phase field model employed here is
designed to simulate solidification using heterogeneous nucleation from
inoculant particles allowing to take into account morphological phenomena
including the columnar-to-equiaxed transition (CET). The phase field model is
first validated against the predictions of the previously developed
steady-state CET theory of Hunt \cite{hunt1984steady}. It is then used under
transient conditions to study microstructure evolution, revealing that the
nucleation rate is noticeably higher in the horizontally built samples due to
larger constitutional undercooling, which is consistent with experimental
observations. We further quantify the effect of building direction on the local
cooling conditions, and consequently on the grain morphology.
