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Metal additive manufacturing (AM) improves the design flexibility of titanium aluminides (TiAl-based alloys) as a new class of high-temperature alloys towards widespread applications. In this work, the underlying mecha- nisms responsible for the site-specific thermal history and grain evolution during laser powder bed fusion (LPBF) of TiAl-based alloys are investigated through an integrated computational and experimental effort. In spe- cific, a multiphysics modeling framework integrating a finite element thermal model with a highly efficient phase-field method is developed to simulate the solidification microstructure at different locations within the melt pool during LPBF processing. The investigation of process-microstructure relationship is accomplished using a Ti-45Al (at.%) alloy for a binary approximation, with a focus on site-specific primary dendrite arm spacing (PDAS) and non-equilibrium microsegregation. The microstructural sensitivity to spatial variations, individual processing parameters, and misorientation angle between the preferred crystalline orientation and the temper- ature gradient direction are studied to thoroughly understand the rapid solidification during LPBF. LPBF experi- ments are carried out to validate the modeling results in terms of melt pool dimensions and site-specific PDAS across the melt pool. The knowledge gained in this work will benefit the development of AM processing routine for fabrication of high-performance TiAl-based alloys towards extensive applications.