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The process of the laser beam welding of Al-Si alloys is simulated on the different length scales. This second part of the work reconstructs the microstructure and microsegregation by direct simulation using the phase field method. In the typical parameter window d/dt T = 1000 K/s - 12000 K/s and ∇T = 500-4000 K/cm systematic investigations by 2D-simulations were carried out in order to describe the morphology diagram. Doublon-dendritic transitions are observed and the primary spacing is evaluated as function of solidfication conditions. Differences in simulation results are discussed for the cases of binary and ternary alloys, two and three dimensional simulations, and different models of crystal anisotropy. The results are compared with the measured microstructure in the weld pool.