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Under directional growth conditions, a strong crystallographic texture is observed in Mg-based alloys due to the anisotropy of the hcp-phase. The aim of the present work is to investigate the fundamental mechanisms of this growth texture evolution by microstructure simulations. For this purpose, a phase-field model has been extended to allow for complex 3D anisotropic interfacial energies and mobilities, calibrated by data from molecular dynamics studies. The model is first applied in 2D to AZ31 (Mg–3%Al–1%Zn). Bicrystal simulations are performed for a systematic study of grain interactions. Extended simulations are compared to experiments. Comprehensive texture evolution is investigated in 3D for Mg–6%Al. Texture is found to evolve mainly due to retarded growth in basal <0001> orientations. Grains with the fast growing <1120> orientation most closely aligned to the temperature gradient commonly prevail …