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International audience; The envelope of the solidification front naturally develops a macroscopic curvature in a multitude of solidification processes. However, its effect on dendritic microstructure formation remains poorly understood. Here we exploit a microgravity environment where convection is suppressed to investigate quantitatively the effect of curvature on dendritic array growth during directional solidification of a transparent succinonitrile 0.46 wt% camphor alloy. In addition, we interpret the results using both theoretical analyses and phase-field simulations. In situ observations reveal that even a weak macroscopic interface curvature can have a major effect on both the array pattern evolution and grain structure. First, convex and concave interfaces lead to a continuous increase and decrease in time of the average primary spacing, respectively, which only attains a stationary value for a flat interface. We show that this results from the formation of drifting velocity gradients along the interface under the combined effect of the crystal misorientation and the interface misorientation. These grains form at sample boundaries and overgrow pre-existing interior grains of smaller misorientation to the detriment of well-oriented crystal growth. In addition, they induce a change of array structure when the directional normal to the sample boundary is parallel to one of axis of secondary branches. These results provide new insights for controlling and optimizing directionally solidified alloy microstructures.