In directional solidification of binary alloys, cellular arrays undergo various instabilities that affect both the average width of growth cells and their dynamics. A fundamental issue in the formation of microstructures consists in understanding the occurrence of these instabilities from the evolution of cell geometry. Towards this goal, we experimentally address the instability diagram, the undercooling and the geometry of growth cells in directional solidification of succinonitrile alloys. In particular, we determine a global parametrization of cell boundaries, from their grooves to their tip, over the whole control parameter space of the system. The implications of these determinations for the onset of sidebranching are discussed. (C) 2002 Elsevier Science B.V. All fights reserved.