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The microstructure evolution of bicrystal samples during directional solidification was studied, both by simulation and experiment, to explore the mechanism of competitive growth. A new orientation relationship of bicrystal samples, the non-uniplanar case, is proposed, which expands the orientation relationship of bicrystal samples from two dimensions to three dimensions. The results show that, in the non-uniplanar case, the favorably oriented grain overgrows the unfavorably oriented grain by developing new dendrites in the lateral gap where the primary dendrites of the unfavorably oriented grain diverge from the mold wall. During this process, the grain boundary is found to move in two directions, one perpendicular to the grain boundary and the other parallel to the grain boundary. To characterize the state of dendrite growth, a three-dimensional reference frame is constructed. In this reference frame, the mechanism of competitive growth can be categorized as a converging case, a non-uniplanar case and a diverging case. Furthermore, the simulation results are in good agreement with the experimental findings. (C) 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.