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The microstructural evolution of Ti-45at.%Al alloy during directional solidification was simulated by applying a solute diffusion controlled solidification model，and the results have showed that under high thermal gradient the stable primary spacing can be adjusted by branching or competitive growth，irrelevant of the initial seed spacing. In addition，under a given pulling speed，increasing thermal gradient decreases primary cell/dendrite spacing，and under a given thermal gradient，increasing pulling velocity，we have observed a cell/dendrite transition region consisting of cells and dendrites，and which varies with the thermal gradient in a contradicting way，i.e. increasing the thermal gradient leading to the decrease of the range of the transition region. The simulated results agree reasonably well with experiment results.