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Constant-pressure molecular dynamics simulation and the pair analysis technique have been performed to study the microstructural evolution of aluminium during rapid solidification. The microstructure characteristics of icosahedral ordering increase with decrease of the cooling rate, whereas the microstructure unit characteristics of hcp crystalline structure decrease. There are two kinds of microstructure units which are similar to those in the fcc crystal containing interstitialcies. These two kinds of microscopic units are nearly independent of the cooling rate. The microscopic structural unit characteristics of fcc crystalline structure do not depend on the cooling rate either. These results may help us understand the microstructure of glass and its stability.