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• The topologically close–packed (TCP) atoms dominate in undercooled Zr liquid. • The TCP atoms are energetic and structural favourable and then stabilize super-cooled liquid. • Three stages between TCP and BCC competition process can be observed. • Crystallization cannot occur until the TCP atoms with T 5 > 1/3 drops in number and interconnect. The crystallization of undercooled liquid zirconium (Zr) during isothermal relaxation was investigated by molecular dynamics simulation. In particular, the dynamic competition mechanism between the topologically close–packed (TCP) and body–centered cubic (BCC) structures during crystallization was deeply studied using the atomic energy, the pair distribution function and the largest standard cluster analysis (LaSCA). The study found that TCP clusters, rather than icosahedral clusters, play an important role in hindering the crystallization of the undercooled liquid. The TCP clusters with T 5 = n 5 /(n 4 + n 5 + n 6) > 1/3 (where n 4 , n 5 and n 6 represent the number of common neighbor sub-cluster: 444, 555 and 666 respectively) stabilize the undercooled liquid and prevent crystallization; while the other TCPs exhibits an evolution trend similar to that of BCC-like clusters. Furthermore, three stages of the competition process between TCP and BCC structures can be observed, and crystallization does not happen until the number of major TCP clusters with T 5 > 1/3 decreases and the average degree of interconnection among them weakens. [ABSTRACT FROM AUTHOR]