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• With a crystallization-like E-T curve Ni 50 Ag 50 amorphization includes a LLT and a LST. • The average cutoff distance exported by LaSCA is useful in identifying state transitions. • LLT can be identified by the evolution of SRO and MRO structures, where MRO shows the glass feature. • In LST, TCP-based MRO and TLRO structures grow rapidly. • TCP structures reflect the essential nature of amorphous systems more effectively than ICOs. A molecular dynamics simulation of rapid cooling at a cooling rate of 1011 K/s for Ni 50 Ag 50 alloys was conducted. The rapid cooling process was analyzed by using the system energy, the pair distribution function, and the largest standard cluster analysis. It is found that with a crystallization-like energy curve the solidification of Ni 50 Ag 50 alloy experiences a liquid-liquid and a liquid-solid transition (LLT and LST), finally result in an amorphous solid. In LLT stage the topologically close-packed (TCP) short-range order structures of both crystal (S666) and glass (S555) increase; whereas only glass medium-range order structures are formed. TCP-based long-range order (LRO) structures of glass do not increase until the beginning of the LST. Even in solid (T < T g) the LRO parameter based on ICO structures fluctuates violently, while that based on TCP structures is quite stable. Therefore, TCP not only is the basic structural characteristics of disordered system but also reasonably represents the metastability of metallic glasses. These findings not only clarify the importance of LLT for the glass forming ability of alloys, but also fully demonstrate the effectiveness and necessity of TCP structures for describing the structure of amorphous systems. [ABSTRACT FROM AUTHOR]