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Understanding the mechanism of metal solidification holds both theoretical significance and practical importance. In this study, we conducted molecular dynamics simulations to investigate the impact of cooling rates on the solidification of a melted ruthenium alloy using the embedded atom method (EAM) potential. The EAM potential is a widely employed interatomic potential for describing the metallic system, which can capture numerous crucial properties, including mechanical properties, the energy of competing crystal structure dynamics, defects, and liquid structures. Our simulations showed that upon quenching with different cooling rates, the system transformed into a supercooled liquid state at 1200 K, and a hexagonal close-packed cluster emerged as a dominant structure that remained stable even in the supercooled state. A critical cooling rate (1011 K/s) marked the transition from crystal to amorphous phase; this transition exhibited an upward trend as the superheating temperature increased until it reached the maximum achievable cooling rate. Our simulations also revealed that the optimal conditions for undercooling and superheating occur at ∼0.4396 and 1.2893 Tm, respectively, where Tm is the melting temperature. Our results provide comprehensive insights into the evolution of melt structures with changing temperatures during deep undercooling, the formation of homogeneous melt-free crystal regions, and the effect of the molten state on solidification phenomena.