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The phase-field crystal (PFC) method has emerged as a promising technique to simulate the evolution of crystalline patterns with atomistic resolution on mesoscopic time scales. We use a 2D PFC model based on Elder et al. [Phy. Rev. B 75, 064107 (2007)] to perform a systematic analysis of a liquid-solid interface for a binary alloy system. We propose the method of determining interfacial energies for a curved liquid-solid interface by stabilizing the circular solid seed in the surrounding liquid phase and the liquid droplet in the solid phase for various seed sizes in a finite system. We also investigate the impact of model parameters on the resulting interface energies. The interface energies are computed with various system sizes in order to study the system size effects. In particular, we compare the simulation results in the form of the interface energy as a function of radius with the existing theories.