This study explores the interplay between particle size disparity and energy polydispersity in shaping the surface morphology of a two-dimensional binary Lennard-Jones (LJ) mixture. Through molecular dynamics (MD) simulations, we analyze how variations in size-ratio (α) influence structural ordering in the solid phase, characterized by the radial distribution function (RDF) and hexatic order parameter (Ψ6). In addition to size disparity, we investigate the role of energy polydispersity in governing particle interactions and phase stability, where varying interaction strengths impact the local and global ordering of the system. The results clearly demonstrate a significant effect of particle size disparity on the positional and six-fold orientational order of the particles in two dimensions. Following this, the research enhances the understanding of how the structure of complex systems near the liquid-solid phase transition depends on the properties of the constituent particles and the quenching protocol, providing valuable insights for designing materials with specific surface characteristics.
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