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Melting/freezing transition in polydisperse Lennard-Jones system: Remarkable agreement between predictions of inherent structure, bifurcation phase diagram, Hansen-Verlet rule and Lindemann criteria

We use polydispersity in size as a control parameter to explore certain aspects of melting and freezing transitions in a system of Lennard-Jones spheres. Both analytical theory and computer simulations are employed to establish a potentially interesting relationship between observed terminal polydispersity in Lennard-Jones polydisperse spheres and prediction of the same in the integral equation based theoretical analysis of liquid-solid transition. As we increase polydispersity, solid becomes inherently unstable because of the strain built up due to the size disparity. This aspect is studied here by calculating the inherent structure (IS) calculation. With polydispersity at constant volume fraction we find initially a sharp rise of the average IS energy of the crystalline solid until transition polydispersity, followed by a cross over to a weaker dependence of IS energy on polydispersity in the amorphous state. This cross over from FCC to amorphous state predicted by IS analysis agrees remarkably well with the solid-liquid phase diagram (with extension into the metastable phase) generated by non-linear integral equation theories of freezing. Two other well-known criteria of freezing/melting transitions, the Hansen-Verlet rule of freezing and the Lindemann criterion of melting are both shown to be remarkably in good agreement with the above two estimates. Together they seem to indicate a small range of metastability in the liquid-solid transition in polydisperse solids.