多分散Lennard-Jones系统的熔融/凝固转变：固有结构、分岔phase diagram、Hansen-Verlet规则和Lindemann准则的预测之间的显著一致性
Melting/freezing transition in polydisperse Lennard-Jones system: Remarkable agreement between predictions of inherent structure, bifurcation phase diagram, Hansen-Verlet rule and Lindemann criteria
摘要：
我们使用多分散性的大小作为一个控制参数，探索在一个系统的Lennard-Jones球的熔化和冻结过渡的某些方面。分析理论和计算机模拟建立一个潜在的有趣的关系之间观察到的终端多分散性Lennard-Jones多分散球和预测相同的积分方程为基础的理论分析的液-固转变。当我们增加多分散性时，固体变得固有地不稳定，这是因为由于尺寸差异而产生的应变。这里通过计算固有结构（IS）计算来研究这方面的问题。随着多分散性在恒定的体积分数，我们发现最初急剧上升的平均IS能量的结晶固体，直到过渡多分散性，随后由一个交叉到一个较弱的依赖性IS能量的多分散性在无定形状态。这种从FCC到无定形状态的交叉由IS分析预测同意非常好的固-液相图（扩展到亚稳相）所产生的非线性积分方程理论的冻结。另外两个著名的标准的冻结/融化的转变，Hansen-Verlet规则的冻结和Lindemann标准的熔化都被证明是非常好的协议与上述两个估计。它们一起似乎表明在多分散固体中的液-固转变中的小范围的亚稳性。
英文摘要：
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.
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