超越Ginzburg-Landau冻结理论：相场晶体模型中界面自由能的各向异性
Beyond the Ginzburg-Landau theory of freezing: Anisotropy of the interfacial free energy in the Phase-Field Crystal model
摘要：
本文重新考察了弱四阶各向异性的Ginzburg-Landau（GL）冻结理论。首先，我们确定的各向异性的界面自由能在相场晶体（PFC）模型的分析，并证明它仍然是有限的临界点作为一个直接后果的一个模式的优势模型。其次，我们推导了首阶PFC振幅模型，并与传统的弱四阶各向异性GL理论进行了形式上的类比。我们的结论是，材料无关的各向异性出现在涌现GL理论与生成PFC模型的残余各向异性相一致。结果表明，在相场晶体模型和新兴的Ginzburg-Landau理论中，约化温度ε都没有进入金属材料的界面自由能各向异性。最后，我们研究了各向异性Ginzburg-Landau理论校准的可能途径。
英文摘要：
This paper re-visits the weakly fourth order anisotropic Ginzburg-Landau (GL) theory of freezing. First we determine the anisotropy of the interfacial free energy in the Phase-Field Crystal (PFC) model analytically, and prove that it remains finite at the critical point as a direct consequence of the one-mode dominance of the model. Next, we derive the leading order PFC amplitude model and show the formal analogy to traditional weakly 4th order anisotropic GL theories. We conclude that the material-independent anisotropy appearing in emergent GL theory coincides with the remnant anisotropy of the generating PFC model. As a result, we show that the reduced temperature ε does not enter into the interfacial free energy anisotropy for metallic materials in both the Phase-Field Crystal model and the emerging Ginzburg-Landau theories. Finally, we investigate the possible pathways of calibrating anisotropic Ginzburg-Landau theories.
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