Beyond the Ginzburg-Landau theory of freezing: Anisotropy of the
interfacial free energy in the Phase-Field Crystal model
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abstract
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 {\epsilon} 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.