Advanced Ginzburg-Landau theory of freezing: A density-functional approach

G. Tóth, Nikolas Provatas

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

This paper revisits the weakly fourth-order anisotropic Ginzburg-Landau (GL) theory of freezing (also known as the Landau-Brazowskii model or theory of weak crystallization) by comparing it to a recent density functional approach, the phase-field crystal (PFC) model. First we study the critical behavior of a generalized PFC model and show that (i) the so-called one-mode approximation is exact in the leading order, and (ii) the direct correlation function has no contribution to the phase diagram near the critical point. Next, we calculate the anisotropy of the crystal-liquid interfacial free energy in the phase-field crystal (PFC) model analytically. For comparison, we also determine the anisotropy numerically and show that no range of parameters can be found for which the phase-field crystal equation can quantitatively model anisotropy for metallic materials. Finally, we derive the leading order PFC amplitude model and show that it coincides with the weakly fourth-order anisotropic GL theory, as a consequence of the assumptions of the GL theory being inherent in the PFC model. We also propose a way to calibrate the anisotropy in the Ginzburg-Landau theory via a generalized gradient operator emerging from the direct correlation function appearing in the generating PFC free energy functional.

Original languageEnglish
Article number104101
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume90
Issue number10
DOIs
Publication statusPublished - Sep 2 2014

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Freezing
freezing
crystal field theory
Crystals
Anisotropy
anisotropy
Free energy
free energy
Liquid Crystals
Crystallization
Liquid crystals
Phase diagrams
Mathematical operators
emerging
critical point
liquid crystals
phase diagrams
crystallization
operators
gradients

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Electronic, Optical and Magnetic Materials

Cite this

Advanced Ginzburg-Landau theory of freezing : A density-functional approach. / Tóth, G.; Provatas, Nikolas.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 90, No. 10, 104101, 02.09.2014.

Research output: Contribution to journalArticle

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