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Advanced Ginzburg–Landau theory of freezing: a density-functional approach

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posted on 06.11.2017 by Gyula Toth, Nikolas Provatas
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.

Funding

This work has been supported by the Postdoctoral Programme of The Hungarian Academy of Sciences and the Natural Sciences and Engineering Research Council of Canada.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Physical Review B

Volume

90

Issue

10

Citation

TOTH, G. and PROVATAS, N., 2014. Advanced Ginzburg–Landau theory of freezing: a density-functional approach. Physical Review. B, Condensed matter and materials physics, 90 (10), DOI: 10.1103/PhysRevB.90.104101.

Publisher

© American Physical Society

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2014

ISSN

1098-0121

eISSN

1550-235X

Language

en

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